id	sid	tid	token	lemma	pos
ejpam-5970	1	1	european	european	PROPN
ejpam-5970	1	2	journal	journal	PROPN
ejpam-5970	1	3	of	of	ADP
ejpam-5970	1	4	pure	pure	ADJ
ejpam-5970	1	5	and	and	CCONJ
ejpam-5970	1	6	applied	applied	ADJ
ejpam-5970	1	7	mathematics	mathematic	NOUN
ejpam-5970	1	8	2025	2025	NUM
ejpam-5970	1	9	,	,	PUNCT
ejpam-5970	1	10	vol	vol	NOUN
ejpam-5970	1	11	.	.	PROPN
ejpam-5970	1	12	18	18	NUM
ejpam-5970	1	13	,	,	PUNCT
ejpam-5970	1	14	issue	issue	NOUN
ejpam-5970	1	15	3	3	NUM
ejpam-5970	1	16	,	,	PUNCT
ejpam-5970	1	17	article	article	NOUN
ejpam-5970	1	18	number	number	NOUN
ejpam-5970	1	19	5970	5970	NUM
ejpam-5970	1	20	issn	issn	PROPN
ejpam-5970	1	21	1307	1307	NUM
ejpam-5970	1	22	-	-	SYM
ejpam-5970	1	23	5543	5543	NUM
ejpam-5970	1	24	–	–	PUNCT
ejpam-5970	1	25	ejpam.com	ejpam.com	X
ejpam-5970	1	26	published	publish	VERB
ejpam-5970	1	27	by	by	ADP
ejpam-5970	1	28	new	new	PROPN
ejpam-5970	1	29	york	york	PROPN
ejpam-5970	1	30	business	business	PROPN
ejpam-5970	1	31	global	global	PROPN
ejpam-5970	1	32	spatio	spatio	PROPN
ejpam-5970	1	33	-	-	PUNCT
ejpam-5970	1	34	temporal	temporal	ADJ
ejpam-5970	1	35	graph	graph	NOUN
ejpam-5970	1	36	neural	neural	ADJ
ejpam-5970	1	37	network	network	NOUN
ejpam-5970	1	38	for	for	ADP
ejpam-5970	1	39	time	time	NOUN
ejpam-5970	1	40	series	series	PROPN
ejpam-5970	1	41	forecasting	forecasting	PROPN
ejpam-5970	1	42	:	:	PUNCT
ejpam-5970	1	43	local	local	ADJ
ejpam-5970	1	44	antimagic	antimagic	ADJ
ejpam-5970	1	45	coloring	coloring	NOUN
ejpam-5970	1	46	-	-	PUNCT
ejpam-5970	1	47	based	base	VERB
ejpam-5970	1	48	companion	companion	NOUN
ejpam-5970	1	49	farming	farming	NOUN
ejpam-5970	1	50	a.	a.	NOUN
ejpam-5970	1	51	i.	i.	PROPN
ejpam-5970	1	52	kristiana1,2	kristiana1,2	PROPN
ejpam-5970	1	53	,	,	PUNCT
ejpam-5970	1	54	r.	r.	PROPN
ejpam-5970	1	55	izza3	izza3	PROPN
ejpam-5970	1	56	,	,	PUNCT
ejpam-5970	1	57	i.	i.	PROPN
ejpam-5970	1	58	h.	h.	PROPN
ejpam-5970	1	59	agustin1,4,∗	agustin1,4,∗	PROPN
ejpam-5970	1	60	,	,	PUNCT
ejpam-5970	1	61	l.	l.	PROPN
ejpam-5970	1	62	a.	a.	PROPN
ejpam-5970	1	63	monalisa2	monalisa2	PROPN
ejpam-5970	1	64	,	,	PUNCT
ejpam-5970	1	65	i.	i.	PROPN
ejpam-5970	1	66	l.	l.	PROPN
ejpam-5970	1	67	mursyidah1	mursyidah1	PROPN
ejpam-5970	1	68	,	,	PUNCT
ejpam-5970	1	69	r.	r.	PROPN
ejpam-5970	1	70	i.	i.	PROPN
ejpam-5970	1	71	baihaki1	baihaki1	PROPN
ejpam-5970	1	72	,	,	PUNCT
ejpam-5970	2	1	k.	k.	PROPN
ejpam-5970	2	2	h.	h.	PROPN
ejpam-5970	2	3	agustina5	agustina5	PROPN
ejpam-5970	2	4	,	,	PUNCT
ejpam-5970	2	5	dafik1,4	dafik1,4	PROPN
ejpam-5970	2	6	1	1	NUM
ejpam-5970	2	7	pui	pui	PROPN
ejpam-5970	2	8	-	-	PUNCT
ejpam-5970	2	9	pt	pt	NOUN
ejpam-5970	2	10	combinatorics	combinatoric	NOUN
ejpam-5970	2	11	and	and	CCONJ
ejpam-5970	2	12	graph	graph	NOUN
ejpam-5970	2	13	,	,	PUNCT
ejpam-5970	2	14	cgant	cgant	ADJ
ejpam-5970	2	15	,	,	PUNCT
ejpam-5970	2	16	university	university	NOUN
ejpam-5970	2	17	of	of	ADP
ejpam-5970	2	18	jember	jember	PROPN
ejpam-5970	2	19	,	,	PUNCT
ejpam-5970	2	20	jember	jember	PROPN
ejpam-5970	2	21	,	,	PUNCT
ejpam-5970	2	22	indonesia	indonesia	PROPN
ejpam-5970	2	23	2	2	NUM
ejpam-5970	2	24	department	department	NOUN
ejpam-5970	2	25	of	of	ADP
ejpam-5970	2	26	mathematics	mathematics	PROPN
ejpam-5970	2	27	education	education	NOUN
ejpam-5970	2	28	,	,	PUNCT
ejpam-5970	2	29	university	university	NOUN
ejpam-5970	2	30	of	of	ADP
ejpam-5970	2	31	jember	jember	PROPN
ejpam-5970	2	32	,	,	PUNCT
ejpam-5970	2	33	jember	jember	PROPN
ejpam-5970	2	34	,	,	PUNCT
ejpam-5970	2	35	indonesia	indonesia	PROPN
ejpam-5970	2	36	3	3	NUM
ejpam-5970	2	37	department	department	PROPN
ejpam-5970	2	38	of	of	ADP
ejpam-5970	2	39	mathematics	mathematics	PROPN
ejpam-5970	2	40	education	education	NOUN
ejpam-5970	2	41	,	,	PUNCT
ejpam-5970	2	42	cordoba	cordoba	PROPN
ejpam-5970	2	43	islamic	islamic	PROPN
ejpam-5970	2	44	university	university	PROPN
ejpam-5970	2	45	,	,	PUNCT
ejpam-5970	2	46	banyuwangi	banyuwangi	PROPN
ejpam-5970	2	47	,	,	PUNCT
ejpam-5970	2	48	indonesia	indonesia	PROPN
ejpam-5970	2	49	4	4	NUM
ejpam-5970	2	50	department	department	NOUN
ejpam-5970	2	51	of	of	ADP
ejpam-5970	2	52	mathematics	mathematic	NOUN
ejpam-5970	2	53	,	,	PUNCT
ejpam-5970	2	54	university	university	PROPN
ejpam-5970	2	55	of	of	ADP
ejpam-5970	2	56	jember	jember	PROPN
ejpam-5970	2	57	,	,	PUNCT
ejpam-5970	2	58	jember	jember	PROPN
ejpam-5970	2	59	indonesia	indonesia	PROPN
ejpam-5970	2	60	5	5	PROPN
ejpam-5970	2	61	department	department	NOUN
ejpam-5970	2	62	of	of	ADP
ejpam-5970	2	63	postgraduate	postgraduate	NOUN
ejpam-5970	2	64	mathematics	mathematic	NOUN
ejpam-5970	2	65	education	education	NOUN
ejpam-5970	2	66	,	,	PUNCT
ejpam-5970	2	67	university	university	NOUN
ejpam-5970	2	68	of	of	ADP
ejpam-5970	2	69	jember	jember	PROPN
ejpam-5970	2	70	,	,	PUNCT
ejpam-5970	2	71	jember	jember	PROPN
ejpam-5970	2	72	,	,	PUNCT
ejpam-5970	2	73	indonesia	indonesia	PROPN
ejpam-5970	2	74	abstract	abstract	NOUN
ejpam-5970	2	75	.	.	PUNCT
ejpam-5970	3	1	let	let	VERB
ejpam-5970	3	2	g(v	g(v	PROPN
ejpam-5970	3	3	,	,	PUNCT
ejpam-5970	3	4	e	e	NOUN
ejpam-5970	3	5	)	)	PUNCT
ejpam-5970	3	6	represent	represent	VERB
ejpam-5970	3	7	a	a	DET
ejpam-5970	3	8	simple	simple	ADJ
ejpam-5970	3	9	,	,	PUNCT
ejpam-5970	3	10	finite	finite	ADJ
ejpam-5970	3	11	,	,	PUNCT
ejpam-5970	3	12	and	and	CCONJ
ejpam-5970	3	13	connected	connected	ADJ
ejpam-5970	3	14	graph	graph	NOUN
ejpam-5970	3	15	with	with	ADP
ejpam-5970	3	16	|v	|v	PROPN
ejpam-5970	4	1	|	|	ADV
ejpam-5970	4	2	=	=	SYM
ejpam-5970	5	1	p	p	NOUN
ejpam-5970	5	2	and	and	CCONJ
ejpam-5970	5	3	|e|	|e|	PROPN
ejpam-5970	5	4	=	=	PUNCT
ejpam-5970	5	5	q.	q.	PROPN
ejpam-5970	5	6	a	a	DET
ejpam-5970	5	7	bijection	bijection	NOUN
ejpam-5970	5	8	f	f	X
ejpam-5970	5	9	:	:	PUNCT
ejpam-5970	5	10	v	v	X
ejpam-5970	5	11	(	(	PUNCT
ejpam-5970	5	12	g	g	NOUN
ejpam-5970	5	13	)	)	PUNCT
ejpam-5970	5	14	−→	−→	NOUN
ejpam-5970	5	15	{	{	PUNCT
ejpam-5970	5	16	1	1	NUM
ejpam-5970	5	17	,	,	PUNCT
ejpam-5970	5	18	2	2	NUM
ejpam-5970	5	19	,	,	PUNCT
ejpam-5970	5	20	3	3	NUM
ejpam-5970	5	21	,	,	PUNCT
ejpam-5970	5	22	.	.	PUNCT
ejpam-5970	5	23	.	.	PUNCT
ejpam-5970	6	1	.	.	PUNCT
ejpam-5970	7	1	,	,	PUNCT
ejpam-5970	7	2	|v	|v	PROPN
ejpam-5970	7	3	(	(	PUNCT
ejpam-5970	7	4	g)|	g)|	PROPN
ejpam-5970	7	5	}	}	PUNCT
ejpam-5970	7	6	is	be	AUX
ejpam-5970	7	7	defined	define	VERB
ejpam-5970	7	8	as	as	ADP
ejpam-5970	7	9	an	an	DET
ejpam-5970	7	10	edge	edge	NOUN
ejpam-5970	7	11	antimagic	antimagic	ADJ
ejpam-5970	7	12	labeling	labeling	NOUN
ejpam-5970	7	13	of	of	ADP
ejpam-5970	7	14	g	g	PROPN
ejpam-5970	7	15	if	if	SCONJ
ejpam-5970	7	16	the	the	DET
ejpam-5970	7	17	edge	edge	NOUN
ejpam-5970	7	18	weights	weight	VERB
ejpam-5970	7	19	w(uv	w(uv	NOUN
ejpam-5970	7	20	)	)	PUNCT
ejpam-5970	7	21	=	=	SYM
ejpam-5970	7	22	f(u	f(u	PROPN
ejpam-5970	7	23	)	)	PUNCT
ejpam-5970	8	1	+	+	NUM
ejpam-5970	8	2	f(v	f(v	NOUN
ejpam-5970	8	3	)	)	PUNCT
ejpam-5970	8	4	,	,	PUNCT
ejpam-5970	8	5	where	where	SCONJ
ejpam-5970	8	6	uv	uv	PROPN
ejpam-5970	8	7	∈	∈	PROPN
ejpam-5970	8	8	e(g	e(g	PROPN
ejpam-5970	8	9	)	)	PUNCT
ejpam-5970	8	10	,	,	PUNCT
ejpam-5970	8	11	are	be	AUX
ejpam-5970	8	12	all	all	ADV
ejpam-5970	8	13	distinct	distinct	ADJ
ejpam-5970	8	14	.	.	PUNCT
ejpam-5970	9	1	this	this	DET
ejpam-5970	9	2	labeling	labeling	NOUN
ejpam-5970	9	3	induces	induce	VERB
ejpam-5970	9	4	a	a	DET
ejpam-5970	9	5	lea	lea	NOUN
ejpam-5970	9	6	coloring	coloring	NOUN
ejpam-5970	9	7	of	of	ADP
ejpam-5970	9	8	g	g	PROPN
ejpam-5970	9	9	,	,	PUNCT
ejpam-5970	9	10	where	where	SCONJ
ejpam-5970	9	11	each	each	DET
ejpam-5970	9	12	edge	edge	NOUN
ejpam-5970	9	13	is	be	AUX
ejpam-5970	9	14	assigned	assign	VERB
ejpam-5970	9	15	a	a	DET
ejpam-5970	9	16	color	color	NOUN
ejpam-5970	9	17	based	base	VERB
ejpam-5970	9	18	on	on	ADP
ejpam-5970	9	19	its	its	PRON
ejpam-5970	9	20	weight	weight	NOUN
ejpam-5970	9	21	w(e	w(e	NOUN
ejpam-5970	9	22	)	)	PUNCT
ejpam-5970	9	23	.	.	PUNCT
ejpam-5970	10	1	the	the	DET
ejpam-5970	10	2	graph	graph	NOUN
ejpam-5970	10	3	g	g	NOUN
ejpam-5970	10	4	is	be	AUX
ejpam-5970	10	5	said	say	VERB
ejpam-5970	10	6	to	to	PART
ejpam-5970	10	7	have	have	VERB
ejpam-5970	10	8	a	a	DET
ejpam-5970	10	9	local	local	ADJ
ejpam-5970	10	10	(	(	PUNCT
ejpam-5970	10	11	a	a	PRON
ejpam-5970	10	12	,	,	PUNCT
ejpam-5970	10	13	d)-edge	d)-edge	NOUN
ejpam-5970	10	14	antimagic	antimagic	ADJ
ejpam-5970	10	15	coloring	coloring	NOUN
ejpam-5970	10	16	if	if	SCONJ
ejpam-5970	10	17	the	the	DET
ejpam-5970	10	18	edge	edge	NOUN
ejpam-5970	10	19	colors	color	NOUN
ejpam-5970	10	20	form	form	VERB
ejpam-5970	10	21	an	an	DET
ejpam-5970	10	22	arithmetic	arithmetic	ADJ
ejpam-5970	10	23	sequence	sequence	NOUN
ejpam-5970	10	24	with	with	ADP
ejpam-5970	10	25	an	an	DET
ejpam-5970	10	26	initial	initial	ADJ
ejpam-5970	10	27	term	term	NOUN
ejpam-5970	10	28	a	a	DET
ejpam-5970	10	29	and	and	CCONJ
ejpam-5970	10	30	a	a	DET
ejpam-5970	10	31	common	common	ADJ
ejpam-5970	10	32	difference	difference	NOUN
ejpam-5970	10	33	d.	d.	PROPN
ejpam-5970	10	34	the	the	DET
ejpam-5970	10	35	edge	edge	NOUN
ejpam-5970	10	36	weights	weight	NOUN
ejpam-5970	10	37	then	then	ADV
ejpam-5970	10	38	belong	belong	VERB
ejpam-5970	10	39	to	to	ADP
ejpam-5970	10	40	an	an	DET
ejpam-5970	10	41	arithmetic	arithmetic	ADJ
ejpam-5970	10	42	progression	progression	NOUN
ejpam-5970	10	43	{	{	PUNCT
ejpam-5970	10	44	a	a	NOUN
ejpam-5970	10	45	,	,	PUNCT
ejpam-5970	10	46	a	a	PRON
ejpam-5970	10	47	+	+	X
ejpam-5970	10	48	d	d	PROPN
ejpam-5970	10	49	,	,	PUNCT
ejpam-5970	10	50	a	a	DET
ejpam-5970	10	51	+	+	X
ejpam-5970	10	52	2d	2d	NOUN
ejpam-5970	10	53	,	,	PUNCT
ejpam-5970	10	54	.	.	PUNCT
ejpam-5970	10	55	.	.	PUNCT
ejpam-5970	11	1	.	.	PUNCT
ejpam-5970	12	1	,	,	PUNCT
ejpam-5970	12	2	a	a	DET
ejpam-5970	12	3	+	+	X
ejpam-5970	12	4	(	(	PUNCT
ejpam-5970	12	5	k	k	PROPN
ejpam-5970	12	6	−	−	PROPN
ejpam-5970	12	7	1)d	1)d	NUM
ejpam-5970	12	8	}	}	PUNCT
ejpam-5970	12	9	,	,	PUNCT
ejpam-5970	12	10	where	where	SCONJ
ejpam-5970	12	11	a	a	X
ejpam-5970	12	12	,	,	PUNCT
ejpam-5970	12	13	d	d	X
ejpam-5970	12	14	≥	≥	NUM
ejpam-5970	12	15	1	1	NUM
ejpam-5970	12	16	are	be	AUX
ejpam-5970	12	17	integers	integer	NOUN
ejpam-5970	12	18	,	,	PUNCT
ejpam-5970	12	19	and	and	CCONJ
ejpam-5970	12	20	k	k	PROPN
ejpam-5970	12	21	represents	represent	VERB
ejpam-5970	12	22	the	the	DET
ejpam-5970	12	23	number	number	NOUN
ejpam-5970	12	24	of	of	ADP
ejpam-5970	12	25	distinct	distinct	ADJ
ejpam-5970	12	26	colors	color	NOUN
ejpam-5970	12	27	used	use	VERB
ejpam-5970	12	28	.	.	PUNCT
ejpam-5970	13	1	the	the	DET
ejpam-5970	13	2	minimum	minimum	ADJ
ejpam-5970	13	3	number	number	NOUN
ejpam-5970	13	4	of	of	ADP
ejpam-5970	13	5	colors	color	NOUN
ejpam-5970	13	6	required	require	VERB
ejpam-5970	13	7	for	for	SCONJ
ejpam-5970	13	8	g	g	PROPN
ejpam-5970	13	9	to	to	PART
ejpam-5970	13	10	admit	admit	VERB
ejpam-5970	13	11	a	a	DET
ejpam-5970	13	12	local	local	ADJ
ejpam-5970	13	13	(	(	PUNCT
ejpam-5970	13	14	a	a	PRON
ejpam-5970	13	15	,	,	PUNCT
ejpam-5970	13	16	d)-edge	d)-edge	ADJ
ejpam-5970	13	17	antimagic	antimagic	ADJ
ejpam-5970	13	18	coloring	coloring	NOUN
ejpam-5970	13	19	is	be	AUX
ejpam-5970	13	20	called	call	VERB
ejpam-5970	13	21	the	the	DET
ejpam-5970	13	22	local	local	ADJ
ejpam-5970	13	23	(	(	PUNCT
ejpam-5970	13	24	a	a	PRON
ejpam-5970	13	25	,	,	PUNCT
ejpam-5970	13	26	d)-edge	d)-edge	ADJ
ejpam-5970	13	27	antimagic	antimagic	ADJ
ejpam-5970	13	28	chromatic	chromatic	ADJ
ejpam-5970	13	29	number	number	NOUN
ejpam-5970	13	30	,	,	PUNCT
ejpam-5970	13	31	denoted	denote	VERB
ejpam-5970	13	32	by	by	ADP
ejpam-5970	13	33	χle(a	χle(a	NOUN
ejpam-5970	13	34	,	,	PUNCT
ejpam-5970	13	35	d)(g	d)(g	PROPN
ejpam-5970	13	36	)	)	PUNCT
ejpam-5970	13	37	.	.	PUNCT
ejpam-5970	14	1	this	this	DET
ejpam-5970	14	2	coloring	coloring	NOUN
ejpam-5970	14	3	is	be	AUX
ejpam-5970	14	4	referred	refer	VERB
ejpam-5970	14	5	to	to	ADP
ejpam-5970	14	6	as	as	ADP
ejpam-5970	14	7	lea(a	lea(a	PROPN
ejpam-5970	14	8	,	,	PUNCT
ejpam-5970	14	9	d	d	NOUN
ejpam-5970	14	10	)	)	PUNCT
ejpam-5970	14	11	coloring	coloring	NOUN
ejpam-5970	14	12	.	.	PUNCT
ejpam-5970	15	1	in	in	ADP
ejpam-5970	15	2	this	this	DET
ejpam-5970	15	3	study	study	NOUN
ejpam-5970	15	4	,	,	PUNCT
ejpam-5970	15	5	we	we	PRON
ejpam-5970	15	6	establish	establish	VERB
ejpam-5970	15	7	both	both	CCONJ
ejpam-5970	15	8	the	the	DET
ejpam-5970	15	9	lower	low	ADJ
ejpam-5970	15	10	and	and	CCONJ
ejpam-5970	15	11	upper	upper	ADJ
ejpam-5970	15	12	bounds	bound	NOUN
ejpam-5970	15	13	of	of	ADP
ejpam-5970	15	14	χle(a	χle(a	PROPN
ejpam-5970	15	15	,	,	PUNCT
ejpam-5970	15	16	d)(g	d)(g	NOUN
ejpam-5970	15	17	)	)	PUNCT
ejpam-5970	15	18	and	and	CCONJ
ejpam-5970	15	19	identify	identify	VERB
ejpam-5970	15	20	the	the	DET
ejpam-5970	15	21	exact	exact	ADJ
ejpam-5970	15	22	values	value	NOUN
ejpam-5970	15	23	for	for	ADP
ejpam-5970	15	24	specific	specific	ADJ
ejpam-5970	15	25	graph	graph	NOUN
ejpam-5970	15	26	classes	class	NOUN
ejpam-5970	15	27	.	.	PUNCT
ejpam-5970	16	1	additionally	additionally	ADV
ejpam-5970	16	2	,	,	PUNCT
ejpam-5970	16	3	we	we	PRON
ejpam-5970	16	4	demonstrate	demonstrate	VERB
ejpam-5970	16	5	the	the	DET
ejpam-5970	16	6	practical	practical	ADJ
ejpam-5970	16	7	application	application	NOUN
ejpam-5970	16	8	of	of	ADP
ejpam-5970	16	9	local	local	ADJ
ejpam-5970	16	10	(	(	PUNCT
ejpam-5970	16	11	a	a	PRON
ejpam-5970	16	12	,	,	PUNCT
ejpam-5970	16	13	d)-edge	d)-edge	NOUN
ejpam-5970	16	14	antimagic	antimagic	ADJ
ejpam-5970	16	15	coloring	coloring	NOUN
ejpam-5970	16	16	by	by	ADP
ejpam-5970	16	17	employing	employ	VERB
ejpam-5970	16	18	it	it	PRON
ejpam-5970	16	19	in	in	ADP
ejpam-5970	16	20	the	the	DET
ejpam-5970	16	21	analysis	analysis	NOUN
ejpam-5970	16	22	of	of	ADP
ejpam-5970	16	23	the	the	DET
ejpam-5970	16	24	spatio	spatio	PROPN
ejpam-5970	16	25	-	-	PUNCT
ejpam-5970	16	26	temporal	temporal	ADJ
ejpam-5970	16	27	graph	graph	NOUN
ejpam-5970	16	28	neural	neural	ADJ
ejpam-5970	16	29	network	network	NOUN
ejpam-5970	16	30	(	(	PUNCT
ejpam-5970	16	31	stgnn	stgnn	NOUN
ejpam-5970	16	32	)	)	PUNCT
ejpam-5970	16	33	model	model	NOUN
ejpam-5970	16	34	to	to	PART
ejpam-5970	16	35	support	support	VERB
ejpam-5970	16	36	autonomous	autonomous	ADJ
ejpam-5970	16	37	controlled	control	VERB
ejpam-5970	16	38	environment	environment	NOUN
ejpam-5970	16	39	agriculture	agriculture	NOUN
ejpam-5970	16	40	(	(	PUNCT
ejpam-5970	16	41	cea	cea	PROPN
ejpam-5970	16	42	)	)	PUNCT
ejpam-5970	16	43	in	in	ADP
ejpam-5970	16	44	forecasting	forecast	VERB
ejpam-5970	16	45	npk	npk	NOUN
ejpam-5970	16	46	concentration	concentration	NOUN
ejpam-5970	16	47	trends	trend	NOUN
ejpam-5970	16	48	for	for	ADP
ejpam-5970	16	49	companion	companion	NOUN
ejpam-5970	16	50	plantations	plantation	NOUN
ejpam-5970	16	51	over	over	ADP
ejpam-5970	16	52	multiple	multiple	ADJ
ejpam-5970	16	53	time	time	NOUN
ejpam-5970	16	54	steps	step	NOUN
ejpam-5970	16	55	.	.	PUNCT
ejpam-5970	17	1	2020	2020	NUM
ejpam-5970	17	2	mathematics	mathematic	NOUN
ejpam-5970	17	3	subject	subject	NOUN
ejpam-5970	17	4	classifications	classification	NOUN
ejpam-5970	17	5	:	:	PUNCT
ejpam-5970	17	6	05c15	05c15	NUM
ejpam-5970	17	7	,	,	PUNCT
ejpam-5970	17	8	05c90	05c90	NUM
ejpam-5970	17	9	,	,	PUNCT
ejpam-5970	17	10	68r01	68r01	NOUN
ejpam-5970	17	11	,	,	PUNCT
ejpam-5970	17	12	68r10	68r10	NUM
ejpam-5970	17	13	key	key	ADJ
ejpam-5970	17	14	words	word	NOUN
ejpam-5970	17	15	and	and	CCONJ
ejpam-5970	17	16	phrases	phrase	NOUN
ejpam-5970	17	17	:	:	PUNCT
ejpam-5970	17	18	local	local	ADJ
ejpam-5970	17	19	(	(	PUNCT
ejpam-5970	17	20	a	a	PRON
ejpam-5970	17	21	,	,	PUNCT
ejpam-5970	17	22	d)-edge	d)-edge	NOUN
ejpam-5970	17	23	antimagic	antimagic	ADJ
ejpam-5970	17	24	coloring	coloring	NOUN
ejpam-5970	17	25	,	,	PUNCT
ejpam-5970	17	26	spatio	spatio	NOUN
ejpam-5970	17	27	-	-	PUNCT
ejpam-5970	17	28	temporal	temporal	ADJ
ejpam-5970	17	29	graph	graph	NOUN
ejpam-5970	17	30	neural	neural	ADJ
ejpam-5970	17	31	network	network	NOUN
ejpam-5970	17	32	(	(	PUNCT
ejpam-5970	17	33	stgnn	stgnn	NOUN
ejpam-5970	17	34	)	)	PUNCT
ejpam-5970	17	35	,	,	PUNCT
ejpam-5970	17	36	npk	npk	NOUN
ejpam-5970	17	37	concentration	concentration	NOUN
ejpam-5970	17	38	forecasting	forecasting	NOUN
ejpam-5970	17	39	∗corresponding	∗corresponde	VERB
ejpam-5970	17	40	author	author	NOUN
ejpam-5970	17	41	.	.	PUNCT
ejpam-5970	18	1	doi	doi	NOUN
ejpam-5970	18	2	:	:	PUNCT
ejpam-5970	18	3	https://doi.org/10.29020/nybg.ejpam.v18i3.5970	https://doi.org/10.29020/nybg.ejpam.v18i3.5970	PROPN
ejpam-5970	18	4	email	email	NOUN
ejpam-5970	18	5	addresses	address	NOUN
ejpam-5970	18	6	:	:	PUNCT
ejpam-5970	18	7	ikahesti.fmipa@unej.ac.id	ikahesti.fmipa@unej.ac.id	NUM
ejpam-5970	18	8	(	(	PUNCT
ejpam-5970	18	9	i.	i.	PROPN
ejpam-5970	18	10	h.	h.	PROPN
ejpam-5970	18	11	agustin	agustin	PROPN
ejpam-5970	18	12	)	)	PUNCT
ejpam-5970	18	13	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5970	19	1	1	1	NUM
ejpam-5970	19	2	copyright	copyright	NOUN
ejpam-5970	19	3	:	:	PUNCT
ejpam-5970	19	4	©	©	PROPN
ejpam-5970	19	5	2025	2025	NUM
ejpam-5970	19	6	the	the	DET
ejpam-5970	19	7	author(s	author(s	NOUN
ejpam-5970	19	8	)	)	PUNCT
ejpam-5970	19	9	.	.	PUNCT
ejpam-5970	20	1	(	(	PUNCT
ejpam-5970	20	2	cc	cc	NOUN
ejpam-5970	20	3	by	by	ADP
ejpam-5970	20	4	-	-	PUNCT
ejpam-5970	20	5	nc	nc	PROPN
ejpam-5970	20	6	4.0	4.0	NUM
ejpam-5970	20	7	)	)	PUNCT
ejpam-5970	20	8	a.	a.	NOUN
ejpam-5970	20	9	i.	i.	PROPN
ejpam-5970	20	10	kristiana	kristiana	PROPN
ejpam-5970	20	11	,	,	PUNCT
ejpam-5970	20	12	et	et	PROPN
ejpam-5970	20	13	al	al	PROPN
ejpam-5970	20	14	.	.	PUNCT
ejpam-5970	20	15	/	/	SYM
ejpam-5970	20	16	eur	eur	PROPN
ejpam-5970	20	17	.	.	PUNCT
ejpam-5970	21	1	j.	j.	PROPN
ejpam-5970	21	2	pure	pure	PROPN
ejpam-5970	21	3	appl	appl	PROPN
ejpam-5970	21	4	.	.	PROPN
ejpam-5970	21	5	math	math	PROPN
ejpam-5970	21	6	,	,	PUNCT
ejpam-5970	21	7	18	18	NUM
ejpam-5970	21	8	(	(	PUNCT
ejpam-5970	21	9	3	3	NUM
ejpam-5970	21	10	)	)	PUNCT
ejpam-5970	21	11	(	(	PUNCT
ejpam-5970	21	12	2025	2025	NUM
ejpam-5970	21	13	)	)	PUNCT
ejpam-5970	21	14	,	,	PUNCT
ejpam-5970	21	15	5970	5970	NUM
ejpam-5970	21	16	2	2	NUM
ejpam-5970	21	17	of	of	ADP
ejpam-5970	21	18	18	18	NUM
ejpam-5970	21	19	1	1	NUM
ejpam-5970	21	20	.	.	PUNCT
ejpam-5970	22	1	introduction	introduction	NOUN
ejpam-5970	22	2	in	in	ADP
ejpam-5970	22	3	addition	addition	NOUN
ejpam-5970	22	4	,	,	PUNCT
ejpam-5970	22	5	a	a	DET
ejpam-5970	22	6	local	local	ADJ
ejpam-5970	22	7	edge	edge	NOUN
ejpam-5970	22	8	antimagic	antimagic	ADJ
ejpam-5970	22	9	coloring	coloring	NOUN
ejpam-5970	22	10	can	can	AUX
ejpam-5970	22	11	also	also	ADV
ejpam-5970	22	12	be	be	AUX
ejpam-5970	22	13	defined	define	VERB
ejpam-5970	22	14	for	for	ADP
ejpam-5970	22	15	graphs	graph	NOUN
ejpam-5970	22	16	[	[	X
ejpam-5970	22	17	1	1	NUM
ejpam-5970	22	18	]	]	PUNCT
ejpam-5970	22	19	.	.	PUNCT
ejpam-5970	23	1	a	a	DET
ejpam-5970	23	2	bijection	bijection	ADJ
ejpam-5970	23	3	f	f	X
ejpam-5970	23	4	:	:	PUNCT
ejpam-5970	23	5	v	v	X
ejpam-5970	23	6	→	→	SYM
ejpam-5970	23	7	{	{	PUNCT
ejpam-5970	23	8	1	1	NUM
ejpam-5970	23	9	,	,	PUNCT
ejpam-5970	23	10	2	2	NUM
ejpam-5970	23	11	,	,	PUNCT
ejpam-5970	23	12	3	3	NUM
ejpam-5970	23	13	,	,	PUNCT
ejpam-5970	23	14	.	.	PUNCT
ejpam-5970	23	15	.	.	PUNCT
ejpam-5970	23	16	.	.	PUNCT
ejpam-5970	24	1	,	,	PUNCT
ejpam-5970	24	2	|v	|v	PROPN
ejpam-5970	24	3	(	(	PUNCT
ejpam-5970	24	4	g)|	g)|	PROPN
ejpam-5970	24	5	}	}	PUNCT
ejpam-5970	24	6	is	be	AUX
ejpam-5970	24	7	referred	refer	VERB
ejpam-5970	24	8	to	to	ADP
ejpam-5970	24	9	as	as	ADP
ejpam-5970	24	10	a	a	DET
ejpam-5970	24	11	lea	lea	NOUN
ejpam-5970	24	12	labeling	labeling	NOUN
ejpam-5970	24	13	if	if	SCONJ
ejpam-5970	24	14	any	any	DET
ejpam-5970	24	15	two	two	NUM
ejpam-5970	24	16	adjacent	adjacent	ADJ
ejpam-5970	24	17	edges	edge	NOUN
ejpam-5970	24	18	e1	e1	PROPN
ejpam-5970	24	19	and	and	CCONJ
ejpam-5970	24	20	e2	e2	PROPN
ejpam-5970	24	21	satisfy	satisfy	PROPN
ejpam-5970	24	22	w(e1	w(e1	NOUN
ejpam-5970	24	23	)	)	PUNCT
ejpam-5970	25	1	̸=	̸=	PROPN
ejpam-5970	25	2	w(e2	w(e2	PROPN
ejpam-5970	25	3	)	)	PUNCT
ejpam-5970	25	4	,	,	PUNCT
ejpam-5970	25	5	where	where	SCONJ
ejpam-5970	25	6	for	for	ADP
ejpam-5970	25	7	e	e	NOUN
ejpam-5970	25	8	=	=	NOUN
ejpam-5970	25	9	uv	uv	PROPN
ejpam-5970	25	10	∈	∈	PROPN
ejpam-5970	25	11	e(g	e(g	PROPN
ejpam-5970	25	12	)	)	PUNCT
ejpam-5970	25	13	,	,	PUNCT
ejpam-5970	25	14	the	the	DET
ejpam-5970	25	15	weight	weight	NOUN
ejpam-5970	25	16	of	of	ADP
ejpam-5970	25	17	the	the	DET
ejpam-5970	25	18	edge	edge	NOUN
ejpam-5970	25	19	is	be	AUX
ejpam-5970	25	20	given	give	VERB
ejpam-5970	25	21	by	by	ADP
ejpam-5970	25	22	w(e	w(e	NOUN
ejpam-5970	25	23	)	)	PUNCT
ejpam-5970	25	24	=	=	SYM
ejpam-5970	25	25	f(u	f(u	PROPN
ejpam-5970	25	26	)	)	PUNCT
ejpam-5970	25	27	+	+	NUM
ejpam-5970	25	28	f(v	f(v	NOUN
ejpam-5970	25	29	)	)	PUNCT
ejpam-5970	25	30	.	.	PUNCT
ejpam-5970	26	1	a	a	DET
ejpam-5970	26	2	proper	proper	ADJ
ejpam-5970	26	3	edge	edge	NOUN
ejpam-5970	26	4	coloring	coloring	NOUN
ejpam-5970	26	5	of	of	ADP
ejpam-5970	26	6	g	g	PROPN
ejpam-5970	26	7	is	be	AUX
ejpam-5970	26	8	induced	induce	VERB
ejpam-5970	26	9	by	by	ADP
ejpam-5970	26	10	the	the	DET
ejpam-5970	26	11	lea	lea	PROPN
ejpam-5970	26	12	labeling	labeling	NOUN
ejpam-5970	26	13	when	when	SCONJ
ejpam-5970	26	14	all	all	DET
ejpam-5970	26	15	edges	edge	NOUN
ejpam-5970	26	16	are	be	AUX
ejpam-5970	26	17	assigned	assign	VERB
ejpam-5970	26	18	colors	color	NOUN
ejpam-5970	26	19	based	base	VERB
ejpam-5970	26	20	on	on	ADP
ejpam-5970	26	21	their	their	PRON
ejpam-5970	26	22	weights	weight	NOUN
ejpam-5970	26	23	w(e	w(e	NOUN
ejpam-5970	26	24	)	)	PUNCT
ejpam-5970	27	1	[	[	X
ejpam-5970	27	2	2	2	NUM
ejpam-5970	27	3	]	]	PUNCT
ejpam-5970	27	4	.	.	PUNCT
ejpam-5970	28	1	the	the	DET
ejpam-5970	28	2	lea	lea	PROPN
ejpam-5970	28	3	chromatic	chromatic	ADJ
ejpam-5970	28	4	number	number	NOUN
ejpam-5970	28	5	,	,	PUNCT
ejpam-5970	28	6	represented	represent	VERB
ejpam-5970	28	7	as	as	ADP
ejpam-5970	28	8	χlea(g	χlea(g	PROPN
ejpam-5970	28	9	)	)	PUNCT
ejpam-5970	28	10	,	,	PUNCT
ejpam-5970	28	11	denotes	denote	VERB
ejpam-5970	28	12	the	the	DET
ejpam-5970	28	13	minimum	minimum	ADJ
ejpam-5970	28	14	number	number	NOUN
ejpam-5970	28	15	of	of	ADP
ejpam-5970	28	16	colors	color	NOUN
ejpam-5970	28	17	required	require	VERB
ejpam-5970	28	18	for	for	ADP
ejpam-5970	28	19	the	the	DET
ejpam-5970	28	20	proper	proper	ADJ
ejpam-5970	28	21	edge	edge	NOUN
ejpam-5970	28	22	coloring	coloring	NOUN
ejpam-5970	28	23	of	of	ADP
ejpam-5970	28	24	g	g	PROPN
ejpam-5970	28	25	based	base	VERB
ejpam-5970	28	26	on	on	ADP
ejpam-5970	28	27	the	the	DET
ejpam-5970	28	28	lea	lea	PROPN
ejpam-5970	28	29	labeling	labeling	NOUN
ejpam-5970	28	30	[	[	X
ejpam-5970	28	31	3	3	NUM
ejpam-5970	28	32	]	]	PUNCT
ejpam-5970	28	33	.	.	PUNCT
ejpam-5970	29	1	several	several	ADJ
ejpam-5970	29	2	findings	finding	NOUN
ejpam-5970	29	3	related	relate	VERB
ejpam-5970	29	4	to	to	ADP
ejpam-5970	29	5	lea	lea	PROPN
ejpam-5970	29	6	coloring	coloring	NOUN
ejpam-5970	29	7	in	in	ADP
ejpam-5970	29	8	graphs	graph	NOUN
ejpam-5970	29	9	are	be	AUX
ejpam-5970	29	10	discussed	discuss	VERB
ejpam-5970	29	11	in	in	ADP
ejpam-5970	29	12	[	[	X
ejpam-5970	29	13	4	4	NUM
ejpam-5970	29	14	]	]	PUNCT
ejpam-5970	29	15	.	.	PUNCT
ejpam-5970	30	1	a	a	DET
ejpam-5970	30	2	graph	graph	NOUN
ejpam-5970	30	3	g	g	NOUN
ejpam-5970	30	4	is	be	AUX
ejpam-5970	30	5	said	say	VERB
ejpam-5970	30	6	to	to	PART
ejpam-5970	30	7	have	have	VERB
ejpam-5970	30	8	a	a	DET
ejpam-5970	30	9	local	local	ADJ
ejpam-5970	30	10	(	(	PUNCT
ejpam-5970	30	11	a	a	PRON
ejpam-5970	30	12	,	,	PUNCT
ejpam-5970	30	13	d)-antimagic	d)-antimagic	NOUN
ejpam-5970	30	14	coloring	color	VERB
ejpam-5970	30	15	if	if	SCONJ
ejpam-5970	30	16	the	the	DET
ejpam-5970	30	17	set	set	NOUN
ejpam-5970	30	18	of	of	ADP
ejpam-5970	30	19	its	its	PRON
ejpam-5970	30	20	edge	edge	NOUN
ejpam-5970	30	21	colors	color	NOUN
ejpam-5970	30	22	forms	form	VERB
ejpam-5970	30	23	an	an	DET
ejpam-5970	30	24	arithmetic	arithmetic	ADJ
ejpam-5970	30	25	progression	progression	NOUN
ejpam-5970	30	26	{	{	PUNCT
ejpam-5970	30	27	a	a	PRON
ejpam-5970	30	28	,	,	PUNCT
ejpam-5970	30	29	a+d	a+d	NUM
ejpam-5970	30	30	,	,	PUNCT
ejpam-5970	30	31	a+2d	a+2d	PROPN
ejpam-5970	30	32	,	,	PUNCT
ejpam-5970	30	33	.	.	PUNCT
ejpam-5970	30	34	.	.	PUNCT
ejpam-5970	31	1	.	.	PUNCT
ejpam-5970	32	1	,	,	PUNCT
ejpam-5970	32	2	a+	a+	PUNCT
ejpam-5970	32	3	(	(	PUNCT
ejpam-5970	32	4	k	k	X
ejpam-5970	32	5	−	−	PROPN
ejpam-5970	32	6	1)d	1)d	NUM
ejpam-5970	32	7	}	}	PUNCT
ejpam-5970	32	8	,	,	PUNCT
ejpam-5970	32	9	where	where	SCONJ
ejpam-5970	32	10	a	a	X
ejpam-5970	32	11	,	,	PUNCT
ejpam-5970	32	12	d	d	X
ejpam-5970	32	13	≥	≥	NUM
ejpam-5970	32	14	1	1	NUM
ejpam-5970	32	15	are	be	AUX
ejpam-5970	32	16	integers	integer	NOUN
ejpam-5970	32	17	,	,	PUNCT
ejpam-5970	32	18	and	and	CCONJ
ejpam-5970	32	19	k	k	PROPN
ejpam-5970	32	20	is	be	AUX
ejpam-5970	32	21	the	the	DET
ejpam-5970	32	22	number	number	NOUN
ejpam-5970	32	23	of	of	ADP
ejpam-5970	32	24	distinct	distinct	ADJ
ejpam-5970	32	25	colors	color	NOUN
ejpam-5970	32	26	used	use	VERB
ejpam-5970	32	27	in	in	ADP
ejpam-5970	32	28	the	the	DET
ejpam-5970	32	29	proper	proper	ADJ
ejpam-5970	32	30	edge	edge	NOUN
ejpam-5970	32	31	coloring	coloring	NOUN
ejpam-5970	32	32	.	.	PUNCT
ejpam-5970	33	1	this	this	DET
ejpam-5970	33	2	type	type	NOUN
ejpam-5970	33	3	of	of	ADP
ejpam-5970	33	4	coloring	coloring	NOUN
ejpam-5970	33	5	is	be	AUX
ejpam-5970	33	6	referred	refer	VERB
ejpam-5970	33	7	to	to	ADP
ejpam-5970	33	8	as	as	ADP
ejpam-5970	33	9	a	a	DET
ejpam-5970	33	10	lea(a	lea(a	PROPN
ejpam-5970	33	11	,	,	PUNCT
ejpam-5970	33	12	d	d	NOUN
ejpam-5970	33	13	)	)	PUNCT
ejpam-5970	33	14	coloring	coloring	NOUN
ejpam-5970	33	15	.	.	PUNCT
ejpam-5970	34	1	the	the	DET
ejpam-5970	34	2	local	local	ADJ
ejpam-5970	34	3	(	(	PUNCT
ejpam-5970	34	4	a	a	PRON
ejpam-5970	34	5	,	,	PUNCT
ejpam-5970	34	6	d)-antimagic	d)-antimagic	NOUN
ejpam-5970	34	7	chromatic	chromatic	ADJ
ejpam-5970	34	8	number	number	NOUN
ejpam-5970	34	9	,	,	PUNCT
ejpam-5970	34	10	denoted	denote	VERB
ejpam-5970	34	11	as	as	ADP
ejpam-5970	34	12	χle(a	χle(a	NOUN
ejpam-5970	34	13	,	,	PUNCT
ejpam-5970	34	14	d)(g	d)(g	NOUN
ejpam-5970	34	15	)	)	PUNCT
ejpam-5970	34	16	,	,	PUNCT
ejpam-5970	34	17	is	be	AUX
ejpam-5970	34	18	defined	define	VERB
ejpam-5970	34	19	as	as	ADP
ejpam-5970	34	20	the	the	DET
ejpam-5970	34	21	minimum	minimum	ADJ
ejpam-5970	34	22	number	number	NOUN
ejpam-5970	34	23	of	of	ADP
ejpam-5970	34	24	colors	color	NOUN
ejpam-5970	34	25	required	require	VERB
ejpam-5970	34	26	to	to	PART
ejpam-5970	34	27	assign	assign	VERB
ejpam-5970	34	28	a	a	DET
ejpam-5970	34	29	local	local	ADJ
ejpam-5970	34	30	(	(	PUNCT
ejpam-5970	34	31	a	a	PRON
ejpam-5970	34	32	,	,	PUNCT
ejpam-5970	34	33	d)-antimagic	d)-antimagic	NOUN
ejpam-5970	34	34	coloring	color	VERB
ejpam-5970	34	35	to	to	ADP
ejpam-5970	34	36	g.	g.	VERB
ejpam-5970	34	37	for	for	ADP
ejpam-5970	34	38	further	further	ADJ
ejpam-5970	34	39	details	detail	NOUN
ejpam-5970	34	40	,	,	PUNCT
ejpam-5970	34	41	refer	refer	VERB
ejpam-5970	34	42	to	to	ADP
ejpam-5970	34	43	[	[	X
ejpam-5970	34	44	5	5	NUM
ejpam-5970	34	45	]	]	PUNCT
ejpam-5970	34	46	.	.	PUNCT
ejpam-5970	35	1	the	the	DET
ejpam-5970	35	2	study	study	NOUN
ejpam-5970	35	3	of	of	ADP
ejpam-5970	35	4	graph	graph	NOUN
ejpam-5970	35	5	colorings	coloring	NOUN
ejpam-5970	35	6	has	have	AUX
ejpam-5970	35	7	been	be	AUX
ejpam-5970	35	8	an	an	DET
ejpam-5970	35	9	essential	essential	ADJ
ejpam-5970	35	10	area	area	NOUN
ejpam-5970	35	11	of	of	ADP
ejpam-5970	35	12	research	research	NOUN
ejpam-5970	35	13	in	in	ADP
ejpam-5970	35	14	combinatorics	combinatoric	NOUN
ejpam-5970	35	15	,	,	PUNCT
ejpam-5970	35	16	particularly	particularly	ADV
ejpam-5970	35	17	due	due	ADP
ejpam-5970	35	18	to	to	ADP
ejpam-5970	35	19	its	its	PRON
ejpam-5970	35	20	wide	wide	ADV
ejpam-5970	35	21	-	-	PUNCT
ejpam-5970	35	22	ranging	range	VERB
ejpam-5970	35	23	applications	application	NOUN
ejpam-5970	35	24	in	in	ADP
ejpam-5970	35	25	network	network	NOUN
ejpam-5970	35	26	optimization	optimization	NOUN
ejpam-5970	35	27	,	,	PUNCT
ejpam-5970	35	28	scheduling	scheduling	NOUN
ejpam-5970	35	29	,	,	PUNCT
ejpam-5970	35	30	and	and	CCONJ
ejpam-5970	35	31	cryptographic	cryptographic	ADJ
ejpam-5970	35	32	systems	system	NOUN
ejpam-5970	35	33	[	[	X
ejpam-5970	35	34	6	6	NUM
ejpam-5970	35	35	,	,	PUNCT
ejpam-5970	35	36	7	7	NUM
ejpam-5970	35	37	]	]	PUNCT
ejpam-5970	35	38	.	.	PUNCT
ejpam-5970	36	1	several	several	ADJ
ejpam-5970	36	2	recent	recent	ADJ
ejpam-5970	36	3	works	work	NOUN
ejpam-5970	36	4	have	have	AUX
ejpam-5970	36	5	contributed	contribute	VERB
ejpam-5970	36	6	significantly	significantly	ADV
ejpam-5970	36	7	to	to	ADP
ejpam-5970	36	8	advancing	advance	VERB
ejpam-5970	36	9	this	this	DET
ejpam-5970	36	10	field	field	NOUN
ejpam-5970	36	11	.	.	PUNCT
ejpam-5970	37	1	for	for	ADP
ejpam-5970	37	2	example	example	NOUN
ejpam-5970	37	3	,	,	PUNCT
ejpam-5970	37	4	alfarisi	alfarisi	PROPN
ejpam-5970	37	5	et	et	PROPN
ejpam-5970	37	6	al	al	PROPN
ejpam-5970	37	7	.	.	PROPN
ejpam-5970	37	8	explored	explore	VERB
ejpam-5970	37	9	the	the	DET
ejpam-5970	37	10	graceful	graceful	ADJ
ejpam-5970	37	11	chromatic	chromatic	ADJ
ejpam-5970	37	12	number	number	NOUN
ejpam-5970	37	13	of	of	ADP
ejpam-5970	37	14	unicyclic	unicyclic	ADJ
ejpam-5970	37	15	graphs	graph	NOUN
ejpam-5970	37	16	,	,	PUNCT
ejpam-5970	37	17	establishing	establish	VERB
ejpam-5970	37	18	critical	critical	ADJ
ejpam-5970	37	19	properties	property	NOUN
ejpam-5970	37	20	and	and	CCONJ
ejpam-5970	37	21	applications	application	NOUN
ejpam-5970	37	22	in	in	ADP
ejpam-5970	37	23	network	network	NOUN
ejpam-5970	37	24	models	model	NOUN
ejpam-5970	37	25	[	[	X
ejpam-5970	37	26	8	8	NUM
ejpam-5970	37	27	]	]	PUNCT
ejpam-5970	37	28	.	.	PUNCT
ejpam-5970	38	1	similarly	similarly	ADV
ejpam-5970	38	2	,	,	PUNCT
ejpam-5970	38	3	dafik	dafik	VERB
ejpam-5970	38	4	et	et	PROPN
ejpam-5970	38	5	al	al	PROPN
ejpam-5970	38	6	.	.	PROPN
ejpam-5970	38	7	examined	examine	VERB
ejpam-5970	38	8	the	the	DET
ejpam-5970	38	9	non	non	ADJ
ejpam-5970	38	10	-	-	ADJ
ejpam-5970	38	11	isolated	isolated	ADJ
ejpam-5970	38	12	resolving	resolving	NOUN
ejpam-5970	38	13	numbers	number	NOUN
ejpam-5970	38	14	of	of	ADP
ejpam-5970	38	15	special	special	ADJ
ejpam-5970	38	16	graphs	graph	NOUN
ejpam-5970	38	17	,	,	PUNCT
ejpam-5970	38	18	offering	offer	VERB
ejpam-5970	38	19	insights	insight	NOUN
ejpam-5970	38	20	into	into	ADP
ejpam-5970	38	21	their	their	PRON
ejpam-5970	38	22	operational	operational	ADJ
ejpam-5970	38	23	characteristics	characteristic	NOUN
ejpam-5970	38	24	and	and	CCONJ
ejpam-5970	38	25	implications	implication	NOUN
ejpam-5970	38	26	for	for	ADP
ejpam-5970	38	27	graph	graph	NOUN
ejpam-5970	38	28	operations	operation	NOUN
ejpam-5970	38	29	[	[	X
ejpam-5970	38	30	9	9	NUM
ejpam-5970	38	31	]	]	PUNCT
ejpam-5970	38	32	.	.	PUNCT
ejpam-5970	39	1	building	build	VERB
ejpam-5970	39	2	on	on	ADP
ejpam-5970	39	3	these	these	DET
ejpam-5970	39	4	foundations	foundation	NOUN
ejpam-5970	39	5	,	,	PUNCT
ejpam-5970	39	6	septyory	septyory	PROPN
ejpam-5970	39	7	et	et	PROPN
ejpam-5970	39	8	al	al	PROPN
ejpam-5970	39	9	.	.	PROPN
ejpam-5970	40	1	(	(	PUNCT
ejpam-5970	40	2	2021	2021	NUM
ejpam-5970	40	3	)	)	PUNCT
ejpam-5970	40	4	focused	focus	VERB
ejpam-5970	40	5	on	on	ADP
ejpam-5970	40	6	rainbow	rainbow	NOUN
ejpam-5970	40	7	antimagic	antimagic	ADJ
ejpam-5970	40	8	coloring	coloring	NOUN
ejpam-5970	40	9	of	of	ADP
ejpam-5970	40	10	special	special	ADJ
ejpam-5970	40	11	graphs	graph	NOUN
ejpam-5970	40	12	,	,	PUNCT
ejpam-5970	40	13	showcasing	showcase	VERB
ejpam-5970	40	14	its	its	PRON
ejpam-5970	40	15	potential	potential	NOUN
ejpam-5970	40	16	in	in	ADP
ejpam-5970	40	17	diverse	diverse	ADJ
ejpam-5970	40	18	computational	computational	ADJ
ejpam-5970	40	19	frameworks	framework	NOUN
ejpam-5970	40	20	[	[	X
ejpam-5970	40	21	10	10	NUM
ejpam-5970	40	22	]	]	PUNCT
ejpam-5970	40	23	.	.	PUNCT
ejpam-5970	41	1	further	far	ADV
ejpam-5970	41	2	,	,	PUNCT
ejpam-5970	41	3	dafik	dafik	VERB
ejpam-5970	41	4	et	et	PROPN
ejpam-5970	41	5	al	al	PROPN
ejpam-5970	41	6	.	.	PROPN
ejpam-5970	42	1	and	and	CCONJ
ejpam-5970	42	2	gembong	gembong	NOUN
ejpam-5970	42	3	et	et	PROPN
ejpam-5970	42	4	al	al	PROPN
ejpam-5970	42	5	.	.	PROPN
ejpam-5970	42	6	investigated	investigate	VERB
ejpam-5970	42	7	edge	edge	NOUN
ejpam-5970	42	8	domination	domination	NOUN
ejpam-5970	42	9	numbers	number	NOUN
ejpam-5970	42	10	and	and	CCONJ
ejpam-5970	42	11	distance	distance	NOUN
ejpam-5970	42	12	domination	domination	NOUN
ejpam-5970	42	13	numbers	number	NOUN
ejpam-5970	42	14	in	in	ADP
ejpam-5970	42	15	comb	comb	NOUN
ejpam-5970	42	16	product	product	NOUN
ejpam-5970	42	17	graphs	graph	NOUN
ejpam-5970	42	18	,	,	PUNCT
ejpam-5970	42	19	respectively	respectively	ADV
ejpam-5970	42	20	,	,	PUNCT
ejpam-5970	42	21	providing	provide	VERB
ejpam-5970	42	22	a	a	DET
ejpam-5970	42	23	deeper	deep	ADJ
ejpam-5970	42	24	understanding	understanding	NOUN
ejpam-5970	42	25	of	of	ADP
ejpam-5970	42	26	their	their	PRON
ejpam-5970	42	27	structural	structural	ADJ
ejpam-5970	42	28	and	and	CCONJ
ejpam-5970	42	29	combinatorial	combinatorial	ADJ
ejpam-5970	42	30	properties	property	NOUN
ejpam-5970	42	31	[	[	X
ejpam-5970	42	32	11	11	NUM
ejpam-5970	42	33	]	]	PUNCT
ejpam-5970	42	34	.	.	PUNCT
ejpam-5970	43	1	as	as	ADP
ejpam-5970	43	2	a	a	DET
ejpam-5970	43	3	subfield	subfield	NOUN
ejpam-5970	43	4	of	of	ADP
ejpam-5970	43	5	graph	graph	NOUN
ejpam-5970	43	6	coloring	coloring	NOUN
ejpam-5970	43	7	,	,	PUNCT
ejpam-5970	43	8	local	local	ADJ
ejpam-5970	43	9	edge	edge	NOUN
ejpam-5970	43	10	-	-	PUNCT
ejpam-5970	43	11	antimagic	antimagic	NOUN
ejpam-5970	43	12	(	(	PUNCT
ejpam-5970	43	13	a	a	PRON
ejpam-5970	43	14	,	,	PUNCT
ejpam-5970	43	15	d)-coloring	d)-colore	VERB
ejpam-5970	43	16	(	(	PUNCT
ejpam-5970	43	17	lea(a	lea(a	PROPN
ejpam-5970	43	18	,	,	PUNCT
ejpam-5970	43	19	d	d	NOUN
ejpam-5970	43	20	)	)	PUNCT
ejpam-5970	43	21	coloring	coloring	NOUN
ejpam-5970	43	22	)	)	PUNCT
ejpam-5970	43	23	has	have	AUX
ejpam-5970	43	24	been	be	AUX
ejpam-5970	43	25	the	the	DET
ejpam-5970	43	26	subject	subject	NOUN
ejpam-5970	43	27	of	of	ADP
ejpam-5970	43	28	numerous	numerous	ADJ
ejpam-5970	43	29	studies	study	NOUN
ejpam-5970	43	30	.	.	PUNCT
ejpam-5970	44	1	rajkumar	rajkumar	PROPN
ejpam-5970	44	2	and	and	CCONJ
ejpam-5970	44	3	nalliah	nalliah	PROPN
ejpam-5970	45	1	[	[	X
ejpam-5970	45	2	12	12	NUM
ejpam-5970	45	3	]	]	PUNCT
ejpam-5970	45	4	computed	compute	VERB
ejpam-5970	45	5	the	the	DET
ejpam-5970	45	6	lea(a	lea(a	PROPN
ejpam-5970	45	7	,	,	PUNCT
ejpam-5970	45	8	d)-chromatic	d)-chromatic	ADJ
ejpam-5970	45	9	number	number	NOUN
ejpam-5970	45	10	for	for	ADP
ejpam-5970	45	11	wheel	wheel	NOUN
ejpam-5970	45	12	graphs	graph	NOUN
ejpam-5970	45	13	.	.	PUNCT
ejpam-5970	46	1	agustin	agustin	PROPN
ejpam-5970	46	2	et	et	PROPN
ejpam-5970	46	3	al	al	PROPN
ejpam-5970	46	4	.	.	PROPN
ejpam-5970	46	5	(	(	PUNCT
ejpam-5970	46	6	2023	2023	NUM
ejpam-5970	46	7	)	)	PUNCT
ejpam-5970	46	8	further	far	ADV
ejpam-5970	46	9	analyzed	analyze	VERB
ejpam-5970	46	10	path	path	NOUN
ejpam-5970	46	11	,	,	PUNCT
ejpam-5970	46	12	fan	fan	NOUN
ejpam-5970	46	13	,	,	PUNCT
ejpam-5970	46	14	friendship	friendship	NOUN
ejpam-5970	46	15	,	,	PUNCT
ejpam-5970	46	16	and	and	CCONJ
ejpam-5970	46	17	star	star	NOUN
ejpam-5970	46	18	graphs	graph	NOUN
ejpam-5970	46	19	to	to	PART
ejpam-5970	46	20	determine	determine	VERB
ejpam-5970	46	21	their	their	PRON
ejpam-5970	46	22	respective	respective	ADJ
ejpam-5970	46	23	lea(a	lea(a	PROPN
ejpam-5970	46	24	,	,	PUNCT
ejpam-5970	46	25	d)-chromatic	d)-chromatic	ADJ
ejpam-5970	46	26	numbers	number	NOUN
ejpam-5970	46	27	[	[	X
ejpam-5970	46	28	13	13	NUM
ejpam-5970	46	29	]	]	PUNCT
ejpam-5970	46	30	.	.	PUNCT
ejpam-5970	47	1	almaidah	almaidah	PROPN
ejpam-5970	47	2	et	et	PROPN
ejpam-5970	47	3	al	al	PROPN
ejpam-5970	47	4	.	.	PROPN
ejpam-5970	48	1	(	(	PUNCT
ejpam-5970	48	2	2023	2023	NUM
ejpam-5970	48	3	)	)	PUNCT
ejpam-5970	48	4	studied	study	VERB
ejpam-5970	48	5	ladder	ladder	NOUN
ejpam-5970	48	6	,	,	PUNCT
ejpam-5970	48	7	cycle	cycle	NOUN
ejpam-5970	48	8	,	,	PUNCT
ejpam-5970	48	9	octopus	octopus	NOUN
ejpam-5970	48	10	,	,	PUNCT
ejpam-5970	48	11	helm	helm	NOUN
ejpam-5970	48	12	,	,	PUNCT
ejpam-5970	48	13	triangular	triangular	NOUN
ejpam-5970	48	14	book	book	NOUN
ejpam-5970	48	15	,	,	PUNCT
ejpam-5970	48	16	and	and	CCONJ
ejpam-5970	48	17	tadpole	tadpole	NOUN
ejpam-5970	48	18	graphs	graph	VERB
ejpam-5970	48	19	[	[	X
ejpam-5970	48	20	14	14	NUM
ejpam-5970	48	21	]	]	PUNCT
ejpam-5970	48	22	.	.	PUNCT
ejpam-5970	49	1	putra	putra	PROPN
ejpam-5970	49	2	et	et	PROPN
ejpam-5970	49	3	al	al	PROPN
ejpam-5970	49	4	.	.	PROPN
ejpam-5970	49	5	extended	extend	VERB
ejpam-5970	49	6	the	the	DET
ejpam-5970	49	7	analysis	analysis	NOUN
ejpam-5970	49	8	to	to	ADP
ejpam-5970	49	9	centipede	centipede	NOUN
ejpam-5970	49	10	,	,	PUNCT
ejpam-5970	49	11	lotus	lotus	PROPN
ejpam-5970	49	12	,	,	PUNCT
ejpam-5970	49	13	caterpillar	caterpillar	NOUN
ejpam-5970	49	14	,	,	PUNCT
ejpam-5970	49	15	double	double	ADJ
ejpam-5970	49	16	star	star	NOUN
ejpam-5970	49	17	,	,	PUNCT
ejpam-5970	49	18	and	and	CCONJ
ejpam-5970	49	19	double	double	ADJ
ejpam-5970	49	20	broom	broom	NOUN
ejpam-5970	49	21	graphs	graph	NOUN
ejpam-5970	49	22	[	[	X
ejpam-5970	49	23	15	15	NUM
ejpam-5970	49	24	]	]	PUNCT
ejpam-5970	49	25	.	.	PUNCT
ejpam-5970	50	1	rifda	rifda	PROPN
ejpam-5970	50	2	et	et	PROPN
ejpam-5970	50	3	al	al	PROPN
ejpam-5970	50	4	.	.	PROPN
ejpam-5970	50	5	(	(	PUNCT
ejpam-5970	50	6	2023	2023	NUM
ejpam-5970	50	7	)	)	PUNCT
ejpam-5970	50	8	explored	explore	VERB
ejpam-5970	50	9	the	the	DET
ejpam-5970	50	10	application	application	NOUN
ejpam-5970	50	11	of	of	ADP
ejpam-5970	50	12	lea(a	lea(a	PROPN
ejpam-5970	50	13	,	,	PUNCT
ejpam-5970	50	14	d	d	NOUN
ejpam-5970	50	15	)	)	PUNCT
ejpam-5970	50	16	coloring	color	VERB
ejpam-5970	50	17	on	on	ADP
ejpam-5970	50	18	broom	broom	NOUN
ejpam-5970	50	19	,	,	PUNCT
ejpam-5970	50	20	book	book	NOUN
ejpam-5970	50	21	,	,	PUNCT
ejpam-5970	50	22	firecracker	firecracker	NOUN
ejpam-5970	50	23	,	,	PUNCT
ejpam-5970	50	24	complete	complete	ADJ
ejpam-5970	50	25	,	,	PUNCT
ejpam-5970	50	26	and	and	CCONJ
ejpam-5970	50	27	dragon	dragon	NOUN
ejpam-5970	50	28	graphs	graph	NOUN
ejpam-5970	50	29	[	[	X
ejpam-5970	50	30	16	16	NUM
ejpam-5970	50	31	]	]	PUNCT
ejpam-5970	50	32	.	.	PUNCT
ejpam-5970	51	1	despite	despite	SCONJ
ejpam-5970	51	2	the	the	DET
ejpam-5970	51	3	significant	significant	ADJ
ejpam-5970	51	4	progress	progress	NOUN
ejpam-5970	51	5	made	make	VERB
ejpam-5970	51	6	in	in	ADP
ejpam-5970	51	7	the	the	DET
ejpam-5970	51	8	study	study	NOUN
ejpam-5970	51	9	of	of	ADP
ejpam-5970	51	10	lea(a	lea(a	PROPN
ejpam-5970	51	11	,	,	PUNCT
ejpam-5970	51	12	d	d	NOUN
ejpam-5970	51	13	)	)	PUNCT
ejpam-5970	51	14	coloring	color	VERB
ejpam-5970	51	15	across	across	ADP
ejpam-5970	51	16	various	various	ADJ
ejpam-5970	51	17	graph	graph	NOUN
ejpam-5970	51	18	classes	class	NOUN
ejpam-5970	51	19	,	,	PUNCT
ejpam-5970	51	20	its	its	PRON
ejpam-5970	51	21	application	application	NOUN
ejpam-5970	51	22	to	to	ADP
ejpam-5970	51	23	real	real	ADJ
ejpam-5970	51	24	-	-	PUNCT
ejpam-5970	51	25	world	world	NOUN
ejpam-5970	51	26	domains	domain	NOUN
ejpam-5970	51	27	remains	remain	VERB
ejpam-5970	51	28	limited	limited	ADJ
ejpam-5970	51	29	.	.	PUNCT
ejpam-5970	52	1	to	to	ADP
ejpam-5970	52	2	the	the	DET
ejpam-5970	52	3	best	good	ADJ
ejpam-5970	52	4	of	of	ADP
ejpam-5970	52	5	our	our	PRON
ejpam-5970	52	6	knowledge	knowledge	NOUN
ejpam-5970	52	7	,	,	PUNCT
ejpam-5970	52	8	no	no	DET
ejpam-5970	52	9	prior	prior	ADJ
ejpam-5970	52	10	work	work	NOUN
ejpam-5970	52	11	has	have	AUX
ejpam-5970	52	12	integrated	integrate	VERB
ejpam-5970	52	13	the	the	DET
ejpam-5970	52	14	concept	concept	NOUN
ejpam-5970	52	15	of	of	ADP
ejpam-5970	52	16	lea(a	lea(a	PROPN
ejpam-5970	52	17	,	,	PUNCT
ejpam-5970	52	18	d	d	NOUN
ejpam-5970	52	19	)	)	PUNCT
ejpam-5970	52	20	coloring	color	VERB
ejpam-5970	52	21	into	into	ADP
ejpam-5970	52	22	smart	smart	ADJ
ejpam-5970	52	23	agriculture	agriculture	NOUN
ejpam-5970	52	24	,	,	PUNCT
ejpam-5970	52	25	particularly	particularly	ADV
ejpam-5970	52	26	within	within	ADP
ejpam-5970	52	27	the	the	DET
ejpam-5970	52	28	framework	framework	NOUN
ejpam-5970	52	29	of	of	ADP
ejpam-5970	52	30	spatio	spatio	PROPN
ejpam-5970	52	31	-	-	PUNCT
ejpam-5970	52	32	temporal	temporal	ADJ
ejpam-5970	52	33	graph	graph	NOUN
ejpam-5970	52	34	neural	neural	ADJ
ejpam-5970	52	35	networks	network	NOUN
ejpam-5970	52	36	(	(	PUNCT
ejpam-5970	52	37	stgnn	stgnn	NOUN
ejpam-5970	52	38	)	)	PUNCT
ejpam-5970	52	39	.	.	PUNCT
ejpam-5970	53	1	this	this	DET
ejpam-5970	53	2	research	research	NOUN
ejpam-5970	53	3	addresses	address	VERB
ejpam-5970	53	4	that	that	SCONJ
ejpam-5970	53	5	gap	gap	NOUN
ejpam-5970	53	6	by	by	ADP
ejpam-5970	53	7	proposing	propose	VERB
ejpam-5970	53	8	a	a	DET
ejpam-5970	53	9	novel	novel	ADJ
ejpam-5970	53	10	integration	integration	NOUN
ejpam-5970	53	11	of	of	ADP
ejpam-5970	53	12	graph	graph	NOUN
ejpam-5970	53	13	labeling	labeling	NOUN
ejpam-5970	53	14	theory	theory	NOUN
ejpam-5970	53	15	and	and	CCONJ
ejpam-5970	53	16	deep	deep	ADJ
ejpam-5970	53	17	learning	learning	NOUN
ejpam-5970	53	18	for	for	ADP
ejpam-5970	53	19	optimized	optimize	VERB
ejpam-5970	53	20	sensor	sensor	NOUN
ejpam-5970	53	21	deployment	deployment	NOUN
ejpam-5970	53	22	and	and	CCONJ
ejpam-5970	53	23	nutrient	nutrient	NOUN
ejpam-5970	53	24	forecasting	forecasting	NOUN
ejpam-5970	53	25	.	.	PUNCT
ejpam-5970	54	1	recent	recent	ADJ
ejpam-5970	54	2	developments	development	NOUN
ejpam-5970	54	3	further	far	ADV
ejpam-5970	54	4	support	support	VERB
ejpam-5970	54	5	the	the	DET
ejpam-5970	54	6	feasibility	feasibility	NOUN
ejpam-5970	54	7	of	of	ADP
ejpam-5970	54	8	incorporating	incorporate	VERB
ejpam-5970	54	9	graph	graph	NOUN
ejpam-5970	54	10	coloring	color	VERB
ejpam-5970	54	11	a.	a.	PROPN
ejpam-5970	54	12	i.	i.	PROPN
ejpam-5970	54	13	kristiana	kristiana	PROPN
ejpam-5970	54	14	,	,	PUNCT
ejpam-5970	54	15	et	et	PROPN
ejpam-5970	54	16	al	al	PROPN
ejpam-5970	54	17	.	.	PUNCT
ejpam-5970	54	18	/	/	SYM
ejpam-5970	54	19	eur	eur	PROPN
ejpam-5970	54	20	.	.	PUNCT
ejpam-5970	55	1	j.	j.	PROPN
ejpam-5970	55	2	pure	pure	PROPN
ejpam-5970	55	3	appl	appl	PROPN
ejpam-5970	55	4	.	.	PROPN
ejpam-5970	55	5	math	math	PROPN
ejpam-5970	55	6	,	,	PUNCT
ejpam-5970	55	7	18	18	NUM
ejpam-5970	55	8	(	(	PUNCT
ejpam-5970	55	9	3	3	NUM
ejpam-5970	55	10	)	)	PUNCT
ejpam-5970	55	11	(	(	PUNCT
ejpam-5970	55	12	2025	2025	NUM
ejpam-5970	55	13	)	)	PUNCT
ejpam-5970	55	14	,	,	PUNCT
ejpam-5970	55	15	5970	5970	NUM
ejpam-5970	55	16	3	3	NUM
ejpam-5970	55	17	of	of	ADP
ejpam-5970	55	18	18	18	NUM
ejpam-5970	55	19	concepts	concept	NOUN
ejpam-5970	55	20	into	into	ADP
ejpam-5970	55	21	deep	deep	ADJ
ejpam-5970	55	22	learning	learning	NOUN
ejpam-5970	55	23	models	model	NOUN
ejpam-5970	55	24	for	for	ADP
ejpam-5970	55	25	agricultural	agricultural	ADJ
ejpam-5970	55	26	forecasting	forecasting	NOUN
ejpam-5970	55	27	.	.	PUNCT
ejpam-5970	56	1	expanding	expand	VERB
ejpam-5970	56	2	the	the	DET
ejpam-5970	56	3	application	application	NOUN
ejpam-5970	56	4	of	of	ADP
ejpam-5970	56	5	graph	graph	NOUN
ejpam-5970	56	6	coloring	coloring	NOUN
ejpam-5970	56	7	,	,	PUNCT
ejpam-5970	56	8	kristiana	kristiana	PROPN
ejpam-5970	56	9	et	et	PROPN
ejpam-5970	56	10	al	al	PROPN
ejpam-5970	56	11	.	.	PROPN
ejpam-5970	57	1	(	(	PUNCT
ejpam-5970	57	2	2024	2024	NUM
ejpam-5970	57	3	)	)	PUNCT
ejpam-5970	57	4	analyzed	analyze	VERB
ejpam-5970	57	5	the	the	DET
ejpam-5970	57	6	b	b	NOUN
ejpam-5970	57	7	-	-	PUNCT
ejpam-5970	57	8	coloring	coloring	NOUN
ejpam-5970	57	9	of	of	ADP
ejpam-5970	57	10	graphs	graph	NOUN
ejpam-5970	57	11	and	and	CCONJ
ejpam-5970	57	12	its	its	PRON
ejpam-5970	57	13	integration	integration	NOUN
ejpam-5970	57	14	into	into	ADP
ejpam-5970	57	15	spatio	spatio	PROPN
ejpam-5970	57	16	-	-	PUNCT
ejpam-5970	57	17	temporal	temporal	ADJ
ejpam-5970	57	18	graph	graph	NOUN
ejpam-5970	57	19	neural	neural	ADJ
ejpam-5970	57	20	networks	network	NOUN
ejpam-5970	57	21	(	(	PUNCT
ejpam-5970	57	22	stgnn	stgnn	NOUN
ejpam-5970	57	23	)	)	PUNCT
ejpam-5970	57	24	for	for	ADP
ejpam-5970	57	25	multi	multi	ADJ
ejpam-5970	57	26	-	-	ADJ
ejpam-5970	57	27	step	step	ADJ
ejpam-5970	57	28	time	time	NOUN
ejpam-5970	57	29	series	series	NOUN
ejpam-5970	57	30	forecasting	forecasting	NOUN
ejpam-5970	57	31	[	[	X
ejpam-5970	57	32	17	17	NUM
ejpam-5970	57	33	]	]	PUNCT
ejpam-5970	57	34	.	.	PUNCT
ejpam-5970	58	1	their	their	PRON
ejpam-5970	58	2	study	study	NOUN
ejpam-5970	58	3	demonstrated	demonstrate	VERB
ejpam-5970	58	4	how	how	SCONJ
ejpam-5970	58	5	graph	graph	NOUN
ejpam-5970	58	6	coloring	coloring	NOUN
ejpam-5970	58	7	techniques	technique	NOUN
ejpam-5970	58	8	could	could	AUX
ejpam-5970	58	9	optimize	optimize	VERB
ejpam-5970	58	10	the	the	DET
ejpam-5970	58	11	monitoring	monitoring	NOUN
ejpam-5970	58	12	of	of	ADP
ejpam-5970	58	13	soil	soil	NOUN
ejpam-5970	58	14	moisture	moisture	NOUN
ejpam-5970	58	15	and	and	CCONJ
ejpam-5970	58	16	ph	ph	ADJ
ejpam-5970	58	17	levels	level	NOUN
ejpam-5970	58	18	in	in	ADP
ejpam-5970	58	19	companion	companion	NOUN
ejpam-5970	58	20	farming	farming	NOUN
ejpam-5970	58	21	systems	system	NOUN
ejpam-5970	58	22	[	[	X
ejpam-5970	58	23	18	18	NUM
ejpam-5970	58	24	]	]	PUNCT
ejpam-5970	58	25	.	.	PUNCT
ejpam-5970	59	1	these	these	DET
ejpam-5970	59	2	findings	finding	NOUN
ejpam-5970	59	3	reinforce	reinforce	VERB
ejpam-5970	59	4	the	the	DET
ejpam-5970	59	5	significance	significance	NOUN
ejpam-5970	59	6	of	of	ADP
ejpam-5970	59	7	graph	graph	NOUN
ejpam-5970	59	8	coloring	color	VERB
ejpam-5970	59	9	not	not	PART
ejpam-5970	59	10	only	only	ADV
ejpam-5970	59	11	in	in	ADP
ejpam-5970	59	12	theoretical	theoretical	ADJ
ejpam-5970	59	13	combinatorial	combinatorial	ADJ
ejpam-5970	59	14	problems	problem	NOUN
ejpam-5970	59	15	but	but	CCONJ
ejpam-5970	59	16	also	also	ADV
ejpam-5970	59	17	in	in	ADP
ejpam-5970	59	18	practical	practical	ADJ
ejpam-5970	59	19	applications	application	NOUN
ejpam-5970	59	20	,	,	PUNCT
ejpam-5970	59	21	particularly	particularly	ADV
ejpam-5970	59	22	in	in	ADP
ejpam-5970	59	23	agricultural	agricultural	ADJ
ejpam-5970	59	24	and	and	CCONJ
ejpam-5970	59	25	environmental	environmental	ADJ
ejpam-5970	59	26	monitoring	monitoring	NOUN
ejpam-5970	59	27	[	[	X
ejpam-5970	59	28	19	19	NUM
ejpam-5970	59	29	]	]	PUNCT
ejpam-5970	59	30	.	.	PUNCT
ejpam-5970	60	1	collectively	collectively	ADV
ejpam-5970	60	2	,	,	PUNCT
ejpam-5970	60	3	these	these	DET
ejpam-5970	60	4	studies	study	NOUN
ejpam-5970	60	5	highlight	highlight	VERB
ejpam-5970	60	6	the	the	DET
ejpam-5970	60	7	growing	grow	VERB
ejpam-5970	60	8	importance	importance	NOUN
ejpam-5970	60	9	of	of	ADP
ejpam-5970	60	10	graph	graph	NOUN
ejpam-5970	60	11	coloring	coloring	NOUN
ejpam-5970	60	12	techniques	technique	NOUN
ejpam-5970	60	13	in	in	ADP
ejpam-5970	60	14	addressing	address	VERB
ejpam-5970	60	15	both	both	DET
ejpam-5970	60	16	theoretical	theoretical	ADJ
ejpam-5970	60	17	challenges	challenge	NOUN
ejpam-5970	60	18	and	and	CCONJ
ejpam-5970	60	19	real	real	ADJ
ejpam-5970	60	20	-	-	PUNCT
ejpam-5970	60	21	world	world	NOUN
ejpam-5970	60	22	problems	problem	NOUN
ejpam-5970	60	23	in	in	ADP
ejpam-5970	60	24	combinatorics	combinatoric	NOUN
ejpam-5970	60	25	and	and	CCONJ
ejpam-5970	60	26	beyond	beyond	ADP
ejpam-5970	60	27	[	[	X
ejpam-5970	60	28	20	20	NUM
ejpam-5970	60	29	]	]	PUNCT
ejpam-5970	60	30	.	.	PUNCT
ejpam-5970	61	1	this	this	DET
ejpam-5970	61	2	research	research	NOUN
ejpam-5970	61	3	is	be	AUX
ejpam-5970	61	4	motivated	motivate	VERB
ejpam-5970	61	5	by	by	ADP
ejpam-5970	61	6	the	the	DET
ejpam-5970	61	7	need	need	NOUN
ejpam-5970	61	8	to	to	PART
ejpam-5970	61	9	bridge	bridge	VERB
ejpam-5970	61	10	the	the	DET
ejpam-5970	61	11	gap	gap	NOUN
ejpam-5970	61	12	between	between	ADP
ejpam-5970	61	13	theoretical	theoretical	ADJ
ejpam-5970	61	14	developments	development	NOUN
ejpam-5970	61	15	in	in	ADP
ejpam-5970	61	16	graph	graph	NOUN
ejpam-5970	61	17	labeling	labeling	NOUN
ejpam-5970	61	18	and	and	CCONJ
ejpam-5970	61	19	their	their	PRON
ejpam-5970	61	20	practical	practical	ADJ
ejpam-5970	61	21	applications	application	NOUN
ejpam-5970	61	22	in	in	ADP
ejpam-5970	61	23	data	data	NOUN
ejpam-5970	61	24	-	-	PUNCT
ejpam-5970	61	25	driven	drive	VERB
ejpam-5970	61	26	systems	system	NOUN
ejpam-5970	61	27	.	.	PUNCT
ejpam-5970	62	1	specifically	specifically	ADV
ejpam-5970	62	2	,	,	PUNCT
ejpam-5970	62	3	this	this	DET
ejpam-5970	62	4	paper	paper	NOUN
ejpam-5970	62	5	aims	aim	VERB
ejpam-5970	62	6	to	to	PART
ejpam-5970	62	7	derive	derive	VERB
ejpam-5970	62	8	sharper	sharper	ADV
ejpam-5970	62	9	lower	low	ADJ
ejpam-5970	62	10	and	and	CCONJ
ejpam-5970	62	11	upper	upper	ADJ
ejpam-5970	62	12	bounds	bound	NOUN
ejpam-5970	62	13	for	for	ADP
ejpam-5970	62	14	the	the	DET
ejpam-5970	62	15	lea(a	lea(a	PROPN
ejpam-5970	62	16	,	,	PUNCT
ejpam-5970	62	17	d)-chromatic	d)-chromatic	ADJ
ejpam-5970	62	18	number	number	NOUN
ejpam-5970	62	19	,	,	PUNCT
ejpam-5970	62	20	χle(a	χle(a	PROPN
ejpam-5970	62	21	,	,	PUNCT
ejpam-5970	62	22	d)(g	d)(g	NOUN
ejpam-5970	62	23	)	)	PUNCT
ejpam-5970	62	24	,	,	PUNCT
ejpam-5970	62	25	and	and	CCONJ
ejpam-5970	62	26	to	to	PART
ejpam-5970	62	27	determine	determine	VERB
ejpam-5970	62	28	its	its	PRON
ejpam-5970	62	29	exact	exact	ADJ
ejpam-5970	62	30	value	value	NOUN
ejpam-5970	62	31	for	for	ADP
ejpam-5970	62	32	selected	select	VERB
ejpam-5970	62	33	classes	class	NOUN
ejpam-5970	62	34	of	of	ADP
ejpam-5970	62	35	graphs	graph	NOUN
ejpam-5970	62	36	.	.	PUNCT
ejpam-5970	63	1	beyond	beyond	ADP
ejpam-5970	63	2	the	the	DET
ejpam-5970	63	3	theoretical	theoretical	ADJ
ejpam-5970	63	4	contributions	contribution	NOUN
ejpam-5970	63	5	,	,	PUNCT
ejpam-5970	63	6	this	this	DET
ejpam-5970	63	7	study	study	NOUN
ejpam-5970	63	8	demonstrates	demonstrate	VERB
ejpam-5970	63	9	the	the	DET
ejpam-5970	63	10	applicability	applicability	NOUN
ejpam-5970	63	11	of	of	ADP
ejpam-5970	63	12	lea(a	lea(a	PROPN
ejpam-5970	63	13	,	,	PUNCT
ejpam-5970	63	14	d	d	NOUN
ejpam-5970	63	15	)	)	PUNCT
ejpam-5970	63	16	coloring	color	VERB
ejpam-5970	63	17	in	in	ADP
ejpam-5970	63	18	real	real	ADJ
ejpam-5970	63	19	-	-	PUNCT
ejpam-5970	63	20	world	world	NOUN
ejpam-5970	63	21	scenarios	scenario	NOUN
ejpam-5970	63	22	by	by	ADP
ejpam-5970	63	23	integrating	integrate	VERB
ejpam-5970	63	24	it	it	PRON
ejpam-5970	63	25	into	into	ADP
ejpam-5970	63	26	the	the	DET
ejpam-5970	63	27	analysis	analysis	NOUN
ejpam-5970	63	28	of	of	ADP
ejpam-5970	63	29	a	a	DET
ejpam-5970	63	30	stgnn	stgnn	NOUN
ejpam-5970	63	31	model	model	NOUN
ejpam-5970	63	32	.	.	PUNCT
ejpam-5970	64	1	this	this	DET
ejpam-5970	64	2	integration	integration	NOUN
ejpam-5970	64	3	is	be	AUX
ejpam-5970	64	4	applied	apply	VERB
ejpam-5970	64	5	in	in	ADP
ejpam-5970	64	6	the	the	DET
ejpam-5970	64	7	context	context	NOUN
ejpam-5970	64	8	of	of	ADP
ejpam-5970	64	9	autonomous	autonomous	ADJ
ejpam-5970	64	10	controlled	control	VERB
ejpam-5970	64	11	environment	environment	NOUN
ejpam-5970	64	12	agriculture	agriculture	NOUN
ejpam-5970	64	13	(	(	PUNCT
ejpam-5970	64	14	cea	cea	PROPN
ejpam-5970	64	15	)	)	PUNCT
ejpam-5970	64	16	,	,	PUNCT
ejpam-5970	64	17	where	where	SCONJ
ejpam-5970	64	18	it	it	PRON
ejpam-5970	64	19	supports	support	VERB
ejpam-5970	64	20	multi	multi	ADJ
ejpam-5970	64	21	-	-	ADJ
ejpam-5970	64	22	step	step	ADJ
ejpam-5970	64	23	time	time	NOUN
ejpam-5970	64	24	series	series	PROPN
ejpam-5970	64	25	forecasting	forecasting	NOUN
ejpam-5970	64	26	of	of	ADP
ejpam-5970	64	27	nitrogen	nitrogen	NOUN
ejpam-5970	64	28	(	(	PUNCT
ejpam-5970	64	29	n	n	CCONJ
ejpam-5970	64	30	)	)	PUNCT
ejpam-5970	64	31	,	,	PUNCT
ejpam-5970	64	32	phosphorus	phosphorus	NOUN
ejpam-5970	64	33	(	(	PUNCT
ejpam-5970	64	34	p	p	NOUN
ejpam-5970	64	35	)	)	PUNCT
ejpam-5970	64	36	,	,	PUNCT
ejpam-5970	64	37	and	and	CCONJ
ejpam-5970	64	38	potassium	potassium	NOUN
ejpam-5970	64	39	(	(	PUNCT
ejpam-5970	64	40	k	k	NOUN
ejpam-5970	64	41	)	)	PUNCT
ejpam-5970	64	42	concentrations	concentration	NOUN
ejpam-5970	64	43	in	in	ADP
ejpam-5970	64	44	companion	companion	NOUN
ejpam-5970	64	45	plantation	plantation	NOUN
ejpam-5970	64	46	systems	system	NOUN
ejpam-5970	64	47	.	.	PUNCT
ejpam-5970	65	1	the	the	DET
ejpam-5970	65	2	proposed	propose	VERB
ejpam-5970	65	3	approach	approach	NOUN
ejpam-5970	65	4	not	not	PART
ejpam-5970	65	5	only	only	ADV
ejpam-5970	65	6	advances	advance	NOUN
ejpam-5970	65	7	graph	graph	NOUN
ejpam-5970	65	8	coloring	coloring	NOUN
ejpam-5970	65	9	theory	theory	NOUN
ejpam-5970	65	10	but	but	CCONJ
ejpam-5970	65	11	also	also	ADV
ejpam-5970	65	12	enhances	enhance	VERB
ejpam-5970	65	13	predictive	predictive	ADJ
ejpam-5970	65	14	accuracy	accuracy	NOUN
ejpam-5970	65	15	and	and	CCONJ
ejpam-5970	65	16	sensor	sensor	NOUN
ejpam-5970	65	17	efficiency	efficiency	NOUN
ejpam-5970	65	18	in	in	ADP
ejpam-5970	65	19	precision	precision	NOUN
ejpam-5970	65	20	agriculture	agriculture	NOUN
ejpam-5970	65	21	.	.	PUNCT
ejpam-5970	66	1	2	2	X
ejpam-5970	66	2	.	.	X
ejpam-5970	66	3	method	method	VERB
ejpam-5970	66	4	this	this	DET
ejpam-5970	66	5	research	research	NOUN
ejpam-5970	66	6	utilizes	utilize	VERB
ejpam-5970	66	7	both	both	CCONJ
ejpam-5970	66	8	analytical	analytical	ADJ
ejpam-5970	66	9	and	and	CCONJ
ejpam-5970	66	10	experimental	experimental	ADJ
ejpam-5970	66	11	methodologies	methodology	NOUN
ejpam-5970	66	12	.	.	PUNCT
ejpam-5970	67	1	in	in	ADP
ejpam-5970	67	2	the	the	DET
ejpam-5970	67	3	analytical	analytical	ADJ
ejpam-5970	67	4	section	section	NOUN
ejpam-5970	67	5	,	,	PUNCT
ejpam-5970	67	6	we	we	PRON
ejpam-5970	67	7	will	will	AUX
ejpam-5970	67	8	apply	apply	VERB
ejpam-5970	67	9	a	a	DET
ejpam-5970	67	10	mathematical	mathematical	ADJ
ejpam-5970	67	11	deductive	deductive	ADJ
ejpam-5970	67	12	approach	approach	NOUN
ejpam-5970	67	13	to	to	PART
ejpam-5970	67	14	obtain	obtain	VERB
ejpam-5970	67	15	some	some	DET
ejpam-5970	67	16	theorems	theorem	NOUN
ejpam-5970	67	17	,	,	PUNCT
ejpam-5970	67	18	we	we	PRON
ejpam-5970	67	19	use	use	VERB
ejpam-5970	67	20	the	the	DET
ejpam-5970	67	21	the	the	DET
ejpam-5970	67	22	following	follow	VERB
ejpam-5970	67	23	some	some	DET
ejpam-5970	67	24	known	know	VERB
ejpam-5970	67	25	lower	low	ADJ
ejpam-5970	67	26	bounds	bound	NOUN
ejpam-5970	67	27	to	to	PART
ejpam-5970	67	28	obtain	obtain	VERB
ejpam-5970	67	29	the	the	DET
ejpam-5970	67	30	new	new	ADJ
ejpam-5970	67	31	theorems	theorem	NOUN
ejpam-5970	67	32	.	.	PUNCT
ejpam-5970	68	1	observation	observation	NOUN
ejpam-5970	68	2	1	1	NUM
ejpam-5970	68	3	.	.	PUNCT
ejpam-5970	69	1	[	[	X
ejpam-5970	69	2	1	1	NUM
ejpam-5970	69	3	]	]	SYM
ejpam-5970	69	4	χlea(g	χlea(g	PROPN
ejpam-5970	69	5	)	)	PUNCT
ejpam-5970	69	6	≥	≥	NOUN
ejpam-5970	69	7	χ(g	χ(g	PROPN
ejpam-5970	69	8	)	)	PUNCT
ejpam-5970	69	9	,	,	PUNCT
ejpam-5970	69	10	where	where	SCONJ
ejpam-5970	69	11	χ(g	χ(g	PROPN
ejpam-5970	69	12	)	)	PUNCT
ejpam-5970	69	13	is	be	AUX
ejpam-5970	69	14	a	a	DET
ejpam-5970	69	15	chromatic	chromatic	ADJ
ejpam-5970	69	16	number	number	NOUN
ejpam-5970	69	17	of	of	ADP
ejpam-5970	69	18	graph	graph	NOUN
ejpam-5970	69	19	coloring	color	VERB
ejpam-5970	69	20	g.	g.	PROPN
ejpam-5970	69	21	observation	observation	NOUN
ejpam-5970	69	22	2	2	NUM
ejpam-5970	69	23	.	.	PUNCT
ejpam-5970	70	1	[	[	X
ejpam-5970	70	2	3	3	X
ejpam-5970	70	3	]	]	PUNCT
ejpam-5970	70	4	χle(a	χle(a	PROPN
ejpam-5970	70	5	,	,	PUNCT
ejpam-5970	70	6	d)(g	d)(g	PROPN
ejpam-5970	70	7	)	)	PUNCT
ejpam-5970	70	8	≥	≥	NOUN
ejpam-5970	70	9	χlea(g	χlea(g	PROPN
ejpam-5970	70	10	)	)	PUNCT
ejpam-5970	70	11	≥	≥	NOUN
ejpam-5970	70	12	χ(g	χ(g	PROPN
ejpam-5970	70	13	)	)	PUNCT
ejpam-5970	70	14	observation	observation	NOUN
ejpam-5970	70	15	3	3	NUM
ejpam-5970	70	16	.	.	PUNCT
ejpam-5970	71	1	[	[	X
ejpam-5970	71	2	1	1	NUM
ejpam-5970	71	3	]	]	SYM
ejpam-5970	71	4	χlea(g	χlea(g	PROPN
ejpam-5970	71	5	)	)	PUNCT
ejpam-5970	71	6	≥	≥	NOUN
ejpam-5970	71	7	∆(g	∆(g	NOUN
ejpam-5970	71	8	)	)	PUNCT
ejpam-5970	71	9	,	,	PUNCT
ejpam-5970	71	10	where	where	SCONJ
ejpam-5970	71	11	∆(g	∆(g	NOUN
ejpam-5970	71	12	)	)	PUNCT
ejpam-5970	71	13	is	be	AUX
ejpam-5970	71	14	maximum	maximum	ADJ
ejpam-5970	71	15	degrees	degree	NOUN
ejpam-5970	71	16	of	of	ADP
ejpam-5970	71	17	g	g	NOUN
ejpam-5970	71	18	observation	observation	NOUN
ejpam-5970	71	19	4	4	NUM
ejpam-5970	71	20	.	.	PUNCT
ejpam-5970	72	1	[	[	X
ejpam-5970	72	2	13	13	NUM
ejpam-5970	72	3	]	]	SYM
ejpam-5970	72	4	χle(a	χle(a	PROPN
ejpam-5970	72	5	,	,	PUNCT
ejpam-5970	72	6	d)(g	d)(g	PROPN
ejpam-5970	72	7	)	)	PUNCT
ejpam-5970	72	8	≥	≥	NOUN
ejpam-5970	72	9	χlea(g	χlea(g	PROPN
ejpam-5970	72	10	)	)	PUNCT
ejpam-5970	72	11	≥	≥	NOUN
ejpam-5970	72	12	∆(g	∆(g	NOUN
ejpam-5970	72	13	)	)	PUNCT
ejpam-5970	72	14	observation	observation	NOUN
ejpam-5970	72	15	5	5	NUM
ejpam-5970	72	16	.	.	PUNCT
ejpam-5970	73	1	[	[	X
ejpam-5970	73	2	16	16	NUM
ejpam-5970	73	3	]	]	PUNCT
ejpam-5970	73	4	χle(a	χle(a	PROPN
ejpam-5970	73	5	,	,	PUNCT
ejpam-5970	73	6	d)(g	d)(g	PROPN
ejpam-5970	73	7	)	)	PUNCT
ejpam-5970	73	8	≥	≥	NOUN
ejpam-5970	73	9	χlea(g	χlea(g	PROPN
ejpam-5970	73	10	)	)	PUNCT
ejpam-5970	73	11	≥	≥	NOUN
ejpam-5970	73	12	χ(g	χ(g	PROPN
ejpam-5970	73	13	)	)	PUNCT
ejpam-5970	73	14	≥	≥	NOUN
ejpam-5970	73	15	∆(g	∆(g	NOUN
ejpam-5970	73	16	)	)	PUNCT
ejpam-5970	73	17	.	.	PUNCT
ejpam-5970	74	1	observation	observation	NOUN
ejpam-5970	74	2	6	6	NUM
ejpam-5970	74	3	.	.	PUNCT
ejpam-5970	75	1	[	[	X
ejpam-5970	75	2	16	16	NUM
ejpam-5970	75	3	]	]	X
ejpam-5970	75	4	if	if	SCONJ
ejpam-5970	75	5	the	the	DET
ejpam-5970	75	6	graph	graph	NOUN
ejpam-5970	75	7	g	g	PROPN
ejpam-5970	75	8	admits	admit	VERB
ejpam-5970	75	9	an	an	DET
ejpam-5970	75	10	local	local	ADJ
ejpam-5970	75	11	(	(	PUNCT
ejpam-5970	75	12	a	a	PRON
ejpam-5970	75	13	,	,	PUNCT
ejpam-5970	75	14	d)-edge	d)-edge	ADJ
ejpam-5970	75	15	antimagic	antimagic	ADJ
ejpam-5970	75	16	labeling	labeling	NOUN
ejpam-5970	75	17	with	with	ADP
ejpam-5970	75	18	k	k	NOUN
ejpam-5970	75	19	-	-	NOUN
ejpam-5970	75	20	colors	color	NOUN
ejpam-5970	75	21	,	,	PUNCT
ejpam-5970	75	22	then	then	ADV
ejpam-5970	75	23	d	d	X
ejpam-5970	75	24	≤	≤	PROPN
ejpam-5970	75	25	2p−4	2p−4	NUM
ejpam-5970	75	26	k−1	k−1	PROPN
ejpam-5970	75	27	.	.	PUNCT
ejpam-5970	76	1	whilst	whilst	SCONJ
ejpam-5970	76	2	,	,	PUNCT
ejpam-5970	76	3	in	in	ADP
ejpam-5970	76	4	the	the	DET
ejpam-5970	76	5	experimental	experimental	ADJ
ejpam-5970	76	6	method	method	NOUN
ejpam-5970	76	7	,	,	PUNCT
ejpam-5970	76	8	we	we	PRON
ejpam-5970	76	9	will	will	AUX
ejpam-5970	76	10	use	use	VERB
ejpam-5970	76	11	a	a	DET
ejpam-5970	76	12	computer	computer	NOUN
ejpam-5970	76	13	programming	programming	NOUN
ejpam-5970	76	14	to	to	PART
ejpam-5970	76	15	do	do	VERB
ejpam-5970	76	16	simulation	simulation	NOUN
ejpam-5970	76	17	on	on	ADP
ejpam-5970	76	18	autonomous	autonomous	ADJ
ejpam-5970	76	19	controlled	control	VERB
ejpam-5970	76	20	environment	environment	NOUN
ejpam-5970	76	21	agriculture	agriculture	NOUN
ejpam-5970	76	22	(	(	PUNCT
ejpam-5970	76	23	cea	cea	PROPN
ejpam-5970	76	24	)	)	PUNCT
ejpam-5970	76	25	development	development	NOUN
ejpam-5970	76	26	on	on	ADP
ejpam-5970	76	27	multistep	multistep	ADJ
ejpam-5970	76	28	time	time	NOUN
ejpam-5970	76	29	series	series	PROPN
ejpam-5970	76	30	forecasting	forecasting	NOUN
ejpam-5970	76	31	for	for	ADP
ejpam-5970	76	32	npk	npk	NOUN
ejpam-5970	76	33	concentration	concentration	NOUN
ejpam-5970	76	34	of	of	ADP
ejpam-5970	76	35	companion	companion	NOUN
ejpam-5970	76	36	plantations	plantation	NOUN
ejpam-5970	76	37	of	of	ADP
ejpam-5970	76	38	rosa	rosa	PROPN
ejpam-5970	76	39	sp	sp	PROPN
ejpam-5970	76	40	.	.	PROPN
ejpam-5970	76	41	a.	a.	PROPN
ejpam-5970	76	42	i.	i.	PROPN
ejpam-5970	76	43	kristiana	kristiana	PROPN
ejpam-5970	76	44	,	,	PUNCT
ejpam-5970	76	45	et	et	PROPN
ejpam-5970	76	46	al	al	PROPN
ejpam-5970	76	47	.	.	PUNCT
ejpam-5970	76	48	/	/	SYM
ejpam-5970	76	49	eur	eur	PROPN
ejpam-5970	76	50	.	.	PUNCT
ejpam-5970	77	1	j.	j.	PROPN
ejpam-5970	77	2	pure	pure	PROPN
ejpam-5970	77	3	appl	appl	PROPN
ejpam-5970	77	4	.	.	PROPN
ejpam-5970	77	5	math	math	PROPN
ejpam-5970	77	6	,	,	PUNCT
ejpam-5970	77	7	18	18	NUM
ejpam-5970	77	8	(	(	PUNCT
ejpam-5970	77	9	3	3	NUM
ejpam-5970	77	10	)	)	PUNCT
ejpam-5970	77	11	(	(	PUNCT
ejpam-5970	77	12	2025	2025	NUM
ejpam-5970	77	13	)	)	PUNCT
ejpam-5970	77	14	,	,	PUNCT
ejpam-5970	77	15	5970	5970	NUM
ejpam-5970	77	16	4	4	NUM
ejpam-5970	77	17	of	of	ADP
ejpam-5970	77	18	18	18	NUM
ejpam-5970	77	19	plantation	plantation	NOUN
ejpam-5970	77	20	,	,	PUNCT
ejpam-5970	77	21	bougainvillea	bougainvillea	PROPN
ejpam-5970	77	22	spectabilis	spectabili	VERB
ejpam-5970	77	23	plantation	plantation	NOUN
ejpam-5970	77	24	,	,	PUNCT
ejpam-5970	77	25	cryptanthus	cryptanthus	ADJ
ejpam-5970	77	26	spp	spp	NOUN
ejpam-5970	77	27	plantation	plantation	NOUN
ejpam-5970	77	28	,	,	PUNCT
ejpam-5970	77	29	and	and	CCONJ
ejpam-5970	77	30	bromeliaceae	bromeliaceae	PROPN
ejpam-5970	77	31	plantation	plantation	NOUN
ejpam-5970	77	32	.	.	PUNCT
ejpam-5970	78	1	first	first	ADV
ejpam-5970	78	2	,	,	PUNCT
ejpam-5970	78	3	we	we	PRON
ejpam-5970	78	4	will	will	AUX
ejpam-5970	78	5	display	display	VERB
ejpam-5970	78	6	the	the	DET
ejpam-5970	78	7	vertex	vertex	NOUN
ejpam-5970	78	8	embedding	embed	VERB
ejpam-5970	78	9	process	process	NOUN
ejpam-5970	78	10	of	of	ADP
ejpam-5970	78	11	a	a	DET
ejpam-5970	78	12	single	single	ADJ
ejpam-5970	78	13	-	-	PUNCT
ejpam-5970	78	14	layer	layer	NOUN
ejpam-5970	78	15	gnn	gnn	NOUN
ejpam-5970	78	16	for	for	ADP
ejpam-5970	78	17	a	a	DET
ejpam-5970	78	18	given	give	VERB
ejpam-5970	78	19	graph	graph	NOUN
ejpam-5970	78	20	that	that	PRON
ejpam-5970	78	21	contains	contain	VERB
ejpam-5970	78	22	three	three	NUM
ejpam-5970	78	23	feature	feature	NOUN
ejpam-5970	78	24	data	datum	NOUN
ejpam-5970	78	25	,	,	PUNCT
ejpam-5970	78	26	namely	namely	ADV
ejpam-5970	78	27	n	n	CCONJ
ejpam-5970	78	28	,	,	PUNCT
ejpam-5970	78	29	p	p	X
ejpam-5970	78	30	,	,	PUNCT
ejpam-5970	78	31	and	and	CCONJ
ejpam-5970	78	32	k	k	PROPN
ejpam-5970	78	33	data	datum	NOUN
ejpam-5970	78	34	for	for	ADP
ejpam-5970	78	35	three	three	NUM
ejpam-5970	78	36	month	month	NOUN
ejpam-5970	78	37	observation	observation	NOUN
ejpam-5970	78	38	.	.	PUNCT
ejpam-5970	79	1	second	second	ADJ
ejpam-5970	79	2	,	,	PUNCT
ejpam-5970	79	3	we	we	PRON
ejpam-5970	79	4	will	will	AUX
ejpam-5970	79	5	write	write	VERB
ejpam-5970	79	6	stgnn	stgnn	NOUN
ejpam-5970	79	7	programming	programming	NOUN
ejpam-5970	79	8	,	,	PUNCT
ejpam-5970	79	9	train	train	VERB
ejpam-5970	79	10	a	a	DET
ejpam-5970	79	11	model	model	NOUN
ejpam-5970	79	12	utilizing	utilize	VERB
ejpam-5970	79	13	80	80	NUM
ejpam-5970	79	14	%	%	NOUN
ejpam-5970	79	15	of	of	ADP
ejpam-5970	79	16	the	the	DET
ejpam-5970	79	17	input	input	NOUN
ejpam-5970	79	18	data	datum	NOUN
ejpam-5970	79	19	obtained	obtain	VERB
ejpam-5970	79	20	from	from	ADP
ejpam-5970	79	21	the	the	DET
ejpam-5970	79	22	vertex	vertex	NOUN
ejpam-5970	79	23	embedding	embed	VERB
ejpam-5970	79	24	process	process	NOUN
ejpam-5970	79	25	,	,	PUNCT
ejpam-5970	79	26	test	test	NOUN
ejpam-5970	79	27	and	and	CCONJ
ejpam-5970	79	28	finally	finally	ADV
ejpam-5970	79	29	forecast	forecast	VERB
ejpam-5970	79	30	the	the	DET
ejpam-5970	79	31	npk	npk	NOUN
ejpam-5970	79	32	fertilization	fertilization	NOUN
ejpam-5970	79	33	to	to	PART
ejpam-5970	79	34	determine	determine	VERB
ejpam-5970	79	35	the	the	DET
ejpam-5970	79	36	time	time	NOUN
ejpam-5970	79	37	of	of	ADP
ejpam-5970	79	38	application	application	NOUN
ejpam-5970	79	39	of	of	ADP
ejpam-5970	79	40	fertilizer	fertilizer	NOUN
ejpam-5970	79	41	to	to	ADP
ejpam-5970	79	42	rosa	rosa	PROPN
ejpam-5970	79	43	sp	sp	PROPN
ejpam-5970	79	44	plantation	plantation	NOUN
ejpam-5970	79	45	,	,	PUNCT
ejpam-5970	79	46	bromeliaceae	bromeliaceae	PROPN
ejpam-5970	79	47	plantation	plantation	NOUN
ejpam-5970	79	48	,	,	PUNCT
ejpam-5970	79	49	bougainvillea	bougainvillea	PROPN
ejpam-5970	79	50	spectabilis	spectabili	VERB
ejpam-5970	79	51	plantation	plantation	NOUN
ejpam-5970	79	52	and	and	CCONJ
ejpam-5970	79	53	cryptanthus	cryptanthus	ADJ
ejpam-5970	79	54	sp	sp	ADP
ejpam-5970	79	55	plantation	plantation	NOUN
ejpam-5970	79	56	.	.	PUNCT
ejpam-5970	80	1	we	we	PRON
ejpam-5970	80	2	use	use	VERB
ejpam-5970	80	3	the	the	DET
ejpam-5970	80	4	algorithm	algorithm	NOUN
ejpam-5970	80	5	1	1	NUM
ejpam-5970	80	6	for	for	ADP
ejpam-5970	80	7	studying	study	VERB
ejpam-5970	80	8	the	the	DET
ejpam-5970	80	9	fuel	fuel	NOUN
ejpam-5970	80	10	purchase	purchase	NOUN
ejpam-5970	80	11	distribution	distribution	NOUN
ejpam-5970	80	12	by	by	ADP
ejpam-5970	80	13	using	use	VERB
ejpam-5970	80	14	stgnn	stgnn	NOUN
ejpam-5970	80	15	combined	combine	VERB
ejpam-5970	80	16	by	by	ADP
ejpam-5970	80	17	lea(a	lea(a	PROPN
ejpam-5970	80	18	,	,	PUNCT
ejpam-5970	80	19	d	d	NOUN
ejpam-5970	80	20	)	)	PUNCT
ejpam-5970	80	21	coloring	coloring	NOUN
ejpam-5970	80	22	.	.	PUNCT
ejpam-5970	81	1	algorithm	algorithm	NOUN
ejpam-5970	81	2	1	1	NUM
ejpam-5970	81	3	(	(	PUNCT
ejpam-5970	81	4	phtb	phtb	PROPN
ejpam-5970	81	5	)	)	PUNCT
ejpam-5970	81	6	.	.	PUNCT
ejpam-5970	82	1	inputinput	inputinput	NOUN
ejpam-5970	82	2	outputoutput	outputoutput	VERB
ejpam-5970	82	3	graph	graph	NOUN
ejpam-5970	82	4	g(v	g(v	PROPN
ejpam-5970	82	5	,	,	PUNCT
ejpam-5970	82	6	e	e	NOUN
ejpam-5970	82	7	)	)	PUNCT
ejpam-5970	82	8	,	,	PUNCT
ejpam-5970	82	9	adjacency	adjacency	NOUN
ejpam-5970	82	10	matrix	matrix	NOUN
ejpam-5970	82	11	a	a	PRON
ejpam-5970	82	12	from	from	ADP
ejpam-5970	82	13	graph	graph	NOUN
ejpam-5970	82	14	g	g	NOUN
ejpam-5970	82	15	,	,	PUNCT
ejpam-5970	82	16	feature	feature	NOUN
ejpam-5970	82	17	matrix	matrix	NOUN
ejpam-5970	82	18	hn×m	hn×m	NOUN
ejpam-5970	82	19	,	,	PUNCT
ejpam-5970	82	20	and	and	CCONJ
ejpam-5970	82	21	threshold	threshold	NOUN
ejpam-5970	82	22	ϵ	ϵ	PRON
ejpam-5970	82	23	time	time	NOUN
ejpam-5970	82	24	series	series	PROPN
ejpam-5970	82	25	prediction	prediction	NOUN
ejpam-5970	82	26	results	result	NOUN
ejpam-5970	82	27	initialize	initialize	VERB
ejpam-5970	82	28	parameters	parameter	NOUN
ejpam-5970	82	29	:	:	PUNCT
ejpam-5970	82	30	weights	weights	PROPN
ejpam-5970	82	31	w	w	PROPN
ejpam-5970	82	32	,	,	PUNCT
ejpam-5970	82	33	bias	bias	NOUN
ejpam-5970	82	34	β	β	NOUN
ejpam-5970	82	35	,	,	PUNCT
ejpam-5970	82	36	and	and	CCONJ
ejpam-5970	82	37	learning	learn	VERB
ejpam-5970	82	38	rate	rate	NOUN
ejpam-5970	82	39	α	α	PROPN
ejpam-5970	82	40	.	.	PUNCT
ejpam-5970	82	41	error	error	NOUN
ejpam-5970	82	42	<	<	X
ejpam-5970	82	43	ϵ	ϵ	X
ejpam-5970	82	44	perform	perform	VERB
ejpam-5970	82	45	message	message	NOUN
ejpam-5970	82	46	propagation	propagation	NOUN
ejpam-5970	82	47	mu	mu	NOUN
ejpam-5970	82	48	λ	λ	PROPN
ejpam-5970	82	49	=	=	PUNCT
ejpam-5970	83	1	msgλ(h	msgλ(h	PROPN
ejpam-5970	83	2	λ−1	λ−1	PROPN
ejpam-5970	83	3	u	u	PROPN
ejpam-5970	83	4	)	)	PUNCT
ejpam-5970	83	5	.	.	PUNCT
ejpam-5970	84	1	compute	compute	PROPN
ejpam-5970	84	2	aggregated	aggregate	VERB
ejpam-5970	84	3	message	message	NOUN
ejpam-5970	84	4	hλv	hλv	NOUN
ejpam-5970	84	5	=	=	SYM
ejpam-5970	84	6	aggλ{mλ−1	aggλ{mλ−1	NOUN
ejpam-5970	84	7	u	u	NOUN
ejpam-5970	84	8	,	,	PUNCT
ejpam-5970	84	9	u	u	PROPN
ejpam-5970	84	10	∈	∈	PROPN
ejpam-5970	84	11	n(v	n(v	PROPN
ejpam-5970	84	12	)	)	PUNCT
ejpam-5970	84	13	}	}	PUNCT
ejpam-5970	84	14	.	.	PUNCT
ejpam-5970	85	1	evaluate	evaluate	VERB
ejpam-5970	85	2	error	error	NOUN
ejpam-5970	85	3	λ	λ	NOUN
ejpam-5970	85	4	=	=	SYM
ejpam-5970	85	5	||hvi−hvj	||hvi−hvj	VERB
ejpam-5970	85	6	||2	||2	NOUN
ejpam-5970	85	7	|e|	|e|	PROPN
ejpam-5970	85	8	.	.	PUNCT
ejpam-5970	86	1	update	update	NOUN
ejpam-5970	86	2	parameters	parameter	NOUN
ejpam-5970	86	3	:	:	PUNCT
ejpam-5970	87	1	w	w	PROPN
ejpam-5970	87	2	λ+1	λ+1	NUM
ejpam-5970	87	3	j	j	NOUN
ejpam-5970	87	4	=	=	PUNCT
ejpam-5970	87	5	w	w	PROPN
ejpam-5970	87	6	λ	λ	PROPN
ejpam-5970	87	7	j	j	PROPN
ejpam-5970	87	8	+	+	CCONJ
ejpam-5970	87	9	α	α	PROPN
ejpam-5970	87	10	·	·	PUNCT
ejpam-5970	87	11	zj	zj	PROPN
ejpam-5970	87	12	·	·	PUNCT
ejpam-5970	87	13	eλ	eλ	PROPN
ejpam-5970	87	14	.	.	PUNCT
ejpam-5970	87	15	store	store	VERB
ejpam-5970	87	16	the	the	DET
ejpam-5970	87	17	final	final	ADJ
ejpam-5970	87	18	node	node	ADJ
ejpam-5970	87	19	representations	representation	NOUN
ejpam-5970	87	20	as	as	ADP
ejpam-5970	87	21	embedding	embed	VERB
ejpam-5970	87	22	vector	vector	NOUN
ejpam-5970	87	23	.	.	PUNCT
ejpam-5970	88	1	load	load	VERB
ejpam-5970	88	2	the	the	DET
ejpam-5970	88	3	feature	feature	NOUN
ejpam-5970	88	4	embedding	embed	VERB
ejpam-5970	88	5	from	from	ADP
ejpam-5970	88	6	saved	save	VERB
ejpam-5970	88	7	data	datum	NOUN
ejpam-5970	88	8	.	.	PUNCT
ejpam-5970	89	1	apply	apply	VERB
ejpam-5970	89	2	forecasting	forecasting	NOUN
ejpam-5970	89	3	using	use	VERB
ejpam-5970	89	4	learned	learn	VERB
ejpam-5970	89	5	representations	representation	NOUN
ejpam-5970	89	6	.	.	PUNCT
ejpam-5970	90	1	output	output	VERB
ejpam-5970	90	2	the	the	DET
ejpam-5970	90	3	best	well	ADV
ejpam-5970	90	4	-	-	PUNCT
ejpam-5970	90	5	fit	fit	ADJ
ejpam-5970	90	6	prediction	prediction	NOUN
ejpam-5970	90	7	based	base	VERB
ejpam-5970	90	8	on	on	ADP
ejpam-5970	90	9	training	training	NOUN
ejpam-5970	90	10	and	and	CCONJ
ejpam-5970	90	11	validation	validation	NOUN
ejpam-5970	90	12	.	.	PUNCT
ejpam-5970	91	1	single	single	ADJ
ejpam-5970	91	2	-	-	PUNCT
ejpam-5970	91	3	layer	layer	NOUN
ejpam-5970	91	4	graph	graph	NOUN
ejpam-5970	91	5	neural	neural	ADJ
ejpam-5970	91	6	network	network	NOUN
ejpam-5970	91	7	for	for	ADP
ejpam-5970	91	8	forecasting	forecast	VERB
ejpam-5970	91	9	3	3	NUM
ejpam-5970	91	10	.	.	PUNCT
ejpam-5970	91	11	main	main	ADJ
ejpam-5970	91	12	result	result	NOUN
ejpam-5970	91	13	3.1	3.1	NUM
ejpam-5970	91	14	.	.	PUNCT
ejpam-5970	92	1	local	local	ADJ
ejpam-5970	92	2	(	(	PUNCT
ejpam-5970	92	3	a	a	PRON
ejpam-5970	92	4	,	,	PUNCT
ejpam-5970	92	5	d)-edge	d)-edge	NOUN
ejpam-5970	92	6	antimagic	antimagic	ADJ
ejpam-5970	92	7	coloring	coloring	NOUN
ejpam-5970	92	8	in	in	ADP
ejpam-5970	92	9	this	this	DET
ejpam-5970	92	10	section	section	NOUN
ejpam-5970	92	11	,	,	PUNCT
ejpam-5970	92	12	we	we	PRON
ejpam-5970	92	13	will	will	AUX
ejpam-5970	92	14	show	show	VERB
ejpam-5970	92	15	the	the	DET
ejpam-5970	92	16	existence	existence	NOUN
ejpam-5970	92	17	of	of	ADP
ejpam-5970	92	18	lea(a	lea(a	PROPN
ejpam-5970	92	19	,	,	PUNCT
ejpam-5970	92	20	d	d	NOUN
ejpam-5970	92	21	)	)	PUNCT
ejpam-5970	92	22	coloring	coloring	NOUN
ejpam-5970	92	23	of	of	ADP
ejpam-5970	92	24	a	a	DET
ejpam-5970	92	25	some	some	DET
ejpam-5970	92	26	specific	specific	ADJ
ejpam-5970	92	27	families	family	NOUN
ejpam-5970	92	28	of	of	ADP
ejpam-5970	92	29	graphs	graph	NOUN
ejpam-5970	92	30	,	,	PUNCT
ejpam-5970	92	31	and	and	CCONJ
ejpam-5970	92	32	determine	determine	VERB
ejpam-5970	92	33	the	the	DET
ejpam-5970	92	34	exact	exact	ADJ
ejpam-5970	92	35	value	value	NOUN
ejpam-5970	92	36	of	of	ADP
ejpam-5970	92	37	the	the	DET
ejpam-5970	92	38	lea(a	lea(a	PROPN
ejpam-5970	92	39	,	,	PUNCT
ejpam-5970	92	40	d	d	NOUN
ejpam-5970	92	41	)	)	PUNCT
ejpam-5970	92	42	chromatic	chromatic	ADJ
ejpam-5970	92	43	number	number	NOUN
ejpam-5970	92	44	of	of	ADP
ejpam-5970	92	45	pn	pn	PROPN
ejpam-5970	92	46	▷	▷	PROPN
ejpam-5970	92	47	pm	pm	NOUN
ejpam-5970	92	48	,	,	PUNCT
ejpam-5970	92	49	amal(fn	amal(fn	NOUN
ejpam-5970	92	50	,	,	PUNCT
ejpam-5970	92	51	v	v	NOUN
ejpam-5970	92	52	,	,	PUNCT
ejpam-5970	92	53	m	m	NOUN
ejpam-5970	92	54	)	)	PUNCT
ejpam-5970	92	55	,	,	PUNCT
ejpam-5970	92	56	and	and	CCONJ
ejpam-5970	92	57	amal(vn	amal(vn	PROPN
ejpam-5970	92	58	,	,	PUNCT
ejpam-5970	92	59	v	v	NOUN
ejpam-5970	92	60	,	,	PUNCT
ejpam-5970	92	61	m	m	NOUN
ejpam-5970	92	62	)	)	PUNCT
ejpam-5970	92	63	.	.	PUNCT
ejpam-5970	93	1	further	far	ADV
ejpam-5970	93	2	,	,	PUNCT
ejpam-5970	93	3	we	we	PRON
ejpam-5970	93	4	will	will	AUX
ejpam-5970	93	5	use	use	VERB
ejpam-5970	93	6	the	the	DET
ejpam-5970	93	7	obtained	obtain	VERB
ejpam-5970	93	8	theorem	theorem	NOUN
ejpam-5970	93	9	for	for	ADP
ejpam-5970	93	10	analysing	analyse	VERB
ejpam-5970	93	11	stgnn	stgnn	NOUN
ejpam-5970	93	12	model	model	NOUN
ejpam-5970	93	13	for	for	ADP
ejpam-5970	93	14	autonomous	autonomous	ADJ
ejpam-5970	93	15	controlled	control	VERB
ejpam-5970	93	16	environment	environment	NOUN
ejpam-5970	93	17	agriculture	agriculture	NOUN
ejpam-5970	93	18	(	(	PUNCT
ejpam-5970	93	19	cea	cea	PROPN
ejpam-5970	93	20	)	)	PUNCT
ejpam-5970	93	21	development	development	NOUN
ejpam-5970	93	22	on	on	ADP
ejpam-5970	93	23	multi	multi	ADJ
ejpam-5970	93	24	-	-	ADJ
ejpam-5970	93	25	step	step	ADJ
ejpam-5970	93	26	time	time	NOUN
ejpam-5970	93	27	series	series	NOUN
ejpam-5970	93	28	forecasting	forecasting	NOUN
ejpam-5970	93	29	for	for	ADP
ejpam-5970	93	30	npk	npk	NOUN
ejpam-5970	93	31	concentration	concentration	NOUN
ejpam-5970	93	32	of	of	ADP
ejpam-5970	93	33	companion	companion	NOUN
ejpam-5970	93	34	plantations	plantation	NOUN
ejpam-5970	93	35	.	.	PUNCT
ejpam-5970	94	1	theorem	theorem	NOUN
ejpam-5970	94	2	1	1	NUM
ejpam-5970	94	3	.	.	PUNCT
ejpam-5970	95	1	let	let	VERB
ejpam-5970	95	2	pn	pn	PROPN
ejpam-5970	95	3	▷pm	▷pm	PROPN
ejpam-5970	95	4	be	be	AUX
ejpam-5970	95	5	a	a	DET
ejpam-5970	95	6	comb	comb	NOUN
ejpam-5970	95	7	product	product	NOUN
ejpam-5970	95	8	between	between	ADP
ejpam-5970	95	9	pn	pn	PROPN
ejpam-5970	95	10	and	and	CCONJ
ejpam-5970	95	11	pm	pm	NOUN
ejpam-5970	95	12	graph	graph	NOUN
ejpam-5970	95	13	with	with	ADP
ejpam-5970	95	14	n	n	CCONJ
ejpam-5970	95	15	,	,	PUNCT
ejpam-5970	95	16	m	m	VERB
ejpam-5970	95	17	≥	≥	NOUN
ejpam-5970	95	18	3	3	X
ejpam-5970	95	19	.	.	PUNCT
ejpam-5970	96	1	we	we	PRON
ejpam-5970	96	2	have	have	VERB
ejpam-5970	96	3	χle(nm−n+3,2)(pn	χle(nm−n+3,2)(pn	NUM
ejpam-5970	96	4	▷	▷	ADJ
ejpam-5970	96	5	pm	pm	NOUN
ejpam-5970	96	6	)	)	PUNCT
ejpam-5970	96	7	=	=	SYM
ejpam-5970	96	8	n	n	CCONJ
ejpam-5970	96	9	,	,	PUNCT
ejpam-5970	96	10	for	for	ADP
ejpam-5970	96	11	m	m	PROPN
ejpam-5970	96	12	≡	≡	PROPN
ejpam-5970	96	13	1(mod	1(mod	NUM
ejpam-5970	96	14	2	2	NUM
ejpam-5970	96	15	)	)	PUNCT
ejpam-5970	96	16	,	,	PUNCT
ejpam-5970	96	17	n	n	NUM
ejpam-5970	96	18	≡	≡	PROPN
ejpam-5970	96	19	0(mod	0(mod	NOUN
ejpam-5970	96	20	2	2	NUM
ejpam-5970	96	21	)	)	PUNCT
ejpam-5970	96	22	;	;	PUNCT
ejpam-5970	96	23	and	and	CCONJ
ejpam-5970	96	24	χle(nm+1,2)(pn	χle(nm+1,2)(pn	PROPN
ejpam-5970	96	25	▷	▷	ADJ
ejpam-5970	96	26	pm	pm	NOUN
ejpam-5970	96	27	)	)	PUNCT
ejpam-5970	96	28	=	=	SYM
ejpam-5970	96	29	n	n	CCONJ
ejpam-5970	96	30	,	,	PUNCT
ejpam-5970	96	31	for	for	ADP
ejpam-5970	96	32	m	m	PROPN
ejpam-5970	96	33	,	,	PUNCT
ejpam-5970	96	34	n	n	PRON
ejpam-5970	96	35	≡	≡	PROPN
ejpam-5970	96	36	0(mod	0(mod	NOUN
ejpam-5970	96	37	2	2	NUM
ejpam-5970	96	38	)	)	PUNCT
ejpam-5970	96	39	.	.	PUNCT
ejpam-5970	97	1	proof	proof	NOUN
ejpam-5970	97	2	.	.	PUNCT
ejpam-5970	98	1	we	we	PRON
ejpam-5970	98	2	begin	begin	VERB
ejpam-5970	98	3	by	by	ADP
ejpam-5970	98	4	recalling	recall	VERB
ejpam-5970	98	5	the	the	DET
ejpam-5970	98	6	structure	structure	NOUN
ejpam-5970	98	7	of	of	ADP
ejpam-5970	98	8	the	the	DET
ejpam-5970	98	9	comb	comb	NOUN
ejpam-5970	98	10	product	product	NOUN
ejpam-5970	98	11	pn	pn	PROPN
ejpam-5970	98	12	▷	▷	ADJ
ejpam-5970	98	13	pm	pm	NOUN
ejpam-5970	98	14	,	,	PUNCT
ejpam-5970	98	15	which	which	PRON
ejpam-5970	98	16	is	be	AUX
ejpam-5970	98	17	a	a	DET
ejpam-5970	98	18	connected	connected	ADJ
ejpam-5970	98	19	graph	graph	NOUN
ejpam-5970	98	20	composed	compose	VERB
ejpam-5970	98	21	of	of	ADP
ejpam-5970	98	22	n	n	NOUN
ejpam-5970	98	23	copies	copy	NOUN
ejpam-5970	98	24	of	of	ADP
ejpam-5970	98	25	the	the	DET
ejpam-5970	98	26	path	path	NOUN
ejpam-5970	98	27	pm	pm	NOUN
ejpam-5970	98	28	,	,	PUNCT
ejpam-5970	98	29	where	where	SCONJ
ejpam-5970	98	30	each	each	DET
ejpam-5970	98	31	pm	pm	NOUN
ejpam-5970	98	32	is	be	AUX
ejpam-5970	98	33	connected	connect	VERB
ejpam-5970	98	34	via	via	ADP
ejpam-5970	98	35	its	its	PRON
ejpam-5970	98	36	a.	a.	NOUN
ejpam-5970	98	37	i.	i.	PROPN
ejpam-5970	98	38	kristiana	kristiana	PROPN
ejpam-5970	98	39	,	,	PUNCT
ejpam-5970	98	40	et	et	PROPN
ejpam-5970	98	41	al	al	PROPN
ejpam-5970	98	42	.	.	PUNCT
ejpam-5970	98	43	/	/	SYM
ejpam-5970	98	44	eur	eur	PROPN
ejpam-5970	98	45	.	.	PUNCT
ejpam-5970	99	1	j.	j.	PROPN
ejpam-5970	99	2	pure	pure	PROPN
ejpam-5970	99	3	appl	appl	PROPN
ejpam-5970	99	4	.	.	PROPN
ejpam-5970	99	5	math	math	PROPN
ejpam-5970	99	6	,	,	PUNCT
ejpam-5970	99	7	18	18	NUM
ejpam-5970	99	8	(	(	PUNCT
ejpam-5970	99	9	3	3	NUM
ejpam-5970	99	10	)	)	PUNCT
ejpam-5970	99	11	(	(	PUNCT
ejpam-5970	99	12	2025	2025	NUM
ejpam-5970	99	13	)	)	PUNCT
ejpam-5970	99	14	,	,	PUNCT
ejpam-5970	99	15	5970	5970	NUM
ejpam-5970	99	16	5	5	NUM
ejpam-5970	99	17	of	of	ADP
ejpam-5970	99	18	18	18	NUM
ejpam-5970	99	19	last	last	ADJ
ejpam-5970	99	20	vertex	vertex	NOUN
ejpam-5970	99	21	to	to	PART
ejpam-5970	99	22	form	form	VERB
ejpam-5970	99	23	a	a	DET
ejpam-5970	99	24	path	path	NOUN
ejpam-5970	99	25	of	of	ADP
ejpam-5970	99	26	n	n	NOUN
ejpam-5970	99	27	vertices	vertex	NOUN
ejpam-5970	99	28	.	.	PUNCT
ejpam-5970	100	1	formally	formally	ADV
ejpam-5970	100	2	,	,	PUNCT
ejpam-5970	100	3	the	the	DET
ejpam-5970	100	4	vertex	vertex	NOUN
ejpam-5970	100	5	set	set	NOUN
ejpam-5970	100	6	is	be	AUX
ejpam-5970	100	7	given	give	VERB
ejpam-5970	100	8	by	by	ADP
ejpam-5970	100	9	v	v	NOUN
ejpam-5970	100	10	(	(	PUNCT
ejpam-5970	100	11	pn	pn	PROPN
ejpam-5970	100	12	▷pm	▷pm	PROPN
ejpam-5970	100	13	)	)	PUNCT
ejpam-5970	100	14	=	=	PRON
ejpam-5970	100	15	{	{	PUNCT
ejpam-5970	100	16	xij	xij	NOUN
ejpam-5970	100	17	:	:	PUNCT
ejpam-5970	100	18	1	1	NUM
ejpam-5970	100	19	≤	≤	NUM
ejpam-5970	100	20	i	i	PRON
ejpam-5970	100	21	≤	≤	PROPN
ejpam-5970	100	22	n	n	CCONJ
ejpam-5970	100	23	,	,	PUNCT
ejpam-5970	100	24	1	1	NUM
ejpam-5970	100	25	≤	≤	NUM
ejpam-5970	100	26	j	j	PROPN
ejpam-5970	100	27	≤	≤	PROPN
ejpam-5970	100	28	m	m	PROPN
ejpam-5970	100	29	}	}	PUNCT
ejpam-5970	100	30	and	and	CCONJ
ejpam-5970	100	31	the	the	DET
ejpam-5970	100	32	edge	edge	NOUN
ejpam-5970	100	33	set	set	NOUN
ejpam-5970	100	34	is	be	AUX
ejpam-5970	100	35	defined	define	VERB
ejpam-5970	100	36	as	as	ADP
ejpam-5970	100	37	e(pn	e(pn	PRON
ejpam-5970	100	38	▷	▷	ADJ
ejpam-5970	100	39	pm	pm	NOUN
ejpam-5970	100	40	)	)	PUNCT
ejpam-5970	100	41	=	=	PRON
ejpam-5970	101	1	{	{	PUNCT
ejpam-5970	101	2	xijxij+1	xijxij+1	NOUN
ejpam-5970	101	3	:	:	PUNCT
ejpam-5970	101	4	1	1	NUM
ejpam-5970	101	5	≤	≤	NUM
ejpam-5970	101	6	j	j	PROPN
ejpam-5970	101	7	≤	≤	PROPN
ejpam-5970	101	8	m−	m−	PROPN
ejpam-5970	101	9	1	1	NUM
ejpam-5970	101	10	,	,	PUNCT
ejpam-5970	101	11	1	1	NUM
ejpam-5970	101	12	≤	≤	NUM
ejpam-5970	101	13	i	i	PRON
ejpam-5970	101	14	≤	≤	NOUN
ejpam-5970	101	15	n	n	CCONJ
ejpam-5970	101	16	}	}	PUNCT
ejpam-5970	101	17	∪	∪	ADJ
ejpam-5970	101	18	{	{	PUNCT
ejpam-5970	101	19	ximxi+1	ximxi+1	NOUN
ejpam-5970	101	20	m	m	VERB
ejpam-5970	101	21	:	:	PUNCT
ejpam-5970	101	22	1	1	NUM
ejpam-5970	101	23	≤	≤	NUM
ejpam-5970	102	1	i	i	PRON
ejpam-5970	102	2	≤	≤	ADJ
ejpam-5970	102	3	n−	n−	NOUN
ejpam-5970	102	4	1	1	NUM
ejpam-5970	102	5	}	}	PUNCT
ejpam-5970	102	6	.	.	PUNCT
ejpam-5970	103	1	consequently	consequently	ADV
ejpam-5970	103	2	,	,	PUNCT
ejpam-5970	103	3	we	we	PRON
ejpam-5970	103	4	have	have	AUX
ejpam-5970	103	5	|v	|v	VERB
ejpam-5970	103	6	|	|	ADV
ejpam-5970	103	7	=	=	SYM
ejpam-5970	103	8	nm	nm	NOUN
ejpam-5970	103	9	and	and	CCONJ
ejpam-5970	103	10	|e|	|e|	ADJ
ejpam-5970	103	11	=	=	SYM
ejpam-5970	103	12	nm−	nm−	PROPN
ejpam-5970	103	13	1	1	NUM
ejpam-5970	103	14	.	.	PUNCT
ejpam-5970	103	15	to	to	PART
ejpam-5970	103	16	prove	prove	VERB
ejpam-5970	103	17	the	the	DET
ejpam-5970	103	18	theorem	theorem	NOUN
ejpam-5970	103	19	,	,	PUNCT
ejpam-5970	103	20	we	we	PRON
ejpam-5970	103	21	determine	determine	VERB
ejpam-5970	103	22	both	both	CCONJ
ejpam-5970	103	23	the	the	DET
ejpam-5970	103	24	lower	low	ADJ
ejpam-5970	103	25	and	and	CCONJ
ejpam-5970	103	26	upper	upper	ADJ
ejpam-5970	103	27	bounds	bound	NOUN
ejpam-5970	103	28	of	of	ADP
ejpam-5970	103	29	the	the	DET
ejpam-5970	103	30	local	local	ADJ
ejpam-5970	103	31	edge	edge	NOUN
ejpam-5970	103	32	(	(	PUNCT
ejpam-5970	103	33	a	a	DET
ejpam-5970	103	34	,	,	PUNCT
ejpam-5970	103	35	d)-antimagic	d)-antimagic	NOUN
ejpam-5970	103	36	chromatic	chromatic	ADJ
ejpam-5970	103	37	number	number	NOUN
ejpam-5970	103	38	and	and	CCONJ
ejpam-5970	103	39	show	show	VERB
ejpam-5970	103	40	that	that	SCONJ
ejpam-5970	103	41	they	they	PRON
ejpam-5970	103	42	are	be	AUX
ejpam-5970	103	43	equal	equal	ADJ
ejpam-5970	103	44	to	to	ADP
ejpam-5970	103	45	n	n	NOUN
ejpam-5970	103	46	under	under	ADP
ejpam-5970	103	47	the	the	DET
ejpam-5970	103	48	given	give	VERB
ejpam-5970	103	49	conditions	condition	NOUN
ejpam-5970	103	50	.	.	PUNCT
ejpam-5970	104	1	from	from	ADP
ejpam-5970	104	2	the	the	DET
ejpam-5970	104	3	result	result	NOUN
ejpam-5970	104	4	by	by	ADP
ejpam-5970	104	5	agustin	agustin	PROPN
ejpam-5970	104	6	et	et	PROPN
ejpam-5970	104	7	al	al	PROPN
ejpam-5970	104	8	.	.	PUNCT
ejpam-5970	105	1	[	[	X
ejpam-5970	105	2	2	2	NUM
ejpam-5970	105	3	]	]	PUNCT
ejpam-5970	105	4	,	,	PUNCT
ejpam-5970	105	5	it	it	PRON
ejpam-5970	105	6	is	be	AUX
ejpam-5970	105	7	known	know	VERB
ejpam-5970	105	8	that	that	SCONJ
ejpam-5970	105	9	χlea(pn	χlea(pn	NOUN
ejpam-5970	105	10	▷	▷	ADJ
ejpam-5970	105	11	pm	pm	NOUN
ejpam-5970	105	12	)	)	PUNCT
ejpam-5970	105	13	=	=	SYM
ejpam-5970	106	1	n	n	PROPN
ejpam-5970	106	2	for	for	ADP
ejpam-5970	106	3	n	n	CCONJ
ejpam-5970	106	4	,	,	PUNCT
ejpam-5970	106	5	m	m	VERB
ejpam-5970	106	6	≥	≥	NOUN
ejpam-5970	106	7	3	3	NUM
ejpam-5970	106	8	.	.	PUNCT
ejpam-5970	107	1	additionally	additionally	ADV
ejpam-5970	107	2	,	,	PUNCT
ejpam-5970	107	3	observation	observation	NOUN
ejpam-5970	107	4	2	2	NUM
ejpam-5970	107	5	implies	imply	VERB
ejpam-5970	107	6	χle(a	χle(a	PROPN
ejpam-5970	107	7	,	,	PUNCT
ejpam-5970	107	8	d)(pn	d)(pn	X
ejpam-5970	107	9	▷pm	▷pm	PROPN
ejpam-5970	107	10	)	)	PUNCT
ejpam-5970	107	11	≥	≥	NOUN
ejpam-5970	107	12	χlea(pn	χlea(pn	PROPN
ejpam-5970	107	13	▷pm	▷pm	PROPN
ejpam-5970	107	14	)	)	PUNCT
ejpam-5970	107	15	=	=	PUNCT
ejpam-5970	108	1	n.	n.	PROPN
ejpam-5970	108	2	thus	thus	ADV
ejpam-5970	108	3	,	,	PUNCT
ejpam-5970	108	4	the	the	DET
ejpam-5970	108	5	lower	lower	ADV
ejpam-5970	108	6	bound	bind	VERB
ejpam-5970	108	7	is	be	AUX
ejpam-5970	108	8	established	establish	VERB
ejpam-5970	108	9	.	.	PUNCT
ejpam-5970	109	1	to	to	PART
ejpam-5970	109	2	construct	construct	VERB
ejpam-5970	109	3	the	the	DET
ejpam-5970	109	4	upper	upper	ADJ
ejpam-5970	109	5	bound	bind	VERB
ejpam-5970	109	6	,	,	PUNCT
ejpam-5970	109	7	we	we	PRON
ejpam-5970	109	8	define	define	VERB
ejpam-5970	109	9	a	a	DET
ejpam-5970	109	10	bijective	bijective	ADJ
ejpam-5970	109	11	labeling	labeling	NOUN
ejpam-5970	109	12	f	f	NOUN
ejpam-5970	109	13	:	:	PUNCT
ejpam-5970	109	14	v	v	X
ejpam-5970	109	15	(	(	PUNCT
ejpam-5970	109	16	pn	pn	PROPN
ejpam-5970	109	17	▷	▷	ADJ
ejpam-5970	109	18	pm	pm	NOUN
ejpam-5970	109	19	)	)	PUNCT
ejpam-5970	109	20	→	→	SYM
ejpam-5970	109	21	{	{	PUNCT
ejpam-5970	109	22	1	1	NUM
ejpam-5970	109	23	,	,	PUNCT
ejpam-5970	109	24	2	2	NUM
ejpam-5970	109	25	,	,	PUNCT
ejpam-5970	109	26	.	.	PUNCT
ejpam-5970	109	27	.	.	PUNCT
ejpam-5970	109	28	.	.	PUNCT
ejpam-5970	110	1	,	,	PUNCT
ejpam-5970	110	2	nm	nm	AUX
ejpam-5970	110	3	}	}	PUNCT
ejpam-5970	110	4	as	as	SCONJ
ejpam-5970	110	5	follows	follow	VERB
ejpam-5970	110	6	:	:	PUNCT
ejpam-5970	110	7	f(xij	f(xij	NOUN
ejpam-5970	110	8	)	)	PUNCT
ejpam-5970	111	1	=	=	PRON
ejpam-5970	111	2	{	{	PUNCT
ejpam-5970	111	3	i+	i+	X
ejpam-5970	111	4	(	(	PUNCT
ejpam-5970	111	5	j−1)n	j−1)n	PROPN
ejpam-5970	111	6	2	2	NUM
ejpam-5970	111	7	,	,	PUNCT
ejpam-5970	111	8	if	if	SCONJ
ejpam-5970	111	9	j	j	PROPN
ejpam-5970	111	10	≡	≡	PROPN
ejpam-5970	111	11	1	1	NUM
ejpam-5970	111	12	(	(	PUNCT
ejpam-5970	111	13	mod	mod	NOUN
ejpam-5970	111	14	2	2	NUM
ejpam-5970	111	15	)	)	PUNCT
ejpam-5970	111	16	nm+	nm+	NOUN
ejpam-5970	111	17	1−	1−	NUM
ejpam-5970	111	18	i+	i+	NUM
ejpam-5970	111	19	n−	n−	NOUN
ejpam-5970	111	20	nj	nj	PROPN
ejpam-5970	111	21	2	2	NUM
ejpam-5970	111	22	,	,	PUNCT
ejpam-5970	111	23	if	if	SCONJ
ejpam-5970	111	24	j	j	PROPN
ejpam-5970	111	25	≡	≡	PROPN
ejpam-5970	111	26	0	0	PUNCT
ejpam-5970	111	27	(	(	PUNCT
ejpam-5970	111	28	mod	mod	NOUN
ejpam-5970	111	29	2	2	X
ejpam-5970	111	30	)	)	PUNCT
ejpam-5970	111	31	this	this	DET
ejpam-5970	111	32	labeling	labeling	NOUN
ejpam-5970	111	33	ensures	ensure	VERB
ejpam-5970	111	34	a	a	DET
ejpam-5970	111	35	proper	proper	ADJ
ejpam-5970	111	36	assignment	assignment	NOUN
ejpam-5970	111	37	of	of	ADP
ejpam-5970	111	38	distinct	distinct	ADJ
ejpam-5970	111	39	values	value	NOUN
ejpam-5970	111	40	to	to	ADP
ejpam-5970	111	41	the	the	DET
ejpam-5970	111	42	vertices	vertex	NOUN
ejpam-5970	111	43	and	and	CCONJ
ejpam-5970	111	44	generates	generate	VERB
ejpam-5970	111	45	edge	edge	VERB
ejpam-5970	111	46	weights	weight	NOUN
ejpam-5970	111	47	that	that	PRON
ejpam-5970	111	48	can	can	AUX
ejpam-5970	111	49	be	be	AUX
ejpam-5970	111	50	analyzed	analyze	VERB
ejpam-5970	111	51	in	in	ADP
ejpam-5970	111	52	two	two	NUM
ejpam-5970	111	53	separate	separate	ADJ
ejpam-5970	111	54	cases	case	NOUN
ejpam-5970	111	55	based	base	VERB
ejpam-5970	111	56	on	on	ADP
ejpam-5970	111	57	the	the	DET
ejpam-5970	111	58	parity	parity	NOUN
ejpam-5970	111	59	of	of	ADP
ejpam-5970	111	60	m	m	PROPN
ejpam-5970	111	61	and	and	CCONJ
ejpam-5970	111	62	n.	n.	NOUN
ejpam-5970	111	63	case	case	NOUN
ejpam-5970	111	64	1	1	NUM
ejpam-5970	111	65	:	:	PUNCT
ejpam-5970	111	66	for	for	ADP
ejpam-5970	111	67	m	m	PROPN
ejpam-5970	111	68	≡	≡	PROPN
ejpam-5970	111	69	1	1	NUM
ejpam-5970	111	70	(	(	PUNCT
ejpam-5970	111	71	mod	mod	NOUN
ejpam-5970	111	72	2	2	NUM
ejpam-5970	111	73	)	)	PUNCT
ejpam-5970	111	74	and	and	CCONJ
ejpam-5970	111	75	n	n	PRON
ejpam-5970	111	76	≡	≡	PROPN
ejpam-5970	111	77	0	0	PUNCT
ejpam-5970	111	78	(	(	PUNCT
ejpam-5970	111	79	mod	mod	NOUN
ejpam-5970	111	80	2	2	NUM
ejpam-5970	111	81	)	)	PUNCT
ejpam-5970	111	82	,	,	PUNCT
ejpam-5970	111	83	the	the	DET
ejpam-5970	111	84	edge	edge	NOUN
ejpam-5970	111	85	weights	weight	VERB
ejpam-5970	111	86	for	for	ADP
ejpam-5970	111	87	horizontal	horizontal	ADJ
ejpam-5970	111	88	edges	edge	NOUN
ejpam-5970	111	89	within	within	ADP
ejpam-5970	111	90	each	each	DET
ejpam-5970	111	91	copy	copy	NOUN
ejpam-5970	111	92	of	of	ADP
ejpam-5970	111	93	pm	pm	NOUN
ejpam-5970	111	94	are	be	AUX
ejpam-5970	111	95	:	:	PUNCT
ejpam-5970	111	96	w(xijx	w(xijx	X
ejpam-5970	112	1	i	i	PRON
ejpam-5970	112	2	j+1	j+1	NOUN
ejpam-5970	112	3	)	)	PUNCT
ejpam-5970	112	4	=	=	NOUN
ejpam-5970	112	5	{	{	PUNCT
ejpam-5970	112	6	nm+	nm+	NOUN
ejpam-5970	112	7	1	1	NUM
ejpam-5970	112	8	,	,	PUNCT
ejpam-5970	112	9	if	if	SCONJ
ejpam-5970	112	10	j	j	PROPN
ejpam-5970	112	11	≡	≡	PROPN
ejpam-5970	112	12	1	1	NUM
ejpam-5970	112	13	(	(	PUNCT
ejpam-5970	112	14	mod	mod	NOUN
ejpam-5970	112	15	2	2	NUM
ejpam-5970	112	16	)	)	PUNCT
ejpam-5970	112	17	nm+	nm+	NOUN
ejpam-5970	112	18	n+	n+	PUNCT
ejpam-5970	112	19	1	1	X
ejpam-5970	112	20	,	,	PUNCT
ejpam-5970	112	21	if	if	SCONJ
ejpam-5970	112	22	j	j	PROPN
ejpam-5970	112	23	≡	≡	PROPN
ejpam-5970	112	24	0	0	PUNCT
ejpam-5970	112	25	(	(	PUNCT
ejpam-5970	112	26	mod	mod	NOUN
ejpam-5970	112	27	2	2	NUM
ejpam-5970	112	28	)	)	PUNCT
ejpam-5970	112	29	for	for	ADP
ejpam-5970	112	30	vertical	vertical	ADJ
ejpam-5970	112	31	edges	edge	NOUN
ejpam-5970	112	32	between	between	ADP
ejpam-5970	112	33	copies	copy	NOUN
ejpam-5970	112	34	:	:	PUNCT
ejpam-5970	112	35	w(ximxi+1	w(ximxi+1	NOUN
ejpam-5970	112	36	m	m	NOUN
ejpam-5970	112	37	)	)	PUNCT
ejpam-5970	112	38	=	=	SYM
ejpam-5970	112	39	nm−	nm−	PROPN
ejpam-5970	112	40	n+	n+	PUNCT
ejpam-5970	112	41	2i+	2i+	NUM
ejpam-5970	112	42	1	1	NUM
ejpam-5970	112	43	,	,	PUNCT
ejpam-5970	112	44	for	for	ADP
ejpam-5970	112	45	1	1	NUM
ejpam-5970	112	46	≤	≤	NUM
ejpam-5970	112	47	i	i	PRON
ejpam-5970	112	48	≤	≤	ADJ
ejpam-5970	112	49	n−	n−	NOUN
ejpam-5970	112	50	1	1	NUM
ejpam-5970	112	51	these	these	DET
ejpam-5970	112	52	edge	edge	NOUN
ejpam-5970	112	53	weights	weight	NOUN
ejpam-5970	112	54	can	can	AUX
ejpam-5970	112	55	be	be	AUX
ejpam-5970	112	56	grouped	group	VERB
ejpam-5970	112	57	into	into	ADP
ejpam-5970	112	58	three	three	NUM
ejpam-5970	112	59	distinct	distinct	ADJ
ejpam-5970	112	60	sets	set	NOUN
ejpam-5970	112	61	:	:	PUNCT
ejpam-5970	112	62	w1	w1	NOUN
ejpam-5970	112	63	=	=	SYM
ejpam-5970	112	64	{	{	PUNCT
ejpam-5970	112	65	nm	nm	NOUN
ejpam-5970	112	66	+	+	NOUN
ejpam-5970	112	67	1	1	NUM
ejpam-5970	112	68	}	}	PUNCT
ejpam-5970	112	69	,	,	PUNCT
ejpam-5970	112	70	w2	w2	NOUN
ejpam-5970	112	71	=	=	SYM
ejpam-5970	112	72	{	{	PUNCT
ejpam-5970	112	73	nm	nm	NOUN
ejpam-5970	112	74	+	+	NUM
ejpam-5970	112	75	n	n	NOUN
ejpam-5970	112	76	+	+	NOUN
ejpam-5970	112	77	1	1	NUM
ejpam-5970	112	78	}	}	PUNCT
ejpam-5970	112	79	,	,	PUNCT
ejpam-5970	112	80	and	and	CCONJ
ejpam-5970	112	81	w3	w3	PROPN
ejpam-5970	112	82	=	=	SYM
ejpam-5970	112	83	{	{	PUNCT
ejpam-5970	112	84	nm	nm	NOUN
ejpam-5970	112	85	−	−	PROPN
ejpam-5970	112	86	n	n	NOUN
ejpam-5970	112	87	+	+	CCONJ
ejpam-5970	112	88	3	3	NUM
ejpam-5970	112	89	,	,	PUNCT
ejpam-5970	112	90	nm	nm	ADV
ejpam-5970	112	91	−	−	PROPN
ejpam-5970	112	92	n	n	NOUN
ejpam-5970	112	93	+	+	NUM
ejpam-5970	112	94	5	5	NUM
ejpam-5970	112	95	,	,	PUNCT
ejpam-5970	112	96	.	.	PUNCT
ejpam-5970	112	97	.	.	PUNCT
ejpam-5970	113	1	.	.	PUNCT
ejpam-5970	114	1	,	,	PUNCT
ejpam-5970	114	2	nm	nm	VERB
ejpam-5970	114	3	+	+	CCONJ
ejpam-5970	114	4	n	n	CCONJ
ejpam-5970	114	5	−	−	PROPN
ejpam-5970	114	6	1	1	NUM
ejpam-5970	114	7	}	}	PUNCT
ejpam-5970	114	8	.	.	PUNCT
ejpam-5970	115	1	we	we	PRON
ejpam-5970	115	2	examine	examine	VERB
ejpam-5970	115	3	their	their	PRON
ejpam-5970	115	4	cardinalities	cardinality	NOUN
ejpam-5970	115	5	and	and	CCONJ
ejpam-5970	115	6	mutual	mutual	ADJ
ejpam-5970	115	7	disjointness	disjointness	NOUN
ejpam-5970	115	8	.	.	PUNCT
ejpam-5970	116	1	to	to	PART
ejpam-5970	116	2	verify	verify	VERB
ejpam-5970	116	3	disjointness	disjointness	NOUN
ejpam-5970	116	4	:	:	PUNCT
ejpam-5970	116	5	suppose	suppose	VERB
ejpam-5970	116	6	w1	w1	PROPN
ejpam-5970	116	7	⊆	⊆	NUM
ejpam-5970	116	8	w3	w3	PROPN
ejpam-5970	116	9	implies	imply	VERB
ejpam-5970	116	10	nm	nm	ADJ
ejpam-5970	116	11	+	+	NOUN
ejpam-5970	116	12	1	1	NUM
ejpam-5970	116	13	=	=	NOUN
ejpam-5970	116	14	nm	nm	ADV
ejpam-5970	116	15	−	−	NOUN
ejpam-5970	116	16	n	n	NOUN
ejpam-5970	116	17	+	+	CCONJ
ejpam-5970	116	18	2i	2i	NUM
ejpam-5970	116	19	+	+	CCONJ
ejpam-5970	116	20	1	1	NUM
ejpam-5970	116	21	,	,	PUNCT
ejpam-5970	116	22	which	which	PRON
ejpam-5970	116	23	leads	lead	VERB
ejpam-5970	116	24	to	to	ADP
ejpam-5970	116	25	i	i	PROPN
ejpam-5970	116	26	=	=	PUNCT
ejpam-5970	116	27	n	n	PRON
ejpam-5970	116	28	2	2	NUM
ejpam-5970	116	29	.	.	PUNCT
ejpam-5970	117	1	since	since	SCONJ
ejpam-5970	117	2	i	i	PRON
ejpam-5970	117	3	=	=	SYM
ejpam-5970	117	4	n	n	PRON
ejpam-5970	117	5	2	2	NUM
ejpam-5970	117	6	is	be	AUX
ejpam-5970	117	7	within	within	ADP
ejpam-5970	117	8	the	the	DET
ejpam-5970	117	9	index	index	NOUN
ejpam-5970	117	10	range	range	NOUN
ejpam-5970	117	11	,	,	PUNCT
ejpam-5970	117	12	it	it	PRON
ejpam-5970	117	13	confirms	confirm	VERB
ejpam-5970	117	14	w1	w1	PROPN
ejpam-5970	117	15	⊂	⊂	PROPN
ejpam-5970	117	16	w3	w3	PROPN
ejpam-5970	117	17	.	.	PUNCT
ejpam-5970	118	1	on	on	ADP
ejpam-5970	118	2	the	the	DET
ejpam-5970	118	3	other	other	ADJ
ejpam-5970	118	4	hand	hand	NOUN
ejpam-5970	118	5	,	,	PUNCT
ejpam-5970	118	6	suppose	suppose	VERB
ejpam-5970	118	7	w2	w2	PROPN
ejpam-5970	118	8	⊆	⊆	NUM
ejpam-5970	118	9	w3	w3	PROPN
ejpam-5970	118	10	implies	imply	VERB
ejpam-5970	118	11	nm	nm	ADP
ejpam-5970	118	12	+	+	SYM
ejpam-5970	118	13	n	n	CCONJ
ejpam-5970	118	14	+	+	CCONJ
ejpam-5970	118	15	1	1	NUM
ejpam-5970	118	16	=	=	NOUN
ejpam-5970	118	17	nm	nm	ADV
ejpam-5970	118	18	−	−	NOUN
ejpam-5970	118	19	n	n	NOUN
ejpam-5970	118	20	+	+	CCONJ
ejpam-5970	118	21	2i	2i	NUM
ejpam-5970	118	22	+	+	CCONJ
ejpam-5970	118	23	1	1	NUM
ejpam-5970	118	24	,	,	PUNCT
ejpam-5970	118	25	which	which	PRON
ejpam-5970	118	26	leads	lead	VERB
ejpam-5970	118	27	to	to	ADP
ejpam-5970	118	28	i	i	PROPN
ejpam-5970	118	29	=	=	SYM
ejpam-5970	118	30	n.	n.	PROPN
ejpam-5970	118	31	however	however	ADV
ejpam-5970	118	32	,	,	PUNCT
ejpam-5970	118	33	i	i	PRON
ejpam-5970	118	34	=	=	PUNCT
ejpam-5970	118	35	n	n	PROPN
ejpam-5970	118	36	lies	lie	VERB
ejpam-5970	118	37	outside	outside	ADP
ejpam-5970	118	38	the	the	DET
ejpam-5970	118	39	valid	valid	ADJ
ejpam-5970	118	40	range	range	NOUN
ejpam-5970	118	41	of	of	ADP
ejpam-5970	118	42	1	1	NUM
ejpam-5970	118	43	≤	≤	NUM
ejpam-5970	119	1	i	i	PRON
ejpam-5970	119	2	≤	≤	ADJ
ejpam-5970	119	3	n−	n−	NOUN
ejpam-5970	119	4	1	1	NUM
ejpam-5970	119	5	,	,	PUNCT
ejpam-5970	119	6	hence	hence	ADV
ejpam-5970	119	7	a	a	DET
ejpam-5970	119	8	contradiction	contradiction	NOUN
ejpam-5970	119	9	.	.	PUNCT
ejpam-5970	120	1	therefore	therefore	ADV
ejpam-5970	120	2	,	,	PUNCT
ejpam-5970	120	3	w2	w2	NOUN
ejpam-5970	120	4	∩w3	∩w3	NOUN
ejpam-5970	120	5	=	=	SYM
ejpam-5970	120	6	∅	∅	NOUN
ejpam-5970	120	7	and	and	CCONJ
ejpam-5970	120	8	w	w	NOUN
ejpam-5970	120	9	=	=	PROPN
ejpam-5970	120	10	w2	w2	NOUN
ejpam-5970	120	11	∪w3	∪w3	VERB
ejpam-5970	120	12	.	.	PUNCT
ejpam-5970	121	1	the	the	DET
ejpam-5970	121	2	cardinality	cardinality	NOUN
ejpam-5970	121	3	is	be	AUX
ejpam-5970	121	4	then	then	ADV
ejpam-5970	121	5	|w2|	|w2|	NOUN
ejpam-5970	121	6	=	=	SYM
ejpam-5970	121	7	1	1	NUM
ejpam-5970	121	8	,	,	PUNCT
ejpam-5970	121	9	and	and	CCONJ
ejpam-5970	121	10	for	for	ADP
ejpam-5970	121	11	w3	w3	PROPN
ejpam-5970	121	12	,	,	PUNCT
ejpam-5970	121	13	let	let	VERB
ejpam-5970	121	14	us	we	PRON
ejpam-5970	121	15	be	be	AUX
ejpam-5970	121	16	the	the	DET
ejpam-5970	121	17	s	s	NOUN
ejpam-5970	121	18	-	-	PUNCT
ejpam-5970	121	19	th	th	ADJ
ejpam-5970	121	20	term	term	NOUN
ejpam-5970	121	21	in	in	ADP
ejpam-5970	121	22	the	the	DET
ejpam-5970	121	23	arithmetic	arithmetic	ADJ
ejpam-5970	121	24	progression	progression	NOUN
ejpam-5970	121	25	with	with	ADP
ejpam-5970	121	26	common	common	ADJ
ejpam-5970	121	27	difference	difference	NOUN
ejpam-5970	121	28	2	2	NUM
ejpam-5970	121	29	.	.	PUNCT
ejpam-5970	121	30	solving	solve	VERB
ejpam-5970	121	31	nm+	nm+	NOUN
ejpam-5970	121	32	n−	n−	NOUN
ejpam-5970	121	33	1	1	NUM
ejpam-5970	121	34	=	=	SYM
ejpam-5970	121	35	nm−	nm−	PROPN
ejpam-5970	121	36	n+	n+	PUNCT
ejpam-5970	121	37	3	3	NUM
ejpam-5970	121	38	+	+	NUM
ejpam-5970	121	39	(	(	PUNCT
ejpam-5970	121	40	|w3|	|w3|	NOUN
ejpam-5970	121	41	−	−	PROPN
ejpam-5970	121	42	1	1	NUM
ejpam-5970	121	43	)	)	PUNCT
ejpam-5970	121	44	·	·	PUNCT
ejpam-5970	122	1	2	2	X
ejpam-5970	122	2	,	,	PUNCT
ejpam-5970	122	3	we	we	PRON
ejpam-5970	122	4	find	find	VERB
ejpam-5970	122	5	|w3|	|w3|	NOUN
ejpam-5970	122	6	=	=	PUNCT
ejpam-5970	122	7	n−	n−	NOUN
ejpam-5970	122	8	1	1	NUM
ejpam-5970	122	9	,	,	PUNCT
ejpam-5970	122	10	so	so	ADV
ejpam-5970	122	11	|w	|w	ADJ
ejpam-5970	122	12	|	|	NOUN
ejpam-5970	122	13	=	=	SYM
ejpam-5970	122	14	n.	n.	NOUN
ejpam-5970	122	15	case	case	NOUN
ejpam-5970	122	16	2	2	NUM
ejpam-5970	122	17	:	:	PUNCT
ejpam-5970	122	18	for	for	ADP
ejpam-5970	122	19	m	m	PROPN
ejpam-5970	122	20	,	,	PUNCT
ejpam-5970	122	21	n	n	PROPN
ejpam-5970	122	22	≡	≡	PROPN
ejpam-5970	122	23	0	0	PUNCT
ejpam-5970	123	1	(	(	PUNCT
ejpam-5970	123	2	mod	mod	NOUN
ejpam-5970	123	3	2	2	NUM
ejpam-5970	123	4	)	)	PUNCT
ejpam-5970	123	5	,	,	PUNCT
ejpam-5970	123	6	we	we	PRON
ejpam-5970	123	7	compute	compute	VERB
ejpam-5970	123	8	:	:	PUNCT
ejpam-5970	123	9	w(ximxi+1	w(ximxi+1	NOUN
ejpam-5970	123	10	m	m	NOUN
ejpam-5970	123	11	)	)	PUNCT
ejpam-5970	124	1	=	=	SYM
ejpam-5970	124	2	nm+	nm+	NOUN
ejpam-5970	125	1	2n−	2n−	PROPN
ejpam-5970	125	2	2i+	2i+	NUM
ejpam-5970	125	3	1	1	NUM
ejpam-5970	125	4	,	,	PUNCT
ejpam-5970	125	5	for	for	ADP
ejpam-5970	125	6	1	1	NUM
ejpam-5970	125	7	≤	≤	NUM
ejpam-5970	125	8	i	i	PRON
ejpam-5970	125	9	≤	≤	ADJ
ejpam-5970	125	10	n−	n−	NOUN
ejpam-5970	125	11	1	1	NUM
ejpam-5970	125	12	a.	a.	NOUN
ejpam-5970	125	13	i.	i.	PROPN
ejpam-5970	125	14	kristiana	kristiana	PROPN
ejpam-5970	125	15	,	,	PUNCT
ejpam-5970	125	16	et	et	PROPN
ejpam-5970	125	17	al	al	PROPN
ejpam-5970	125	18	.	.	PUNCT
ejpam-5970	125	19	/	/	SYM
ejpam-5970	125	20	eur	eur	PROPN
ejpam-5970	125	21	.	.	PUNCT
ejpam-5970	126	1	j.	j.	PROPN
ejpam-5970	126	2	pure	pure	PROPN
ejpam-5970	126	3	appl	appl	PROPN
ejpam-5970	126	4	.	.	PROPN
ejpam-5970	126	5	math	math	PROPN
ejpam-5970	126	6	,	,	PUNCT
ejpam-5970	126	7	18	18	NUM
ejpam-5970	126	8	(	(	PUNCT
ejpam-5970	126	9	3	3	NUM
ejpam-5970	126	10	)	)	PUNCT
ejpam-5970	126	11	(	(	PUNCT
ejpam-5970	126	12	2025	2025	NUM
ejpam-5970	126	13	)	)	PUNCT
ejpam-5970	126	14	,	,	PUNCT
ejpam-5970	126	15	5970	5970	NUM
ejpam-5970	126	16	6	6	NUM
ejpam-5970	126	17	of	of	ADP
ejpam-5970	126	18	18	18	NUM
ejpam-5970	126	19	the	the	DET
ejpam-5970	126	20	weight	weight	NOUN
ejpam-5970	126	21	sets	set	NOUN
ejpam-5970	126	22	in	in	ADP
ejpam-5970	126	23	this	this	DET
ejpam-5970	126	24	case	case	NOUN
ejpam-5970	126	25	are	be	AUX
ejpam-5970	126	26	w1	w1	NOUN
ejpam-5970	126	27	=	=	SYM
ejpam-5970	126	28	{	{	PUNCT
ejpam-5970	126	29	nm	nm	NOUN
ejpam-5970	126	30	+	+	NOUN
ejpam-5970	126	31	1	1	NUM
ejpam-5970	126	32	}	}	PUNCT
ejpam-5970	126	33	,	,	PUNCT
ejpam-5970	126	34	w2	w2	NOUN
ejpam-5970	126	35	=	=	SYM
ejpam-5970	126	36	{	{	PUNCT
ejpam-5970	126	37	nm	nm	NOUN
ejpam-5970	126	38	+	+	NUM
ejpam-5970	126	39	n	n	NOUN
ejpam-5970	126	40	+	+	NOUN
ejpam-5970	126	41	1	1	NUM
ejpam-5970	126	42	}	}	PUNCT
ejpam-5970	126	43	,	,	PUNCT
ejpam-5970	126	44	and	and	CCONJ
ejpam-5970	126	45	w3	w3	PROPN
ejpam-5970	126	46	=	=	PUNCT
ejpam-5970	126	47	{	{	PUNCT
ejpam-5970	126	48	nm+	nm+	NOUN
ejpam-5970	126	49	2n−	2n−	NUM
ejpam-5970	126	50	1	1	NUM
ejpam-5970	126	51	,	,	PUNCT
ejpam-5970	126	52	nm+	nm+	NOUN
ejpam-5970	126	53	2n−	2n−	PROPN
ejpam-5970	126	54	3	3	NUM
ejpam-5970	126	55	,	,	PUNCT
ejpam-5970	126	56	.	.	PUNCT
ejpam-5970	126	57	.	.	PUNCT
ejpam-5970	126	58	.	.	PUNCT
ejpam-5970	127	1	,	,	PUNCT
ejpam-5970	127	2	nm+	nm+	NOUN
ejpam-5970	127	3	3	3	NUM
ejpam-5970	127	4	}	}	PUNCT
ejpam-5970	127	5	.	.	PUNCT
ejpam-5970	128	1	to	to	PART
ejpam-5970	128	2	verify	verify	VERB
ejpam-5970	128	3	disjointness	disjointness	NOUN
ejpam-5970	128	4	:	:	PUNCT
ejpam-5970	128	5	suppose	suppose	VERB
ejpam-5970	128	6	w1	w1	PROPN
ejpam-5970	128	7	⊆	⊆	NUM
ejpam-5970	128	8	w3	w3	PROPN
ejpam-5970	128	9	implies	imply	VERB
ejpam-5970	128	10	nm	nm	ADJ
ejpam-5970	128	11	+	+	NOUN
ejpam-5970	128	12	1	1	NUM
ejpam-5970	128	13	=	=	SYM
ejpam-5970	128	14	nm	nm	ADJ
ejpam-5970	128	15	+	+	NOUN
ejpam-5970	128	16	2n	2n	NUM
ejpam-5970	128	17	−	−	NOUN
ejpam-5970	128	18	2i	2i	NOUN
ejpam-5970	128	19	+	+	CCONJ
ejpam-5970	128	20	1	1	NUM
ejpam-5970	128	21	,	,	PUNCT
ejpam-5970	128	22	which	which	PRON
ejpam-5970	128	23	gives	give	VERB
ejpam-5970	128	24	i	i	PRON
ejpam-5970	128	25	=	=	PUNCT
ejpam-5970	128	26	n.	n.	NOUN
ejpam-5970	128	27	since	since	SCONJ
ejpam-5970	128	28	i	i	PROPN
ejpam-5970	128	29	=	=	PUNCT
ejpam-5970	128	30	n	n	X
ejpam-5970	128	31	is	be	AUX
ejpam-5970	128	32	out	out	ADP
ejpam-5970	128	33	of	of	ADP
ejpam-5970	128	34	range	range	NOUN
ejpam-5970	128	35	,	,	PUNCT
ejpam-5970	128	36	this	this	PRON
ejpam-5970	128	37	leads	lead	VERB
ejpam-5970	128	38	to	to	ADP
ejpam-5970	128	39	a	a	DET
ejpam-5970	128	40	contradiction	contradiction	NOUN
ejpam-5970	128	41	.	.	PUNCT
ejpam-5970	129	1	hence	hence	ADV
ejpam-5970	129	2	w1∩w3	w1∩w3	PROPN
ejpam-5970	129	3	=	=	PRON
ejpam-5970	129	4	∅.	∅.	NOUN
ejpam-5970	129	5	now	now	ADV
ejpam-5970	129	6	suppose	suppose	VERB
ejpam-5970	129	7	w2	w2	NOUN
ejpam-5970	129	8	⊆w3	⊆w3	PROPN
ejpam-5970	129	9	implies	imply	VERB
ejpam-5970	129	10	nm+	nm+	NOUN
ejpam-5970	129	11	n+	n+	PUNCT
ejpam-5970	129	12	1	1	NUM
ejpam-5970	129	13	=	=	PUNCT
ejpam-5970	129	14	nm+	nm+	NOUN
ejpam-5970	129	15	2n−	2n−	PROPN
ejpam-5970	129	16	2i+	2i+	NUM
ejpam-5970	129	17	1	1	NUM
ejpam-5970	129	18	,	,	PUNCT
ejpam-5970	129	19	which	which	PRON
ejpam-5970	129	20	gives	give	VERB
ejpam-5970	129	21	i	i	PRON
ejpam-5970	129	22	=	=	PUNCT
ejpam-5970	129	23	n	n	PRON
ejpam-5970	129	24	2	2	NUM
ejpam-5970	129	25	.	.	PUNCT
ejpam-5970	130	1	since	since	SCONJ
ejpam-5970	130	2	this	this	PRON
ejpam-5970	130	3	i	i	PRON
ejpam-5970	130	4	lies	lie	VERB
ejpam-5970	130	5	within	within	ADP
ejpam-5970	130	6	the	the	DET
ejpam-5970	130	7	valid	valid	ADJ
ejpam-5970	130	8	range	range	NOUN
ejpam-5970	130	9	,	,	PUNCT
ejpam-5970	130	10	w2	w2	NOUN
ejpam-5970	130	11	⊂w3	⊂w3	NOUN
ejpam-5970	130	12	,	,	PUNCT
ejpam-5970	130	13	and	and	CCONJ
ejpam-5970	130	14	thus	thus	ADV
ejpam-5970	130	15	w	w	PROPN
ejpam-5970	130	16	=	=	SYM
ejpam-5970	130	17	w1	w1	NOUN
ejpam-5970	130	18	∪w3	∪w3	NOUN
ejpam-5970	130	19	.	.	PUNCT
ejpam-5970	131	1	the	the	DET
ejpam-5970	131	2	cardinality	cardinality	NOUN
ejpam-5970	131	3	is	be	AUX
ejpam-5970	131	4	|w1|	|w1|	NOUN
ejpam-5970	131	5	=	=	SYM
ejpam-5970	131	6	1	1	X
ejpam-5970	131	7	.	.	PUNCT
ejpam-5970	131	8	to	to	PART
ejpam-5970	131	9	compute	compute	VERB
ejpam-5970	131	10	|w3|	|w3|	PRON
ejpam-5970	131	11	,	,	PUNCT
ejpam-5970	131	12	let	let	VERB
ejpam-5970	131	13	us	we	PRON
ejpam-5970	131	14	=	=	PUNCT
ejpam-5970	131	15	nm+3	nm+3	PROPN
ejpam-5970	131	16	and	and	CCONJ
ejpam-5970	131	17	u1	u1	NOUN
ejpam-5970	131	18	=	=	SYM
ejpam-5970	131	19	nm+2n−1	nm+2n−1	PROPN
ejpam-5970	131	20	.	.	PUNCT
ejpam-5970	132	1	solving	solve	VERB
ejpam-5970	132	2	us	we	PRON
ejpam-5970	132	3	=	=	PUNCT
ejpam-5970	132	4	u1	u1	PROPN
ejpam-5970	132	5	+	+	CCONJ
ejpam-5970	132	6	(	(	PUNCT
ejpam-5970	132	7	s−	s−	PROPN
ejpam-5970	132	8	1)(−2	1)(−2	NUM
ejpam-5970	132	9	)	)	PUNCT
ejpam-5970	132	10	,	,	PUNCT
ejpam-5970	132	11	we	we	PRON
ejpam-5970	132	12	obtain	obtain	VERB
ejpam-5970	132	13	s	s	VERB
ejpam-5970	132	14	=	=	PUNCT
ejpam-5970	132	15	n−	n−	NOUN
ejpam-5970	132	16	1	1	NUM
ejpam-5970	132	17	,	,	PUNCT
ejpam-5970	132	18	so	so	ADV
ejpam-5970	132	19	again	again	ADV
ejpam-5970	132	20	|w	|w	ADJ
ejpam-5970	133	1	|	|	NOUN
ejpam-5970	133	2	=	=	SYM
ejpam-5970	133	3	n.	n.	PROPN
ejpam-5970	133	4	therefore	therefore	ADV
ejpam-5970	133	5	,	,	PUNCT
ejpam-5970	133	6	in	in	ADP
ejpam-5970	133	7	both	both	DET
ejpam-5970	133	8	cases	case	NOUN
ejpam-5970	133	9	,	,	PUNCT
ejpam-5970	133	10	we	we	PRON
ejpam-5970	133	11	have	have	VERB
ejpam-5970	133	12	χle(a	χle(a	NOUN
ejpam-5970	133	13	,	,	PUNCT
ejpam-5970	133	14	d)(pn	d)(pn	ADJ
ejpam-5970	133	15	▷	▷	ADJ
ejpam-5970	133	16	pm	pm	NOUN
ejpam-5970	133	17	)	)	PUNCT
ejpam-5970	133	18	≤	≤	NOUN
ejpam-5970	133	19	n	n	CCONJ
ejpam-5970	133	20	and	and	CCONJ
ejpam-5970	133	21	from	from	ADP
ejpam-5970	133	22	the	the	DET
ejpam-5970	133	23	lower	lower	ADV
ejpam-5970	133	24	bound	bind	VERB
ejpam-5970	133	25	,	,	PUNCT
ejpam-5970	133	26	equality	equality	NOUN
ejpam-5970	133	27	holds	hold	VERB
ejpam-5970	133	28	.	.	PUNCT
ejpam-5970	134	1	hence	hence	ADV
ejpam-5970	134	2	the	the	DET
ejpam-5970	134	3	theorem	theorem	NOUN
ejpam-5970	134	4	is	be	AUX
ejpam-5970	134	5	proved	prove	VERB
ejpam-5970	134	6	.	.	PUNCT
ejpam-5970	135	1	theorem	theorem	NOUN
ejpam-5970	135	2	2	2	NUM
ejpam-5970	135	3	.	.	PUNCT
ejpam-5970	136	1	let	let	VERB
ejpam-5970	136	2	amal(fn	amal(fn	NOUN
ejpam-5970	136	3	,	,	PUNCT
ejpam-5970	136	4	x	x	X
ejpam-5970	136	5	,	,	PUNCT
ejpam-5970	136	6	m	m	VERB
ejpam-5970	136	7	)	)	PUNCT
ejpam-5970	136	8	be	be	VERB
ejpam-5970	136	9	an	an	DET
ejpam-5970	136	10	amalgamation	amalgamation	NOUN
ejpam-5970	136	11	of	of	ADP
ejpam-5970	136	12	fan	fan	NOUN
ejpam-5970	136	13	graph	graph	NOUN
ejpam-5970	136	14	with	with	ADP
ejpam-5970	136	15	n	n	NUM
ejpam-5970	136	16	≥	≥	NOUN
ejpam-5970	136	17	3	3	NUM
ejpam-5970	136	18	and	and	CCONJ
ejpam-5970	136	19	m	m	PROPN
ejpam-5970	136	20	≥	≥	NOUN
ejpam-5970	136	21	2	2	NUM
ejpam-5970	136	22	.	.	PUNCT
ejpam-5970	137	1	we	we	PRON
ejpam-5970	137	2	have	have	VERB
ejpam-5970	137	3	nm	nm	PRON
ejpam-5970	137	4	≤	≤	NUM
ejpam-5970	137	5	χle(nm+1,1)(amal(fn	χle(nm+1,1)(amal(fn	NOUN
ejpam-5970	137	6	,	,	PUNCT
ejpam-5970	137	7	x	x	X
ejpam-5970	137	8	,	,	PUNCT
ejpam-5970	137	9	m	m	NOUN
ejpam-5970	137	10	)	)	PUNCT
ejpam-5970	137	11	)	)	PUNCT
ejpam-5970	137	12	≤	≤	NUM
ejpam-5970	137	13	nm+	nm+	NOUN
ejpam-5970	137	14	1	1	NUM
ejpam-5970	137	15	.	.	PUNCT
ejpam-5970	138	1	proof	proof	NOUN
ejpam-5970	138	2	.	.	PUNCT
ejpam-5970	139	1	amalgamation	amalgamation	NOUN
ejpam-5970	139	2	of	of	ADP
ejpam-5970	139	3	fan	fan	PROPN
ejpam-5970	139	4	graph	graph	NOUN
ejpam-5970	139	5	amal(fn	amal(fn	PROPN
ejpam-5970	139	6	,	,	PUNCT
ejpam-5970	139	7	x	x	X
ejpam-5970	139	8	,	,	PUNCT
ejpam-5970	139	9	m	m	VERB
ejpam-5970	139	10	)	)	PUNCT
ejpam-5970	139	11	is	be	AUX
ejpam-5970	139	12	a	a	DET
ejpam-5970	139	13	connected	connected	ADJ
ejpam-5970	139	14	graph	graph	NOUN
ejpam-5970	139	15	with	with	ADP
ejpam-5970	139	16	vertex	vertex	NOUN
ejpam-5970	139	17	set	set	VERB
ejpam-5970	139	18	v	v	NOUN
ejpam-5970	139	19	(	(	PUNCT
ejpam-5970	139	20	amal(fn	amal(fn	NOUN
ejpam-5970	139	21	,	,	PUNCT
ejpam-5970	139	22	x	x	X
ejpam-5970	139	23	,	,	PUNCT
ejpam-5970	139	24	m	m	NOUN
ejpam-5970	139	25	)	)	PUNCT
ejpam-5970	139	26	)	)	PUNCT
ejpam-5970	140	1	=	=	PRON
ejpam-5970	140	2	{	{	PUNCT
ejpam-5970	140	3	x	x	NOUN
ejpam-5970	140	4	}	}	PUNCT
ejpam-5970	140	5	∪	∪	X
ejpam-5970	140	6	{	{	PUNCT
ejpam-5970	140	7	xji	xji	NOUN
ejpam-5970	140	8	;	;	PUNCT
ejpam-5970	140	9	1	1	NUM
ejpam-5970	140	10	≤	≤	NUM
ejpam-5970	140	11	i	i	PRON
ejpam-5970	140	12	≤	≤	PROPN
ejpam-5970	140	13	n	n	CCONJ
ejpam-5970	140	14	,	,	PUNCT
ejpam-5970	140	15	1	1	NUM
ejpam-5970	140	16	≤	≤	NUM
ejpam-5970	140	17	j	j	PROPN
ejpam-5970	140	18	≤	≤	PROPN
ejpam-5970	140	19	m	m	PROPN
ejpam-5970	140	20	}	}	PUNCT
ejpam-5970	140	21	and	and	CCONJ
ejpam-5970	140	22	edge	edge	VERB
ejpam-5970	140	23	set	set	VERB
ejpam-5970	140	24	e(amal(fn	e(amal(fn	NOUN
ejpam-5970	140	25	,	,	PUNCT
ejpam-5970	140	26	v	v	NOUN
ejpam-5970	140	27	,	,	PUNCT
ejpam-5970	140	28	m	m	NOUN
ejpam-5970	140	29	)	)	PUNCT
ejpam-5970	140	30	)	)	PUNCT
ejpam-5970	141	1	=	=	PRON
ejpam-5970	141	2	{	{	PUNCT
ejpam-5970	141	3	xxji	xxji	NOUN
ejpam-5970	141	4	;	;	PUNCT
ejpam-5970	141	5	1	1	NUM
ejpam-5970	141	6	≤	≤	NUM
ejpam-5970	141	7	i	i	PRON
ejpam-5970	141	8	≤	≤	PROPN
ejpam-5970	141	9	n	n	CCONJ
ejpam-5970	141	10	,	,	PUNCT
ejpam-5970	141	11	1	1	NUM
ejpam-5970	141	12	≤	≤	NUM
ejpam-5970	141	13	j	j	PROPN
ejpam-5970	141	14	≤	≤	PROPN
ejpam-5970	141	15	m	m	VERB
ejpam-5970	141	16	}	}	PUNCT
ejpam-5970	141	17	∪	∪	X
ejpam-5970	141	18	{	{	PUNCT
ejpam-5970	141	19	xjix	xjix	PROPN
ejpam-5970	141	20	j	j	PROPN
ejpam-5970	141	21	i+1	i+1	PRON
ejpam-5970	141	22	;	;	PUNCT
ejpam-5970	141	23	1	1	NUM
ejpam-5970	141	24	≤	≤	NUM
ejpam-5970	141	25	i	i	PRON
ejpam-5970	141	26	≤	≤	ADJ
ejpam-5970	141	27	n	n	CCONJ
ejpam-5970	141	28	−	−	PROPN
ejpam-5970	141	29	1	1	NUM
ejpam-5970	141	30	,	,	PUNCT
ejpam-5970	141	31	1	1	NUM
ejpam-5970	141	32	≤	≤	NUM
ejpam-5970	141	33	j	j	PROPN
ejpam-5970	141	34	≤	≤	PROPN
ejpam-5970	141	35	m	m	PROPN
ejpam-5970	141	36	}	}	PUNCT
ejpam-5970	141	37	.	.	PUNCT
ejpam-5970	142	1	the	the	DET
ejpam-5970	142	2	cardinality	cardinality	NOUN
ejpam-5970	142	3	of	of	ADP
ejpam-5970	142	4	the	the	DET
ejpam-5970	142	5	vertices	vertex	NOUN
ejpam-5970	142	6	set	set	VERB
ejpam-5970	142	7	|v	|v	PROPN
ejpam-5970	142	8	(	(	PUNCT
ejpam-5970	142	9	amal(fn	amal(fn	NOUN
ejpam-5970	142	10	,	,	PUNCT
ejpam-5970	142	11	x	x	NOUN
ejpam-5970	142	12	,	,	PUNCT
ejpam-5970	142	13	m))|	m))|	PROPN
ejpam-5970	142	14	=	=	PUNCT
ejpam-5970	142	15	nm	nm	PROPN
ejpam-5970	143	1	+	+	ADJ
ejpam-5970	143	2	1	1	NUM
ejpam-5970	143	3	,	,	PUNCT
ejpam-5970	143	4	and	and	CCONJ
ejpam-5970	143	5	the	the	DET
ejpam-5970	143	6	cardinality	cardinality	NOUN
ejpam-5970	143	7	of	of	ADP
ejpam-5970	143	8	the	the	DET
ejpam-5970	143	9	edges	edge	NOUN
ejpam-5970	143	10	set	set	VERB
ejpam-5970	143	11	|e(amal(fn	|e(amal(fn	PROPN
ejpam-5970	143	12	,	,	PUNCT
ejpam-5970	143	13	x	x	NOUN
ejpam-5970	143	14	,	,	PUNCT
ejpam-5970	143	15	m))|	m))|	PROPN
ejpam-5970	143	16	=	=	PUNCT
ejpam-5970	143	17	2nm−m	2nm−m	NUM
ejpam-5970	143	18	.	.	PUNCT
ejpam-5970	144	1	to	to	PART
ejpam-5970	144	2	prove	prove	VERB
ejpam-5970	144	3	,	,	PUNCT
ejpam-5970	144	4	first	first	ADV
ejpam-5970	144	5	we	we	PRON
ejpam-5970	144	6	need	need	VERB
ejpam-5970	144	7	to	to	PART
ejpam-5970	144	8	show	show	VERB
ejpam-5970	144	9	the	the	DET
ejpam-5970	144	10	lower	low	ADJ
ejpam-5970	144	11	bound	bind	VERB
ejpam-5970	144	12	of	of	ADP
ejpam-5970	144	13	χle(nm+1,1)(amal(fn	χle(nm+1,1)(amal(fn	NOUN
ejpam-5970	144	14	,	,	PUNCT
ejpam-5970	144	15	x	x	X
ejpam-5970	144	16	,	,	PUNCT
ejpam-5970	144	17	m	m	NOUN
ejpam-5970	144	18	)	)	PUNCT
ejpam-5970	144	19	)	)	PUNCT
ejpam-5970	144	20	.	.	PUNCT
ejpam-5970	145	1	based	base	VERB
ejpam-5970	145	2	on	on	ADP
ejpam-5970	145	3	observation	observation	NOUN
ejpam-5970	145	4	4	4	NUM
ejpam-5970	145	5	,	,	PUNCT
ejpam-5970	145	6	we	we	PRON
ejpam-5970	145	7	have	have	VERB
ejpam-5970	145	8	χle(a	χle(a	NOUN
ejpam-5970	145	9	,	,	PUNCT
ejpam-5970	145	10	d)(amal(fn	d)(amal(fn	PROPN
ejpam-5970	145	11	,	,	PUNCT
ejpam-5970	145	12	x	x	NOUN
ejpam-5970	145	13	,	,	PUNCT
ejpam-5970	145	14	m	m	NOUN
ejpam-5970	145	15	)	)	PUNCT
ejpam-5970	145	16	)	)	PUNCT
ejpam-5970	145	17	≥	≥	NUM
ejpam-5970	146	1	χlea(amal(fn	χlea(amal(fn	NOUN
ejpam-5970	146	2	,	,	PUNCT
ejpam-5970	146	3	x	x	X
ejpam-5970	146	4	,	,	PUNCT
ejpam-5970	146	5	m	m	NOUN
ejpam-5970	146	6	)	)	PUNCT
ejpam-5970	146	7	)	)	PUNCT
ejpam-5970	146	8	≥	≥	NOUN
ejpam-5970	147	1	∆(amal	∆(amal	PROPN
ejpam-5970	147	2	(	(	PUNCT
ejpam-5970	147	3	fn	fn	NOUN
ejpam-5970	147	4	,	,	PUNCT
ejpam-5970	147	5	x	x	NOUN
ejpam-5970	147	6	,	,	PUNCT
ejpam-5970	147	7	m	m	NOUN
ejpam-5970	147	8	)	)	PUNCT
ejpam-5970	147	9	)	)	PUNCT
ejpam-5970	147	10	.	.	PUNCT
ejpam-5970	148	1	the	the	DET
ejpam-5970	148	2	maximum	maximum	ADJ
ejpam-5970	148	3	degree	degree	NOUN
ejpam-5970	148	4	is	be	AUX
ejpam-5970	148	5	∆(amal(fn	∆(amal(fn	PROPN
ejpam-5970	148	6	,	,	PUNCT
ejpam-5970	148	7	x	x	X
ejpam-5970	148	8	,	,	PUNCT
ejpam-5970	148	9	m	m	NOUN
ejpam-5970	148	10	)	)	PUNCT
ejpam-5970	148	11	)	)	PUNCT
ejpam-5970	149	1	=	=	PUNCT
ejpam-5970	149	2	nm	nm	X
ejpam-5970	149	3	.	.	PUNCT
ejpam-5970	150	1	thus	thus	ADV
ejpam-5970	150	2	,	,	PUNCT
ejpam-5970	150	3	the	the	DET
ejpam-5970	150	4	lower	lower	ADV
ejpam-5970	150	5	bound	bind	VERB
ejpam-5970	150	6	is	be	AUX
ejpam-5970	150	7	χle(a	χle(a	PROPN
ejpam-5970	150	8	,	,	PUNCT
ejpam-5970	150	9	d)(amal(fn	d)(amal(fn	PROPN
ejpam-5970	150	10	,	,	PUNCT
ejpam-5970	150	11	x	x	NOUN
ejpam-5970	150	12	,	,	PUNCT
ejpam-5970	150	13	m	m	NOUN
ejpam-5970	150	14	)	)	PUNCT
ejpam-5970	150	15	)	)	PUNCT
ejpam-5970	150	16	≥	≥	PROPN
ejpam-5970	150	17	nm	nm	NOUN
ejpam-5970	150	18	.	.	PUNCT
ejpam-5970	151	1	to	to	PART
ejpam-5970	151	2	show	show	VERB
ejpam-5970	151	3	the	the	DET
ejpam-5970	151	4	upper	upper	ADJ
ejpam-5970	151	5	bound	bind	VERB
ejpam-5970	151	6	,	,	PUNCT
ejpam-5970	151	7	we	we	PRON
ejpam-5970	151	8	define	define	VERB
ejpam-5970	151	9	the	the	DET
ejpam-5970	151	10	bijection	bijection	NOUN
ejpam-5970	151	11	as	as	ADP
ejpam-5970	151	12	follow	follow	NOUN
ejpam-5970	151	13	f	f	PROPN
ejpam-5970	151	14	:	:	PUNCT
ejpam-5970	151	15	v	v	X
ejpam-5970	151	16	(	(	PUNCT
ejpam-5970	151	17	amal(fn	amal(fn	NOUN
ejpam-5970	151	18	,	,	PUNCT
ejpam-5970	151	19	x	x	X
ejpam-5970	151	20	,	,	PUNCT
ejpam-5970	151	21	m	m	NOUN
ejpam-5970	151	22	)	)	PUNCT
ejpam-5970	151	23	)	)	PUNCT
ejpam-5970	151	24	→	→	PUNCT
ejpam-5970	151	25	{	{	PUNCT
ejpam-5970	151	26	1	1	NUM
ejpam-5970	151	27	,	,	PUNCT
ejpam-5970	151	28	2	2	NUM
ejpam-5970	151	29	,	,	PUNCT
ejpam-5970	151	30	3	3	NUM
ejpam-5970	151	31	,	,	PUNCT
ejpam-5970	151	32	.	.	PUNCT
ejpam-5970	151	33	.	.	PUNCT
ejpam-5970	152	1	.	.	PUNCT
ejpam-5970	153	1	,	,	PUNCT
ejpam-5970	153	2	|v	|v	PROPN
ejpam-5970	153	3	(	(	PUNCT
ejpam-5970	153	4	amal(fn	amal(fn	NOUN
ejpam-5970	153	5	,	,	PUNCT
ejpam-5970	153	6	x	x	X
ejpam-5970	153	7	,	,	PUNCT
ejpam-5970	153	8	m))|	m))|	PROPN
ejpam-5970	153	9	}	}	PUNCT
ejpam-5970	153	10	.	.	PUNCT
ejpam-5970	154	1	to	to	PART
ejpam-5970	154	2	prove	prove	VERB
ejpam-5970	154	3	upperbound	upperbound	PROPN
ejpam-5970	154	4	,	,	PUNCT
ejpam-5970	154	5	we	we	PRON
ejpam-5970	154	6	show	show	VERB
ejpam-5970	154	7	into	into	ADP
ejpam-5970	154	8	two	two	NUM
ejpam-5970	154	9	cases	case	NOUN
ejpam-5970	154	10	.	.	PUNCT
ejpam-5970	155	1	case	case	NOUN
ejpam-5970	155	2	1	1	NUM
ejpam-5970	155	3	.	.	X
ejpam-5970	155	4	for	for	ADP
ejpam-5970	155	5	n	n	PRON
ejpam-5970	155	6	≡	≡	PROPN
ejpam-5970	155	7	1(mod2	1(mod2	NUM
ejpam-5970	155	8	)	)	PUNCT
ejpam-5970	155	9	,	,	PUNCT
ejpam-5970	155	10	we	we	PRON
ejpam-5970	155	11	have	have	VERB
ejpam-5970	155	12	the	the	DET
ejpam-5970	155	13	following	following	NOUN
ejpam-5970	155	14	.	.	PUNCT
ejpam-5970	156	1	firstly	firstly	ADV
ejpam-5970	156	2	,	,	PUNCT
ejpam-5970	156	3	we	we	PRON
ejpam-5970	156	4	show	show	VERB
ejpam-5970	156	5	the	the	DET
ejpam-5970	156	6	bijective	bijective	ADJ
ejpam-5970	156	7	function	function	NOUN
ejpam-5970	156	8	of	of	ADP
ejpam-5970	156	9	vertex	vertex	NOUN
ejpam-5970	156	10	labels	label	NOUN
ejpam-5970	156	11	as	as	SCONJ
ejpam-5970	156	12	follows	follow	VERB
ejpam-5970	156	13	f(x	f(x	PROPN
ejpam-5970	156	14	)	)	PUNCT
ejpam-5970	157	1	=	=	PUNCT
ejpam-5970	157	2	nm+	nm+	NOUN
ejpam-5970	157	3	1	1	NUM
ejpam-5970	157	4	f(xji	f(xji	NOUN
ejpam-5970	157	5	)	)	PUNCT
ejpam-5970	157	6	=	=	PUNCT
ejpam-5970	158	1			NUM
ejpam-5970	158	2	nj+n+i+1	nj+n+i+1	NUM
ejpam-5970	158	3	2	2	NUM
ejpam-5970	158	4	−	−	NOUN
ejpam-5970	158	5	n	n	CCONJ
ejpam-5970	158	6	,	,	PUNCT
ejpam-5970	158	7	for	for	ADP
ejpam-5970	158	8	i	i	PRON
ejpam-5970	158	9	,	,	PUNCT
ejpam-5970	158	10	j	j	PROPN
ejpam-5970	158	11	≡	≡	PROPN
ejpam-5970	158	12	1(mod	1(mod	NUM
ejpam-5970	158	13	2	2	X
ejpam-5970	158	14	)	)	PUNCT
ejpam-5970	158	15	nm−	nm−	PUNCT
ejpam-5970	158	16	nj+n+i	nj+n+i	NOUN
ejpam-5970	158	17	2	2	NUM
ejpam-5970	158	18	+	+	CCONJ
ejpam-5970	158	19	n+	n+	NUM
ejpam-5970	158	20	1	1	NUM
ejpam-5970	158	21	,	,	PUNCT
ejpam-5970	158	22	for	for	ADP
ejpam-5970	158	23	i	i	PROPN
ejpam-5970	158	24	≡	≡	PROPN
ejpam-5970	158	25	1(mod	1(mod	NUM
ejpam-5970	158	26	2	2	NUM
ejpam-5970	158	27	)	)	PUNCT
ejpam-5970	158	28	,	,	PUNCT
ejpam-5970	158	29	j	j	PROPN
ejpam-5970	158	30	≡	≡	PROPN
ejpam-5970	158	31	0(mod	0(mod	NOUN
ejpam-5970	158	32	2	2	X
ejpam-5970	158	33	)	)	PUNCT
ejpam-5970	158	34	nj+n+i+1	nj+n+i+1	NUM
ejpam-5970	158	35	2	2	NUM
ejpam-5970	158	36	−	−	NOUN
ejpam-5970	158	37	n	n	CCONJ
ejpam-5970	158	38	,	,	PUNCT
ejpam-5970	158	39	for	for	ADP
ejpam-5970	158	40	i	i	PRON
ejpam-5970	158	41	,	,	PUNCT
ejpam-5970	158	42	j	j	PROPN
ejpam-5970	158	43	≡	≡	PROPN
ejpam-5970	158	44	0(mod	0(mod	NOUN
ejpam-5970	158	45	2	2	X
ejpam-5970	158	46	)	)	PUNCT
ejpam-5970	158	47	nm−	nm−	PUNCT
ejpam-5970	158	48	nj+n+i	nj+n+i	PROPN
ejpam-5970	158	49	2	2	NUM
ejpam-5970	158	50	+	+	CCONJ
ejpam-5970	158	51	n+	n+	NUM
ejpam-5970	158	52	1	1	NUM
ejpam-5970	158	53	,	,	PUNCT
ejpam-5970	158	54	for	for	ADP
ejpam-5970	158	55	i	i	PROPN
ejpam-5970	158	56	≡	≡	ADJ
ejpam-5970	158	57	0(mod	0(mod	NOUN
ejpam-5970	158	58	2	2	NUM
ejpam-5970	158	59	)	)	PUNCT
ejpam-5970	158	60	,	,	PUNCT
ejpam-5970	158	61	j	j	PROPN
ejpam-5970	158	62	≡	≡	PROPN
ejpam-5970	158	63	1(mod	1(mod	NUM
ejpam-5970	158	64	2	2	X
ejpam-5970	158	65	)	)	PUNCT
ejpam-5970	158	66	under	under	ADP
ejpam-5970	158	67	the	the	DET
ejpam-5970	158	68	bijection	bijection	ADJ
ejpam-5970	158	69	f	f	NOUN
ejpam-5970	158	70	,	,	PUNCT
ejpam-5970	158	71	the	the	DET
ejpam-5970	158	72	edge	edge	NOUN
ejpam-5970	158	73	weights	weight	NOUN
ejpam-5970	158	74	can	can	AUX
ejpam-5970	158	75	be	be	AUX
ejpam-5970	158	76	presented	present	VERB
ejpam-5970	158	77	as	as	SCONJ
ejpam-5970	158	78	follows	follow	VERB
ejpam-5970	158	79	w(xjix	w(xjix	PROPN
ejpam-5970	158	80	j	j	PROPN
ejpam-5970	158	81	i+1	i+1	NUM
ejpam-5970	158	82	)	)	PUNCT
ejpam-5970	158	83	=	=	SYM
ejpam-5970	158	84			PUNCT
ejpam-5970	158	85	nm+	nm+	NOUN
ejpam-5970	158	86	1	1	NUM
ejpam-5970	158	87	,	,	PUNCT
ejpam-5970	158	88	for	for	ADP
ejpam-5970	158	89	m	m	PROPN
ejpam-5970	158	90	,	,	PUNCT
ejpam-5970	158	91	i	i	PRON
ejpam-5970	158	92	≡	≡	PROPN
ejpam-5970	158	93	1(mod	1(mod	NUM
ejpam-5970	158	94	2	2	X
ejpam-5970	158	95	)	)	PUNCT
ejpam-5970	158	96	nm+	nm+	NOUN
ejpam-5970	158	97	2	2	NUM
ejpam-5970	158	98	,	,	PUNCT
ejpam-5970	158	99	for	for	ADP
ejpam-5970	158	100	m	m	PROPN
ejpam-5970	158	101	≡	≡	PROPN
ejpam-5970	158	102	1(mod	1(mod	NUM
ejpam-5970	158	103	2	2	NUM
ejpam-5970	158	104	)	)	PUNCT
ejpam-5970	158	105	,	,	PUNCT
ejpam-5970	158	106	i	i	PRON
ejpam-5970	158	107	≡	≡	PROPN
ejpam-5970	158	108	0(mod	0(mod	NOUN
ejpam-5970	159	1	2	2	X
ejpam-5970	159	2	)	)	PUNCT
ejpam-5970	159	3	nm+	nm+	NOUN
ejpam-5970	159	4	1	1	NUM
ejpam-5970	159	5	,	,	PUNCT
ejpam-5970	159	6	for	for	ADP
ejpam-5970	159	7	m	m	PROPN
ejpam-5970	159	8	,	,	PUNCT
ejpam-5970	159	9	i	i	PRON
ejpam-5970	159	10	≡	≡	PROPN
ejpam-5970	159	11	0(mod	0(mod	NOUN
ejpam-5970	159	12	2	2	X
ejpam-5970	159	13	)	)	PUNCT
ejpam-5970	159	14	nm+	nm+	NOUN
ejpam-5970	159	15	2	2	NUM
ejpam-5970	159	16	,	,	PUNCT
ejpam-5970	159	17	for	for	ADP
ejpam-5970	159	18	m	m	PROPN
ejpam-5970	159	19	≡	≡	ADJ
ejpam-5970	159	20	0(mod	0(mod	NOUN
ejpam-5970	159	21	2	2	NUM
ejpam-5970	159	22	)	)	PUNCT
ejpam-5970	159	23	,	,	PUNCT
ejpam-5970	159	24	i	i	PRON
ejpam-5970	159	25	≡	≡	PROPN
ejpam-5970	159	26	1(mod	1(mod	NUM
ejpam-5970	159	27	2	2	X
ejpam-5970	159	28	)	)	PUNCT
ejpam-5970	159	29	w(xxji	w(xxji	NOUN
ejpam-5970	159	30	)	)	PUNCT
ejpam-5970	160	1	=	=	X
ejpam-5970	160	2			NUM
ejpam-5970	160	3	nj+n+i+1	nj+n+i+1	NUM
ejpam-5970	160	4	2	2	NUM
ejpam-5970	160	5	−	−	NOUN
ejpam-5970	160	6	n+	n+	SYM
ejpam-5970	160	7	nm+	nm+	NOUN
ejpam-5970	160	8	1	1	NUM
ejpam-5970	160	9	,	,	PUNCT
ejpam-5970	160	10	for	for	ADP
ejpam-5970	160	11	i	i	PRON
ejpam-5970	160	12	,	,	PUNCT
ejpam-5970	160	13	j	j	PROPN
ejpam-5970	160	14	≡	≡	PROPN
ejpam-5970	160	15	1(mod	1(mod	NUM
ejpam-5970	160	16	2	2	NUM
ejpam-5970	160	17	)	)	PUNCT
ejpam-5970	160	18	,	,	PUNCT
ejpam-5970	160	19	1	1	NUM
ejpam-5970	160	20	≤	≤	NUM
ejpam-5970	160	21	i	i	PRON
ejpam-5970	160	22	≤	≤	PROPN
ejpam-5970	160	23	n	n	CCONJ
ejpam-5970	160	24	,	,	PUNCT
ejpam-5970	160	25	1	1	NUM
ejpam-5970	160	26	≤	≤	NUM
ejpam-5970	160	27	j	j	PROPN
ejpam-5970	160	28	≤	≤	NUM
ejpam-5970	160	29	m	m	VERB
ejpam-5970	160	30	2nm−	2nm−	NUM
ejpam-5970	160	31	jn+n+i	jn+n+i	PROPN
ejpam-5970	160	32	2	2	NUM
ejpam-5970	160	33	+	+	CCONJ
ejpam-5970	160	34	n+	n+	NUM
ejpam-5970	160	35	2	2	NUM
ejpam-5970	160	36	,	,	PUNCT
ejpam-5970	160	37	for	for	ADP
ejpam-5970	160	38	i	i	PROPN
ejpam-5970	160	39	≡	≡	PROPN
ejpam-5970	160	40	1(mod	1(mod	NUM
ejpam-5970	160	41	2	2	NUM
ejpam-5970	160	42	)	)	PUNCT
ejpam-5970	160	43	,	,	PUNCT
ejpam-5970	160	44	j	j	PROPN
ejpam-5970	160	45	≡	≡	PROPN
ejpam-5970	160	46	0(mod	0(mod	NOUN
ejpam-5970	160	47	2	2	NUM
ejpam-5970	160	48	)	)	PUNCT
ejpam-5970	160	49	,	,	PUNCT
ejpam-5970	160	50	1	1	NUM
ejpam-5970	160	51	≤	≤	NUM
ejpam-5970	160	52	i	i	PRON
ejpam-5970	160	53	≤	≤	PROPN
ejpam-5970	160	54	n	n	CCONJ
ejpam-5970	160	55	,	,	PUNCT
ejpam-5970	160	56	2	2	NUM
ejpam-5970	160	57	≤	≤	NUM
ejpam-5970	160	58	j	j	PROPN
ejpam-5970	160	59	≤	≤	NUM
ejpam-5970	160	60	m	m	VERB
ejpam-5970	160	61	nj+n+i+1	nj+n+i+1	PROPN
ejpam-5970	160	62	2	2	NUM
ejpam-5970	160	63	−	−	NOUN
ejpam-5970	160	64	n+	n+	SYM
ejpam-5970	160	65	nm+	nm+	NOUN
ejpam-5970	160	66	1	1	NUM
ejpam-5970	160	67	,	,	PUNCT
ejpam-5970	160	68	for	for	ADP
ejpam-5970	160	69	i	i	PRON
ejpam-5970	160	70	,	,	PUNCT
ejpam-5970	160	71	j	j	PROPN
ejpam-5970	160	72	≡	≡	PROPN
ejpam-5970	160	73	0(mod	0(mod	NOUN
ejpam-5970	161	1	2	2	NUM
ejpam-5970	161	2	)	)	PUNCT
ejpam-5970	161	3	,	,	PUNCT
ejpam-5970	161	4	2	2	NUM
ejpam-5970	161	5	≤	≤	NUM
ejpam-5970	161	6	i	i	PRON
ejpam-5970	161	7	≤	≤	PROPN
ejpam-5970	161	8	n	n	CCONJ
ejpam-5970	161	9	,	,	PUNCT
ejpam-5970	161	10	2	2	NUM
ejpam-5970	161	11	≤	≤	NUM
ejpam-5970	161	12	j	j	PROPN
ejpam-5970	161	13	≤	≤	NUM
ejpam-5970	161	14	m	m	VERB
ejpam-5970	161	15	2nm−	2nm−	NUM
ejpam-5970	161	16	jn+n+i	jn+n+i	PROPN
ejpam-5970	161	17	2	2	NUM
ejpam-5970	161	18	+	+	CCONJ
ejpam-5970	161	19	n+	n+	NUM
ejpam-5970	161	20	2	2	NUM
ejpam-5970	161	21	,	,	PUNCT
ejpam-5970	161	22	for	for	ADP
ejpam-5970	161	23	i	i	PROPN
ejpam-5970	161	24	≡	≡	ADJ
ejpam-5970	161	25	0(mod	0(mod	NOUN
ejpam-5970	161	26	2	2	NUM
ejpam-5970	161	27	)	)	PUNCT
ejpam-5970	161	28	,	,	PUNCT
ejpam-5970	161	29	j	j	PROPN
ejpam-5970	161	30	≡	≡	PROPN
ejpam-5970	161	31	1(mod	1(mod	NUM
ejpam-5970	161	32	2	2	NUM
ejpam-5970	161	33	)	)	PUNCT
ejpam-5970	161	34	,	,	PUNCT
ejpam-5970	161	35	2	2	NUM
ejpam-5970	161	36	≤	≤	NUM
ejpam-5970	161	37	i	i	PRON
ejpam-5970	161	38	≤	≤	PROPN
ejpam-5970	161	39	n	n	CCONJ
ejpam-5970	161	40	,	,	PUNCT
ejpam-5970	161	41	1	1	NUM
ejpam-5970	161	42	≤	≤	NUM
ejpam-5970	161	43	j	j	PROPN
ejpam-5970	161	44	≤	≤	PROPN
ejpam-5970	161	45	m	m	VERB
ejpam-5970	161	46	a.	a.	PROPN
ejpam-5970	161	47	i.	i.	PROPN
ejpam-5970	161	48	kristiana	kristiana	PROPN
ejpam-5970	161	49	,	,	PUNCT
ejpam-5970	161	50	et	et	PROPN
ejpam-5970	161	51	al	al	PROPN
ejpam-5970	161	52	.	.	PUNCT
ejpam-5970	161	53	/	/	SYM
ejpam-5970	161	54	eur	eur	PROPN
ejpam-5970	161	55	.	.	PUNCT
ejpam-5970	162	1	j.	j.	PROPN
ejpam-5970	162	2	pure	pure	PROPN
ejpam-5970	162	3	appl	appl	PROPN
ejpam-5970	162	4	.	.	PROPN
ejpam-5970	162	5	math	math	PROPN
ejpam-5970	162	6	,	,	PUNCT
ejpam-5970	162	7	18	18	NUM
ejpam-5970	162	8	(	(	PUNCT
ejpam-5970	162	9	3	3	NUM
ejpam-5970	162	10	)	)	PUNCT
ejpam-5970	162	11	(	(	PUNCT
ejpam-5970	162	12	2025	2025	NUM
ejpam-5970	162	13	)	)	PUNCT
ejpam-5970	162	14	,	,	PUNCT
ejpam-5970	162	15	5970	5970	NUM
ejpam-5970	162	16	7	7	NUM
ejpam-5970	162	17	of	of	ADP
ejpam-5970	162	18	18	18	NUM
ejpam-5970	162	19	thus	thus	ADV
ejpam-5970	162	20	,	,	PUNCT
ejpam-5970	162	21	we	we	PRON
ejpam-5970	162	22	can	can	AUX
ejpam-5970	162	23	write	write	VERB
ejpam-5970	162	24	in	in	ADP
ejpam-5970	162	25	the	the	DET
ejpam-5970	162	26	form	form	NOUN
ejpam-5970	162	27	of	of	ADP
ejpam-5970	162	28	the	the	DET
ejpam-5970	162	29	set	set	NOUN
ejpam-5970	162	30	w	w	PROPN
ejpam-5970	162	31	of	of	ADP
ejpam-5970	162	32	edge	edge	NOUN
ejpam-5970	162	33	weight	weight	NOUN
ejpam-5970	162	34	of	of	ADP
ejpam-5970	162	35	amal(fn	amal(fn	NOUN
ejpam-5970	162	36	,	,	PUNCT
ejpam-5970	162	37	x	x	X
ejpam-5970	162	38	,	,	PUNCT
ejpam-5970	162	39	m	m	NOUN
ejpam-5970	162	40	)	)	PUNCT
ejpam-5970	162	41	.	.	PUNCT
ejpam-5970	163	1	it	it	PRON
ejpam-5970	163	2	includes	include	VERB
ejpam-5970	163	3	four	four	NUM
ejpam-5970	163	4	sets	set	NOUN
ejpam-5970	163	5	of	of	ADP
ejpam-5970	163	6	edge	edge	NOUN
ejpam-5970	163	7	weights	weight	NOUN
ejpam-5970	163	8	,	,	PUNCT
ejpam-5970	163	9	namely	namely	ADV
ejpam-5970	163	10	w1	w1	NOUN
ejpam-5970	163	11	=	=	SYM
ejpam-5970	163	12	{	{	PUNCT
ejpam-5970	163	13	nm+1	nm+1	X
ejpam-5970	163	14	}	}	PUNCT
ejpam-5970	163	15	,	,	PUNCT
ejpam-5970	163	16	w2	w2	NOUN
ejpam-5970	163	17	=	=	SYM
ejpam-5970	163	18	{	{	PUNCT
ejpam-5970	163	19	nm+2	nm+2	NOUN
ejpam-5970	163	20	}	}	PUNCT
ejpam-5970	163	21	,	,	PUNCT
ejpam-5970	163	22	w3	w3	PROPN
ejpam-5970	163	23	=	=	PUNCT
ejpam-5970	163	24	{	{	PUNCT
ejpam-5970	163	25	nm+	nm+	NOUN
ejpam-5970	163	26	2	2	NUM
ejpam-5970	163	27	,	,	PUNCT
ejpam-5970	163	28	nm+3	nm+3	NUM
ejpam-5970	163	29	,	,	PUNCT
ejpam-5970	163	30	nm+4	nm+4	NUM
ejpam-5970	163	31	.	.	PUNCT
ejpam-5970	163	32	.	.	PUNCT
ejpam-5970	163	33	.	.	PUNCT
ejpam-5970	164	1	,	,	PUNCT
ejpam-5970	164	2	nm+1	nm+1	NUM
ejpam-5970	164	3	+	+	SYM
ejpam-5970	164	4	nm+1	nm+1	PROPN
ejpam-5970	164	5	2	2	NUM
ejpam-5970	164	6	}	}	PUNCT
ejpam-5970	164	7	,	,	PUNCT
ejpam-5970	164	8	andw4	andw4	NOUN
ejpam-5970	164	9	=	=	PRON
ejpam-5970	164	10	{	{	PUNCT
ejpam-5970	164	11	nm+2	nm+2	X
ejpam-5970	164	12	+	+	NUM
ejpam-5970	164	13	nm+1	nm+1	PROPN
ejpam-5970	164	14	2	2	NUM
ejpam-5970	164	15	,	,	PUNCT
ejpam-5970	164	16	nm+3	nm+3	NUM
ejpam-5970	164	17	+	+	NUM
ejpam-5970	164	18	nm+1	nm+1	PROPN
ejpam-5970	164	19	2	2	NUM
ejpam-5970	164	20	,	,	PUNCT
ejpam-5970	164	21	.	.	PUNCT
ejpam-5970	164	22	.	.	PUNCT
ejpam-5970	165	1	.	.	PUNCT
ejpam-5970	166	1	,	,	PUNCT
ejpam-5970	166	2	2nm+	2nm+	PROPN
ejpam-5970	166	3	1	1	NUM
ejpam-5970	166	4	}	}	PUNCT
ejpam-5970	166	5	.	.	PUNCT
ejpam-5970	167	1	our	our	PRON
ejpam-5970	167	2	task	task	NOUN
ejpam-5970	167	3	is	be	AUX
ejpam-5970	167	4	to	to	PART
ejpam-5970	167	5	determine	determine	VERB
ejpam-5970	167	6	the	the	DET
ejpam-5970	167	7	cardinality	cardinality	NOUN
ejpam-5970	167	8	of	of	ADP
ejpam-5970	167	9	those	those	DET
ejpam-5970	167	10	sets	set	NOUN
ejpam-5970	167	11	to	to	PART
ejpam-5970	167	12	obtain	obtain	VERB
ejpam-5970	167	13	the	the	DET
ejpam-5970	167	14	upper	upper	ADJ
ejpam-5970	167	15	bound	bound	NOUN
ejpam-5970	167	16	,	,	PUNCT
ejpam-5970	167	17	but	but	CCONJ
ejpam-5970	167	18	we	we	PRON
ejpam-5970	167	19	need	need	VERB
ejpam-5970	167	20	to	to	PART
ejpam-5970	167	21	check	check	VERB
ejpam-5970	167	22	whether	whether	SCONJ
ejpam-5970	167	23	all	all	DET
ejpam-5970	167	24	three	three	NUM
ejpam-5970	167	25	sets	set	NOUN
ejpam-5970	167	26	are	be	AUX
ejpam-5970	167	27	disjoint	disjoint	ADJ
ejpam-5970	167	28	or	or	CCONJ
ejpam-5970	167	29	not	not	PART
ejpam-5970	167	30	first	first	ADJ
ejpam-5970	167	31	.	.	PUNCT
ejpam-5970	168	1	under	under	ADP
ejpam-5970	168	2	the	the	DET
ejpam-5970	168	3	contradiction	contradiction	NOUN
ejpam-5970	168	4	proof	proof	NOUN
ejpam-5970	168	5	,	,	PUNCT
ejpam-5970	168	6	we	we	PRON
ejpam-5970	168	7	suppose	suppose	VERB
ejpam-5970	168	8	w1	w1	NOUN
ejpam-5970	168	9	⊆w3	⊆w3	PROPN
ejpam-5970	169	1	←→	←→	ADP
ejpam-5970	169	2	nm+1	nm+1	PROPN
ejpam-5970	169	3	=	=	SYM
ejpam-5970	169	4	nj+n+i+1	nj+n+i+1	PROPN
ejpam-5970	169	5	2	2	NUM
ejpam-5970	169	6	−n+nm+1←→	−n+nm+1←→	NOUN
ejpam-5970	169	7	i	i	PRON
ejpam-5970	169	8	=	=	NOUN
ejpam-5970	169	9	−3n−nj−	−3n−nj−	NOUN
ejpam-5970	169	10	1	1	X
ejpam-5970	169	11	.	.	PUNCT
ejpam-5970	170	1	since	since	SCONJ
ejpam-5970	170	2	w(xxji	w(xxji	NOUN
ejpam-5970	170	3	)	)	PUNCT
ejpam-5970	171	1	=	=	PUNCT
ejpam-5970	171	2	nj+n+i+1	nj+n+i+1	NUM
ejpam-5970	171	3	2	2	NUM
ejpam-5970	171	4	−n+nm+1	−n+nm+1	NOUN
ejpam-5970	171	5	,	,	PUNCT
ejpam-5970	171	6	for	for	ADP
ejpam-5970	171	7	1	1	NUM
ejpam-5970	171	8	≤	≤	NUM
ejpam-5970	171	9	i	i	PRON
ejpam-5970	171	10	≤	≤	NOUN
ejpam-5970	171	11	nm+1	nm+1	PROPN
ejpam-5970	171	12	2	2	NUM
ejpam-5970	171	13	,	,	PUNCT
ejpam-5970	171	14	therefore	therefore	ADV
ejpam-5970	171	15	i	i	PRON
ejpam-5970	171	16	=	=	NOUN
ejpam-5970	172	1	−3n−nj−	−3n−nj−	NOUN
ejpam-5970	172	2	1	1	NUM
ejpam-5970	172	3	does	do	AUX
ejpam-5970	172	4	not	not	PART
ejpam-5970	172	5	lie	lie	VERB
ejpam-5970	172	6	in	in	ADP
ejpam-5970	172	7	the	the	DET
ejpam-5970	172	8	interval	interval	NOUN
ejpam-5970	172	9	,	,	PUNCT
ejpam-5970	172	10	it	it	PRON
ejpam-5970	172	11	is	be	AUX
ejpam-5970	172	12	a	a	DET
ejpam-5970	172	13	contradiction	contradiction	NOUN
ejpam-5970	172	14	.	.	PUNCT
ejpam-5970	173	1	we	we	PRON
ejpam-5970	173	2	conclude	conclude	VERB
ejpam-5970	173	3	that	that	DET
ejpam-5970	173	4	w1∩w3	w1∩w3	PROPN
ejpam-5970	173	5	=	=	PUNCT
ejpam-5970	173	6	∅.	∅.	VERB
ejpam-5970	173	7	furthermore	furthermore	ADV
ejpam-5970	173	8	,	,	PUNCT
ejpam-5970	173	9	in	in	ADP
ejpam-5970	173	10	the	the	DET
ejpam-5970	173	11	contradiction	contradiction	NOUN
ejpam-5970	173	12	proof	proof	NOUN
ejpam-5970	173	13	,	,	PUNCT
ejpam-5970	173	14	we	we	PRON
ejpam-5970	173	15	suppose	suppose	VERB
ejpam-5970	173	16	w1	w1	NOUN
ejpam-5970	173	17	⊆w4	⊆w4	PROPN
ejpam-5970	173	18	←→	←→	PROPN
ejpam-5970	173	19	nm+1	nm+1	PROPN
ejpam-5970	173	20	=	=	SYM
ejpam-5970	173	21	2nm−	2nm−	NUM
ejpam-5970	173	22	nj+n+i	nj+n+i	NOUN
ejpam-5970	173	23	2	2	NUM
ejpam-5970	174	1	+	+	NOUN
ejpam-5970	174	2	n+2←→	n+2←→	ADJ
ejpam-5970	174	3	i	i	NOUN
ejpam-5970	174	4	=	=	SYM
ejpam-5970	174	5	2	2	NUM
ejpam-5970	174	6	nm	nm	NOUN
ejpam-5970	174	7	−	−	PROPN
ejpam-5970	174	8	nj	nj	PROPN
ejpam-5970	174	9	+	+	CCONJ
ejpam-5970	174	10	2	2	X
ejpam-5970	174	11	.	.	PUNCT
ejpam-5970	174	12	since	since	SCONJ
ejpam-5970	174	13	w(xxji	w(xxji	NOUN
ejpam-5970	174	14	)	)	PUNCT
ejpam-5970	175	1	=	=	SYM
ejpam-5970	175	2	2	2	NUM
ejpam-5970	175	3	nm	nm	NOUN
ejpam-5970	175	4	−	−	PROPN
ejpam-5970	175	5	nj+n+i	nj+n+i	NOUN
ejpam-5970	175	6	2	2	NUM
ejpam-5970	175	7	+	+	CCONJ
ejpam-5970	175	8	n	n	PROPN
ejpam-5970	175	9	+	+	NUM
ejpam-5970	175	10	2	2	NUM
ejpam-5970	175	11	,	,	PUNCT
ejpam-5970	175	12	for	for	ADP
ejpam-5970	175	13	nm+3	nm+3	NUM
ejpam-5970	175	14	2	2	NUM
ejpam-5970	175	15	≤	≤	NUM
ejpam-5970	175	16	i	i	PRON
ejpam-5970	175	17	≤	≤	PROPN
ejpam-5970	175	18	nm	nm	ADP
ejpam-5970	175	19	,	,	PUNCT
ejpam-5970	175	20	therefore	therefore	ADV
ejpam-5970	175	21	i	i	NOUN
ejpam-5970	175	22	=	=	SYM
ejpam-5970	175	23	2	2	NUM
ejpam-5970	175	24	nm	nm	NOUN
ejpam-5970	175	25	−	−	PROPN
ejpam-5970	175	26	nj	nj	NOUN
ejpam-5970	175	27	+	+	CCONJ
ejpam-5970	175	28	2	2	NUM
ejpam-5970	175	29	does	do	AUX
ejpam-5970	175	30	not	not	PART
ejpam-5970	175	31	lie	lie	VERB
ejpam-5970	175	32	in	in	ADP
ejpam-5970	175	33	the	the	DET
ejpam-5970	175	34	interval	interval	NOUN
ejpam-5970	175	35	,	,	PUNCT
ejpam-5970	175	36	it	it	PRON
ejpam-5970	175	37	is	be	AUX
ejpam-5970	175	38	a	a	DET
ejpam-5970	175	39	contradiction	contradiction	NOUN
ejpam-5970	175	40	.	.	PUNCT
ejpam-5970	176	1	we	we	PRON
ejpam-5970	176	2	conclude	conclude	VERB
ejpam-5970	176	3	that	that	DET
ejpam-5970	176	4	w1	w1	NOUN
ejpam-5970	176	5	∩w4	∩w4	PROPN
ejpam-5970	177	1	=	=	PUNCT
ejpam-5970	177	2	∅.	∅.	NOUN
ejpam-5970	177	3	finally	finally	ADV
ejpam-5970	177	4	,	,	PUNCT
ejpam-5970	177	5	we	we	PRON
ejpam-5970	177	6	have	have	VERB
ejpam-5970	177	7	w	w	NOUN
ejpam-5970	177	8	=	=	NOUN
ejpam-5970	177	9	w1	w1	PROPN
ejpam-5970	177	10	∪w3	∪w3	PROPN
ejpam-5970	177	11	∪w4	∪w4	PROPN
ejpam-5970	177	12	.	.	PUNCT
ejpam-5970	178	1	now	now	ADV
ejpam-5970	178	2	,	,	PUNCT
ejpam-5970	178	3	we	we	PRON
ejpam-5970	178	4	can	can	AUX
ejpam-5970	178	5	determine	determine	VERB
ejpam-5970	178	6	the	the	DET
ejpam-5970	178	7	cardinality	cardinality	NOUN
ejpam-5970	178	8	of	of	ADP
ejpam-5970	178	9	w.	w.	PROPN
ejpam-5970	178	10	first	first	PROPN
ejpam-5970	178	11	,	,	PUNCT
ejpam-5970	178	12	it	it	PRON
ejpam-5970	178	13	is	be	AUX
ejpam-5970	178	14	easy	easy	ADJ
ejpam-5970	178	15	to	to	PART
ejpam-5970	178	16	see	see	VERB
ejpam-5970	178	17	that	that	DET
ejpam-5970	178	18	|w1|	|w1|	NOUN
ejpam-5970	178	19	=	=	SYM
ejpam-5970	178	20	1	1	NUM
ejpam-5970	178	21	,	,	PUNCT
ejpam-5970	178	22	secondly	secondly	ADV
ejpam-5970	178	23	we	we	PRON
ejpam-5970	178	24	will	will	AUX
ejpam-5970	178	25	determine	determine	VERB
ejpam-5970	178	26	|w3	|w3	NOUN
ejpam-5970	178	27	∪w4|	∪w4|	ADJ
ejpam-5970	178	28	,	,	PUNCT
ejpam-5970	178	29	under	under	ADP
ejpam-5970	178	30	the	the	DET
ejpam-5970	178	31	following	follow	VERB
ejpam-5970	178	32	calculation	calculation	NOUN
ejpam-5970	178	33	.	.	PUNCT
ejpam-5970	179	1	let	let	VERB
ejpam-5970	179	2	us	we	PRON
ejpam-5970	180	1	and	and	CCONJ
ejpam-5970	180	2	d	d	X
ejpam-5970	180	3	be	be	AUX
ejpam-5970	180	4	the	the	DET
ejpam-5970	180	5	s	s	NOUN
ejpam-5970	180	6	term	term	NOUN
ejpam-5970	180	7	and	and	CCONJ
ejpam-5970	180	8	different	different	ADJ
ejpam-5970	180	9	from	from	ADP
ejpam-5970	180	10	the	the	DET
ejpam-5970	180	11	arithmetic	arithmetic	ADJ
ejpam-5970	180	12	sequence	sequence	NOUN
ejpam-5970	180	13	of	of	ADP
ejpam-5970	180	14	w3	w3	PROPN
ejpam-5970	180	15	∪w4	∪w4	NOUN
ejpam-5970	180	16	,	,	PUNCT
ejpam-5970	180	17	consequently	consequently	ADV
ejpam-5970	180	18	.	.	PUNCT
ejpam-5970	181	1	we	we	PRON
ejpam-5970	181	2	have	have	VERB
ejpam-5970	181	3	u|w3∪w4|	u|w3∪w4|	NOUN
ejpam-5970	181	4	=	=	PUNCT
ejpam-5970	181	5	a+(|w3∪w4|−1)d←→	a+(|w3∪w4|−1)d←→	PROPN
ejpam-5970	181	6	2nm+1	2nm+1	X
ejpam-5970	181	7	=	=	SYM
ejpam-5970	181	8	nm+2+(|w3∪w4|−1)1←→	nm+2+(|w3∪w4|−1)1←→	NOUN
ejpam-5970	181	9	|w3∪w4|	|w3∪w4|	PUNCT
ejpam-5970	182	1	=	=	SYM
ejpam-5970	182	2	nm	nm	AUX
ejpam-5970	182	3	.	.	PUNCT
ejpam-5970	182	4	w3∪w4	w3∪w4	NOUN
ejpam-5970	182	5	form	form	VERB
ejpam-5970	182	6	an	an	DET
ejpam-5970	182	7	arithmetic	arithmetic	ADJ
ejpam-5970	182	8	sequence	sequence	NOUN
ejpam-5970	182	9	with	with	ADP
ejpam-5970	182	10	initial	initial	ADJ
ejpam-5970	182	11	value	value	NOUN
ejpam-5970	182	12	a	a	DET
ejpam-5970	182	13	=	=	SYM
ejpam-5970	182	14	nm+2	nm+2	PROPN
ejpam-5970	182	15	and	and	CCONJ
ejpam-5970	182	16	w2	w2	NOUN
ejpam-5970	182	17	=	=	SYM
ejpam-5970	182	18	nm+2	nm+2	PROPN
ejpam-5970	182	19	.	.	PUNCT
ejpam-5970	183	1	thus	thus	ADV
ejpam-5970	183	2	,	,	PUNCT
ejpam-5970	183	3	we	we	PRON
ejpam-5970	183	4	have	have	VERB
ejpam-5970	183	5	w2	w2	PROPN
ejpam-5970	183	6	⊂	⊂	PROPN
ejpam-5970	183	7	(	(	PUNCT
ejpam-5970	183	8	w3	w3	PROPN
ejpam-5970	183	9	∪w4	∪w4	NOUN
ejpam-5970	183	10	)	)	PUNCT
ejpam-5970	183	11	.	.	PUNCT
ejpam-5970	184	1	this	this	PRON
ejpam-5970	184	2	implies	imply	VERB
ejpam-5970	184	3	|w	|w	ADJ
ejpam-5970	184	4	|	|	NOUN
ejpam-5970	184	5	=	=	SYM
ejpam-5970	184	6	|w1|+	|w1|+	PROPN
ejpam-5970	184	7	|w3	|w3	NOUN
ejpam-5970	184	8	∪w4|	∪w4|	ADJ
ejpam-5970	184	9	=	=	SYM
ejpam-5970	184	10	1	1	NUM
ejpam-5970	184	11	+	+	NUM
ejpam-5970	184	12	nm	nm	NOUN
ejpam-5970	184	13	.	.	PUNCT
ejpam-5970	185	1	finally	finally	ADV
ejpam-5970	185	2	,	,	PUNCT
ejpam-5970	185	3	we	we	PRON
ejpam-5970	185	4	have	have	VERB
ejpam-5970	185	5	χle(nm+1,1)(amal(fn	χle(nm+1,1)(amal(fn	NOUN
ejpam-5970	185	6	,	,	PUNCT
ejpam-5970	185	7	x	x	X
ejpam-5970	185	8	,	,	PUNCT
ejpam-5970	185	9	m	m	NOUN
ejpam-5970	185	10	)	)	PUNCT
ejpam-5970	185	11	)	)	PUNCT
ejpam-5970	185	12	≤	≤	NUM
ejpam-5970	185	13	nm+	nm+	NOUN
ejpam-5970	185	14	1	1	NUM
ejpam-5970	185	15	for	for	ADP
ejpam-5970	185	16	n	n	PRON
ejpam-5970	185	17	≡	≡	PROPN
ejpam-5970	185	18	1(mod	1(mod	ADJ
ejpam-5970	185	19	2	2	NUM
ejpam-5970	185	20	)	)	PUNCT
ejpam-5970	185	21	.	.	PUNCT
ejpam-5970	186	1	case	case	NOUN
ejpam-5970	186	2	2	2	NUM
ejpam-5970	186	3	.	.	X
ejpam-5970	186	4	for	for	ADP
ejpam-5970	186	5	n	n	PRON
ejpam-5970	186	6	≡	≡	PROPN
ejpam-5970	186	7	0(mod2	0(mod2	PROPN
ejpam-5970	186	8	)	)	PUNCT
ejpam-5970	186	9	,	,	PUNCT
ejpam-5970	186	10	we	we	PRON
ejpam-5970	186	11	have	have	VERB
ejpam-5970	186	12	the	the	DET
ejpam-5970	186	13	following	following	NOUN
ejpam-5970	186	14	.	.	PUNCT
ejpam-5970	187	1	firstly	firstly	ADV
ejpam-5970	187	2	,	,	PUNCT
ejpam-5970	187	3	we	we	PRON
ejpam-5970	187	4	show	show	VERB
ejpam-5970	187	5	the	the	DET
ejpam-5970	187	6	bijective	bijective	ADJ
ejpam-5970	187	7	function	function	NOUN
ejpam-5970	187	8	of	of	ADP
ejpam-5970	187	9	vertex	vertex	NOUN
ejpam-5970	187	10	labels	label	NOUN
ejpam-5970	187	11	as	as	SCONJ
ejpam-5970	187	12	follows	follow	VERB
ejpam-5970	187	13	.	.	PUNCT
ejpam-5970	188	1	f(x	f(x	NOUN
ejpam-5970	188	2	)	)	PUNCT
ejpam-5970	189	1	=	=	PUNCT
ejpam-5970	189	2	nm+	nm+	NOUN
ejpam-5970	189	3	1	1	NUM
ejpam-5970	189	4	f(xji	f(xji	NOUN
ejpam-5970	189	5	)	)	PUNCT
ejpam-5970	189	6	=	=	PRON
ejpam-5970	189	7	{	{	PUNCT
ejpam-5970	189	8	nj−n+i+1	nj−n+i+1	DET
ejpam-5970	189	9	2	2	NUM
ejpam-5970	189	10	,	,	PUNCT
ejpam-5970	189	11	for	for	ADP
ejpam-5970	189	12	i	i	PROPN
ejpam-5970	189	13	≡	≡	PROPN
ejpam-5970	189	14	1(mod	1(mod	NUM
ejpam-5970	189	15	2	2	NUM
ejpam-5970	189	16	)	)	PUNCT
ejpam-5970	189	17	,	,	PUNCT
ejpam-5970	189	18	1	1	NUM
ejpam-5970	189	19	≤	≤	NUM
ejpam-5970	189	20	i	i	PRON
ejpam-5970	189	21	≤	≤	PROPN
ejpam-5970	189	22	n	n	CCONJ
ejpam-5970	189	23	,	,	PUNCT
ejpam-5970	189	24	1	1	NUM
ejpam-5970	189	25	≤	≤	NUM
ejpam-5970	189	26	j	j	PROPN
ejpam-5970	189	27	≤	≤	NUM
ejpam-5970	189	28	m	m	VERB
ejpam-5970	189	29	nm−	nm−	PROPN
ejpam-5970	189	30	i+nj−n	i+nj−n	ADV
ejpam-5970	189	31	2	2	NUM
ejpam-5970	189	32	+	+	NUM
ejpam-5970	189	33	1	1	NUM
ejpam-5970	189	34	,	,	PUNCT
ejpam-5970	189	35	for	for	ADP
ejpam-5970	189	36	i	i	PROPN
ejpam-5970	189	37	≡	≡	ADJ
ejpam-5970	189	38	0(mod	0(mod	NOUN
ejpam-5970	189	39	2	2	NUM
ejpam-5970	189	40	)	)	PUNCT
ejpam-5970	189	41	,	,	PUNCT
ejpam-5970	189	42	2	2	NUM
ejpam-5970	189	43	≤	≤	NUM
ejpam-5970	189	44	i	i	PRON
ejpam-5970	189	45	≤	≤	PROPN
ejpam-5970	189	46	n	n	CCONJ
ejpam-5970	189	47	,	,	PUNCT
ejpam-5970	189	48	1	1	NUM
ejpam-5970	189	49	≤	≤	NUM
ejpam-5970	189	50	j	j	PROPN
ejpam-5970	189	51	≤	≤	NUM
ejpam-5970	189	52	m	m	VERB
ejpam-5970	189	53	under	under	ADP
ejpam-5970	189	54	bijection	bijection	PROPN
ejpam-5970	189	55	f	f	PROPN
ejpam-5970	189	56	,	,	PUNCT
ejpam-5970	189	57	the	the	DET
ejpam-5970	189	58	edge	edge	NOUN
ejpam-5970	189	59	weights	weight	NOUN
ejpam-5970	189	60	can	can	AUX
ejpam-5970	189	61	be	be	AUX
ejpam-5970	189	62	presented	present	VERB
ejpam-5970	189	63	as	as	SCONJ
ejpam-5970	189	64	follows	follow	VERB
ejpam-5970	189	65	.	.	PUNCT
ejpam-5970	190	1	w(xjix	w(xjix	INTJ
ejpam-5970	190	2	j	j	NOUN
ejpam-5970	190	3	i+1	i+1	NUM
ejpam-5970	190	4	)	)	PUNCT
ejpam-5970	190	5	=	=	PRON
ejpam-5970	190	6	{	{	PUNCT
ejpam-5970	190	7	nm+	nm+	NOUN
ejpam-5970	190	8	1	1	NUM
ejpam-5970	190	9	,	,	PUNCT
ejpam-5970	190	10	for	for	ADP
ejpam-5970	190	11	i	i	PROPN
ejpam-5970	190	12	≡	≡	PROPN
ejpam-5970	190	13	1(mod	1(mod	NUM
ejpam-5970	190	14	2	2	NUM
ejpam-5970	190	15	)	)	PUNCT
ejpam-5970	190	16	,	,	PUNCT
ejpam-5970	190	17	1	1	NUM
ejpam-5970	190	18	≤	≤	NUM
ejpam-5970	191	1	i	i	PRON
ejpam-5970	191	2	≤	≤	ADJ
ejpam-5970	191	3	n−	n−	PROPN
ejpam-5970	191	4	1	1	NUM
ejpam-5970	191	5	,	,	PUNCT
ejpam-5970	191	6	1	1	NUM
ejpam-5970	191	7	≤	≤	NUM
ejpam-5970	191	8	j	j	PROPN
ejpam-5970	191	9	≤	≤	PROPN
ejpam-5970	191	10	m	m	VERB
ejpam-5970	191	11	nm+	nm+	NOUN
ejpam-5970	191	12	2	2	NUM
ejpam-5970	191	13	,	,	PUNCT
ejpam-5970	191	14	for	for	ADP
ejpam-5970	191	15	i	i	PROPN
ejpam-5970	191	16	≡	≡	ADJ
ejpam-5970	191	17	0(mod	0(mod	NOUN
ejpam-5970	191	18	2	2	NUM
ejpam-5970	191	19	)	)	PUNCT
ejpam-5970	191	20	,	,	PUNCT
ejpam-5970	191	21	2	2	NUM
ejpam-5970	191	22	≤	≤	NUM
ejpam-5970	192	1	i	i	PRON
ejpam-5970	192	2	≤	≤	ADJ
ejpam-5970	192	3	n−	n−	PROPN
ejpam-5970	192	4	1	1	NUM
ejpam-5970	192	5	,	,	PUNCT
ejpam-5970	192	6	1	1	NUM
ejpam-5970	192	7	≤	≤	NUM
ejpam-5970	192	8	j	j	PROPN
ejpam-5970	192	9	≤	≤	PROPN
ejpam-5970	192	10	m	m	VERB
ejpam-5970	192	11	w(xxji	w(xxji	NOUN
ejpam-5970	192	12	)	)	PUNCT
ejpam-5970	193	1	=	=	PRON
ejpam-5970	193	2	{	{	PUNCT
ejpam-5970	193	3	nm+	nm+	NOUN
ejpam-5970	193	4	1	1	NUM
ejpam-5970	193	5	+	+	CCONJ
ejpam-5970	193	6	nj−n+i+1	nj−n+i+1	DET
ejpam-5970	193	7	2	2	NUM
ejpam-5970	193	8	,	,	PUNCT
ejpam-5970	193	9	for	for	ADP
ejpam-5970	193	10	i	i	PROPN
ejpam-5970	193	11	≡	≡	PROPN
ejpam-5970	193	12	1(mod	1(mod	NUM
ejpam-5970	193	13	2	2	NUM
ejpam-5970	193	14	)	)	PUNCT
ejpam-5970	193	15	,	,	PUNCT
ejpam-5970	193	16	1	1	NUM
ejpam-5970	193	17	≤	≤	NUM
ejpam-5970	193	18	i	i	PRON
ejpam-5970	193	19	≤	≤	PROPN
ejpam-5970	193	20	n	n	CCONJ
ejpam-5970	193	21	,	,	PUNCT
ejpam-5970	193	22	1	1	NUM
ejpam-5970	193	23	≤	≤	NUM
ejpam-5970	193	24	j	j	PROPN
ejpam-5970	193	25	≤	≤	NUM
ejpam-5970	193	26	m	m	VERB
ejpam-5970	193	27	2nm+	2nm+	PROPN
ejpam-5970	193	28	2−	2−	NUM
ejpam-5970	193	29	i+nj−n	i+nj−n	NUM
ejpam-5970	193	30	2	2	NUM
ejpam-5970	193	31	,	,	PUNCT
ejpam-5970	193	32	for	for	ADP
ejpam-5970	193	33	i	i	PROPN
ejpam-5970	193	34	≡	≡	ADJ
ejpam-5970	193	35	0(mod	0(mod	NOUN
ejpam-5970	193	36	2	2	NUM
ejpam-5970	193	37	)	)	PUNCT
ejpam-5970	193	38	,	,	PUNCT
ejpam-5970	193	39	2	2	NUM
ejpam-5970	193	40	≤	≤	NUM
ejpam-5970	193	41	i	i	PRON
ejpam-5970	193	42	≤	≤	PROPN
ejpam-5970	193	43	n	n	CCONJ
ejpam-5970	193	44	,	,	PUNCT
ejpam-5970	193	45	1	1	NUM
ejpam-5970	193	46	≤	≤	NUM
ejpam-5970	193	47	j	j	PROPN
ejpam-5970	193	48	≤	≤	NUM
ejpam-5970	193	49	m	m	VERB
ejpam-5970	193	50	thus	thus	ADV
ejpam-5970	193	51	,	,	PUNCT
ejpam-5970	193	52	we	we	PRON
ejpam-5970	193	53	can	can	AUX
ejpam-5970	193	54	write	write	VERB
ejpam-5970	193	55	in	in	ADP
ejpam-5970	193	56	the	the	DET
ejpam-5970	193	57	form	form	NOUN
ejpam-5970	193	58	of	of	ADP
ejpam-5970	193	59	the	the	DET
ejpam-5970	193	60	set	set	NOUN
ejpam-5970	193	61	w	w	PROPN
ejpam-5970	193	62	of	of	ADP
ejpam-5970	193	63	edge	edge	NOUN
ejpam-5970	193	64	weight	weight	NOUN
ejpam-5970	193	65	of	of	ADP
ejpam-5970	193	66	amal(fn	amal(fn	NOUN
ejpam-5970	193	67	,	,	PUNCT
ejpam-5970	193	68	x	x	X
ejpam-5970	193	69	,	,	PUNCT
ejpam-5970	193	70	m	m	NOUN
ejpam-5970	193	71	)	)	PUNCT
ejpam-5970	193	72	.	.	PUNCT
ejpam-5970	194	1	it	it	PRON
ejpam-5970	194	2	includes	include	VERB
ejpam-5970	194	3	four	four	NUM
ejpam-5970	194	4	sets	set	NOUN
ejpam-5970	194	5	of	of	ADP
ejpam-5970	194	6	edge	edge	NOUN
ejpam-5970	194	7	weights	weight	NOUN
ejpam-5970	194	8	,	,	PUNCT
ejpam-5970	194	9	namely	namely	ADV
ejpam-5970	194	10	w1	w1	NOUN
ejpam-5970	194	11	=	=	SYM
ejpam-5970	194	12	{	{	PUNCT
ejpam-5970	194	13	nm+	nm+	NOUN
ejpam-5970	194	14	1	1	NUM
ejpam-5970	194	15	}	}	PUNCT
ejpam-5970	194	16	,	,	PUNCT
ejpam-5970	194	17	w2	w2	NOUN
ejpam-5970	194	18	=	=	SYM
ejpam-5970	194	19	{	{	PUNCT
ejpam-5970	194	20	nm+	nm+	NOUN
ejpam-5970	194	21	2	2	NUM
ejpam-5970	194	22	}	}	PUNCT
ejpam-5970	194	23	,	,	PUNCT
ejpam-5970	194	24	w3	w3	PROPN
ejpam-5970	194	25	=	=	PUNCT
ejpam-5970	194	26	{	{	PUNCT
ejpam-5970	194	27	nm+	nm+	NOUN
ejpam-5970	194	28	2	2	NUM
ejpam-5970	194	29	,	,	PUNCT
ejpam-5970	194	30	nm+	nm+	NOUN
ejpam-5970	194	31	3	3	NUM
ejpam-5970	194	32	,	,	PUNCT
ejpam-5970	194	33	nm+4	nm+4	NUM
ejpam-5970	194	34	,	,	PUNCT
ejpam-5970	194	35	.	.	PUNCT
ejpam-5970	194	36	.	.	PUNCT
ejpam-5970	194	37	.	.	PUNCT
ejpam-5970	195	1	,	,	PUNCT
ejpam-5970	195	2	nm+1+nm	nm+1+nm	ADV
ejpam-5970	195	3	2	2	NUM
ejpam-5970	195	4	}	}	PUNCT
ejpam-5970	195	5	,	,	PUNCT
ejpam-5970	195	6	andw4	andw4	NOUN
ejpam-5970	195	7	=	=	PRON
ejpam-5970	195	8	{	{	PUNCT
ejpam-5970	195	9	nm+2+nm	nm+2+nm	NOUN
ejpam-5970	195	10	2	2	NUM
ejpam-5970	195	11	,	,	PUNCT
ejpam-5970	195	12	nm+3+nm	nm+3+nm	ADV
ejpam-5970	195	13	2	2	NUM
ejpam-5970	195	14	,	,	PUNCT
ejpam-5970	195	15	nm+4+nm	nm+4+nm	NOUN
ejpam-5970	195	16	2	2	NUM
ejpam-5970	195	17	.	.	PUNCT
ejpam-5970	195	18	.	.	PUNCT
ejpam-5970	196	1	.	.	PUNCT
ejpam-5970	197	1	,	,	PUNCT
ejpam-5970	197	2	2nm+1	2nm+1	NUM
ejpam-5970	197	3	}	}	PUNCT
ejpam-5970	197	4	.	.	PUNCT
ejpam-5970	198	1	our	our	PRON
ejpam-5970	198	2	task	task	NOUN
ejpam-5970	198	3	is	be	AUX
ejpam-5970	198	4	to	to	PART
ejpam-5970	198	5	determine	determine	VERB
ejpam-5970	198	6	the	the	DET
ejpam-5970	198	7	cardinality	cardinality	NOUN
ejpam-5970	198	8	of	of	ADP
ejpam-5970	198	9	those	those	DET
ejpam-5970	198	10	sets	set	NOUN
ejpam-5970	198	11	to	to	PART
ejpam-5970	198	12	obtain	obtain	VERB
ejpam-5970	198	13	the	the	DET
ejpam-5970	198	14	upper	upper	ADJ
ejpam-5970	198	15	bound	bound	NOUN
ejpam-5970	198	16	,	,	PUNCT
ejpam-5970	198	17	but	but	CCONJ
ejpam-5970	198	18	we	we	PRON
ejpam-5970	198	19	need	need	VERB
ejpam-5970	198	20	to	to	PART
ejpam-5970	198	21	check	check	VERB
ejpam-5970	198	22	whether	whether	SCONJ
ejpam-5970	198	23	all	all	DET
ejpam-5970	198	24	three	three	NUM
ejpam-5970	198	25	sets	set	NOUN
ejpam-5970	198	26	are	be	AUX
ejpam-5970	198	27	disjoint	disjoint	ADJ
ejpam-5970	198	28	or	or	CCONJ
ejpam-5970	198	29	not	not	PART
ejpam-5970	198	30	first	first	ADJ
ejpam-5970	198	31	.	.	PUNCT
ejpam-5970	199	1	under	under	ADP
ejpam-5970	199	2	the	the	DET
ejpam-5970	199	3	contradiction	contradiction	NOUN
ejpam-5970	199	4	proof	proof	NOUN
ejpam-5970	199	5	,	,	PUNCT
ejpam-5970	199	6	we	we	PRON
ejpam-5970	199	7	suppose	suppose	VERB
ejpam-5970	199	8	w1	w1	PROPN
ejpam-5970	199	9	⊆	⊆	NUM
ejpam-5970	199	10	w3	w3	PROPN
ejpam-5970	199	11	←→	←→	PROPN
ejpam-5970	199	12	nm	nm	PROPN
ejpam-5970	199	13	+	+	NOUN
ejpam-5970	199	14	1	1	NUM
ejpam-5970	199	15	=	=	NOUN
ejpam-5970	199	16	nm	nm	NOUN
ejpam-5970	199	17	+	+	NOUN
ejpam-5970	199	18	1	1	NUM
ejpam-5970	199	19	+	+	X
ejpam-5970	199	20	nj−n+i+1	nj−n+i+1	DET
ejpam-5970	199	21	2	2	NUM
ejpam-5970	199	22	←→	←→	PROPN
ejpam-5970	199	23	i	i	PRON
ejpam-5970	199	24	=	=	SYM
ejpam-5970	199	25	n	n	PROPN
ejpam-5970	199	26	−	−	PROPN
ejpam-5970	199	27	nj	nj	PROPN
ejpam-5970	199	28	−	−	PROPN
ejpam-5970	200	1	1	1	X
ejpam-5970	200	2	.	.	PUNCT
ejpam-5970	201	1	since	since	SCONJ
ejpam-5970	201	2	w(xxji	w(xxji	NOUN
ejpam-5970	201	3	)	)	PUNCT
ejpam-5970	202	1	=	=	PUNCT
ejpam-5970	202	2	nm	nm	ADJ
ejpam-5970	203	1	+	+	NOUN
ejpam-5970	203	2	1	1	NUM
ejpam-5970	203	3	+	+	SYM
ejpam-5970	203	4	nj−n+i+1	nj−n+i+1	DET
ejpam-5970	203	5	2	2	NUM
ejpam-5970	203	6	,	,	PUNCT
ejpam-5970	203	7	for	for	ADP
ejpam-5970	203	8	1	1	NUM
ejpam-5970	203	9	≤	≤	NUM
ejpam-5970	203	10	i	i	PRON
ejpam-5970	203	11	≤	≤	NUM
ejpam-5970	203	12	nm	nm	PRON
ejpam-5970	203	13	2	2	NUM
ejpam-5970	203	14	,	,	PUNCT
ejpam-5970	203	15	therefore	therefore	ADV
ejpam-5970	203	16	i	i	PRON
ejpam-5970	203	17	=	=	SYM
ejpam-5970	203	18	n	n	NUM
ejpam-5970	203	19	−	−	PROPN
ejpam-5970	203	20	nj	nj	PROPN
ejpam-5970	204	1	−	−	NOUN
ejpam-5970	204	2	1	1	NUM
ejpam-5970	204	3	does	do	AUX
ejpam-5970	204	4	not	not	PART
ejpam-5970	204	5	lie	lie	VERB
ejpam-5970	204	6	in	in	ADP
ejpam-5970	204	7	the	the	DET
ejpam-5970	204	8	interval	interval	NOUN
ejpam-5970	204	9	,	,	PUNCT
ejpam-5970	204	10	it	it	PRON
ejpam-5970	204	11	is	be	AUX
ejpam-5970	204	12	a	a	DET
ejpam-5970	204	13	contradiction	contradiction	NOUN
ejpam-5970	204	14	.	.	PUNCT
ejpam-5970	205	1	we	we	PRON
ejpam-5970	205	2	conclude	conclude	VERB
ejpam-5970	205	3	that	that	DET
ejpam-5970	205	4	w1	w1	NOUN
ejpam-5970	205	5	∩w3	∩w3	NOUN
ejpam-5970	205	6	=	=	PUNCT
ejpam-5970	205	7	∅.	∅.	VERB
ejpam-5970	205	8	furthermore	furthermore	ADV
ejpam-5970	205	9	,	,	PUNCT
ejpam-5970	205	10	in	in	ADP
ejpam-5970	205	11	the	the	DET
ejpam-5970	205	12	contradiction	contradiction	NOUN
ejpam-5970	205	13	proof	proof	NOUN
ejpam-5970	205	14	,	,	PUNCT
ejpam-5970	205	15	we	we	PRON
ejpam-5970	205	16	suppose	suppose	VERB
ejpam-5970	205	17	w1	w1	NOUN
ejpam-5970	205	18	⊆	⊆	NUM
ejpam-5970	205	19	w4	w4	NOUN
ejpam-5970	205	20	←→	←→	PROPN
ejpam-5970	205	21	nm	nm	NOUN
ejpam-5970	205	22	+	+	NOUN
ejpam-5970	205	23	1	1	NUM
ejpam-5970	205	24	=	=	SYM
ejpam-5970	205	25	2	2	NUM
ejpam-5970	205	26	nm	nm	NOUN
ejpam-5970	205	27	+	+	NUM
ejpam-5970	205	28	3	3	NUM
ejpam-5970	205	29	−	−	NOUN
ejpam-5970	205	30	i+nj−n	i+nj−n	NOUN
ejpam-5970	205	31	2	2	NUM
ejpam-5970	205	32	←→	←→	PROPN
ejpam-5970	205	33	a.	a.	PROPN
ejpam-5970	205	34	i.	i.	PROPN
ejpam-5970	205	35	kristiana	kristiana	PROPN
ejpam-5970	205	36	,	,	PUNCT
ejpam-5970	205	37	et	et	PROPN
ejpam-5970	205	38	al	al	PROPN
ejpam-5970	205	39	.	.	PUNCT
ejpam-5970	205	40	/	/	SYM
ejpam-5970	205	41	eur	eur	PROPN
ejpam-5970	205	42	.	.	PUNCT
ejpam-5970	206	1	j.	j.	PROPN
ejpam-5970	206	2	pure	pure	PROPN
ejpam-5970	206	3	appl	appl	PROPN
ejpam-5970	206	4	.	.	PROPN
ejpam-5970	206	5	math	math	PROPN
ejpam-5970	206	6	,	,	PUNCT
ejpam-5970	206	7	18	18	NUM
ejpam-5970	206	8	(	(	PUNCT
ejpam-5970	206	9	3	3	NUM
ejpam-5970	206	10	)	)	PUNCT
ejpam-5970	206	11	(	(	PUNCT
ejpam-5970	206	12	2025	2025	NUM
ejpam-5970	206	13	)	)	PUNCT
ejpam-5970	206	14	,	,	PUNCT
ejpam-5970	206	15	5970	5970	NUM
ejpam-5970	206	16	8	8	NUM
ejpam-5970	206	17	of	of	ADP
ejpam-5970	206	18	18	18	NUM
ejpam-5970	206	19	i	i	NOUN
ejpam-5970	206	20	=	=	SYM
ejpam-5970	206	21	2	2	NUM
ejpam-5970	206	22	nm	nm	NOUN
ejpam-5970	206	23	−	−	PROPN
ejpam-5970	206	24	nj	nj	NOUN
ejpam-5970	206	25	+	+	CCONJ
ejpam-5970	206	26	n	n	PROPN
ejpam-5970	206	27	+	+	NOUN
ejpam-5970	206	28	4	4	NUM
ejpam-5970	206	29	.	.	PUNCT
ejpam-5970	206	30	since	since	SCONJ
ejpam-5970	206	31	w(xxji	w(xxji	NOUN
ejpam-5970	206	32	)	)	PUNCT
ejpam-5970	207	1	=	=	SYM
ejpam-5970	207	2	2	2	NUM
ejpam-5970	207	3	nm	nm	NOUN
ejpam-5970	207	4	+	+	NUM
ejpam-5970	207	5	3	3	NUM
ejpam-5970	207	6	−	−	NOUN
ejpam-5970	207	7	i+nj−n	i+nj−n	NUM
ejpam-5970	207	8	2	2	NUM
ejpam-5970	207	9	,	,	PUNCT
ejpam-5970	207	10	for	for	ADP
ejpam-5970	207	11	nm+1	nm+1	PROPN
ejpam-5970	207	12	2	2	NUM
ejpam-5970	207	13	≤	≤	NUM
ejpam-5970	207	14	i	i	PRON
ejpam-5970	207	15	≤	≤	PROPN
ejpam-5970	207	16	nm	nm	ADP
ejpam-5970	207	17	,	,	PUNCT
ejpam-5970	207	18	therefore	therefore	ADV
ejpam-5970	207	19	i	i	PRON
ejpam-5970	207	20	=	=	PUNCT
ejpam-5970	207	21	2nm−	2nm−	NUM
ejpam-5970	207	22	nj	nj	PROPN
ejpam-5970	207	23	+	+	CCONJ
ejpam-5970	207	24	n+	n+	X
ejpam-5970	207	25	4	4	NUM
ejpam-5970	207	26	does	do	AUX
ejpam-5970	207	27	not	not	PART
ejpam-5970	207	28	lie	lie	VERB
ejpam-5970	207	29	in	in	ADP
ejpam-5970	207	30	the	the	DET
ejpam-5970	207	31	interval	interval	NOUN
ejpam-5970	207	32	,	,	PUNCT
ejpam-5970	207	33	it	it	PRON
ejpam-5970	207	34	is	be	AUX
ejpam-5970	207	35	a	a	DET
ejpam-5970	207	36	contradiction	contradiction	NOUN
ejpam-5970	207	37	.	.	PUNCT
ejpam-5970	208	1	we	we	PRON
ejpam-5970	208	2	conclude	conclude	VERB
ejpam-5970	208	3	that	that	DET
ejpam-5970	208	4	w1	w1	NOUN
ejpam-5970	208	5	∩w4	∩w4	PROPN
ejpam-5970	209	1	=	=	PUNCT
ejpam-5970	209	2	∅.	∅.	NOUN
ejpam-5970	209	3	finally	finally	ADV
ejpam-5970	209	4	,	,	PUNCT
ejpam-5970	209	5	we	we	PRON
ejpam-5970	209	6	have	have	VERB
ejpam-5970	209	7	w	w	NOUN
ejpam-5970	209	8	=	=	NOUN
ejpam-5970	209	9	w1	w1	PROPN
ejpam-5970	209	10	∪w3	∪w3	PROPN
ejpam-5970	209	11	∪w4	∪w4	PROPN
ejpam-5970	209	12	.	.	PUNCT
ejpam-5970	210	1	now	now	ADV
ejpam-5970	210	2	,	,	PUNCT
ejpam-5970	210	3	we	we	PRON
ejpam-5970	210	4	can	can	AUX
ejpam-5970	210	5	determine	determine	VERB
ejpam-5970	210	6	the	the	DET
ejpam-5970	210	7	cardinality	cardinality	NOUN
ejpam-5970	210	8	of	of	ADP
ejpam-5970	210	9	w.	w.	PROPN
ejpam-5970	210	10	first	first	PROPN
ejpam-5970	210	11	,	,	PUNCT
ejpam-5970	210	12	it	it	PRON
ejpam-5970	210	13	is	be	AUX
ejpam-5970	210	14	easy	easy	ADJ
ejpam-5970	210	15	to	to	PART
ejpam-5970	210	16	see	see	VERB
ejpam-5970	210	17	that	that	DET
ejpam-5970	210	18	|w1|	|w1|	NOUN
ejpam-5970	210	19	=	=	SYM
ejpam-5970	210	20	1	1	NUM
ejpam-5970	210	21	,	,	PUNCT
ejpam-5970	210	22	secondly	secondly	ADV
ejpam-5970	210	23	we	we	PRON
ejpam-5970	210	24	will	will	AUX
ejpam-5970	210	25	determine	determine	VERB
ejpam-5970	210	26	|w3	|w3	NOUN
ejpam-5970	210	27	∪w4|	∪w4|	ADJ
ejpam-5970	210	28	,	,	PUNCT
ejpam-5970	210	29	under	under	ADP
ejpam-5970	210	30	the	the	DET
ejpam-5970	210	31	following	follow	VERB
ejpam-5970	210	32	calculation	calculation	NOUN
ejpam-5970	210	33	.	.	PUNCT
ejpam-5970	211	1	let	let	VERB
ejpam-5970	211	2	us	we	PRON
ejpam-5970	212	1	and	and	CCONJ
ejpam-5970	212	2	d	d	X
ejpam-5970	212	3	be	be	AUX
ejpam-5970	212	4	the	the	DET
ejpam-5970	212	5	s	s	NOUN
ejpam-5970	212	6	term	term	NOUN
ejpam-5970	212	7	and	and	CCONJ
ejpam-5970	212	8	different	different	ADJ
ejpam-5970	212	9	from	from	ADP
ejpam-5970	212	10	the	the	DET
ejpam-5970	212	11	arithmetic	arithmetic	ADJ
ejpam-5970	212	12	sequence	sequence	NOUN
ejpam-5970	212	13	of	of	ADP
ejpam-5970	212	14	w3	w3	PROPN
ejpam-5970	212	15	∪w4	∪w4	NOUN
ejpam-5970	212	16	,	,	PUNCT
ejpam-5970	212	17	consequently	consequently	ADV
ejpam-5970	212	18	.	.	PUNCT
ejpam-5970	213	1	we	we	PRON
ejpam-5970	213	2	have	have	VERB
ejpam-5970	213	3	u|w3∪w4|	u|w3∪w4|	NOUN
ejpam-5970	213	4	=	=	PUNCT
ejpam-5970	213	5	a+(|w3∪w4|−1)d←→	a+(|w3∪w4|−1)d←→	PROPN
ejpam-5970	213	6	2nm+1	2nm+1	X
ejpam-5970	213	7	=	=	SYM
ejpam-5970	213	8	nm+2+(|w3∪w4|−1)1←→	nm+2+(|w3∪w4|−1)1←→	NOUN
ejpam-5970	213	9	|w3∪w4|	|w3∪w4|	PUNCT
ejpam-5970	214	1	=	=	SYM
ejpam-5970	214	2	nm	nm	AUX
ejpam-5970	214	3	.	.	PUNCT
ejpam-5970	214	4	w3∪w4	w3∪w4	NOUN
ejpam-5970	214	5	form	form	VERB
ejpam-5970	214	6	an	an	DET
ejpam-5970	214	7	arithmetic	arithmetic	ADJ
ejpam-5970	214	8	sequence	sequence	NOUN
ejpam-5970	214	9	with	with	ADP
ejpam-5970	214	10	initial	initial	ADJ
ejpam-5970	214	11	value	value	NOUN
ejpam-5970	214	12	a	a	DET
ejpam-5970	214	13	=	=	SYM
ejpam-5970	214	14	nm+2	nm+2	PROPN
ejpam-5970	214	15	and	and	CCONJ
ejpam-5970	214	16	w2	w2	NOUN
ejpam-5970	214	17	=	=	SYM
ejpam-5970	214	18	nm+2	nm+2	PROPN
ejpam-5970	215	1	then	then	ADV
ejpam-5970	215	2	we	we	PRON
ejpam-5970	215	3	have	have	VERB
ejpam-5970	215	4	w2	w2	PROPN
ejpam-5970	215	5	⊂	⊂	PROPN
ejpam-5970	215	6	(	(	PUNCT
ejpam-5970	215	7	w3∪w4	w3∪w4	NOUN
ejpam-5970	215	8	)	)	PUNCT
ejpam-5970	215	9	.	.	PUNCT
ejpam-5970	216	1	it	it	PRON
ejpam-5970	216	2	implies	imply	VERB
ejpam-5970	216	3	that	that	SCONJ
ejpam-5970	216	4	|w	|w	ADJ
ejpam-5970	217	1	|	|	NOUN
ejpam-5970	217	2	=	=	SYM
ejpam-5970	217	3	|w1|+	|w1|+	NOUN
ejpam-5970	217	4	|w3∪w4|	|w3∪w4|	NOUN
ejpam-5970	218	1	=	=	SYM
ejpam-5970	218	2	1+nm	1+nm	X
ejpam-5970	218	3	.	.	PUNCT
ejpam-5970	219	1	finally	finally	ADV
ejpam-5970	219	2	,	,	PUNCT
ejpam-5970	219	3	we	we	PRON
ejpam-5970	219	4	have	have	VERB
ejpam-5970	219	5	χle(nm+1,1)(amal(fn	χle(nm+1,1)(amal(fn	NOUN
ejpam-5970	219	6	,	,	PUNCT
ejpam-5970	219	7	x	x	X
ejpam-5970	219	8	,	,	PUNCT
ejpam-5970	219	9	m	m	NOUN
ejpam-5970	219	10	)	)	PUNCT
ejpam-5970	219	11	)	)	PUNCT
ejpam-5970	219	12	≤	≤	NUM
ejpam-5970	219	13	nm+	nm+	NOUN
ejpam-5970	219	14	1	1	NUM
ejpam-5970	219	15	for	for	ADP
ejpam-5970	219	16	n	n	PRON
ejpam-5970	219	17	≡	≡	PROPN
ejpam-5970	219	18	1(mod	1(mod	ADJ
ejpam-5970	219	19	2	2	NUM
ejpam-5970	219	20	)	)	PUNCT
ejpam-5970	219	21	.	.	PUNCT
ejpam-5970	220	1	thus	thus	ADV
ejpam-5970	220	2	,	,	PUNCT
ejpam-5970	220	3	we	we	PRON
ejpam-5970	220	4	will	will	AUX
ejpam-5970	220	5	have	have	VERB
ejpam-5970	220	6	χle(nm+1,1)(amal(fn	χle(nm+1,1)(amal(fn	NOUN
ejpam-5970	220	7	,	,	PUNCT
ejpam-5970	220	8	x	x	X
ejpam-5970	220	9	,	,	PUNCT
ejpam-5970	220	10	m	m	NOUN
ejpam-5970	220	11	)	)	PUNCT
ejpam-5970	220	12	)	)	PUNCT
ejpam-5970	221	1	≤	≤	NUM
ejpam-5970	221	2	nm	nm	NOUN
ejpam-5970	221	3	+	+	NOUN
ejpam-5970	221	4	1	1	X
ejpam-5970	221	5	.	.	X
ejpam-5970	222	1	it	it	PRON
ejpam-5970	222	2	can	can	AUX
ejpam-5970	222	3	be	be	AUX
ejpam-5970	222	4	concluded	conclude	VERB
ejpam-5970	222	5	that	that	SCONJ
ejpam-5970	222	6	nm	nm	ADJ
ejpam-5970	222	7	≤	≤	NUM
ejpam-5970	222	8	χle(nm+1,1)(amal(fn	χle(nm+1,1)(amal(fn	NOUN
ejpam-5970	222	9	,	,	PUNCT
ejpam-5970	222	10	x	x	X
ejpam-5970	222	11	,	,	PUNCT
ejpam-5970	222	12	m	m	NOUN
ejpam-5970	222	13	)	)	PUNCT
ejpam-5970	222	14	)	)	PUNCT
ejpam-5970	222	15	≤	≤	NUM
ejpam-5970	222	16	nm+	nm+	NOUN
ejpam-5970	222	17	1	1	NUM
ejpam-5970	222	18	.	.	PUNCT
ejpam-5970	222	19	theorem	theorem	NOUN
ejpam-5970	222	20	3	3	X
ejpam-5970	222	21	.	.	PUNCT
ejpam-5970	223	1	let	let	VERB
ejpam-5970	223	2	amal(vn	amal(vn	PROPN
ejpam-5970	223	3	,	,	PUNCT
ejpam-5970	223	4	x	x	NOUN
ejpam-5970	223	5	,	,	PUNCT
ejpam-5970	223	6	m	m	VERB
ejpam-5970	223	7	)	)	PUNCT
ejpam-5970	223	8	be	be	VERB
ejpam-5970	223	9	an	an	DET
ejpam-5970	223	10	amalgamation	amalgamation	NOUN
ejpam-5970	223	11	of	of	ADP
ejpam-5970	223	12	volcano	volcano	NOUN
ejpam-5970	223	13	graph	graph	NOUN
ejpam-5970	223	14	with	with	ADP
ejpam-5970	223	15	n	n	CCONJ
ejpam-5970	223	16	,	,	PUNCT
ejpam-5970	223	17	m	m	VERB
ejpam-5970	223	18	≥	≥	NOUN
ejpam-5970	223	19	2	2	X
ejpam-5970	223	20	.	.	PUNCT
ejpam-5970	224	1	we	we	PRON
ejpam-5970	224	2	have	have	VERB
ejpam-5970	224	3	χle(3,1)(amal(vn	χle(3,1)(amal(vn	PROPN
ejpam-5970	224	4	,	,	PUNCT
ejpam-5970	224	5	x	x	NOUN
ejpam-5970	224	6	,	,	PUNCT
ejpam-5970	224	7	m	m	NOUN
ejpam-5970	224	8	)	)	PUNCT
ejpam-5970	224	9	)	)	PUNCT
ejpam-5970	225	1	=	=	SYM
ejpam-5970	225	2	2m+	2m+	NUM
ejpam-5970	225	3	nm	nm	NOUN
ejpam-5970	225	4	.	.	PUNCT
ejpam-5970	226	1	proof	proof	NOUN
ejpam-5970	226	2	.	.	PUNCT
ejpam-5970	227	1	amalgamation	amalgamation	NOUN
ejpam-5970	227	2	of	of	ADP
ejpam-5970	227	3	volcano	volcano	NOUN
ejpam-5970	227	4	graph	graph	NOUN
ejpam-5970	227	5	amal(vn	amal(vn	PROPN
ejpam-5970	227	6	,	,	PUNCT
ejpam-5970	227	7	x	x	NOUN
ejpam-5970	227	8	,	,	PUNCT
ejpam-5970	227	9	m	m	VERB
ejpam-5970	227	10	)	)	PUNCT
ejpam-5970	227	11	is	be	AUX
ejpam-5970	227	12	a	a	DET
ejpam-5970	227	13	connected	connected	ADJ
ejpam-5970	227	14	graph	graph	NOUN
ejpam-5970	227	15	with	with	ADP
ejpam-5970	227	16	vertex	vertex	NOUN
ejpam-5970	227	17	set	set	VERB
ejpam-5970	227	18	v	v	NOUN
ejpam-5970	227	19	(	(	PUNCT
ejpam-5970	227	20	amal(vn	amal(vn	PROPN
ejpam-5970	227	21	,	,	PUNCT
ejpam-5970	227	22	x	x	NOUN
ejpam-5970	227	23	,	,	PUNCT
ejpam-5970	227	24	m	m	NOUN
ejpam-5970	227	25	)	)	PUNCT
ejpam-5970	227	26	)	)	PUNCT
ejpam-5970	228	1	=	=	PRON
ejpam-5970	228	2	{	{	PUNCT
ejpam-5970	228	3	x	x	NOUN
ejpam-5970	228	4	}	}	PUNCT
ejpam-5970	228	5	∪	∪	X
ejpam-5970	228	6	{	{	PUNCT
ejpam-5970	228	7	xi	xi	PROPN
ejpam-5970	228	8	;	;	PUNCT
ejpam-5970	228	9	1	1	NUM
ejpam-5970	228	10	≤	≤	NUM
ejpam-5970	228	11	i	i	X
ejpam-5970	228	12	≤	≤	NOUN
ejpam-5970	228	13	m	m	VERB
ejpam-5970	228	14	}	}	PUNCT
ejpam-5970	228	15	∪	∪	ADJ
ejpam-5970	228	16	{	{	PUNCT
ejpam-5970	228	17	zi	zi	NOUN
ejpam-5970	228	18	;	;	PUNCT
ejpam-5970	228	19	1	1	NUM
ejpam-5970	228	20	≤	≤	NUM
ejpam-5970	228	21	i	i	X
ejpam-5970	228	22	≤	≤	NOUN
ejpam-5970	228	23	m	m	VERB
ejpam-5970	228	24	}	}	PUNCT
ejpam-5970	228	25	∪	∪	ADJ
ejpam-5970	228	26	{	{	PUNCT
ejpam-5970	228	27	yi	yi	NOUN
ejpam-5970	228	28	;	;	PUNCT
ejpam-5970	228	29	1	1	NUM
ejpam-5970	228	30	≤	≤	NUM
ejpam-5970	228	31	i	i	PRON
ejpam-5970	228	32	≤	≤	X
ejpam-5970	228	33	nm	nm	VERB
ejpam-5970	228	34	}	}	PUNCT
ejpam-5970	228	35	and	and	CCONJ
ejpam-5970	228	36	edge	edge	VERB
ejpam-5970	228	37	set	set	PROPN
ejpam-5970	228	38	e(amal(vn	e(amal(vn	PROPN
ejpam-5970	228	39	,	,	PUNCT
ejpam-5970	228	40	x	x	X
ejpam-5970	228	41	,	,	PUNCT
ejpam-5970	228	42	m	m	NOUN
ejpam-5970	228	43	)	)	PUNCT
ejpam-5970	228	44	)	)	PUNCT
ejpam-5970	229	1	=	=	PRON
ejpam-5970	229	2	{	{	PUNCT
ejpam-5970	229	3	xizi	xizi	ADJ
ejpam-5970	229	4	;	;	PUNCT
ejpam-5970	229	5	1	1	NUM
ejpam-5970	229	6	≤	≤	NUM
ejpam-5970	229	7	i	i	X
ejpam-5970	229	8	≤	≤	NOUN
ejpam-5970	229	9	m	m	VERB
ejpam-5970	229	10	}	}	PUNCT
ejpam-5970	229	11	∪	∪	ADJ
ejpam-5970	229	12	{	{	PUNCT
ejpam-5970	229	13	xxi	xxi	ADJ
ejpam-5970	229	14	;	;	PUNCT
ejpam-5970	229	15	1	1	NUM
ejpam-5970	229	16	≤	≤	NUM
ejpam-5970	229	17	i	i	X
ejpam-5970	229	18	≤	≤	NOUN
ejpam-5970	229	19	m	m	VERB
ejpam-5970	229	20	}	}	PUNCT
ejpam-5970	229	21	∪	∪	ADJ
ejpam-5970	229	22	{	{	PUNCT
ejpam-5970	229	23	xzi	xzi	PROPN
ejpam-5970	229	24	;	;	PUNCT
ejpam-5970	229	25	1	1	NUM
ejpam-5970	229	26	≤	≤	NUM
ejpam-5970	229	27	i	i	X
ejpam-5970	229	28	≤	≤	NOUN
ejpam-5970	229	29	m	m	VERB
ejpam-5970	229	30	}	}	PUNCT
ejpam-5970	229	31	∪	∪	ADJ
ejpam-5970	229	32	{	{	PUNCT
ejpam-5970	229	33	xyi	xyi	NOUN
ejpam-5970	229	34	;	;	PUNCT
ejpam-5970	229	35	1	1	NUM
ejpam-5970	229	36	≤	≤	NUM
ejpam-5970	229	37	i	i	PRON
ejpam-5970	229	38	≤	≤	NUM
ejpam-5970	229	39	nm	nm	VERB
ejpam-5970	229	40	}	}	PUNCT
ejpam-5970	229	41	.	.	PUNCT
ejpam-5970	230	1	the	the	DET
ejpam-5970	230	2	cardinality	cardinality	NOUN
ejpam-5970	230	3	of	of	ADP
ejpam-5970	230	4	the	the	DET
ejpam-5970	230	5	vertices	vertex	NOUN
ejpam-5970	230	6	set	set	VERB
ejpam-5970	230	7	|v	|v	PROPN
ejpam-5970	230	8	(	(	PUNCT
ejpam-5970	230	9	amal(vn	amal(vn	PROPN
ejpam-5970	230	10	,	,	PUNCT
ejpam-5970	230	11	x	x	NOUN
ejpam-5970	230	12	,	,	PUNCT
ejpam-5970	230	13	m))|	m))|	PROPN
ejpam-5970	230	14	=	=	SYM
ejpam-5970	230	15	nm+2m+1	nm+2m+1	PROPN
ejpam-5970	230	16	,	,	PUNCT
ejpam-5970	230	17	and	and	CCONJ
ejpam-5970	230	18	the	the	DET
ejpam-5970	230	19	cardinality	cardinality	NOUN
ejpam-5970	230	20	of	of	ADP
ejpam-5970	230	21	the	the	DET
ejpam-5970	230	22	edges	edge	NOUN
ejpam-5970	230	23	set	set	VERB
ejpam-5970	230	24	|e(amal(vn	|e(amal(vn	PROPN
ejpam-5970	230	25	,	,	PUNCT
ejpam-5970	230	26	x	x	NOUN
ejpam-5970	230	27	,	,	PUNCT
ejpam-5970	230	28	m))|	m))|	PROPN
ejpam-5970	230	29	=	=	PRON
ejpam-5970	230	30	nm+	nm+	NOUN
ejpam-5970	230	31	3	3	NUM
ejpam-5970	230	32	m.	m.	NOUN
ejpam-5970	230	33	to	to	PART
ejpam-5970	230	34	prove	prove	VERB
ejpam-5970	230	35	this	this	DET
ejpam-5970	230	36	theorem	theorem	NOUN
ejpam-5970	230	37	,	,	PUNCT
ejpam-5970	230	38	first	first	ADV
ejpam-5970	230	39	,	,	PUNCT
ejpam-5970	230	40	we	we	PRON
ejpam-5970	230	41	need	need	VERB
ejpam-5970	230	42	to	to	PART
ejpam-5970	230	43	show	show	VERB
ejpam-5970	230	44	the	the	DET
ejpam-5970	230	45	lower	low	ADJ
ejpam-5970	230	46	bound	bind	VERB
ejpam-5970	230	47	of	of	ADP
ejpam-5970	230	48	χle(3,1)(amal(vn	χle(3,1)(amal(vn	PROPN
ejpam-5970	230	49	,	,	PUNCT
ejpam-5970	230	50	x	x	NOUN
ejpam-5970	230	51	,	,	PUNCT
ejpam-5970	230	52	m	m	NOUN
ejpam-5970	230	53	)	)	PUNCT
ejpam-5970	230	54	)	)	PUNCT
ejpam-5970	230	55	.	.	PUNCT
ejpam-5970	231	1	agustin	agustin	PROPN
ejpam-5970	231	2	et	et	PROPN
ejpam-5970	231	3	al	al	PROPN
ejpam-5970	231	4	in	in	ADP
ejpam-5970	231	5	[	[	X
ejpam-5970	231	6	1	1	X
ejpam-5970	231	7	]	]	PUNCT
ejpam-5970	231	8	if	if	SCONJ
ejpam-5970	231	9	∆(g	∆(g	PROPN
ejpam-5970	231	10	)	)	PUNCT
ejpam-5970	231	11	is	be	AUX
ejpam-5970	231	12	maximum	maximum	ADJ
ejpam-5970	231	13	degrees	degree	NOUN
ejpam-5970	231	14	of	of	ADP
ejpam-5970	231	15	g	g	PROPN
ejpam-5970	232	1	then	then	ADV
ejpam-5970	232	2	we	we	PRON
ejpam-5970	232	3	have	have	VERB
ejpam-5970	232	4	the	the	DET
ejpam-5970	232	5	local	local	ADJ
ejpam-5970	232	6	edge	edge	NOUN
ejpam-5970	232	7	antimagic	antimagic	ADJ
ejpam-5970	232	8	chromatic	chromatic	ADJ
ejpam-5970	232	9	number	number	NOUN
ejpam-5970	232	10	of	of	ADP
ejpam-5970	232	11	χlea(g	χlea(g	PROPN
ejpam-5970	232	12	)	)	PUNCT
ejpam-5970	232	13	≥	≥	NOUN
ejpam-5970	232	14	∆(g	∆(g	NOUN
ejpam-5970	232	15	)	)	PUNCT
ejpam-5970	232	16	.	.	PUNCT
ejpam-5970	233	1	based	base	VERB
ejpam-5970	233	2	on	on	ADP
ejpam-5970	233	3	observation	observation	NOUN
ejpam-5970	233	4	3	3	NUM
ejpam-5970	233	5	we	we	PRON
ejpam-5970	233	6	have	have	VERB
ejpam-5970	233	7	χle(a	χle(a	PROPN
ejpam-5970	233	8	,	,	PUNCT
ejpam-5970	233	9	d)(amal(vn	d)(amal(vn	PROPN
ejpam-5970	233	10	,	,	PUNCT
ejpam-5970	233	11	x	x	NOUN
ejpam-5970	233	12	,	,	PUNCT
ejpam-5970	233	13	m	m	NOUN
ejpam-5970	233	14	)	)	PUNCT
ejpam-5970	233	15	)	)	PUNCT
ejpam-5970	233	16	≥	≥	PROPN
ejpam-5970	234	1	χlea(amal(vn	χlea(amal(vn	PROPN
ejpam-5970	234	2	,	,	PUNCT
ejpam-5970	234	3	x	x	NOUN
ejpam-5970	234	4	,	,	PUNCT
ejpam-5970	234	5	m	m	NOUN
ejpam-5970	234	6	)	)	PUNCT
ejpam-5970	234	7	)	)	PUNCT
ejpam-5970	234	8	≥	≥	PROPN
ejpam-5970	234	9	∆(amal(vn	∆(amal(vn	PROPN
ejpam-5970	234	10	,	,	PUNCT
ejpam-5970	234	11	x	x	X
ejpam-5970	234	12	,	,	PUNCT
ejpam-5970	234	13	m	m	NOUN
ejpam-5970	234	14	)	)	PUNCT
ejpam-5970	234	15	)	)	PUNCT
ejpam-5970	234	16	.	.	PUNCT
ejpam-5970	235	1	∆(amal(vn	∆(amal(vn	PROPN
ejpam-5970	235	2	,	,	PUNCT
ejpam-5970	235	3	x	x	NOUN
ejpam-5970	235	4	,	,	PUNCT
ejpam-5970	235	5	m	m	NOUN
ejpam-5970	235	6	)	)	PUNCT
ejpam-5970	235	7	)	)	PUNCT
ejpam-5970	235	8	is	be	AUX
ejpam-5970	235	9	2	2	NUM
ejpam-5970	235	10	m	m	NOUN
ejpam-5970	235	11	+	+	NOUN
ejpam-5970	235	12	nm	nm	VERB
ejpam-5970	235	13	.	.	PUNCT
ejpam-5970	236	1	thus	thus	ADV
ejpam-5970	236	2	,	,	PUNCT
ejpam-5970	236	3	the	the	DET
ejpam-5970	236	4	lower	lower	ADV
ejpam-5970	236	5	bound	bind	VERB
ejpam-5970	236	6	is	be	AUX
ejpam-5970	236	7	χle(a	χle(a	PROPN
ejpam-5970	236	8	,	,	PUNCT
ejpam-5970	236	9	d)(amal(vn	d)(amal(vn	PROPN
ejpam-5970	236	10	,	,	PUNCT
ejpam-5970	236	11	x	x	NOUN
ejpam-5970	236	12	,	,	PUNCT
ejpam-5970	236	13	m	m	NOUN
ejpam-5970	236	14	)	)	PUNCT
ejpam-5970	236	15	)	)	PUNCT
ejpam-5970	236	16	≥	≥	NOUN
ejpam-5970	237	1	2	2	NUM
ejpam-5970	237	2	m	m	VERB
ejpam-5970	237	3	+	+	NOUN
ejpam-5970	237	4	nm	nm	VERB
ejpam-5970	237	5	.	.	PUNCT
ejpam-5970	237	6	to	to	PART
ejpam-5970	237	7	show	show	VERB
ejpam-5970	237	8	the	the	DET
ejpam-5970	237	9	upper	upper	ADJ
ejpam-5970	237	10	bound	bind	VERB
ejpam-5970	237	11	,	,	PUNCT
ejpam-5970	237	12	we	we	PRON
ejpam-5970	237	13	define	define	VERB
ejpam-5970	237	14	the	the	DET
ejpam-5970	237	15	bijection	bijection	NOUN
ejpam-5970	237	16	as	as	ADP
ejpam-5970	237	17	follow	follow	NOUN
ejpam-5970	237	18	f	f	PROPN
ejpam-5970	237	19	:	:	PUNCT
ejpam-5970	237	20	v	v	X
ejpam-5970	237	21	(	(	PUNCT
ejpam-5970	237	22	amal(vn	amal(vn	PROPN
ejpam-5970	237	23	,	,	PUNCT
ejpam-5970	237	24	x	x	NOUN
ejpam-5970	237	25	,	,	PUNCT
ejpam-5970	237	26	m	m	NOUN
ejpam-5970	237	27	)	)	PUNCT
ejpam-5970	237	28	)	)	PUNCT
ejpam-5970	238	1	→	→	PUNCT
ejpam-5970	238	2	{	{	PUNCT
ejpam-5970	238	3	1	1	NUM
ejpam-5970	238	4	,	,	PUNCT
ejpam-5970	238	5	2	2	NUM
ejpam-5970	238	6	,	,	PUNCT
ejpam-5970	238	7	3	3	NUM
ejpam-5970	238	8	,	,	PUNCT
ejpam-5970	238	9	.	.	PUNCT
ejpam-5970	238	10	.	.	PUNCT
ejpam-5970	239	1	.	.	PUNCT
ejpam-5970	240	1	,	,	PUNCT
ejpam-5970	240	2	|v	|v	PROPN
ejpam-5970	240	3	(	(	PUNCT
ejpam-5970	240	4	amal(vn	amal(vn	PROPN
ejpam-5970	240	5	,	,	PUNCT
ejpam-5970	240	6	x	x	NOUN
ejpam-5970	240	7	,	,	PUNCT
ejpam-5970	240	8	m))|	m))|	PROPN
ejpam-5970	240	9	}	}	PUNCT
ejpam-5970	240	10	.	.	PUNCT
ejpam-5970	241	1	f(x	f(x	NOUN
ejpam-5970	241	2	)	)	PUNCT
ejpam-5970	242	1	=	=	NOUN
ejpam-5970	242	2	1	1	NUM
ejpam-5970	242	3	f(xi	f(xi	NUM
ejpam-5970	242	4	)	)	PUNCT
ejpam-5970	243	1	=	=	NOUN
ejpam-5970	243	2	i+	i+	NUM
ejpam-5970	243	3	1	1	NUM
ejpam-5970	243	4	,	,	PUNCT
ejpam-5970	243	5	for	for	ADP
ejpam-5970	243	6	1	1	NUM
ejpam-5970	243	7	≤	≤	NUM
ejpam-5970	243	8	i	i	PRON
ejpam-5970	243	9	≤	≤	NOUN
ejpam-5970	243	10	m	m	VERB
ejpam-5970	243	11	f(yi	f(yi	NUM
ejpam-5970	243	12	)	)	PUNCT
ejpam-5970	244	1	=	=	SYM
ejpam-5970	244	2	2m+	2m+	NUM
ejpam-5970	244	3	i+	i+	NUM
ejpam-5970	244	4	1	1	NUM
ejpam-5970	244	5	,	,	PUNCT
ejpam-5970	244	6	for	for	ADP
ejpam-5970	244	7	1	1	NUM
ejpam-5970	244	8	≤	≤	NUM
ejpam-5970	244	9	i	i	PRON
ejpam-5970	244	10	≤	≤	NUM
ejpam-5970	244	11	nm	nm	PRON
ejpam-5970	244	12	f(zi	f(zi	NOUN
ejpam-5970	244	13	)	)	PUNCT
ejpam-5970	244	14	=	=	SYM
ejpam-5970	245	1	2m−	2m−	PROPN
ejpam-5970	245	2	i+	i+	NUM
ejpam-5970	245	3	2	2	NUM
ejpam-5970	245	4	,	,	PUNCT
ejpam-5970	245	5	for	for	ADP
ejpam-5970	245	6	1	1	NUM
ejpam-5970	245	7	≤	≤	NUM
ejpam-5970	245	8	i	i	PRON
ejpam-5970	246	1	≤	≤	NOUN
ejpam-5970	246	2	m	m	VERB
ejpam-5970	246	3	under	under	ADP
ejpam-5970	246	4	the	the	DET
ejpam-5970	246	5	bijection	bijection	ADJ
ejpam-5970	246	6	f	f	NOUN
ejpam-5970	246	7	,	,	PUNCT
ejpam-5970	246	8	the	the	DET
ejpam-5970	246	9	edge	edge	NOUN
ejpam-5970	246	10	weights	weight	NOUN
ejpam-5970	246	11	can	can	AUX
ejpam-5970	246	12	be	be	AUX
ejpam-5970	246	13	presented	present	VERB
ejpam-5970	246	14	as	as	SCONJ
ejpam-5970	246	15	follows	follow	VERB
ejpam-5970	246	16	w(xxi	w(xxi	NOUN
ejpam-5970	246	17	)	)	PUNCT
ejpam-5970	246	18	=	=	NOUN
ejpam-5970	247	1	i+	i+	NUM
ejpam-5970	247	2	2	2	NUM
ejpam-5970	247	3	,	,	PUNCT
ejpam-5970	247	4	for	for	ADP
ejpam-5970	247	5	1	1	NUM
ejpam-5970	247	6	≤	≤	NUM
ejpam-5970	248	1	i	i	PRON
ejpam-5970	249	1	≤	≤	NOUN
ejpam-5970	249	2	m	m	VERB
ejpam-5970	249	3	w(xizi	w(xizi	ADJ
ejpam-5970	249	4	)	)	PUNCT
ejpam-5970	250	1	=	=	SYM
ejpam-5970	251	1	2m+	2m+	NUM
ejpam-5970	251	2	3	3	NUM
ejpam-5970	251	3	,	,	PUNCT
ejpam-5970	251	4	for	for	ADP
ejpam-5970	251	5	1	1	NUM
ejpam-5970	251	6	≤	≤	NUM
ejpam-5970	251	7	i	i	PRON
ejpam-5970	251	8	≤	≤	NOUN
ejpam-5970	251	9	m	m	VERB
ejpam-5970	251	10	w(xzi	w(xzi	PROPN
ejpam-5970	251	11	)	)	PUNCT
ejpam-5970	252	1	=	=	PUNCT
ejpam-5970	252	2	2m−	2m−	PROPN
ejpam-5970	252	3	i+	i+	NUM
ejpam-5970	252	4	3	3	NUM
ejpam-5970	252	5	,	,	PUNCT
ejpam-5970	252	6	for	for	ADP
ejpam-5970	252	7	1	1	NUM
ejpam-5970	252	8	≤	≤	NUM
ejpam-5970	252	9	i	i	PRON
ejpam-5970	252	10	≤	≤	NOUN
ejpam-5970	252	11	m	m	VERB
ejpam-5970	252	12	a.	a.	PROPN
ejpam-5970	252	13	i.	i.	PROPN
ejpam-5970	252	14	kristiana	kristiana	PROPN
ejpam-5970	252	15	,	,	PUNCT
ejpam-5970	252	16	et	et	PROPN
ejpam-5970	252	17	al	al	PROPN
ejpam-5970	252	18	.	.	PUNCT
ejpam-5970	252	19	/	/	SYM
ejpam-5970	252	20	eur	eur	PROPN
ejpam-5970	252	21	.	.	PUNCT
ejpam-5970	253	1	j.	j.	PROPN
ejpam-5970	253	2	pure	pure	PROPN
ejpam-5970	253	3	appl	appl	PROPN
ejpam-5970	253	4	.	.	PROPN
ejpam-5970	253	5	math	math	PROPN
ejpam-5970	253	6	,	,	PUNCT
ejpam-5970	253	7	18	18	NUM
ejpam-5970	253	8	(	(	PUNCT
ejpam-5970	253	9	3	3	NUM
ejpam-5970	253	10	)	)	PUNCT
ejpam-5970	253	11	(	(	PUNCT
ejpam-5970	253	12	2025	2025	NUM
ejpam-5970	253	13	)	)	PUNCT
ejpam-5970	253	14	,	,	PUNCT
ejpam-5970	253	15	5970	5970	NUM
ejpam-5970	253	16	9	9	NUM
ejpam-5970	253	17	of	of	ADP
ejpam-5970	253	18	18	18	NUM
ejpam-5970	253	19	w(xyi	w(xyi	NOUN
ejpam-5970	253	20	)	)	PUNCT
ejpam-5970	253	21	=	=	SYM
ejpam-5970	253	22	2m+	2m+	NUM
ejpam-5970	253	23	2	2	NUM
ejpam-5970	254	1	+	+	CCONJ
ejpam-5970	254	2	i	i	PRON
ejpam-5970	254	3	,	,	PUNCT
ejpam-5970	254	4	for	for	ADP
ejpam-5970	254	5	1	1	NUM
ejpam-5970	254	6	≤	≤	NUM
ejpam-5970	254	7	i	i	PRON
ejpam-5970	254	8	≤	≤	NOUN
ejpam-5970	254	9	mn	mn	PROPN
ejpam-5970	255	1	thus	thus	ADV
ejpam-5970	255	2	we	we	PRON
ejpam-5970	255	3	can	can	AUX
ejpam-5970	255	4	write	write	VERB
ejpam-5970	255	5	in	in	ADP
ejpam-5970	255	6	the	the	DET
ejpam-5970	255	7	form	form	NOUN
ejpam-5970	255	8	of	of	ADP
ejpam-5970	255	9	set	set	NOUN
ejpam-5970	255	10	w	w	PROPN
ejpam-5970	255	11	of	of	ADP
ejpam-5970	255	12	edge	edge	NOUN
ejpam-5970	255	13	weight	weight	NOUN
ejpam-5970	255	14	of	of	ADP
ejpam-5970	255	15	amal(vn	amal(vn	PROPN
ejpam-5970	255	16	,	,	PUNCT
ejpam-5970	255	17	x	x	X
ejpam-5970	255	18	,	,	PUNCT
ejpam-5970	255	19	m	m	NOUN
ejpam-5970	255	20	)	)	PUNCT
ejpam-5970	255	21	.	.	PUNCT
ejpam-5970	256	1	it	it	PRON
ejpam-5970	256	2	includes	include	VERB
ejpam-5970	256	3	three	three	NUM
ejpam-5970	256	4	edge	edge	NOUN
ejpam-5970	256	5	weight	weight	NOUN
ejpam-5970	256	6	sets	set	NOUN
ejpam-5970	256	7	,	,	PUNCT
ejpam-5970	256	8	namely	namely	ADV
ejpam-5970	256	9	w1	w1	NOUN
ejpam-5970	256	10	=	=	SYM
ejpam-5970	256	11	{	{	PUNCT
ejpam-5970	256	12	3	3	NUM
ejpam-5970	256	13	,	,	PUNCT
ejpam-5970	256	14	5	5	NUM
ejpam-5970	256	15	,	,	PUNCT
ejpam-5970	256	16	·	·	PUNCT
ejpam-5970	256	17	·	·	PUNCT
ejpam-5970	256	18	·	·	PUNCT
ejpam-5970	256	19	,	,	PUNCT
ejpam-5970	256	20	2	2	NUM
ejpam-5970	256	21	+	+	NUM
ejpam-5970	256	22	m},w2	m},w2	NOUN
ejpam-5970	256	23	=	=	SYM
ejpam-5970	256	24	{	{	PUNCT
ejpam-5970	256	25	2	2	NUM
ejpam-5970	256	26	m	m	NOUN
ejpam-5970	256	27	+	+	NOUN
ejpam-5970	256	28	3	3	NUM
ejpam-5970	256	29	}	}	PUNCT
ejpam-5970	256	30	,	,	PUNCT
ejpam-5970	256	31	w3	w3	PROPN
ejpam-5970	256	32	=	=	SYM
ejpam-5970	256	33	{	{	PUNCT
ejpam-5970	256	34	2	2	NUM
ejpam-5970	256	35	m	m	NOUN
ejpam-5970	256	36	+	+	NOUN
ejpam-5970	256	37	2	2	NUM
ejpam-5970	256	38	,	,	PUNCT
ejpam-5970	256	39	2	2	NUM
ejpam-5970	256	40	m	m	NOUN
ejpam-5970	256	41	+	+	ADJ
ejpam-5970	256	42	1	1	NUM
ejpam-5970	256	43	·	·	PUNCT
ejpam-5970	256	44	·	·	PUNCT
ejpam-5970	256	45	·	·	PUNCT
ejpam-5970	256	46	,	,	PUNCT
ejpam-5970	256	47	m	m	VERB
ejpam-5970	256	48	+	+	ADJ
ejpam-5970	256	49	3	3	NUM
ejpam-5970	256	50	}	}	PUNCT
ejpam-5970	256	51	,	,	PUNCT
ejpam-5970	256	52	and	and	CCONJ
ejpam-5970	256	53	w4	w4	NOUN
ejpam-5970	256	54	=	=	SYM
ejpam-5970	256	55	{	{	PUNCT
ejpam-5970	256	56	2	2	NUM
ejpam-5970	256	57	m	m	NOUN
ejpam-5970	256	58	+	+	NOUN
ejpam-5970	256	59	3	3	NUM
ejpam-5970	256	60	,	,	PUNCT
ejpam-5970	256	61	2	2	NUM
ejpam-5970	256	62	m	m	NOUN
ejpam-5970	256	63	+	+	NOUN
ejpam-5970	256	64	4	4	NUM
ejpam-5970	256	65	,	,	PUNCT
ejpam-5970	256	66	·	·	PUNCT
ejpam-5970	256	67	·	·	PUNCT
ejpam-5970	256	68	·	·	PUNCT
ejpam-5970	256	69	,	,	PUNCT
ejpam-5970	256	70	2	2	NUM
ejpam-5970	256	71	m	m	NOUN
ejpam-5970	256	72	+	+	NUM
ejpam-5970	256	73	2	2	NUM
ejpam-5970	256	74	+	+	NUM
ejpam-5970	256	75	n	n	CCONJ
ejpam-5970	256	76	}	}	PUNCT
ejpam-5970	256	77	.	.	PUNCT
ejpam-5970	257	1	our	our	PRON
ejpam-5970	257	2	task	task	NOUN
ejpam-5970	257	3	is	be	AUX
ejpam-5970	257	4	to	to	PART
ejpam-5970	257	5	determine	determine	VERB
ejpam-5970	257	6	the	the	DET
ejpam-5970	257	7	cardinality	cardinality	NOUN
ejpam-5970	257	8	of	of	ADP
ejpam-5970	257	9	those	those	DET
ejpam-5970	257	10	sets	set	NOUN
ejpam-5970	257	11	to	to	PART
ejpam-5970	257	12	obtain	obtain	VERB
ejpam-5970	257	13	the	the	DET
ejpam-5970	257	14	upper	upper	ADJ
ejpam-5970	257	15	bound	bound	NOUN
ejpam-5970	257	16	,	,	PUNCT
ejpam-5970	257	17	but	but	CCONJ
ejpam-5970	257	18	we	we	PRON
ejpam-5970	257	19	need	need	VERB
ejpam-5970	257	20	to	to	PART
ejpam-5970	257	21	check	check	VERB
ejpam-5970	257	22	weather	weather	NOUN
ejpam-5970	257	23	all	all	DET
ejpam-5970	257	24	three	three	NUM
ejpam-5970	257	25	sets	set	NOUN
ejpam-5970	257	26	are	be	AUX
ejpam-5970	257	27	disjoint	disjoint	ADJ
ejpam-5970	257	28	or	or	CCONJ
ejpam-5970	257	29	not	not	PART
ejpam-5970	257	30	first	first	ADJ
ejpam-5970	257	31	.	.	PUNCT
ejpam-5970	258	1	under	under	ADP
ejpam-5970	258	2	the	the	DET
ejpam-5970	258	3	contradiction	contradiction	NOUN
ejpam-5970	258	4	proof	proof	NOUN
ejpam-5970	258	5	,	,	PUNCT
ejpam-5970	258	6	we	we	PRON
ejpam-5970	258	7	suppose	suppose	VERB
ejpam-5970	258	8	w2	w2	NOUN
ejpam-5970	258	9	⊆	⊆	NUM
ejpam-5970	258	10	w1	w1	NOUN
ejpam-5970	258	11	←→	←→	ADP
ejpam-5970	258	12	2m+	2m+	NUM
ejpam-5970	258	13	3	3	NUM
ejpam-5970	258	14	=	=	SYM
ejpam-5970	258	15	2	2	NUM
ejpam-5970	258	16	+	+	NUM
ejpam-5970	258	17	i←→	i←→	NOUN
ejpam-5970	258	18	i	i	NOUN
ejpam-5970	258	19	=	=	NOUN
ejpam-5970	258	20	2m+	2m+	NUM
ejpam-5970	258	21	1	1	NUM
ejpam-5970	258	22	.	.	PUNCT
ejpam-5970	259	1	since	since	SCONJ
ejpam-5970	259	2	w(xxi	w(xxi	PROPN
ejpam-5970	259	3	)	)	PUNCT
ejpam-5970	259	4	=	=	SYM
ejpam-5970	259	5	2	2	NUM
ejpam-5970	259	6	+	+	CCONJ
ejpam-5970	259	7	i	i	PROPN
ejpam-5970	259	8	,	,	PUNCT
ejpam-5970	259	9	for	for	ADP
ejpam-5970	259	10	1	1	NUM
ejpam-5970	259	11	≤	≤	NUM
ejpam-5970	259	12	i	i	PRON
ejpam-5970	259	13	≤	≤	NOUN
ejpam-5970	259	14	m	m	ADP
ejpam-5970	259	15	,	,	PUNCT
ejpam-5970	259	16	thus	thus	ADV
ejpam-5970	259	17	i	i	PRON
ejpam-5970	260	1	=	=	SYM
ejpam-5970	260	2	2m+1	2m+1	PROPN
ejpam-5970	260	3	does	do	AUX
ejpam-5970	260	4	not	not	PART
ejpam-5970	260	5	lie	lie	VERB
ejpam-5970	260	6	in	in	ADP
ejpam-5970	260	7	the	the	DET
ejpam-5970	260	8	interval	interval	NOUN
ejpam-5970	260	9	,	,	PUNCT
ejpam-5970	260	10	it	it	PRON
ejpam-5970	260	11	is	be	AUX
ejpam-5970	260	12	a	a	DET
ejpam-5970	260	13	contradiction	contradiction	NOUN
ejpam-5970	260	14	.	.	PUNCT
ejpam-5970	261	1	it	it	PRON
ejpam-5970	261	2	concludes	conclude	VERB
ejpam-5970	261	3	that	that	SCONJ
ejpam-5970	261	4	w2∩w1	w2∩w1	NOUN
ejpam-5970	261	5	=	=	PUNCT
ejpam-5970	261	6	∅.	∅.	NOUN
ejpam-5970	261	7	under	under	ADP
ejpam-5970	261	8	the	the	DET
ejpam-5970	261	9	contradiction	contradiction	NOUN
ejpam-5970	261	10	proof	proof	NOUN
ejpam-5970	261	11	,	,	PUNCT
ejpam-5970	261	12	we	we	PRON
ejpam-5970	261	13	suppose	suppose	VERB
ejpam-5970	261	14	w1	w1	NOUN
ejpam-5970	261	15	⊆w3	⊆w3	PROPN
ejpam-5970	262	1	←→	←→	ADP
ejpam-5970	262	2	2+i	2+i	NUM
ejpam-5970	262	3	=	=	SYM
ejpam-5970	262	4	2m−i+3←→	2m−i+3←→	NOUN
ejpam-5970	263	1	i	i	NOUN
ejpam-5970	263	2	=	=	PUNCT
ejpam-5970	263	3	2m+1	2m+1	PROPN
ejpam-5970	263	4	2	2	NUM
ejpam-5970	263	5	.	.	PUNCT
ejpam-5970	264	1	since	since	SCONJ
ejpam-5970	264	2	w(xzi	w(xzi	PROPN
ejpam-5970	264	3	)	)	PUNCT
ejpam-5970	265	1	=	=	PUNCT
ejpam-5970	266	1	2m−	2m−	NUM
ejpam-5970	266	2	i+3	i+3	NOUN
ejpam-5970	266	3	,	,	PUNCT
ejpam-5970	266	4	for	for	ADP
ejpam-5970	266	5	1	1	NUM
ejpam-5970	266	6	≤	≤	NUM
ejpam-5970	266	7	i	i	PRON
ejpam-5970	266	8	≤	≤	NOUN
ejpam-5970	266	9	m	m	ADP
ejpam-5970	266	10	,	,	PUNCT
ejpam-5970	266	11	thus	thus	ADV
ejpam-5970	266	12	i	i	PRON
ejpam-5970	266	13	=	=	SYM
ejpam-5970	266	14	2m+1	2m+1	NOUN
ejpam-5970	266	15	2	2	NUM
ejpam-5970	266	16	does	do	AUX
ejpam-5970	266	17	not	not	PART
ejpam-5970	266	18	lie	lie	VERB
ejpam-5970	266	19	in	in	ADP
ejpam-5970	266	20	the	the	DET
ejpam-5970	266	21	interval	interval	NOUN
ejpam-5970	266	22	,	,	PUNCT
ejpam-5970	266	23	it	it	PRON
ejpam-5970	266	24	is	be	AUX
ejpam-5970	266	25	a	a	DET
ejpam-5970	266	26	contradiction	contradiction	NOUN
ejpam-5970	266	27	.	.	PUNCT
ejpam-5970	267	1	it	it	PRON
ejpam-5970	267	2	concludes	conclude	VERB
ejpam-5970	267	3	that	that	SCONJ
ejpam-5970	267	4	w1	w1	NOUN
ejpam-5970	267	5	∩w3	∩w3	NOUN
ejpam-5970	267	6	=	=	SYM
ejpam-5970	267	7	∅.under	∅.under	NOUN
ejpam-5970	267	8	the	the	DET
ejpam-5970	267	9	contradiction	contradiction	NOUN
ejpam-5970	267	10	proof	proof	NOUN
ejpam-5970	267	11	,	,	PUNCT
ejpam-5970	267	12	we	we	PRON
ejpam-5970	267	13	suppose	suppose	VERB
ejpam-5970	267	14	w1	w1	NOUN
ejpam-5970	267	15	⊆w4	⊆w4	PUNCT
ejpam-5970	267	16	←→	←→	ADP
ejpam-5970	267	17	2	2	NUM
ejpam-5970	268	1	+	+	CCONJ
ejpam-5970	268	2	i	i	NOUN
ejpam-5970	268	3	=	=	NOUN
ejpam-5970	268	4	2m+	2m+	NUM
ejpam-5970	268	5	2	2	NUM
ejpam-5970	268	6	+	+	NUM
ejpam-5970	268	7	i←→	i←→	NOUN
ejpam-5970	268	8	m	m	NOUN
ejpam-5970	268	9	=	=	NOUN
ejpam-5970	268	10	0	0	NUM
ejpam-5970	268	11	.	.	PUNCT
ejpam-5970	269	1	since	since	SCONJ
ejpam-5970	269	2	w(xyi	w(xyi	PROPN
ejpam-5970	269	3	)	)	PUNCT
ejpam-5970	269	4	=	=	SYM
ejpam-5970	269	5	2m+	2m+	NUM
ejpam-5970	269	6	2	2	NUM
ejpam-5970	269	7	+	+	NUM
ejpam-5970	269	8	i	i	PRON
ejpam-5970	269	9	,	,	PUNCT
ejpam-5970	269	10	for	for	ADP
ejpam-5970	269	11	1	1	NUM
ejpam-5970	269	12	≤	≤	NUM
ejpam-5970	269	13	i	i	PROPN
ejpam-5970	269	14	≤	≤	PROPN
ejpam-5970	269	15	mn	mn	PROPN
ejpam-5970	269	16	,	,	PUNCT
ejpam-5970	269	17	thusm	thusm	NOUN
ejpam-5970	269	18	=	=	SYM
ejpam-5970	269	19	0	0	NUM
ejpam-5970	269	20	does	do	AUX
ejpam-5970	269	21	not	not	PART
ejpam-5970	269	22	lie	lie	VERB
ejpam-5970	269	23	in	in	ADP
ejpam-5970	269	24	the	the	DET
ejpam-5970	269	25	interval	interval	NOUN
ejpam-5970	269	26	,	,	PUNCT
ejpam-5970	269	27	it	it	PRON
ejpam-5970	269	28	is	be	AUX
ejpam-5970	269	29	a	a	DET
ejpam-5970	269	30	contradiction	contradiction	NOUN
ejpam-5970	269	31	.	.	PUNCT
ejpam-5970	270	1	it	it	PRON
ejpam-5970	270	2	concludes	conclude	VERB
ejpam-5970	270	3	thatw1∩w4	thatw1∩w4	NOUN
ejpam-5970	270	4	=	=	PUNCT
ejpam-5970	270	5	∅.	∅.	NOUN
ejpam-5970	270	6	under	under	ADP
ejpam-5970	270	7	the	the	DET
ejpam-5970	270	8	contradiction	contradiction	NOUN
ejpam-5970	270	9	proof	proof	NOUN
ejpam-5970	270	10	,	,	PUNCT
ejpam-5970	270	11	we	we	PRON
ejpam-5970	270	12	suppose	suppose	VERB
ejpam-5970	270	13	w2	w2	NOUN
ejpam-5970	270	14	⊆w3	⊆w3	NOUN
ejpam-5970	271	1	←→	←→	PROPN
ejpam-5970	271	2	2m+3	2m+3	NUM
ejpam-5970	271	3	=	=	SYM
ejpam-5970	271	4	2m−	2m−	NUM
ejpam-5970	271	5	i+3←→	i+3←→	NOUN
ejpam-5970	272	1	i	i	NOUN
ejpam-5970	272	2	=	=	NOUN
ejpam-5970	272	3	0	0	X
ejpam-5970	272	4	.	.	PUNCT
ejpam-5970	273	1	since	since	SCONJ
ejpam-5970	273	2	w(xzi	w(xzi	PROPN
ejpam-5970	273	3	)	)	PUNCT
ejpam-5970	273	4	=	=	PUNCT
ejpam-5970	273	5	2	2	NUM
ejpam-5970	273	6	m	m	NOUN
ejpam-5970	273	7	−	−	NOUN
ejpam-5970	274	1	i	i	PRON
ejpam-5970	274	2	+	+	NOUN
ejpam-5970	274	3	3	3	NUM
ejpam-5970	274	4	,	,	PUNCT
ejpam-5970	274	5	for	for	ADP
ejpam-5970	274	6	1	1	NUM
ejpam-5970	274	7	≤	≤	NUM
ejpam-5970	274	8	i	i	PRON
ejpam-5970	274	9	≤	≤	NOUN
ejpam-5970	274	10	m	m	ADP
ejpam-5970	274	11	,	,	PUNCT
ejpam-5970	274	12	thus	thus	ADV
ejpam-5970	274	13	i	i	PRON
ejpam-5970	274	14	=	=	NOUN
ejpam-5970	274	15	0	0	PUNCT
ejpam-5970	274	16	does	do	AUX
ejpam-5970	274	17	not	not	PART
ejpam-5970	274	18	lie	lie	VERB
ejpam-5970	274	19	in	in	ADP
ejpam-5970	274	20	the	the	DET
ejpam-5970	274	21	interval	interval	NOUN
ejpam-5970	274	22	,	,	PUNCT
ejpam-5970	274	23	it	it	PRON
ejpam-5970	274	24	is	be	AUX
ejpam-5970	274	25	a	a	DET
ejpam-5970	274	26	contradiction	contradiction	NOUN
ejpam-5970	274	27	.	.	PUNCT
ejpam-5970	275	1	it	it	PRON
ejpam-5970	275	2	concludes	conclude	VERB
ejpam-5970	275	3	that	that	SCONJ
ejpam-5970	275	4	w2∩w3	w2∩w3	NOUN
ejpam-5970	275	5	=	=	VERB
ejpam-5970	275	6	∅.	∅.	NOUN
ejpam-5970	275	7	under	under	ADP
ejpam-5970	275	8	the	the	DET
ejpam-5970	275	9	contradiction	contradiction	NOUN
ejpam-5970	275	10	proof	proof	NOUN
ejpam-5970	275	11	,	,	PUNCT
ejpam-5970	275	12	we	we	PRON
ejpam-5970	275	13	suppose	suppose	VERB
ejpam-5970	275	14	w2	w2	NOUN
ejpam-5970	275	15	⊆w4	⊆w4	PROPN
ejpam-5970	275	16	←→	←→	PROPN
ejpam-5970	275	17	2nm+3	2nm+3	NUM
ejpam-5970	275	18	=	=	SYM
ejpam-5970	275	19	2m+2	2m+2	PROPN
ejpam-5970	275	20	+	+	CCONJ
ejpam-5970	275	21	i←→	i←→	NOUN
ejpam-5970	275	22	i	i	NOUN
ejpam-5970	275	23	=	=	NOUN
ejpam-5970	275	24	1	1	X
ejpam-5970	275	25	.	.	PUNCT
ejpam-5970	275	26	since	since	SCONJ
ejpam-5970	275	27	w(xyi	w(xyi	PROPN
ejpam-5970	275	28	)	)	PUNCT
ejpam-5970	276	1	=	=	SYM
ejpam-5970	276	2	2m+2	2m+2	PROPN
ejpam-5970	276	3	+	+	CCONJ
ejpam-5970	276	4	i	i	PROPN
ejpam-5970	276	5	,	,	PUNCT
ejpam-5970	276	6	for	for	ADP
ejpam-5970	276	7	1	1	NUM
ejpam-5970	276	8	≤	≤	NUM
ejpam-5970	276	9	i	i	PROPN
ejpam-5970	276	10	≤	≤	PROPN
ejpam-5970	276	11	mn	mn	PROPN
ejpam-5970	276	12	,	,	PUNCT
ejpam-5970	276	13	thus	thus	ADV
ejpam-5970	276	14	i	i	PRON
ejpam-5970	276	15	=	=	SYM
ejpam-5970	276	16	1	1	NUM
ejpam-5970	276	17	lies	lie	VERB
ejpam-5970	276	18	in	in	ADP
ejpam-5970	276	19	the	the	DET
ejpam-5970	276	20	interval	interval	NOUN
ejpam-5970	276	21	.	.	PUNCT
ejpam-5970	277	1	it	it	PRON
ejpam-5970	277	2	concludes	conclude	VERB
ejpam-5970	277	3	that	that	SCONJ
ejpam-5970	277	4	w2	w2	PROPN
ejpam-5970	277	5	⊂	⊂	PROPN
ejpam-5970	277	6	w4	w4	PROPN
ejpam-5970	277	7	.	.	PUNCT
ejpam-5970	278	1	furthermore	furthermore	ADV
ejpam-5970	278	2	,	,	PUNCT
ejpam-5970	278	3	under	under	ADP
ejpam-5970	278	4	the	the	DET
ejpam-5970	278	5	contradiction	contradiction	NOUN
ejpam-5970	278	6	proof	proof	NOUN
ejpam-5970	278	7	,	,	PUNCT
ejpam-5970	278	8	we	we	PRON
ejpam-5970	278	9	suppose	suppose	VERB
ejpam-5970	278	10	w3	w3	PROPN
ejpam-5970	278	11	⊆	⊆	NUM
ejpam-5970	278	12	w4	w4	NOUN
ejpam-5970	278	13	←→	←→	PROPN
ejpam-5970	278	14	2	2	NUM
ejpam-5970	278	15	nm	nm	NOUN
ejpam-5970	278	16	−	−	NOUN
ejpam-5970	278	17	1	1	NUM
ejpam-5970	278	18	+	+	CCONJ
ejpam-5970	278	19	3	3	NUM
ejpam-5970	278	20	=	=	SYM
ejpam-5970	278	21	2	2	NUM
ejpam-5970	278	22	m	m	NOUN
ejpam-5970	278	23	+	+	NUM
ejpam-5970	278	24	2	2	NUM
ejpam-5970	278	25	+	+	NUM
ejpam-5970	278	26	i	i	PRON
ejpam-5970	278	27	←→	←→	PROPN
ejpam-5970	278	28	i	i	NOUN
ejpam-5970	278	29	=	=	NOUN
ejpam-5970	278	30	1	1	NUM
ejpam-5970	278	31	2	2	NUM
ejpam-5970	278	32	.	.	PUNCT
ejpam-5970	279	1	since	since	SCONJ
ejpam-5970	279	2	w(xyi	w(xyi	PROPN
ejpam-5970	279	3	)	)	PUNCT
ejpam-5970	279	4	=	=	SYM
ejpam-5970	279	5	2m+	2m+	NUM
ejpam-5970	279	6	2	2	NUM
ejpam-5970	279	7	+	+	CCONJ
ejpam-5970	279	8	i	i	PRON
ejpam-5970	279	9	,	,	PUNCT
ejpam-5970	279	10	for	for	ADP
ejpam-5970	279	11	1	1	NUM
ejpam-5970	279	12	≤	≤	NUM
ejpam-5970	279	13	i	i	PROPN
ejpam-5970	279	14	≤	≤	PROPN
ejpam-5970	279	15	mn	mn	PROPN
ejpam-5970	279	16	,	,	PUNCT
ejpam-5970	279	17	thus	thus	ADV
ejpam-5970	279	18	i	i	PRON
ejpam-5970	279	19	=	=	NOUN
ejpam-5970	279	20	1	1	NUM
ejpam-5970	279	21	2	2	NUM
ejpam-5970	279	22	does	do	AUX
ejpam-5970	279	23	not	not	PART
ejpam-5970	279	24	lie	lie	VERB
ejpam-5970	279	25	in	in	ADP
ejpam-5970	279	26	the	the	DET
ejpam-5970	279	27	interval	interval	NOUN
ejpam-5970	279	28	,	,	PUNCT
ejpam-5970	279	29	it	it	PRON
ejpam-5970	279	30	is	be	AUX
ejpam-5970	279	31	a	a	DET
ejpam-5970	279	32	contradiction	contradiction	NOUN
ejpam-5970	279	33	.	.	PUNCT
ejpam-5970	280	1	it	it	PRON
ejpam-5970	280	2	concludes	conclude	VERB
ejpam-5970	280	3	that	that	SCONJ
ejpam-5970	280	4	w3	w3	PROPN
ejpam-5970	280	5	∩w4	∩w4	PROPN
ejpam-5970	281	1	=	=	PUNCT
ejpam-5970	281	2	∅.	∅.	NOUN
ejpam-5970	281	3	finally	finally	ADV
ejpam-5970	281	4	,	,	PUNCT
ejpam-5970	281	5	we	we	PRON
ejpam-5970	281	6	have	have	VERB
ejpam-5970	281	7	w	w	NOUN
ejpam-5970	281	8	=	=	NOUN
ejpam-5970	281	9	w1	w1	PROPN
ejpam-5970	281	10	∪w3	∪w3	PROPN
ejpam-5970	281	11	∪w4	∪w4	PROPN
ejpam-5970	281	12	.	.	PUNCT
ejpam-5970	282	1	now	now	ADV
ejpam-5970	282	2	,	,	PUNCT
ejpam-5970	282	3	we	we	PRON
ejpam-5970	282	4	can	can	AUX
ejpam-5970	282	5	determine	determine	VERB
ejpam-5970	282	6	the	the	DET
ejpam-5970	282	7	cardinality	cardinality	NOUN
ejpam-5970	282	8	of	of	ADP
ejpam-5970	282	9	w	w	PROPN
ejpam-5970	282	10	.	.	PUNCT
ejpam-5970	283	1	first	first	ADV
ejpam-5970	283	2	,	,	PUNCT
ejpam-5970	283	3	it	it	PRON
ejpam-5970	283	4	is	be	AUX
ejpam-5970	283	5	easy	easy	ADJ
ejpam-5970	283	6	to	to	PART
ejpam-5970	283	7	see	see	VERB
ejpam-5970	283	8	that	that	DET
ejpam-5970	283	9	w2	w2	PROPN
ejpam-5970	283	10	⊂	⊂	PROPN
ejpam-5970	283	11	w4	w4	PROPN
ejpam-5970	283	12	,	,	PUNCT
ejpam-5970	283	13	secondly	secondly	ADV
ejpam-5970	283	14	we	we	PRON
ejpam-5970	283	15	will	will	AUX
ejpam-5970	283	16	determine	determine	VERB
ejpam-5970	283	17	|w1|	|w1|	NOUN
ejpam-5970	283	18	,	,	PUNCT
ejpam-5970	283	19	|w3|	|w3|	NOUN
ejpam-5970	283	20	and	and	CCONJ
ejpam-5970	283	21	|w4|	|w4|	NOUN
ejpam-5970	283	22	under	under	ADP
ejpam-5970	283	23	the	the	DET
ejpam-5970	283	24	following	follow	VERB
ejpam-5970	283	25	calculation	calculation	NOUN
ejpam-5970	283	26	.	.	PUNCT
ejpam-5970	284	1	let	let	VERB
ejpam-5970	284	2	us	we	PRON
ejpam-5970	285	1	and	and	CCONJ
ejpam-5970	285	2	d	d	X
ejpam-5970	285	3	be	be	AUX
ejpam-5970	285	4	the	the	DET
ejpam-5970	285	5	s	s	NOUN
ejpam-5970	285	6	-	-	NOUN
ejpam-5970	285	7	term	term	NOUN
ejpam-5970	285	8	and	and	CCONJ
ejpam-5970	285	9	the	the	DET
ejpam-5970	285	10	different	different	ADJ
ejpam-5970	285	11	of	of	ADP
ejpam-5970	285	12	arithmetic	arithmetic	ADJ
ejpam-5970	285	13	sequence	sequence	NOUN
ejpam-5970	285	14	of	of	ADP
ejpam-5970	285	15	w1	w1	NOUN
ejpam-5970	285	16	,	,	PUNCT
ejpam-5970	285	17	w2	w2	NOUN
ejpam-5970	285	18	and	and	CCONJ
ejpam-5970	285	19	w3	w3	PROPN
ejpam-5970	285	20	,	,	PUNCT
ejpam-5970	285	21	consequently	consequently	ADV
ejpam-5970	285	22	.	.	PUNCT
ejpam-5970	286	1	we	we	PRON
ejpam-5970	286	2	have	have	VERB
ejpam-5970	286	3	u|w1|	u|w1|	ADJ
ejpam-5970	286	4	=	=	SYM
ejpam-5970	286	5	a	a	DET
ejpam-5970	286	6	+	+	NOUN
ejpam-5970	286	7	(	(	PUNCT
ejpam-5970	286	8	|w1|	|w1|	NOUN
ejpam-5970	286	9	−	−	PROPN
ejpam-5970	286	10	1)d	1)d	NUM
ejpam-5970	286	11	←→	←→	PROPN
ejpam-5970	286	12	2	2	NUM
ejpam-5970	286	13	+	+	NOUN
ejpam-5970	286	14	m	m	VERB
ejpam-5970	286	15	=	=	SYM
ejpam-5970	286	16	3	3	NUM
ejpam-5970	286	17	+	+	CCONJ
ejpam-5970	286	18	(	(	PUNCT
ejpam-5970	286	19	|w1|	|w1|	NOUN
ejpam-5970	286	20	−	−	PROPN
ejpam-5970	286	21	1)1	1)1	NUM
ejpam-5970	286	22	←→	←→	PROPN
ejpam-5970	286	23	|w1|	|w1|	NOUN
ejpam-5970	286	24	=	=	SYM
ejpam-5970	286	25	m	m	NOUN
ejpam-5970	286	26	,	,	PUNCT
ejpam-5970	286	27	u|w3|	u|w3|	PROPN
ejpam-5970	286	28	=	=	PUNCT
ejpam-5970	286	29	a+(|w3|−1)d←→	a+(|w3|−1)d←→	ADJ
ejpam-5970	286	30	m+3	m+3	PROPN
ejpam-5970	286	31	=	=	SYM
ejpam-5970	286	32	2m+2+(|w3|−1)(−1)←→	2m+2+(|w3|−1)(−1)←→	NUM
ejpam-5970	286	33	|w3|	|w3|	NOUN
ejpam-5970	287	1	=	=	NOUN
ejpam-5970	287	2	m	m	NOUN
ejpam-5970	287	3	,	,	PUNCT
ejpam-5970	287	4	and	and	CCONJ
ejpam-5970	287	5	u|w4|	u|w4|	PROPN
ejpam-5970	287	6	=	=	SYM
ejpam-5970	287	7	a+(|w4|−	a+(|w4|−	PROPN
ejpam-5970	288	1	1)d←→	1)d←→	NUM
ejpam-5970	288	2	nm+2m+2	nm+2m+2	NOUN
ejpam-5970	288	3	=	=	SYM
ejpam-5970	288	4	2m+3+(|w4|−1)1←→	2m+3+(|w4|−1)1←→	NUM
ejpam-5970	288	5	|w4|	|w4|	NOUN
ejpam-5970	289	1	=	=	SYM
ejpam-5970	289	2	nm	nm	PROPN
ejpam-5970	289	3	.	.	PUNCT
ejpam-5970	290	1	it	it	PRON
ejpam-5970	290	2	implies	imply	VERB
ejpam-5970	290	3	that	that	SCONJ
ejpam-5970	290	4	|w	|w	ADJ
ejpam-5970	290	5	|	|	NOUN
ejpam-5970	290	6	=	=	SYM
ejpam-5970	290	7	|w1|+	|w1|+	PRON
ejpam-5970	290	8	|w3|+|w4|	|w3|+|w4|	X
ejpam-5970	290	9	=	=	SYM
ejpam-5970	290	10	m+m+nm	m+m+nm	PROPN
ejpam-5970	290	11	=	=	SYM
ejpam-5970	290	12	2m+nm	2m+nm	PROPN
ejpam-5970	290	13	.	.	PUNCT
ejpam-5970	291	1	finally	finally	ADV
ejpam-5970	291	2	,	,	PUNCT
ejpam-5970	291	3	we	we	PRON
ejpam-5970	291	4	have	have	VERB
ejpam-5970	291	5	χle(3,1)(amal(vn	χle(3,1)(amal(vn	PROPN
ejpam-5970	291	6	,	,	PUNCT
ejpam-5970	291	7	x	x	NOUN
ejpam-5970	291	8	,	,	PUNCT
ejpam-5970	291	9	m	m	NOUN
ejpam-5970	291	10	)	)	PUNCT
ejpam-5970	291	11	)	)	PUNCT
ejpam-5970	291	12	≤	≤	ADV
ejpam-5970	291	13	2m+nm	2m+nm	NUM
ejpam-5970	291	14	.	.	PUNCT
ejpam-5970	292	1	based	base	VERB
ejpam-5970	292	2	on	on	ADP
ejpam-5970	292	3	the	the	DET
ejpam-5970	292	4	lower	low	ADJ
ejpam-5970	292	5	and	and	CCONJ
ejpam-5970	292	6	upper	upper	ADJ
ejpam-5970	292	7	bounds	bound	NOUN
ejpam-5970	292	8	,	,	PUNCT
ejpam-5970	292	9	we	we	PRON
ejpam-5970	292	10	have	have	VERB
ejpam-5970	292	11	2	2	NUM
ejpam-5970	292	12	m	m	NOUN
ejpam-5970	292	13	+	+	NUM
ejpam-5970	292	14	nm	nm	ADJ
ejpam-5970	292	15	≤	≤	NUM
ejpam-5970	292	16	χle(3,1)(amal(vn	χle(3,1)(amal(vn	PROPN
ejpam-5970	292	17	,	,	PUNCT
ejpam-5970	292	18	x	x	NOUN
ejpam-5970	292	19	,	,	PUNCT
ejpam-5970	292	20	m	m	NOUN
ejpam-5970	292	21	)	)	PUNCT
ejpam-5970	292	22	)	)	PUNCT
ejpam-5970	292	23	≤	≤	NOUN
ejpam-5970	292	24	2m+	2m+	NUM
ejpam-5970	292	25	nm	nm	NOUN
ejpam-5970	292	26	.	.	PUNCT
ejpam-5970	293	1	it	it	PRON
ejpam-5970	293	2	can	can	AUX
ejpam-5970	293	3	be	be	AUX
ejpam-5970	293	4	concluded	conclude	VERB
ejpam-5970	293	5	that	that	SCONJ
ejpam-5970	293	6	χle(3,1)(amal(vn	χle(3,1)(amal(vn	PROPN
ejpam-5970	293	7	,	,	PUNCT
ejpam-5970	293	8	x	x	NOUN
ejpam-5970	293	9	,	,	PUNCT
ejpam-5970	293	10	m	m	NOUN
ejpam-5970	293	11	)	)	PUNCT
ejpam-5970	293	12	)	)	PUNCT
ejpam-5970	294	1	=	=	SYM
ejpam-5970	294	2	2m+	2m+	NUM
ejpam-5970	294	3	nm	nm	NOUN
ejpam-5970	294	4	for	for	ADP
ejpam-5970	294	5	n	n	CCONJ
ejpam-5970	294	6	,	,	PUNCT
ejpam-5970	294	7	m	m	VERB
ejpam-5970	294	8	≥	≥	NOUN
ejpam-5970	294	9	2	2	NUM
ejpam-5970	294	10	.	.	PUNCT
ejpam-5970	295	1	now	now	ADV
ejpam-5970	295	2	,	,	PUNCT
ejpam-5970	295	3	we	we	PRON
ejpam-5970	295	4	will	will	AUX
ejpam-5970	295	5	characterize	characterize	VERB
ejpam-5970	295	6	the	the	DET
ejpam-5970	295	7	non	non	NOUN
ejpam-5970	295	8	-	-	NOUN
ejpam-5970	295	9	existence	existence	NOUN
ejpam-5970	295	10	of	of	ADP
ejpam-5970	295	11	lea	lea	PROPN
ejpam-5970	295	12	(	(	PUNCT
ejpam-5970	295	13	a	a	DET
ejpam-5970	295	14	,	,	PUNCT
ejpam-5970	295	15	d	d	NOUN
ejpam-5970	295	16	)	)	PUNCT
ejpam-5970	295	17	coloring	coloring	NOUN
ejpam-5970	295	18	of	of	ADP
ejpam-5970	295	19	amal(k1+gn	amal(k1+gn	PROPN
ejpam-5970	295	20	,	,	PUNCT
ejpam-5970	295	21	k1,m	k1,m	PROPN
ejpam-5970	295	22	)	)	PUNCT
ejpam-5970	295	23	,	,	PUNCT
ejpam-5970	295	24	for	for	SCONJ
ejpam-5970	295	25	any	any	DET
ejpam-5970	295	26	grah	grah	PROPN
ejpam-5970	295	27	g	g	NOUN
ejpam-5970	295	28	of	of	ADP
ejpam-5970	295	29	order	order	NOUN
ejpam-5970	295	30	n.	n.	NOUN
ejpam-5970	295	31	we	we	PRON
ejpam-5970	295	32	present	present	VERB
ejpam-5970	295	33	it	it	PRON
ejpam-5970	295	34	in	in	ADP
ejpam-5970	295	35	the	the	DET
ejpam-5970	295	36	following	follow	VERB
ejpam-5970	295	37	theorem	theorem	PROPN
ejpam-5970	295	38	.	.	PUNCT
ejpam-5970	295	39	theorem	theorem	NOUN
ejpam-5970	295	40	4	4	NUM
ejpam-5970	295	41	.	.	NOUN
ejpam-5970	295	42	for	for	ADP
ejpam-5970	295	43	n	n	CCONJ
ejpam-5970	295	44	,	,	PUNCT
ejpam-5970	295	45	m	m	VERB
ejpam-5970	295	46	≥	≥	NOUN
ejpam-5970	295	47	2	2	NUM
ejpam-5970	295	48	,	,	PUNCT
ejpam-5970	295	49	the	the	DET
ejpam-5970	295	50	lea(a	lea(a	PROPN
ejpam-5970	295	51	,	,	PUNCT
ejpam-5970	295	52	d	d	NOUN
ejpam-5970	295	53	)	)	PUNCT
ejpam-5970	295	54	coloring	coloring	NOUN
ejpam-5970	295	55	of	of	ADP
ejpam-5970	295	56	graph	graph	NOUN
ejpam-5970	295	57	amal(k1+gn	amal(k1+gn	PROPN
ejpam-5970	295	58	,	,	PUNCT
ejpam-5970	295	59	k1,m	k1,m	PROPN
ejpam-5970	295	60	)	)	PUNCT
ejpam-5970	295	61	does	do	AUX
ejpam-5970	295	62	not	not	PART
ejpam-5970	295	63	exist	exist	VERB
ejpam-5970	295	64	for	for	ADP
ejpam-5970	295	65	d	d	PROPN
ejpam-5970	295	66	∈	∈	PROPN
ejpam-5970	295	67	{	{	PUNCT
ejpam-5970	295	68	0	0	NUM
ejpam-5970	295	69	,	,	PUNCT
ejpam-5970	295	70	2	2	NUM
ejpam-5970	295	71	}	}	PUNCT
ejpam-5970	295	72	.	.	PUNCT
ejpam-5970	296	1	proof	proof	NOUN
ejpam-5970	296	2	.	.	PUNCT
ejpam-5970	297	1	the	the	DET
ejpam-5970	297	2	graph	graph	NOUN
ejpam-5970	297	3	amal(k1	amal(k1	PROPN
ejpam-5970	297	4	+	+	CCONJ
ejpam-5970	297	5	gn	gn	PROPN
ejpam-5970	297	6	,	,	PUNCT
ejpam-5970	297	7	k1,m	k1,m	PROPN
ejpam-5970	297	8	)	)	PUNCT
ejpam-5970	297	9	is	be	AUX
ejpam-5970	297	10	a	a	DET
ejpam-5970	297	11	connected	connected	ADJ
ejpam-5970	297	12	and	and	CCONJ
ejpam-5970	297	13	simple	simple	ADJ
ejpam-5970	297	14	graph	graph	NOUN
ejpam-5970	297	15	with	with	ADP
ejpam-5970	297	16	vertex	vertex	NOUN
ejpam-5970	297	17	set	set	VERB
ejpam-5970	297	18	v	v	NOUN
ejpam-5970	297	19	(	(	PUNCT
ejpam-5970	297	20	amal(k1	amal(k1	PROPN
ejpam-5970	297	21	+	+	CCONJ
ejpam-5970	297	22	gn	gn	PROPN
ejpam-5970	297	23	,	,	PUNCT
ejpam-5970	297	24	k1,m	k1,m	PROPN
ejpam-5970	297	25	)	)	PUNCT
ejpam-5970	297	26	)	)	PUNCT
ejpam-5970	298	1	=	=	PRON
ejpam-5970	298	2	{	{	PUNCT
ejpam-5970	298	3	x	x	NOUN
ejpam-5970	298	4	}	}	PUNCT
ejpam-5970	298	5	∪	∪	X
ejpam-5970	298	6	{	{	PUNCT
ejpam-5970	298	7	xi	xi	PROPN
ejpam-5970	298	8	,	,	PUNCT
ejpam-5970	298	9	j	j	PROPN
ejpam-5970	298	10	;	;	PUNCT
ejpam-5970	298	11	1	1	NUM
ejpam-5970	298	12	≤	≤	NUM
ejpam-5970	298	13	i	i	PRON
ejpam-5970	298	14	≤	≤	PROPN
ejpam-5970	298	15	n	n	CCONJ
ejpam-5970	298	16	,	,	PUNCT
ejpam-5970	298	17	1	1	NUM
ejpam-5970	298	18	≤	≤	NUM
ejpam-5970	298	19	j	j	PROPN
ejpam-5970	298	20	≤	≤	PROPN
ejpam-5970	298	21	m	m	PROPN
ejpam-5970	298	22	}	}	PUNCT
ejpam-5970	298	23	and	and	CCONJ
ejpam-5970	298	24	edge	edge	NOUN
ejpam-5970	298	25	set	set	VERB
ejpam-5970	298	26	e(amal(k1	e(amal(k1	PROPN
ejpam-5970	298	27	+	+	CCONJ
ejpam-5970	298	28	gn	gn	PROPN
ejpam-5970	298	29	,	,	PUNCT
ejpam-5970	298	30	k1,m	k1,m	PROPN
ejpam-5970	298	31	)	)	PUNCT
ejpam-5970	298	32	)	)	PUNCT
ejpam-5970	299	1	=	=	PRON
ejpam-5970	299	2	{	{	PUNCT
ejpam-5970	299	3	xxi	xxi	PROPN
ejpam-5970	299	4	,	,	PUNCT
ejpam-5970	299	5	j	j	PROPN
ejpam-5970	299	6	;	;	PUNCT
ejpam-5970	299	7	1	1	NUM
ejpam-5970	299	8	≤	≤	NUM
ejpam-5970	299	9	i	i	PRON
ejpam-5970	299	10	≤	≤	PROPN
ejpam-5970	299	11	n	n	CCONJ
ejpam-5970	299	12	,	,	PUNCT
ejpam-5970	299	13	1	1	NUM
ejpam-5970	299	14	≤	≤	NUM
ejpam-5970	299	15	j	j	PROPN
ejpam-5970	299	16	≤	≤	PROPN
ejpam-5970	299	17	m	m	VERB
ejpam-5970	299	18	}	}	PUNCT
ejpam-5970	299	19	∪	∪	X
ejpam-5970	299	20	{	{	PUNCT
ejpam-5970	299	21	xj	xj	PROPN
ejpam-5970	299	22	,	,	PUNCT
ejpam-5970	299	23	kxj	kxj	NOUN
ejpam-5970	299	24	,	,	PUNCT
ejpam-5970	299	25	l	l	NOUN
ejpam-5970	299	26	;	;	PUNCT
ejpam-5970	299	27	1	1	NUM
ejpam-5970	299	28	≤	≤	NUM
ejpam-5970	299	29	j	j	PROPN
ejpam-5970	299	30	≤	≤	PROPN
ejpam-5970	299	31	m	m	PROPN
ejpam-5970	299	32	,	,	PUNCT
ejpam-5970	299	33	{	{	PUNCT
ejpam-5970	299	34	k	k	NOUN
ejpam-5970	299	35	,	,	PUNCT
ejpam-5970	299	36	l	l	NOUN
ejpam-5970	299	37	}	}	PUNCT
ejpam-5970	299	38	∈	∈	PROPN
ejpam-5970	299	39	v	v	NOUN
ejpam-5970	299	40	(	(	PUNCT
ejpam-5970	299	41	gn	gn	PROPN
ejpam-5970	299	42	)	)	PUNCT
ejpam-5970	299	43	}	}	PUNCT
ejpam-5970	299	44	.	.	PUNCT
ejpam-5970	300	1	thus	thus	ADV
ejpam-5970	300	2	|v	|v	PROPN
ejpam-5970	300	3	(	(	PUNCT
ejpam-5970	300	4	amal(k1	amal(k1	PROPN
ejpam-5970	300	5	+	+	CCONJ
ejpam-5970	300	6	gn	gn	PROPN
ejpam-5970	300	7	,	,	PUNCT
ejpam-5970	300	8	k1,m))|	k1,m))|	NOUN
ejpam-5970	300	9	=	=	SYM
ejpam-5970	300	10	|v	|v	PROPN
ejpam-5970	300	11	(	(	PUNCT
ejpam-5970	300	12	gn)|m	gn)|m	NOUN
ejpam-5970	300	13	+	+	NOUN
ejpam-5970	300	14	1	1	NUM
ejpam-5970	300	15	=	=	NOUN
ejpam-5970	300	16	nm	nm	NOUN
ejpam-5970	300	17	+	+	NOUN
ejpam-5970	300	18	1	1	NUM
ejpam-5970	300	19	and	and	CCONJ
ejpam-5970	300	20	|e(amal(k1	|e(amal(k1	PROPN
ejpam-5970	300	21	+	+	CCONJ
ejpam-5970	300	22	gn	gn	PROPN
ejpam-5970	300	23	,	,	PUNCT
ejpam-5970	300	24	k1,m)|	k1,m)|	X
ejpam-5970	300	25	=	=	PUNCT
ejpam-5970	300	26	nm	nm	ADJ
ejpam-5970	300	27	+	+	CCONJ
ejpam-5970	300	28	m|e(g)|	m|e(g)|	NUM
ejpam-5970	300	29	.	.	PUNCT
ejpam-5970	301	1	based	base	VERB
ejpam-5970	301	2	on	on	ADP
ejpam-5970	301	3	observation	observation	NOUN
ejpam-5970	301	4	6	6	NUM
ejpam-5970	301	5	,	,	PUNCT
ejpam-5970	301	6	we	we	PRON
ejpam-5970	301	7	have	have	VERB
ejpam-5970	301	8	d	d	NOUN
ejpam-5970	301	9	≤	≤	X
ejpam-5970	301	10	2p−4	2p−4	NUM
ejpam-5970	301	11	k−1	k−1	PROPN
ejpam-5970	302	1	←→	←→	PROPN
ejpam-5970	302	2	d	d	PROPN
ejpam-5970	302	3	≤	≤	PROPN
ejpam-5970	302	4	2|v	2|v	PROPN
ejpam-5970	302	5	(	(	PUNCT
ejpam-5970	302	6	amal(k1+gn	amal(k1+gn	PROPN
ejpam-5970	302	7	,	,	PUNCT
ejpam-5970	302	8	k1,m))|−4	k1,m))|−4	ADJ
ejpam-5970	302	9	|v	|v	X
ejpam-5970	302	10	(	(	PUNCT
ejpam-5970	302	11	amal(k1+gn	amal(k1+gn	PROPN
ejpam-5970	302	12	,	,	PUNCT
ejpam-5970	302	13	k1,m))|−2	k1,m))|−2	NOUN
ejpam-5970	302	14	←→	←→	PROPN
ejpam-5970	302	15	d	d	PROPN
ejpam-5970	302	16	≤	≤	ADV
ejpam-5970	302	17	2	2	NUM
ejpam-5970	302	18	.	.	PUNCT
ejpam-5970	302	19	a.	a.	PROPN
ejpam-5970	302	20	i.	i.	PROPN
ejpam-5970	302	21	kristiana	kristiana	PROPN
ejpam-5970	302	22	,	,	PUNCT
ejpam-5970	302	23	et	et	PROPN
ejpam-5970	302	24	al	al	PROPN
ejpam-5970	302	25	.	.	PUNCT
ejpam-5970	302	26	/	/	SYM
ejpam-5970	302	27	eur	eur	PROPN
ejpam-5970	302	28	.	.	PUNCT
ejpam-5970	303	1	j.	j.	PROPN
ejpam-5970	303	2	pure	pure	PROPN
ejpam-5970	303	3	appl	appl	PROPN
ejpam-5970	303	4	.	.	PROPN
ejpam-5970	303	5	math	math	PROPN
ejpam-5970	303	6	,	,	PUNCT
ejpam-5970	303	7	18	18	NUM
ejpam-5970	303	8	(	(	PUNCT
ejpam-5970	303	9	3	3	NUM
ejpam-5970	303	10	)	)	PUNCT
ejpam-5970	303	11	(	(	PUNCT
ejpam-5970	303	12	2025	2025	NUM
ejpam-5970	303	13	)	)	PUNCT
ejpam-5970	303	14	,	,	PUNCT
ejpam-5970	303	15	5970	5970	NUM
ejpam-5970	303	16	10	10	NUM
ejpam-5970	303	17	of	of	ADP
ejpam-5970	303	18	18	18	NUM
ejpam-5970	303	19	now	now	ADV
ejpam-5970	303	20	,	,	PUNCT
ejpam-5970	303	21	we	we	PRON
ejpam-5970	303	22	will	will	AUX
ejpam-5970	303	23	show	show	VERB
ejpam-5970	303	24	the	the	DET
ejpam-5970	303	25	non	non	NOUN
ejpam-5970	303	26	-	-	NOUN
ejpam-5970	303	27	existence	existence	NOUN
ejpam-5970	303	28	of	of	ADP
ejpam-5970	303	29	lea(a	lea(a	PROPN
ejpam-5970	303	30	,	,	PUNCT
ejpam-5970	303	31	d	d	NOUN
ejpam-5970	303	32	)	)	PUNCT
ejpam-5970	303	33	coloring	coloring	NOUN
ejpam-5970	303	34	of	of	ADP
ejpam-5970	303	35	amal(k1	amal(k1	PROPN
ejpam-5970	303	36	+	+	PROPN
ejpam-5970	303	37	gn	gn	PROPN
ejpam-5970	303	38	,	,	PUNCT
ejpam-5970	303	39	k1,m	k1,m	PROPN
ejpam-5970	303	40	)	)	PUNCT
ejpam-5970	303	41	by	by	ADP
ejpam-5970	303	42	defining	define	VERB
ejpam-5970	303	43	f	f	X
ejpam-5970	303	44	:	:	PUNCT
ejpam-5970	303	45	v	v	X
ejpam-5970	303	46	(	(	PUNCT
ejpam-5970	303	47	amal(k1	amal(k1	PROPN
ejpam-5970	303	48	+	+	PROPN
ejpam-5970	303	49	gn	gn	PROPN
ejpam-5970	303	50	,	,	PUNCT
ejpam-5970	303	51	k1,m))→	k1,m))→	PROPN
ejpam-5970	303	52	{	{	PUNCT
ejpam-5970	303	53	1	1	NUM
ejpam-5970	303	54	,	,	PUNCT
ejpam-5970	303	55	2	2	NUM
ejpam-5970	303	56	,	,	PUNCT
ejpam-5970	303	57	3	3	NUM
ejpam-5970	303	58	,	,	PUNCT
ejpam-5970	303	59	.	.	PUNCT
ejpam-5970	303	60	.	.	PUNCT
ejpam-5970	304	1	.	.	PUNCT
ejpam-5970	305	1	,	,	PUNCT
ejpam-5970	305	2	|v	|v	PROPN
ejpam-5970	305	3	(	(	PUNCT
ejpam-5970	305	4	amal(k1	amal(k1	PROPN
ejpam-5970	305	5	+	+	PROPN
ejpam-5970	305	6	gn	gn	PROPN
ejpam-5970	305	7	,	,	PUNCT
ejpam-5970	305	8	k1	k1	PROPN
ejpam-5970	305	9	,	,	PUNCT
ejpam-5970	305	10	m))|	m))|	PROPN
ejpam-5970	305	11	}	}	PUNCT
ejpam-5970	305	12	as	as	ADP
ejpam-5970	305	13	vertex	vertex	NOUN
ejpam-5970	305	14	labels	label	NOUN
ejpam-5970	305	15	of	of	ADP
ejpam-5970	305	16	amal(k1	amal(k1	PROPN
ejpam-5970	305	17	+	+	CCONJ
ejpam-5970	305	18	gn	gn	PROPN
ejpam-5970	305	19	,	,	PUNCT
ejpam-5970	305	20	k1,m	k1,m	PROPN
ejpam-5970	305	21	)	)	PUNCT
ejpam-5970	305	22	.	.	PUNCT
ejpam-5970	306	1	first	first	ADV
ejpam-5970	306	2	,	,	PUNCT
ejpam-5970	306	3	for	for	ADP
ejpam-5970	306	4	the	the	DET
ejpam-5970	306	5	non	non	ADJ
ejpam-5970	306	6	-	-	NOUN
ejpam-5970	306	7	existence	existence	NOUN
ejpam-5970	306	8	(	(	PUNCT
ejpam-5970	306	9	a	a	X
ejpam-5970	306	10	,	,	PUNCT
ejpam-5970	306	11	0)-edge	0)-edge	NUM
ejpam-5970	306	12	antimagic	antimagic	ADJ
ejpam-5970	306	13	coloring	coloring	NOUN
ejpam-5970	306	14	.	.	PUNCT
ejpam-5970	307	1	assume	assume	VERB
ejpam-5970	307	2	that	that	SCONJ
ejpam-5970	307	3	we	we	PRON
ejpam-5970	307	4	have	have	VERB
ejpam-5970	307	5	d	d	NOUN
ejpam-5970	307	6	=	=	SYM
ejpam-5970	307	7	0	0	NUM
ejpam-5970	307	8	.	.	PUNCT
ejpam-5970	308	1	for	for	ADP
ejpam-5970	308	2	any	any	DET
ejpam-5970	308	3	{	{	PUNCT
ejpam-5970	308	4	xi	xi	PROPN
ejpam-5970	308	5	,	,	PUNCT
ejpam-5970	308	6	j	j	PROPN
ejpam-5970	308	7	,	,	PUNCT
ejpam-5970	308	8	xi	xi	PROPN
ejpam-5970	308	9	,	,	PUNCT
ejpam-5970	308	10	k	k	NOUN
ejpam-5970	308	11	}	}	PUNCT
ejpam-5970	308	12	∈	∈	PROPN
ejpam-5970	308	13	v	v	NOUN
ejpam-5970	308	14	(	(	PUNCT
ejpam-5970	308	15	amal(k1	amal(k1	PROPN
ejpam-5970	308	16	+	+	CCONJ
ejpam-5970	308	17	gn	gn	PROPN
ejpam-5970	308	18	,	,	PUNCT
ejpam-5970	308	19	k1,m	k1,m	PROPN
ejpam-5970	308	20	)	)	PUNCT
ejpam-5970	308	21	)	)	PUNCT
ejpam-5970	308	22	and	and	CCONJ
ejpam-5970	308	23	1	1	NUM
ejpam-5970	308	24	≤	≤	NUM
ejpam-5970	308	25	i	i	PRON
ejpam-5970	308	26	≤	≤	PROPN
ejpam-5970	308	27	n	n	CCONJ
ejpam-5970	308	28	,	,	PUNCT
ejpam-5970	308	29	1	1	NUM
ejpam-5970	308	30	≤	≤	PROPN
ejpam-5970	308	31	j	j	PROPN
ejpam-5970	308	32	,	,	PUNCT
ejpam-5970	308	33	k	k	PROPN
ejpam-5970	308	34	≤	≤	PROPN
ejpam-5970	308	35	m	m	ADP
ejpam-5970	308	36	,	,	PUNCT
ejpam-5970	308	37	we	we	PRON
ejpam-5970	308	38	will	will	AUX
ejpam-5970	308	39	have	have	VERB
ejpam-5970	308	40	w(xxi	w(xxi	PROPN
ejpam-5970	308	41	,	,	PUNCT
ejpam-5970	308	42	j	j	NOUN
ejpam-5970	308	43	)	)	PUNCT
ejpam-5970	308	44	=	=	PUNCT
ejpam-5970	309	1	w(xxi	w(xxi	PROPN
ejpam-5970	309	2	,	,	PUNCT
ejpam-5970	309	3	k	k	NOUN
ejpam-5970	309	4	)	)	PUNCT
ejpam-5970	309	5	.	.	PUNCT
ejpam-5970	310	1	it	it	PRON
ejpam-5970	310	2	contradicts	contradict	VERB
ejpam-5970	310	3	with	with	ADP
ejpam-5970	310	4	the	the	DET
ejpam-5970	310	5	definition	definition	NOUN
ejpam-5970	310	6	of	of	ADP
ejpam-5970	310	7	local	local	ADJ
ejpam-5970	310	8	antimagic	antimagic	ADJ
ejpam-5970	310	9	coloring	coloring	NOUN
ejpam-5970	310	10	,	,	PUNCT
ejpam-5970	310	11	since	since	SCONJ
ejpam-5970	310	12	xxi	xxi	PROPN
ejpam-5970	310	13	,	,	PUNCT
ejpam-5970	310	14	j	j	PROPN
ejpam-5970	310	15	and	and	CCONJ
ejpam-5970	310	16	xxi	xxi	PROPN
ejpam-5970	310	17	,	,	PUNCT
ejpam-5970	310	18	k	k	PROPN
ejpam-5970	310	19	are	be	AUX
ejpam-5970	310	20	incident	incident	NOUN
ejpam-5970	310	21	,	,	PUNCT
ejpam-5970	310	22	they	they	PRON
ejpam-5970	310	23	should	should	AUX
ejpam-5970	310	24	have	have	VERB
ejpam-5970	310	25	distinct	distinct	ADJ
ejpam-5970	310	26	edge	edge	NOUN
ejpam-5970	310	27	weight	weight	NOUN
ejpam-5970	310	28	as	as	ADP
ejpam-5970	310	29	the	the	DET
ejpam-5970	310	30	colors	color	NOUN
ejpam-5970	310	31	.	.	PUNCT
ejpam-5970	311	1	thus	thus	ADV
ejpam-5970	311	2	(	(	PUNCT
ejpam-5970	311	3	a	a	X
ejpam-5970	311	4	,	,	PUNCT
ejpam-5970	311	5	0)-edge	0)-edge	NUM
ejpam-5970	311	6	antimagic	antimagic	ADJ
ejpam-5970	311	7	coloring	coloring	NOUN
ejpam-5970	311	8	of	of	ADP
ejpam-5970	311	9	amal(k1	amal(k1	PROPN
ejpam-5970	311	10	+	+	PROPN
ejpam-5970	311	11	gn	gn	PROPN
ejpam-5970	311	12	,	,	PUNCT
ejpam-5970	311	13	k1,m	k1,m	PROPN
ejpam-5970	311	14	)	)	PUNCT
ejpam-5970	311	15	does	do	AUX
ejpam-5970	311	16	not	not	PART
ejpam-5970	311	17	exist	exist	VERB
ejpam-5970	311	18	.	.	PUNCT
ejpam-5970	312	1	furthermore	furthermore	ADV
ejpam-5970	312	2	,	,	PUNCT
ejpam-5970	312	3	we	we	PRON
ejpam-5970	312	4	will	will	AUX
ejpam-5970	312	5	prove	prove	VERB
ejpam-5970	312	6	the	the	DET
ejpam-5970	312	7	non	non	NOUN
ejpam-5970	312	8	-	-	NOUN
ejpam-5970	312	9	existence	existence	NOUN
ejpam-5970	312	10	of	of	ADP
ejpam-5970	312	11	local	local	ADJ
ejpam-5970	312	12	(	(	PUNCT
ejpam-5970	312	13	a	a	PRON
ejpam-5970	312	14	,	,	PUNCT
ejpam-5970	312	15	2)-edge	2)-edge	NUM
ejpam-5970	312	16	antimagic	antimagic	ADJ
ejpam-5970	312	17	coloring	coloring	NOUN
ejpam-5970	312	18	of	of	ADP
ejpam-5970	312	19	amal(k1+gn	amal(k1+gn	PROPN
ejpam-5970	312	20	,	,	PUNCT
ejpam-5970	312	21	k1,m	k1,m	PROPN
ejpam-5970	312	22	)	)	PUNCT
ejpam-5970	312	23	.	.	PUNCT
ejpam-5970	313	1	since	since	SCONJ
ejpam-5970	313	2	,	,	PUNCT
ejpam-5970	313	3	we	we	PRON
ejpam-5970	313	4	have	have	VERB
ejpam-5970	313	5	f	f	X
ejpam-5970	313	6	:	:	PUNCT
ejpam-5970	313	7	v	v	X
ejpam-5970	313	8	(	(	PUNCT
ejpam-5970	313	9	amal(k1+gn	amal(k1+gn	PROPN
ejpam-5970	313	10	,	,	PUNCT
ejpam-5970	313	11	k1,m))→	k1,m))→	PROPN
ejpam-5970	313	12	{	{	PUNCT
ejpam-5970	313	13	1	1	NUM
ejpam-5970	313	14	,	,	PUNCT
ejpam-5970	313	15	2	2	NUM
ejpam-5970	313	16	,	,	PUNCT
ejpam-5970	313	17	3	3	NUM
ejpam-5970	313	18	,	,	PUNCT
ejpam-5970	313	19	.	.	PUNCT
ejpam-5970	313	20	.	.	PUNCT
ejpam-5970	314	1	.	.	PUNCT
ejpam-5970	315	1	,	,	PUNCT
ejpam-5970	315	2	|v	|v	PROPN
ejpam-5970	315	3	(	(	PUNCT
ejpam-5970	315	4	amal	amal	PROPN
ejpam-5970	315	5	(	(	PUNCT
ejpam-5970	315	6	k1	k1	PROPN
ejpam-5970	315	7	+	+	PROPN
ejpam-5970	315	8	gn	gn	PROPN
ejpam-5970	315	9	,	,	PUNCT
ejpam-5970	315	10	k1,m)|	k1,m)|	PROPN
ejpam-5970	315	11	}	}	PUNCT
ejpam-5970	315	12	as	as	ADP
ejpam-5970	315	13	vertex	vertex	NOUN
ejpam-5970	315	14	labels	label	NOUN
ejpam-5970	315	15	of	of	ADP
ejpam-5970	315	16	amal(k1	amal(k1	NOUN
ejpam-5970	315	17	+	+	PROPN
ejpam-5970	315	18	gn	gn	PROPN
ejpam-5970	315	19	,	,	PUNCT
ejpam-5970	315	20	k1,m	k1,m	PROPN
ejpam-5970	315	21	)	)	PUNCT
ejpam-5970	315	22	.	.	PUNCT
ejpam-5970	316	1	we	we	PRON
ejpam-5970	316	2	have	have	VERB
ejpam-5970	316	3	three	three	NUM
ejpam-5970	316	4	possible	possible	ADJ
ejpam-5970	316	5	labels	label	NOUN
ejpam-5970	316	6	of	of	ADP
ejpam-5970	316	7	the	the	DET
ejpam-5970	316	8	label	label	NOUN
ejpam-5970	316	9	of	of	ADP
ejpam-5970	316	10	f(x	f(x	PROPN
ejpam-5970	316	11	)	)	PUNCT
ejpam-5970	316	12	.	.	PUNCT
ejpam-5970	317	1	first	first	ADJ
ejpam-5970	317	2	f(x	f(x	PROPN
ejpam-5970	317	3	)	)	PUNCT
ejpam-5970	317	4	=	=	SYM
ejpam-5970	318	1	1	1	NUM
ejpam-5970	318	2	,	,	PUNCT
ejpam-5970	318	3	otherwise	otherwise	ADV
ejpam-5970	318	4	f	f	X
ejpam-5970	318	5	:	:	PUNCT
ejpam-5970	318	6	v	v	X
ejpam-5970	318	7	(	(	PUNCT
ejpam-5970	318	8	amal(k1	amal(k1	PROPN
ejpam-5970	318	9	+	+	CCONJ
ejpam-5970	318	10	gn	gn	PROPN
ejpam-5970	318	11	,	,	PUNCT
ejpam-5970	318	12	k1,m)\{x	k1,m)\{x	PROPN
ejpam-5970	318	13	}	}	PUNCT
ejpam-5970	318	14	→	→	SYM
ejpam-5970	318	15	{	{	PUNCT
ejpam-5970	318	16	2	2	NUM
ejpam-5970	318	17	,	,	PUNCT
ejpam-5970	318	18	3	3	NUM
ejpam-5970	318	19	,	,	PUNCT
ejpam-5970	318	20	.	.	PUNCT
ejpam-5970	318	21	.	.	PUNCT
ejpam-5970	318	22	.	.	PUNCT
ejpam-5970	319	1	,	,	PUNCT
ejpam-5970	319	2	|v	|v	PROPN
ejpam-5970	319	3	(	(	PUNCT
ejpam-5970	319	4	amal(k1	amal(k1	PROPN
ejpam-5970	319	5	+	+	PROPN
ejpam-5970	319	6	gn	gn	PROPN
ejpam-5970	319	7	,	,	PUNCT
ejpam-5970	319	8	k1,m)|	k1,m)|	PROPN
ejpam-5970	319	9	}	}	PUNCT
ejpam-5970	319	10	.	.	PUNCT
ejpam-5970	320	1	the	the	DET
ejpam-5970	320	2	edge	edge	NOUN
ejpam-5970	320	3	weight	weight	NOUN
ejpam-5970	320	4	will	will	AUX
ejpam-5970	320	5	be	be	AUX
ejpam-5970	320	6	w	w	ADP
ejpam-5970	320	7	(	(	PUNCT
ejpam-5970	320	8	xxi	xxi	PROPN
ejpam-5970	320	9	,	,	PUNCT
ejpam-5970	320	10	j	j	PROPN
ejpam-5970	320	11	)	)	PUNCT
ejpam-5970	320	12	=	=	PUNCT
ejpam-5970	320	13	{	{	PUNCT
ejpam-5970	320	14	3	3	NUM
ejpam-5970	320	15	,	,	PUNCT
ejpam-5970	320	16	4	4	NUM
ejpam-5970	320	17	,	,	PUNCT
ejpam-5970	320	18	5	5	NUM
ejpam-5970	320	19	,	,	PUNCT
ejpam-5970	320	20	.	.	PUNCT
ejpam-5970	320	21	.	.	PUNCT
ejpam-5970	321	1	.	.	PUNCT
ejpam-5970	322	1	,	,	PUNCT
ejpam-5970	322	2	|v	|v	PROPN
ejpam-5970	322	3	(	(	PUNCT
ejpam-5970	322	4	amal(k1	amal(k1	PROPN
ejpam-5970	322	5	+	+	CCONJ
ejpam-5970	322	6	gn	gn	PROPN
ejpam-5970	322	7	,	,	PUNCT
ejpam-5970	322	8	k1,m))|	k1,m))|	NOUN
ejpam-5970	322	9	+	+	NOUN
ejpam-5970	322	10	1	1	NUM
ejpam-5970	322	11	}	}	PUNCT
ejpam-5970	322	12	.	.	PUNCT
ejpam-5970	323	1	this	this	PRON
ejpam-5970	323	2	form	form	VERB
ejpam-5970	323	3	an	an	DET
ejpam-5970	323	4	arithmetic	arithmetic	ADJ
ejpam-5970	323	5	sequence	sequence	NOUN
ejpam-5970	323	6	of	of	ADP
ejpam-5970	323	7	d	d	PROPN
ejpam-5970	323	8	=	=	SYM
ejpam-5970	323	9	1	1	NUM
ejpam-5970	323	10	,	,	PUNCT
ejpam-5970	323	11	since	since	SCONJ
ejpam-5970	323	12	all	all	PRON
ejpam-5970	323	13	xij	xij	NOUN
ejpam-5970	323	14	connects	connect	VERB
ejpam-5970	323	15	to	to	ADP
ejpam-5970	323	16	x.	x.	NOUN
ejpam-5970	323	17	it	it	PRON
ejpam-5970	323	18	proves	prove	VERB
ejpam-5970	323	19	the	the	DET
ejpam-5970	323	20	non	non	NOUN
ejpam-5970	323	21	-	-	NOUN
ejpam-5970	323	22	existence	existence	NOUN
ejpam-5970	323	23	of	of	ADP
ejpam-5970	323	24	d	d	PROPN
ejpam-5970	323	25	=	=	SYM
ejpam-5970	323	26	2	2	X
ejpam-5970	323	27	.	.	PUNCT
ejpam-5970	324	1	the	the	DET
ejpam-5970	324	2	second	second	ADJ
ejpam-5970	324	3	possibility	possibility	NOUN
ejpam-5970	324	4	is	be	AUX
ejpam-5970	324	5	to	to	PART
ejpam-5970	324	6	assign	assign	VERB
ejpam-5970	324	7	the	the	DET
ejpam-5970	324	8	vertex	vertex	NOUN
ejpam-5970	324	9	labels	label	NOUN
ejpam-5970	324	10	with	with	ADP
ejpam-5970	324	11	2	2	NUM
ejpam-5970	324	12	≤	≤	NUM
ejpam-5970	324	13	f(x	f(x	PROPN
ejpam-5970	324	14	)	)	PUNCT
ejpam-5970	324	15	≤	≤	PUNCT
ejpam-5970	324	16	|v	|v	X
ejpam-5970	324	17	(	(	PUNCT
ejpam-5970	324	18	amal(k1	amal(k1	PROPN
ejpam-5970	324	19	+	+	CCONJ
ejpam-5970	324	20	gn	gn	PROPN
ejpam-5970	324	21	,	,	PUNCT
ejpam-5970	324	22	k1,m))|	k1,m))|	NOUN
ejpam-5970	324	23	−	−	PROPN
ejpam-5970	324	24	1	1	X
ejpam-5970	324	25	.	.	PUNCT
ejpam-5970	324	26	given	give	VERB
ejpam-5970	324	27	that	that	DET
ejpam-5970	324	28	s	s	PART
ejpam-5970	324	29	∈	∈	PROPN
ejpam-5970	324	30	{	{	PUNCT
ejpam-5970	324	31	2	2	NUM
ejpam-5970	324	32	,	,	PUNCT
ejpam-5970	324	33	3	3	NUM
ejpam-5970	324	34	,	,	PUNCT
ejpam-5970	324	35	·	·	PUNCT
ejpam-5970	324	36	·	·	PUNCT
ejpam-5970	324	37	·	·	PUNCT
ejpam-5970	324	38	,	,	PUNCT
ejpam-5970	324	39	|v	|v	PROPN
ejpam-5970	324	40	(	(	PUNCT
ejpam-5970	324	41	amal(k1	amal(k1	PROPN
ejpam-5970	324	42	+	+	CCONJ
ejpam-5970	324	43	gn	gn	PROPN
ejpam-5970	324	44	,	,	PUNCT
ejpam-5970	324	45	k1,m))|	k1,m))|	NOUN
ejpam-5970	324	46	−	−	PROPN
ejpam-5970	324	47	1	1	NUM
ejpam-5970	324	48	}	}	PUNCT
ejpam-5970	324	49	,	,	PUNCT
ejpam-5970	324	50	choose	choose	VERB
ejpam-5970	324	51	any	any	DET
ejpam-5970	324	52	s	s	NOUN
ejpam-5970	324	53	for	for	ADP
ejpam-5970	324	54	f(x	f(x	NOUN
ejpam-5970	324	55	)	)	PUNCT
ejpam-5970	324	56	=	=	VERB
ejpam-5970	325	1	s.	s.	PROPN
ejpam-5970	325	2	the	the	DET
ejpam-5970	325	3	edge	edge	NOUN
ejpam-5970	325	4	weight	weight	NOUN
ejpam-5970	325	5	will	will	AUX
ejpam-5970	325	6	be	be	AUX
ejpam-5970	325	7	w	w	ADP
ejpam-5970	325	8	(	(	PUNCT
ejpam-5970	325	9	xxi	xxi	PROPN
ejpam-5970	325	10	,	,	PUNCT
ejpam-5970	325	11	j	j	PROPN
ejpam-5970	325	12	)	)	PUNCT
ejpam-5970	325	13	=	=	PRON
ejpam-5970	325	14	{	{	PUNCT
ejpam-5970	325	15	·	·	PUNCT
ejpam-5970	325	16	·	·	PUNCT
ejpam-5970	325	17	·	·	PUNCT
ejpam-5970	325	18	,	,	PUNCT
ejpam-5970	325	19	2s−	2s−	NUM
ejpam-5970	325	20	3	3	NUM
ejpam-5970	325	21	,	,	PUNCT
ejpam-5970	325	22	2s−	2s−	NUM
ejpam-5970	325	23	2	2	NUM
ejpam-5970	325	24	,	,	PUNCT
ejpam-5970	325	25	2s−	2s−	NUM
ejpam-5970	325	26	1	1	NUM
ejpam-5970	325	27	,	,	PUNCT
ejpam-5970	325	28	2s+1	2s+1	PROPN
ejpam-5970	325	29	,	,	PUNCT
ejpam-5970	325	30	2s+2	2s+2	PROPN
ejpam-5970	325	31	,	,	PUNCT
ejpam-5970	325	32	2s+3	2s+3	PROPN
ejpam-5970	325	33	,	,	PUNCT
ejpam-5970	325	34	·	·	PUNCT
ejpam-5970	325	35	·	·	PUNCT
ejpam-5970	325	36	·	·	PUNCT
ejpam-5970	325	37	}	}	PUNCT
ejpam-5970	325	38	.	.	PUNCT
ejpam-5970	326	1	this	this	DET
ejpam-5970	326	2	edge	edge	NOUN
ejpam-5970	326	3	weight	weight	NOUN
ejpam-5970	326	4	does	do	AUX
ejpam-5970	326	5	not	not	PART
ejpam-5970	326	6	form	form	VERB
ejpam-5970	326	7	an	an	DET
ejpam-5970	326	8	arithmetic	arithmetic	ADJ
ejpam-5970	326	9	sequence	sequence	NOUN
ejpam-5970	326	10	of	of	ADP
ejpam-5970	326	11	different	different	ADJ
ejpam-5970	326	12	d	d	NOUN
ejpam-5970	326	13	,	,	PUNCT
ejpam-5970	326	14	since	since	SCONJ
ejpam-5970	326	15	even	even	ADV
ejpam-5970	326	16	the	the	DET
ejpam-5970	326	17	different	different	ADJ
ejpam-5970	326	18	of	of	ADP
ejpam-5970	326	19	the	the	DET
ejpam-5970	326	20	left	left	NOUN
ejpam-5970	326	21	and	and	CCONJ
ejpam-5970	326	22	the	the	DET
ejpam-5970	326	23	right	right	ADJ
ejpam-5970	326	24	terms	term	NOUN
ejpam-5970	326	25	shows	show	VERB
ejpam-5970	326	26	d	d	NOUN
ejpam-5970	326	27	=	=	SYM
ejpam-5970	326	28	1	1	NUM
ejpam-5970	326	29	,	,	PUNCT
ejpam-5970	326	30	but	but	CCONJ
ejpam-5970	326	31	the	the	DET
ejpam-5970	326	32	middle	middle	ADJ
ejpam-5970	326	33	terms	term	NOUN
ejpam-5970	326	34	2s+1−	2s+1−	NUM
ejpam-5970	326	35	(	(	PUNCT
ejpam-5970	326	36	2s−	2s−	NUM
ejpam-5970	326	37	1	1	NUM
ejpam-5970	326	38	)	)	PUNCT
ejpam-5970	326	39	=	=	SYM
ejpam-5970	326	40	2	2	X
ejpam-5970	326	41	.	.	PUNCT
ejpam-5970	327	1	it	it	PRON
ejpam-5970	327	2	shows	show	VERB
ejpam-5970	327	3	that	that	SCONJ
ejpam-5970	327	4	for	for	ADP
ejpam-5970	327	5	any	any	DET
ejpam-5970	327	6	f(x	f(x	NOUN
ejpam-5970	327	7	)	)	PUNCT
ejpam-5970	328	1	=	=	SYM
ejpam-5970	328	2	s	s	VERB
ejpam-5970	328	3	where	where	SCONJ
ejpam-5970	328	4	s	s	VERB
ejpam-5970	328	5	∈	∈	PROPN
ejpam-5970	328	6	{	{	PUNCT
ejpam-5970	328	7	2	2	NUM
ejpam-5970	328	8	,	,	PUNCT
ejpam-5970	328	9	3	3	NUM
ejpam-5970	328	10	,	,	PUNCT
ejpam-5970	328	11	·	·	PUNCT
ejpam-5970	328	12	·	·	PUNCT
ejpam-5970	328	13	·	·	PUNCT
ejpam-5970	328	14	,	,	PUNCT
ejpam-5970	328	15	|v	|v	PROPN
ejpam-5970	328	16	(	(	PUNCT
ejpam-5970	328	17	amal(k1+gn	amal(k1+gn	PROPN
ejpam-5970	328	18	,	,	PUNCT
ejpam-5970	328	19	k1,m))|−1	k1,m))|−1	PROPN
ejpam-5970	328	20	}	}	PUNCT
ejpam-5970	328	21	,	,	PUNCT
ejpam-5970	328	22	the	the	DET
ejpam-5970	328	23	local	local	ADJ
ejpam-5970	328	24	(	(	PUNCT
ejpam-5970	328	25	a	a	PRON
ejpam-5970	328	26	,	,	PUNCT
ejpam-5970	328	27	2)edge	2)edge	NUM
ejpam-5970	328	28	antimagic	antimagic	ADJ
ejpam-5970	328	29	coloring	coloring	NOUN
ejpam-5970	328	30	of	of	ADP
ejpam-5970	328	31	amal(k1	amal(k1	PROPN
ejpam-5970	328	32	+	+	PROPN
ejpam-5970	328	33	gn	gn	PROPN
ejpam-5970	328	34	,	,	PUNCT
ejpam-5970	328	35	k1,m	k1,m	PROPN
ejpam-5970	328	36	)	)	PUNCT
ejpam-5970	328	37	does	do	AUX
ejpam-5970	328	38	not	not	PART
ejpam-5970	328	39	exist	exist	VERB
ejpam-5970	328	40	.	.	PUNCT
ejpam-5970	329	1	the	the	DET
ejpam-5970	329	2	third	third	ADJ
ejpam-5970	329	3	,	,	PUNCT
ejpam-5970	329	4	assume	assume	VERB
ejpam-5970	329	5	that	that	SCONJ
ejpam-5970	329	6	f(x	f(x	PROPN
ejpam-5970	329	7	)	)	PUNCT
ejpam-5970	330	1	=	=	SYM
ejpam-5970	330	2	|v	|v	PROPN
ejpam-5970	330	3	(	(	PUNCT
ejpam-5970	330	4	amal(k1	amal(k1	PROPN
ejpam-5970	330	5	+	+	CCONJ
ejpam-5970	330	6	gn	gn	PROPN
ejpam-5970	330	7	,	,	PUNCT
ejpam-5970	330	8	k1,m))|	k1,m))|	PROPN
ejpam-5970	330	9	,	,	PUNCT
ejpam-5970	330	10	the	the	DET
ejpam-5970	330	11	edge	edge	NOUN
ejpam-5970	330	12	weight	weight	NOUN
ejpam-5970	330	13	will	will	AUX
ejpam-5970	330	14	be	be	AUX
ejpam-5970	330	15	w	w	ADP
ejpam-5970	330	16	(	(	PUNCT
ejpam-5970	330	17	xxi	xxi	PROPN
ejpam-5970	330	18	,	,	PUNCT
ejpam-5970	330	19	j	j	PROPN
ejpam-5970	330	20	)	)	PUNCT
ejpam-5970	330	21	=	=	PRON
ejpam-5970	330	22	{	{	PUNCT
ejpam-5970	330	23	|v	|v	X
ejpam-5970	330	24	(	(	PUNCT
ejpam-5970	330	25	amal(k1	amal(k1	PROPN
ejpam-5970	330	26	+	+	CCONJ
ejpam-5970	330	27	gn	gn	PROPN
ejpam-5970	330	28	,	,	PUNCT
ejpam-5970	330	29	k1,m))|	k1,m))|	NOUN
ejpam-5970	330	30	+	+	PUNCT
ejpam-5970	330	31	1	1	NUM
ejpam-5970	330	32	,	,	PUNCT
ejpam-5970	330	33	|v	|v	PROPN
ejpam-5970	330	34	(	(	PUNCT
ejpam-5970	330	35	amal(k1	amal(k1	PROPN
ejpam-5970	330	36	+	+	CCONJ
ejpam-5970	330	37	gn	gn	PROPN
ejpam-5970	330	38	,	,	PUNCT
ejpam-5970	330	39	k1,m))|	k1,m))|	NOUN
ejpam-5970	330	40	+	+	PUNCT
ejpam-5970	330	41	2	2	NUM
ejpam-5970	330	42	,	,	PUNCT
ejpam-5970	330	43	·	·	PUNCT
ejpam-5970	330	44	·	·	PUNCT
ejpam-5970	330	45	·	·	PUNCT
ejpam-5970	330	46	,	,	PUNCT
ejpam-5970	330	47	2|v	2|v	PROPN
ejpam-5970	330	48	(	(	PUNCT
ejpam-5970	330	49	amal(k1	amal(k1	PROPN
ejpam-5970	330	50	+	+	CCONJ
ejpam-5970	330	51	gn	gn	PROPN
ejpam-5970	330	52	,	,	PUNCT
ejpam-5970	330	53	k1,m))|	k1,m))|	NOUN
ejpam-5970	330	54	−	−	NOUN
ejpam-5970	330	55	1	1	NUM
ejpam-5970	330	56	}	}	PUNCT
ejpam-5970	330	57	.	.	PUNCT
ejpam-5970	331	1	this	this	PRON
ejpam-5970	331	2	form	form	VERB
ejpam-5970	331	3	an	an	DET
ejpam-5970	331	4	arithmetic	arithmetic	ADJ
ejpam-5970	331	5	sequence	sequence	NOUN
ejpam-5970	331	6	of	of	ADP
ejpam-5970	331	7	d	d	PROPN
ejpam-5970	331	8	=	=	SYM
ejpam-5970	331	9	1	1	NUM
ejpam-5970	331	10	,	,	PUNCT
ejpam-5970	331	11	since	since	SCONJ
ejpam-5970	331	12	all	all	PRON
ejpam-5970	331	13	xij	xij	NOUN
ejpam-5970	331	14	connects	connect	VERB
ejpam-5970	331	15	to	to	ADP
ejpam-5970	331	16	x.	x.	NOUN
ejpam-5970	331	17	it	it	PRON
ejpam-5970	331	18	proves	prove	VERB
ejpam-5970	331	19	the	the	DET
ejpam-5970	331	20	non	non	NOUN
ejpam-5970	331	21	-	-	NOUN
ejpam-5970	331	22	existence	existence	NOUN
ejpam-5970	331	23	of	of	ADP
ejpam-5970	331	24	d	d	PROPN
ejpam-5970	331	25	=	=	SYM
ejpam-5970	331	26	2	2	NUM
ejpam-5970	331	27	.	.	PUNCT
ejpam-5970	332	1	thus	thus	ADV
ejpam-5970	332	2	(	(	PUNCT
ejpam-5970	332	3	a	a	X
ejpam-5970	332	4	,	,	PUNCT
ejpam-5970	332	5	2)-edge	2)-edge	NUM
ejpam-5970	332	6	antimagic	antimagic	ADJ
ejpam-5970	332	7	coloring	coloring	NOUN
ejpam-5970	332	8	of	of	ADP
ejpam-5970	332	9	amal(k1+gn	amal(k1+gn	PROPN
ejpam-5970	332	10	,	,	PUNCT
ejpam-5970	332	11	k1,m	k1,m	PROPN
ejpam-5970	332	12	)	)	PUNCT
ejpam-5970	332	13	does	do	AUX
ejpam-5970	332	14	not	not	PART
ejpam-5970	332	15	exist	exist	VERB
ejpam-5970	332	16	.	.	PUNCT
ejpam-5970	333	1	it	it	PRON
ejpam-5970	333	2	concludes	conclude	VERB
ejpam-5970	333	3	the	the	DET
ejpam-5970	333	4	proof	proof	NOUN
ejpam-5970	333	5	.	.	PUNCT
ejpam-5970	334	1	3.2	3.2	NUM
ejpam-5970	334	2	.	.	PUNCT
ejpam-5970	335	1	modeling	model	VERB
ejpam-5970	335	2	temporal	temporal	ADJ
ejpam-5970	335	3	-	-	PUNCT
ejpam-5970	335	4	spatial	spatial	ADJ
ejpam-5970	335	5	dependencies	dependency	NOUN
ejpam-5970	335	6	with	with	ADP
ejpam-5970	335	7	graph	graph	NOUN
ejpam-5970	335	8	-	-	PUNCT
ejpam-5970	335	9	based	base	VERB
ejpam-5970	335	10	deep	deep	ADJ
ejpam-5970	335	11	learning	learning	NOUN
ejpam-5970	335	12	in	in	ADP
ejpam-5970	335	13	this	this	DET
ejpam-5970	335	14	work	work	NOUN
ejpam-5970	335	15	,	,	PUNCT
ejpam-5970	335	16	we	we	PRON
ejpam-5970	335	17	propose	propose	VERB
ejpam-5970	335	18	a	a	DET
ejpam-5970	335	19	spatio	spatio	PROPN
ejpam-5970	335	20	-	-	PUNCT
ejpam-5970	335	21	temporal	temporal	ADJ
ejpam-5970	335	22	graph	graph	NOUN
ejpam-5970	335	23	neural	neural	ADJ
ejpam-5970	335	24	network	network	NOUN
ejpam-5970	335	25	(	(	PUNCT
ejpam-5970	335	26	stgnn	stgnn	NOUN
ejpam-5970	335	27	)	)	PUNCT
ejpam-5970	335	28	architecture	architecture	NOUN
ejpam-5970	335	29	tailored	tailor	VERB
ejpam-5970	335	30	to	to	PART
ejpam-5970	335	31	forecast	forecast	VERB
ejpam-5970	335	32	multivariate	multivariate	NOUN
ejpam-5970	335	33	time	time	NOUN
ejpam-5970	335	34	series	series	PROPN
ejpam-5970	335	35	data	datum	NOUN
ejpam-5970	335	36	derived	derive	VERB
ejpam-5970	335	37	from	from	ADP
ejpam-5970	335	38	structured	structured	ADJ
ejpam-5970	335	39	spatial	spatial	ADJ
ejpam-5970	335	40	observations	observation	NOUN
ejpam-5970	335	41	such	such	ADJ
ejpam-5970	335	42	as	as	ADP
ejpam-5970	335	43	nutrient	nutrient	NOUN
ejpam-5970	335	44	content	content	NOUN
ejpam-5970	335	45	(	(	PUNCT
ejpam-5970	335	46	e.g.	e.g.	ADV
ejpam-5970	335	47	,	,	PUNCT
ejpam-5970	335	48	nitrogen	nitrogen	NOUN
ejpam-5970	335	49	,	,	PUNCT
ejpam-5970	335	50	phosphorus	phosphorus	NOUN
ejpam-5970	335	51	,	,	PUNCT
ejpam-5970	335	52	potassium	potassium	NOUN
ejpam-5970	335	53	)	)	PUNCT
ejpam-5970	335	54	.	.	PUNCT
ejpam-5970	336	1	the	the	DET
ejpam-5970	336	2	model	model	NOUN
ejpam-5970	336	3	is	be	AUX
ejpam-5970	336	4	designed	design	VERB
ejpam-5970	336	5	to	to	PART
ejpam-5970	336	6	jointly	jointly	ADV
ejpam-5970	336	7	capture	capture	VERB
ejpam-5970	336	8	spatial	spatial	ADJ
ejpam-5970	336	9	dependencies	dependency	NOUN
ejpam-5970	336	10	across	across	ADP
ejpam-5970	336	11	graph	graph	NOUN
ejpam-5970	336	12	-	-	PUNCT
ejpam-5970	336	13	structured	structure	VERB
ejpam-5970	336	14	nodes	node	NOUN
ejpam-5970	336	15	and	and	CCONJ
ejpam-5970	336	16	temporal	temporal	ADJ
ejpam-5970	336	17	dynamics	dynamic	NOUN
ejpam-5970	336	18	across	across	ADP
ejpam-5970	336	19	multiple	multiple	ADJ
ejpam-5970	336	20	time	time	NOUN
ejpam-5970	336	21	steps	step	NOUN
ejpam-5970	336	22	,	,	PUNCT
ejpam-5970	336	23	as	as	SCONJ
ejpam-5970	336	24	illustrated	illustrate	VERB
ejpam-5970	336	25	in	in	ADP
ejpam-5970	336	26	figure	figure	NOUN
ejpam-5970	336	27	1	1	NUM
ejpam-5970	336	28	and	and	CCONJ
ejpam-5970	336	29	detailed	detailed	ADJ
ejpam-5970	336	30	in	in	ADP
ejpam-5970	336	31	table	table	NOUN
ejpam-5970	336	32	1	1	NUM
ejpam-5970	336	33	.	.	PUNCT
ejpam-5970	337	1	the	the	DET
ejpam-5970	337	2	input	input	NOUN
ejpam-5970	337	3	feature	feature	NOUN
ejpam-5970	337	4	matrix	matrix	NOUN
ejpam-5970	337	5	consists	consist	VERB
ejpam-5970	337	6	of	of	ADP
ejpam-5970	337	7	sequential	sequential	ADJ
ejpam-5970	337	8	observations	observation	NOUN
ejpam-5970	337	9	mapped	map	VERB
ejpam-5970	337	10	onto	onto	ADP
ejpam-5970	337	11	a	a	DET
ejpam-5970	337	12	spatial	spatial	ADJ
ejpam-5970	337	13	graph	graph	NOUN
ejpam-5970	337	14	,	,	PUNCT
ejpam-5970	337	15	where	where	SCONJ
ejpam-5970	337	16	each	each	DET
ejpam-5970	337	17	node	node	NOUN
ejpam-5970	337	18	represents	represent	VERB
ejpam-5970	337	19	a	a	DET
ejpam-5970	337	20	measurement	measurement	NOUN
ejpam-5970	337	21	location	location	NOUN
ejpam-5970	337	22	and	and	CCONJ
ejpam-5970	337	23	edges	edge	NOUN
ejpam-5970	337	24	encode	encode	ADJ
ejpam-5970	337	25	spatial	spatial	ADJ
ejpam-5970	337	26	adjacency	adjacency	NOUN
ejpam-5970	337	27	or	or	CCONJ
ejpam-5970	337	28	correlation	correlation	NOUN
ejpam-5970	337	29	.	.	PUNCT
ejpam-5970	338	1	the	the	DET
ejpam-5970	338	2	preprocessing	preprocessing	NOUN
ejpam-5970	338	3	layer	layer	NOUN
ejpam-5970	338	4	performs	perform	VERB
ejpam-5970	338	5	normalization	normalization	NOUN
ejpam-5970	338	6	and	and	CCONJ
ejpam-5970	338	7	an	an	DET
ejpam-5970	338	8	initial	initial	ADJ
ejpam-5970	338	9	fully	fully	ADV
ejpam-5970	338	10	connected	connect	VERB
ejpam-5970	338	11	transformation	transformation	NOUN
ejpam-5970	338	12	to	to	PART
ejpam-5970	338	13	enhance	enhance	VERB
ejpam-5970	338	14	feature	feature	NOUN
ejpam-5970	338	15	richness	richness	NOUN
ejpam-5970	338	16	.	.	PUNCT
ejpam-5970	339	1	these	these	DET
ejpam-5970	339	2	features	feature	NOUN
ejpam-5970	339	3	are	be	AUX
ejpam-5970	339	4	then	then	ADV
ejpam-5970	339	5	passed	pass	VERB
ejpam-5970	339	6	into	into	ADP
ejpam-5970	339	7	a	a	DET
ejpam-5970	339	8	graph	graph	NOUN
ejpam-5970	339	9	convolutional	convolutional	ADJ
ejpam-5970	339	10	layer	layer	NOUN
ejpam-5970	339	11	,	,	PUNCT
ejpam-5970	339	12	which	which	PRON
ejpam-5970	339	13	extracts	extract	VERB
ejpam-5970	339	14	spatial	spatial	ADJ
ejpam-5970	339	15	relationships	relationship	NOUN
ejpam-5970	339	16	via	via	ADP
ejpam-5970	339	17	topological	topological	ADJ
ejpam-5970	339	18	filtering	filtering	NOUN
ejpam-5970	339	19	using	use	VERB
ejpam-5970	339	20	graph	graph	NOUN
ejpam-5970	339	21	convolutional	convolutional	ADJ
ejpam-5970	339	22	networks	network	NOUN
ejpam-5970	339	23	(	(	PUNCT
ejpam-5970	339	24	gcns	gcns	PROPN
ejpam-5970	339	25	)	)	PUNCT
ejpam-5970	339	26	.	.	PUNCT
ejpam-5970	340	1	a.	a.	PROPN
ejpam-5970	340	2	i.	i.	PROPN
ejpam-5970	340	3	kristiana	kristiana	PROPN
ejpam-5970	340	4	,	,	PUNCT
ejpam-5970	340	5	et	et	PROPN
ejpam-5970	340	6	al	al	PROPN
ejpam-5970	340	7	.	.	PUNCT
ejpam-5970	340	8	/	/	SYM
ejpam-5970	340	9	eur	eur	PROPN
ejpam-5970	340	10	.	.	PUNCT
ejpam-5970	341	1	j.	j.	PROPN
ejpam-5970	341	2	pure	pure	PROPN
ejpam-5970	341	3	appl	appl	PROPN
ejpam-5970	341	4	.	.	PROPN
ejpam-5970	341	5	math	math	PROPN
ejpam-5970	341	6	,	,	PUNCT
ejpam-5970	341	7	18	18	NUM
ejpam-5970	341	8	(	(	PUNCT
ejpam-5970	341	9	3	3	NUM
ejpam-5970	341	10	)	)	PUNCT
ejpam-5970	341	11	(	(	PUNCT
ejpam-5970	341	12	2025	2025	NUM
ejpam-5970	341	13	)	)	PUNCT
ejpam-5970	341	14	,	,	PUNCT
ejpam-5970	341	15	5970	5970	NUM
ejpam-5970	341	16	11	11	NUM
ejpam-5970	341	17	of	of	ADP
ejpam-5970	341	18	18	18	NUM
ejpam-5970	341	19	figure	figure	NOUN
ejpam-5970	341	20	1	1	NUM
ejpam-5970	341	21	:	:	PUNCT
ejpam-5970	341	22	stgnn	stgnn	NOUN
ejpam-5970	341	23	model	model	NOUN
ejpam-5970	341	24	architecture	architecture	NOUN
ejpam-5970	341	25	visualization	visualization	NOUN
ejpam-5970	341	26	.	.	PUNCT
ejpam-5970	342	1	for	for	ADP
ejpam-5970	342	2	temporal	temporal	ADJ
ejpam-5970	342	3	modeling	modeling	NOUN
ejpam-5970	342	4	,	,	PUNCT
ejpam-5970	342	5	the	the	DET
ejpam-5970	342	6	architecture	architecture	NOUN
ejpam-5970	342	7	stacks	stack	VERB
ejpam-5970	342	8	a	a	DET
ejpam-5970	342	9	series	series	NOUN
ejpam-5970	342	10	of	of	ADP
ejpam-5970	342	11	stgnn	stgnn	NOUN
ejpam-5970	342	12	blocks	block	NOUN
ejpam-5970	342	13	,	,	PUNCT
ejpam-5970	342	14	each	each	PRON
ejpam-5970	342	15	combining	combine	VERB
ejpam-5970	342	16	spatial	spatial	ADJ
ejpam-5970	342	17	representations	representation	NOUN
ejpam-5970	342	18	with	with	ADP
ejpam-5970	342	19	gated	gate	VERB
ejpam-5970	342	20	recurrent	recurrent	ADJ
ejpam-5970	342	21	unit	unit	NOUN
ejpam-5970	342	22	(	(	PUNCT
ejpam-5970	342	23	gru)-based	gru)-base	VERB
ejpam-5970	342	24	processing	processing	NOUN
ejpam-5970	342	25	to	to	PART
ejpam-5970	342	26	capture	capture	VERB
ejpam-5970	342	27	sequential	sequential	ADJ
ejpam-5970	342	28	dependencies	dependency	NOUN
ejpam-5970	342	29	.	.	PUNCT
ejpam-5970	343	1	each	each	DET
ejpam-5970	343	2	temporal	temporal	ADJ
ejpam-5970	343	3	slice	slice	NOUN
ejpam-5970	343	4	of	of	ADP
ejpam-5970	343	5	the	the	DET
ejpam-5970	343	6	enhanced	enhance	VERB
ejpam-5970	343	7	hidden	hide	VERB
ejpam-5970	343	8	features	feature	NOUN
ejpam-5970	343	9	is	be	AUX
ejpam-5970	343	10	individually	individually	ADV
ejpam-5970	343	11	passed	pass	VERB
ejpam-5970	343	12	through	through	ADP
ejpam-5970	343	13	an	an	DET
ejpam-5970	343	14	stgnn	stgnn	NOUN
ejpam-5970	343	15	-	-	PUNCT
ejpam-5970	343	16	gru	gru	NOUN
ejpam-5970	343	17	unit	unit	NOUN
ejpam-5970	343	18	,	,	PUNCT
ejpam-5970	343	19	enabling	enable	VERB
ejpam-5970	343	20	the	the	DET
ejpam-5970	343	21	model	model	NOUN
ejpam-5970	343	22	to	to	PART
ejpam-5970	343	23	learn	learn	VERB
ejpam-5970	343	24	both	both	DET
ejpam-5970	343	25	short	short	ADJ
ejpam-5970	343	26	-	-	PUNCT
ejpam-5970	343	27	term	term	NOUN
ejpam-5970	343	28	and	and	CCONJ
ejpam-5970	343	29	long	long	ADJ
ejpam-5970	343	30	-	-	PUNCT
ejpam-5970	343	31	term	term	NOUN
ejpam-5970	343	32	trends	trend	NOUN
ejpam-5970	343	33	.	.	PUNCT
ejpam-5970	344	1	an	an	DET
ejpam-5970	344	2	attention	attention	NOUN
ejpam-5970	344	3	mechanism	mechanism	NOUN
ejpam-5970	344	4	further	far	ADV
ejpam-5970	344	5	refines	refine	VERB
ejpam-5970	344	6	the	the	DET
ejpam-5970	344	7	temporal	temporal	ADJ
ejpam-5970	344	8	features	feature	NOUN
ejpam-5970	344	9	by	by	ADP
ejpam-5970	344	10	weighting	weight	VERB
ejpam-5970	344	11	them	they	PRON
ejpam-5970	344	12	based	base	VERB
ejpam-5970	344	13	on	on	ADP
ejpam-5970	344	14	relevance	relevance	NOUN
ejpam-5970	344	15	to	to	ADP
ejpam-5970	344	16	the	the	DET
ejpam-5970	344	17	forecasting	forecasting	NOUN
ejpam-5970	344	18	task	task	NOUN
ejpam-5970	344	19	.	.	PUNCT
ejpam-5970	345	1	the	the	DET
ejpam-5970	345	2	aggregated	aggregate	VERB
ejpam-5970	345	3	output	output	NOUN
ejpam-5970	345	4	is	be	AUX
ejpam-5970	345	5	then	then	ADV
ejpam-5970	345	6	passed	pass	VERB
ejpam-5970	345	7	through	through	ADP
ejpam-5970	345	8	multiple	multiple	ADJ
ejpam-5970	345	9	fully	fully	ADV
ejpam-5970	345	10	connected	connected	ADJ
ejpam-5970	345	11	layers	layer	NOUN
ejpam-5970	345	12	to	to	PART
ejpam-5970	345	13	project	project	VERB
ejpam-5970	345	14	the	the	DET
ejpam-5970	345	15	learned	learn	VERB
ejpam-5970	345	16	embeddings	embedding	NOUN
ejpam-5970	345	17	into	into	ADP
ejpam-5970	345	18	the	the	DET
ejpam-5970	345	19	prediction	prediction	NOUN
ejpam-5970	345	20	space	space	NOUN
ejpam-5970	345	21	.	.	PUNCT
ejpam-5970	346	1	the	the	DET
ejpam-5970	346	2	final	final	ADJ
ejpam-5970	346	3	prediction	prediction	NOUN
ejpam-5970	346	4	layer	layer	NOUN
ejpam-5970	346	5	outputs	output	VERB
ejpam-5970	346	6	three	three	NUM
ejpam-5970	346	7	continuous	continuous	ADJ
ejpam-5970	346	8	values	value	NOUN
ejpam-5970	346	9	per	per	ADP
ejpam-5970	346	10	node	node	NOUN
ejpam-5970	346	11	,	,	PUNCT
ejpam-5970	346	12	corresponding	correspond	VERB
ejpam-5970	346	13	to	to	PART
ejpam-5970	346	14	target	target	VERB
ejpam-5970	346	15	variables	variable	NOUN
ejpam-5970	346	16	(	(	PUNCT
ejpam-5970	346	17	e.g.	e.g.	ADV
ejpam-5970	346	18	,	,	PUNCT
ejpam-5970	346	19	discharge	discharge	NOUN
ejpam-5970	346	20	,	,	PUNCT
ejpam-5970	346	21	depth	depth	NOUN
ejpam-5970	346	22	,	,	PUNCT
ejpam-5970	346	23	and	and	CCONJ
ejpam-5970	346	24	width	width	ADJ
ejpam-5970	346	25	)	)	PUNCT
ejpam-5970	346	26	.	.	PUNCT
ejpam-5970	347	1	the	the	DET
ejpam-5970	347	2	model	model	NOUN
ejpam-5970	347	3	is	be	AUX
ejpam-5970	347	4	trained	train	VERB
ejpam-5970	347	5	using	use	VERB
ejpam-5970	347	6	the	the	DET
ejpam-5970	347	7	adam	adam	PROPN
ejpam-5970	347	8	optimizer	optimizer	NOUN
ejpam-5970	347	9	for	for	ADP
ejpam-5970	347	10	200	200	NUM
ejpam-5970	347	11	epochs	epoch	NOUN
ejpam-5970	347	12	,	,	PUNCT
ejpam-5970	347	13	with	with	ADP
ejpam-5970	347	14	a	a	DET
ejpam-5970	347	15	learning	learn	VERB
ejpam-5970	347	16	rate	rate	NOUN
ejpam-5970	347	17	of	of	ADP
ejpam-5970	347	18	0.01	0.01	NUM
ejpam-5970	347	19	,	,	PUNCT
ejpam-5970	347	20	and	and	CCONJ
ejpam-5970	347	21	optimized	optimize	VERB
ejpam-5970	347	22	using	using	NOUN
ejpam-5970	347	23	mean	mean	NOUN
ejpam-5970	347	24	squared	square	VERB
ejpam-5970	347	25	error	error	NOUN
ejpam-5970	347	26	(	(	PUNCT
ejpam-5970	347	27	mse	mse	NOUN
ejpam-5970	347	28	)	)	PUNCT
ejpam-5970	347	29	loss	loss	NOUN
ejpam-5970	347	30	.	.	PUNCT
ejpam-5970	348	1	the	the	DET
ejpam-5970	348	2	use	use	NOUN
ejpam-5970	348	3	of	of	ADP
ejpam-5970	348	4	optional	optional	ADJ
ejpam-5970	348	5	components	component	NOUN
ejpam-5970	348	6	such	such	ADJ
ejpam-5970	348	7	as	as	ADP
ejpam-5970	348	8	dilated	dilate	VERB
ejpam-5970	348	9	convolution	convolution	NOUN
ejpam-5970	348	10	enhances	enhance	VERB
ejpam-5970	348	11	the	the	DET
ejpam-5970	348	12	temporal	temporal	ADJ
ejpam-5970	348	13	receptive	receptive	ADJ
ejpam-5970	348	14	field	field	NOUN
ejpam-5970	348	15	,	,	PUNCT
ejpam-5970	348	16	while	while	SCONJ
ejpam-5970	348	17	regularization	regularization	NOUN
ejpam-5970	348	18	strategies	strategy	NOUN
ejpam-5970	348	19	(	(	PUNCT
ejpam-5970	348	20	e.g.	e.g.	ADV
ejpam-5970	348	21	,	,	PUNCT
ejpam-5970	348	22	dropout	dropout	NOUN
ejpam-5970	348	23	)	)	PUNCT
ejpam-5970	348	24	can	can	AUX
ejpam-5970	348	25	be	be	AUX
ejpam-5970	348	26	applied	apply	VERB
ejpam-5970	348	27	for	for	ADP
ejpam-5970	348	28	improved	improved	ADJ
ejpam-5970	348	29	generalization	generalization	NOUN
ejpam-5970	348	30	.	.	PUNCT
ejpam-5970	349	1	overall	overall	ADV
ejpam-5970	349	2	,	,	PUNCT
ejpam-5970	349	3	the	the	DET
ejpam-5970	349	4	architecture	architecture	NOUN
ejpam-5970	349	5	demonstrates	demonstrate	VERB
ejpam-5970	349	6	strong	strong	ADJ
ejpam-5970	349	7	performance	performance	NOUN
ejpam-5970	349	8	in	in	ADP
ejpam-5970	349	9	learning	learn	VERB
ejpam-5970	349	10	spatial	spatial	ADJ
ejpam-5970	349	11	-	-	PUNCT
ejpam-5970	349	12	temporal	temporal	ADJ
ejpam-5970	349	13	patterns	pattern	NOUN
ejpam-5970	349	14	from	from	ADP
ejpam-5970	349	15	graph	graph	NOUN
ejpam-5970	349	16	-	-	PUNCT
ejpam-5970	349	17	structured	structure	VERB
ejpam-5970	349	18	data	datum	NOUN
ejpam-5970	349	19	.	.	PUNCT
ejpam-5970	350	1	3.3	3.3	NUM
ejpam-5970	350	2	.	.	PUNCT
ejpam-5970	351	1	spatio	spatio	NOUN
ejpam-5970	351	2	-	-	PUNCT
ejpam-5970	351	3	temporal	temporal	ADJ
ejpam-5970	351	4	graph	graph	NOUN
ejpam-5970	351	5	encoding	encode	VERB
ejpam-5970	351	6	for	for	ADP
ejpam-5970	351	7	nutrient	nutrient	NOUN
ejpam-5970	351	8	forecasting	forecast	VERB
ejpam-5970	351	9	the	the	DET
ejpam-5970	351	10	next	next	ADJ
ejpam-5970	351	11	research	research	NOUN
ejpam-5970	351	12	result	result	NOUN
ejpam-5970	351	13	is	be	AUX
ejpam-5970	351	14	the	the	DET
ejpam-5970	351	15	implementation	implementation	NOUN
ejpam-5970	351	16	of	of	ADP
ejpam-5970	351	17	the	the	DET
ejpam-5970	351	18	χle(a	χle(a	PROPN
ejpam-5970	351	19	,	,	PUNCT
ejpam-5970	351	20	d	d	NOUN
ejpam-5970	351	21	)	)	PUNCT
ejpam-5970	351	22	coloring	color	VERB
ejpam-5970	351	23	scheme	scheme	NOUN
ejpam-5970	351	24	on	on	ADP
ejpam-5970	351	25	precision	precision	NOUN
ejpam-5970	351	26	agriculture	agriculture	NOUN
ejpam-5970	351	27	.	.	PUNCT
ejpam-5970	352	1	from	from	ADP
ejpam-5970	352	2	now	now	ADV
ejpam-5970	352	3	on	on	ADV
ejpam-5970	352	4	,	,	PUNCT
ejpam-5970	352	5	we	we	PRON
ejpam-5970	352	6	will	will	AUX
ejpam-5970	352	7	do	do	VERB
ejpam-5970	352	8	time	time	NOUN
ejpam-5970	352	9	series	series	PROPN
ejpam-5970	352	10	forecasting	forecasting	NOUN
ejpam-5970	352	11	on	on	ADP
ejpam-5970	352	12	precision	precision	NOUN
ejpam-5970	352	13	agriculture	agriculture	NOUN
ejpam-5970	352	14	soil	soil	NOUN
ejpam-5970	352	15	nutrient	nutrient	NOUN
ejpam-5970	352	16	dataset	dataset	NOUN
ejpam-5970	352	17	,	,	PUNCT
ejpam-5970	352	18	namely	namely	ADV
ejpam-5970	352	19	nitrogen	nitrogen	NOUN
ejpam-5970	352	20	,	,	PUNCT
ejpam-5970	352	21	phosporus	phosporus	NOUN
ejpam-5970	352	22	,	,	PUNCT
ejpam-5970	352	23	and	and	CCONJ
ejpam-5970	352	24	potassium	potassium	NOUN
ejpam-5970	352	25	.	.	PUNCT
ejpam-5970	353	1	the	the	DET
ejpam-5970	353	2	dataset	dataset	NOUN
ejpam-5970	353	3	is	be	AUX
ejpam-5970	353	4	obtained	obtain	VERB
ejpam-5970	353	5	from	from	ADP
ejpam-5970	353	6	the	the	DET
ejpam-5970	353	7	simulation	simulation	NOUN
ejpam-5970	353	8	of	of	ADP
ejpam-5970	353	9	placing	place	VERB
ejpam-5970	353	10	the	the	DET
ejpam-5970	353	11	capacitive	capacitive	ADJ
ejpam-5970	353	12	sensor	sensor	NOUN
ejpam-5970	353	13	for	for	ADP
ejpam-5970	353	14	soil	soil	NOUN
ejpam-5970	353	15	nutrients	nutrient	NOUN
ejpam-5970	353	16	.	.	PUNCT
ejpam-5970	354	1	the	the	DET
ejpam-5970	354	2	placement	placement	NOUN
ejpam-5970	354	3	of	of	ADP
ejpam-5970	354	4	those	those	DET
ejpam-5970	354	5	sensors	sensor	NOUN
ejpam-5970	354	6	respects	respect	NOUN
ejpam-5970	354	7	to	to	ADP
ejpam-5970	354	8	the	the	DET
ejpam-5970	354	9	planting	planting	NOUN
ejpam-5970	354	10	topology	topology	NOUN
ejpam-5970	354	11	derived	derive	VERB
ejpam-5970	354	12	from	from	ADP
ejpam-5970	354	13	theorem	theorem	ADJ
ejpam-5970	354	14	1	1	NUM
ejpam-5970	354	15	,	,	PUNCT
ejpam-5970	354	16	and	and	CCONJ
ejpam-5970	354	17	the	the	DET
ejpam-5970	354	18	number	number	NOUN
ejpam-5970	354	19	of	of	ADP
ejpam-5970	354	20	soil	soil	NOUN
ejpam-5970	354	21	nutrient	nutrient	NOUN
ejpam-5970	354	22	sensors	sensor	NOUN
ejpam-5970	354	23	is	be	AUX
ejpam-5970	354	24	equalto	equalto	NOUN
ejpam-5970	354	25	the	the	DET
ejpam-5970	354	26	obtained	obtain	VERB
ejpam-5970	354	27	lea(a	lea(a	PROPN
ejpam-5970	354	28	,	,	PUNCT
ejpam-5970	354	29	d	d	NOUN
ejpam-5970	354	30	)	)	PUNCT
ejpam-5970	354	31	chromatic	chromatic	ADJ
ejpam-5970	354	32	number	number	NOUN
ejpam-5970	354	33	χle(a	χle(a	PROPN
ejpam-5970	354	34	,	,	PUNCT
ejpam-5970	354	35	d)(g	d)(g	NOUN
ejpam-5970	354	36	)	)	PUNCT
ejpam-5970	354	37	.	.	PUNCT
ejpam-5970	355	1	the	the	DET
ejpam-5970	355	2	soil	soil	NOUN
ejpam-5970	355	3	nutrient	nutrient	NOUN
ejpam-5970	355	4	dataset	dataset	VERB
ejpam-5970	355	5	that	that	SCONJ
ejpam-5970	355	6	we	we	PRON
ejpam-5970	355	7	obtained	obtain	VERB
ejpam-5970	355	8	is	be	AUX
ejpam-5970	355	9	subsequently	subsequently	ADV
ejpam-5970	355	10	used	use	VERB
ejpam-5970	355	11	as	as	ADP
ejpam-5970	355	12	the	the	DET
ejpam-5970	355	13	input	input	NOUN
ejpam-5970	355	14	for	for	ADP
ejpam-5970	355	15	training	training	NOUN
ejpam-5970	355	16	a.	a.	PROPN
ejpam-5970	355	17	i.	i.	PROPN
ejpam-5970	355	18	kristiana	kristiana	PROPN
ejpam-5970	355	19	,	,	PUNCT
ejpam-5970	355	20	et	et	PROPN
ejpam-5970	355	21	al	al	PROPN
ejpam-5970	355	22	.	.	PUNCT
ejpam-5970	355	23	/	/	SYM
ejpam-5970	355	24	eur	eur	PROPN
ejpam-5970	355	25	.	.	PUNCT
ejpam-5970	356	1	j.	j.	PROPN
ejpam-5970	356	2	pure	pure	PROPN
ejpam-5970	356	3	appl	appl	PROPN
ejpam-5970	356	4	.	.	PROPN
ejpam-5970	356	5	math	math	PROPN
ejpam-5970	356	6	,	,	PUNCT
ejpam-5970	356	7	18	18	NUM
ejpam-5970	356	8	(	(	PUNCT
ejpam-5970	356	9	3	3	NUM
ejpam-5970	356	10	)	)	PUNCT
ejpam-5970	356	11	(	(	PUNCT
ejpam-5970	356	12	2025	2025	NUM
ejpam-5970	356	13	)	)	PUNCT
ejpam-5970	356	14	,	,	PUNCT
ejpam-5970	356	15	5970	5970	NUM
ejpam-5970	356	16	12	12	NUM
ejpam-5970	356	17	of	of	ADP
ejpam-5970	356	18	18	18	NUM
ejpam-5970	356	19	table	table	NOUN
ejpam-5970	356	20	1	1	NUM
ejpam-5970	356	21	:	:	PUNCT
ejpam-5970	356	22	architectural	architectural	ADJ
ejpam-5970	356	23	components	component	NOUN
ejpam-5970	356	24	and	and	CCONJ
ejpam-5970	356	25	parameters	parameter	NOUN
ejpam-5970	356	26	of	of	ADP
ejpam-5970	356	27	the	the	DET
ejpam-5970	356	28	proposed	propose	VERB
ejpam-5970	356	29	stgnn	stgnn	PROPN
ejpam-5970	356	30	model	model	PROPN
ejpam-5970	356	31	no	no	PROPN
ejpam-5970	356	32	.	.	PUNCT
ejpam-5970	357	1	component	component	NOUN
ejpam-5970	357	2	description	description	NOUN
ejpam-5970	357	3	1	1	NUM
ejpam-5970	357	4	input	input	NOUN
ejpam-5970	357	5	spatial	spatial	ADJ
ejpam-5970	357	6	graph	graph	NOUN
ejpam-5970	357	7	represents	represent	VERB
ejpam-5970	357	8	spatial	spatial	ADJ
ejpam-5970	357	9	structure	structure	NOUN
ejpam-5970	357	10	over	over	ADP
ejpam-5970	357	11	time	time	NOUN
ejpam-5970	357	12	.	.	PUNCT
ejpam-5970	358	1	nodes	node	NOUN
ejpam-5970	358	2	correspond	correspond	VERB
ejpam-5970	358	3	to	to	ADP
ejpam-5970	358	4	measurement	measurement	NOUN
ejpam-5970	358	5	units	unit	NOUN
ejpam-5970	358	6	;	;	PUNCT
ejpam-5970	358	7	edges	edge	NOUN
ejpam-5970	358	8	reflect	reflect	VERB
ejpam-5970	358	9	proximity	proximity	NOUN
ejpam-5970	358	10	or	or	CCONJ
ejpam-5970	358	11	correlations	correlation	NOUN
ejpam-5970	358	12	.	.	PUNCT
ejpam-5970	359	1	3	3	NUM
ejpam-5970	359	2	preprocessing	preprocessing	NOUN
ejpam-5970	359	3	layer	layer	NOUN
ejpam-5970	359	4	applies	apply	VERB
ejpam-5970	359	5	normalization	normalization	NOUN
ejpam-5970	359	6	and	and	CCONJ
ejpam-5970	359	7	temporal	temporal	ADJ
ejpam-5970	359	8	alignment	alignment	NOUN
ejpam-5970	359	9	.	.	PUNCT
ejpam-5970	360	1	initial	initial	ADJ
ejpam-5970	360	2	fully	fully	ADV
ejpam-5970	360	3	connected	connect	VERB
ejpam-5970	360	4	(	(	PUNCT
ejpam-5970	360	5	fc	fc	INTJ
ejpam-5970	360	6	)	)	PUNCT
ejpam-5970	360	7	transformation	transformation	NOUN
ejpam-5970	360	8	to	to	PART
ejpam-5970	360	9	increase	increase	VERB
ejpam-5970	360	10	feature	feature	NOUN
ejpam-5970	360	11	richness	richness	NOUN
ejpam-5970	360	12	.	.	PUNCT
ejpam-5970	361	1	4	4	NUM
ejpam-5970	361	2	convolutional	convolutional	ADJ
ejpam-5970	361	3	layer	layer	NOUN
ejpam-5970	361	4	applies	apply	VERB
ejpam-5970	361	5	gcn	gcn	NOUN
ejpam-5970	361	6	operation	operation	NOUN
ejpam-5970	361	7	over	over	ADP
ejpam-5970	361	8	the	the	DET
ejpam-5970	361	9	input	input	NOUN
ejpam-5970	361	10	spatial	spatial	ADJ
ejpam-5970	361	11	graph	graph	NOUN
ejpam-5970	361	12	to	to	PART
ejpam-5970	361	13	learn	learn	VERB
ejpam-5970	361	14	spatial	spatial	ADJ
ejpam-5970	361	15	dependencies	dependency	NOUN
ejpam-5970	361	16	from	from	ADP
ejpam-5970	361	17	graph	graph	NOUN
ejpam-5970	361	18	topology	topology	NOUN
ejpam-5970	361	19	.	.	PUNCT
ejpam-5970	362	1	5	5	NUM
ejpam-5970	362	2	stgnn	stgnn	NOUN
ejpam-5970	362	3	block	block	NOUN
ejpam-5970	362	4	(	(	PUNCT
ejpam-5970	362	5	temporal	temporal	ADJ
ejpam-5970	362	6	stack	stack	NOUN
ejpam-5970	362	7	)	)	PUNCT
ejpam-5970	362	8	sequence	sequence	NOUN
ejpam-5970	362	9	of	of	ADP
ejpam-5970	362	10	stgnn	stgnn	NOUN
ejpam-5970	362	11	-	-	PUNCT
ejpam-5970	362	12	gru	gru	NOUN
ejpam-5970	362	13	units	unit	NOUN
ejpam-5970	362	14	processing	process	VERB
ejpam-5970	362	15	temporal	temporal	ADJ
ejpam-5970	362	16	slices	slice	NOUN
ejpam-5970	362	17	of	of	ADP
ejpam-5970	362	18	graph	graph	NOUN
ejpam-5970	362	19	-	-	PUNCT
ejpam-5970	362	20	encoded	encode	VERB
ejpam-5970	362	21	data	datum	NOUN
ejpam-5970	362	22	(	(	PUNCT
ejpam-5970	362	23	e.g.	e.g.	ADV
ejpam-5970	362	24	,	,	PUNCT
ejpam-5970	362	25	xθ−t+3	xθ−t+3	VERB
ejpam-5970	362	26	to	to	PART
ejpam-5970	362	27	xθ	xθ	PROPN
ejpam-5970	362	28	)	)	PUNCT
ejpam-5970	362	29	.	.	PUNCT
ejpam-5970	362	30	captures	capture	VERB
ejpam-5970	362	31	temporal	temporal	ADJ
ejpam-5970	362	32	dynamics	dynamic	NOUN
ejpam-5970	362	33	.	.	PUNCT
ejpam-5970	363	1	6	6	NUM
ejpam-5970	363	2	attention	attention	NOUN
ejpam-5970	363	3	mechanism	mechanism	NOUN
ejpam-5970	363	4	includes	include	VERB
ejpam-5970	363	5	dense	dense	ADJ
ejpam-5970	363	6	projections	projection	NOUN
ejpam-5970	363	7	and	and	CCONJ
ejpam-5970	363	8	softmax	softmax	NOUN
ejpam-5970	363	9	weighting	weight	VERB
ejpam-5970	363	10	to	to	PART
ejpam-5970	363	11	emphasize	emphasize	VERB
ejpam-5970	363	12	relevant	relevant	ADJ
ejpam-5970	363	13	temporal	temporal	ADJ
ejpam-5970	363	14	features	feature	NOUN
ejpam-5970	363	15	.	.	PUNCT
ejpam-5970	364	1	dot	dot	NOUN
ejpam-5970	364	2	product	product	NOUN
ejpam-5970	364	3	used	use	VERB
ejpam-5970	364	4	to	to	PART
ejpam-5970	364	5	compute	compute	VERB
ejpam-5970	364	6	weighted	weighted	ADJ
ejpam-5970	364	7	representation	representation	NOUN
ejpam-5970	364	8	.	.	PUNCT
ejpam-5970	365	1	7	7	NUM
ejpam-5970	365	2	dilated	dilated	ADJ
ejpam-5970	365	3	convolution	convolution	NOUN
ejpam-5970	365	4	(	(	PUNCT
ejpam-5970	365	5	optional	optional	ADJ
ejpam-5970	365	6	)	)	PUNCT
ejpam-5970	365	7	extracts	extract	VERB
ejpam-5970	365	8	multi	multi	ADJ
ejpam-5970	365	9	-	-	ADJ
ejpam-5970	365	10	scale	scale	ADJ
ejpam-5970	365	11	temporal	temporal	ADJ
ejpam-5970	365	12	features	feature	NOUN
ejpam-5970	365	13	through	through	ADP
ejpam-5970	365	14	dilated	dilated	ADJ
ejpam-5970	365	15	convolutions	convolution	NOUN
ejpam-5970	365	16	across	across	ADP
ejpam-5970	365	17	timedelayed	timedelayed	ADJ
ejpam-5970	365	18	embeddings	embedding	NOUN
ejpam-5970	365	19	.	.	PUNCT
ejpam-5970	366	1	enhances	enhance	VERB
ejpam-5970	366	2	long	long	ADJ
ejpam-5970	366	3	-	-	PUNCT
ejpam-5970	366	4	range	range	NOUN
ejpam-5970	366	5	dependencies	dependency	NOUN
ejpam-5970	366	6	.	.	PUNCT
ejpam-5970	367	1	8	8	NUM
ejpam-5970	367	2	fully	fully	ADV
ejpam-5970	367	3	connected	connect	VERB
ejpam-5970	367	4	layers	layer	NOUN
ejpam-5970	367	5	maps	map	VERB
ejpam-5970	367	6	temporal	temporal	ADJ
ejpam-5970	367	7	-	-	PUNCT
ejpam-5970	367	8	spatial	spatial	ADJ
ejpam-5970	367	9	feature	feature	NOUN
ejpam-5970	367	10	embeddings	embedding	NOUN
ejpam-5970	367	11	to	to	PART
ejpam-5970	367	12	prediction	prediction	VERB
ejpam-5970	367	13	space	space	NOUN
ejpam-5970	367	14	via	via	ADP
ejpam-5970	367	15	dense	dense	ADJ
ejpam-5970	367	16	layers	layer	NOUN
ejpam-5970	367	17	.	.	PUNCT
ejpam-5970	368	1	usually	usually	ADV
ejpam-5970	368	2	two	two	NUM
ejpam-5970	368	3	stacked	stack	VERB
ejpam-5970	368	4	layers	layer	NOUN
ejpam-5970	368	5	.	.	PUNCT
ejpam-5970	369	1	9	9	NUM
ejpam-5970	369	2	prediction	prediction	NOUN
ejpam-5970	369	3	layer	layer	NOUN
ejpam-5970	369	4	outputs	output	VERB
ejpam-5970	369	5	3	3	NUM
ejpam-5970	369	6	-	-	PUNCT
ejpam-5970	369	7	dimensional	dimensional	ADJ
ejpam-5970	369	8	predictions	prediction	NOUN
ejpam-5970	369	9	(	(	PUNCT
ejpam-5970	369	10	e.g.	e.g.	ADV
ejpam-5970	369	11	,	,	PUNCT
ejpam-5970	369	12	nitrogen	nitrogen	NOUN
ejpam-5970	369	13	(	(	PUNCT
ejpam-5970	369	14	n	n	CCONJ
ejpam-5970	369	15	)	)	PUNCT
ejpam-5970	369	16	,	,	PUNCT
ejpam-5970	369	17	phosporus	phosporus	NOUN
ejpam-5970	369	18	(	(	PUNCT
ejpam-5970	369	19	p	p	NOUN
ejpam-5970	369	20	)	)	PUNCT
ejpam-5970	369	21	,	,	PUNCT
ejpam-5970	369	22	and	and	CCONJ
ejpam-5970	369	23	potassium	potassium	NOUN
ejpam-5970	369	24	(	(	PUNCT
ejpam-5970	369	25	k	k	NOUN
ejpam-5970	369	26	)	)	PUNCT
ejpam-5970	369	27	per	per	ADP
ejpam-5970	369	28	node	node	NOUN
ejpam-5970	369	29	per	per	ADP
ejpam-5970	369	30	time	time	NOUN
ejpam-5970	369	31	step	step	NOUN
ejpam-5970	369	32	.	.	PUNCT
ejpam-5970	370	1	the	the	DET
ejpam-5970	370	2	stgnn	stgnn	PROPN
ejpam-5970	370	3	model	model	PROPN
ejpam-5970	370	4	.	.	PUNCT
ejpam-5970	371	1	we	we	PRON
ejpam-5970	371	2	analyze	analyze	VERB
ejpam-5970	371	3	the	the	DET
ejpam-5970	371	4	npk	npk	NOUN
ejpam-5970	371	5	nutrient	nutrient	NOUN
ejpam-5970	371	6	fertilization	fertilization	NOUN
ejpam-5970	371	7	levels	level	NOUN
ejpam-5970	371	8	of	of	ADP
ejpam-5970	371	9	plants	plant	NOUN
ejpam-5970	371	10	across	across	ADP
ejpam-5970	371	11	twenty	twenty	NUM
ejpam-5970	371	12	-	-	PUNCT
ejpam-5970	371	13	three	three	NUM
ejpam-5970	371	14	plantations	plantation	NOUN
ejpam-5970	371	15	.	.	PUNCT
ejpam-5970	372	1	first	first	ADV
ejpam-5970	372	2	,	,	PUNCT
ejpam-5970	372	3	we	we	PRON
ejpam-5970	372	4	perform	perform	VERB
ejpam-5970	372	5	the	the	DET
ejpam-5970	372	6	vertex	vertex	NOUN
ejpam-5970	372	7	embedding	embed	VERB
ejpam-5970	372	8	process	process	NOUN
ejpam-5970	372	9	using	use	VERB
ejpam-5970	372	10	a	a	DET
ejpam-5970	372	11	singlelayer	singlelayer	NOUN
ejpam-5970	372	12	stgnn	stgnn	NOUN
ejpam-5970	372	13	applied	apply	VERB
ejpam-5970	372	14	to	to	ADP
ejpam-5970	372	15	a	a	DET
ejpam-5970	372	16	graph	graph	NOUN
ejpam-5970	372	17	with	with	ADP
ejpam-5970	372	18	three	three	NUM
ejpam-5970	372	19	feature	feature	NOUN
ejpam-5970	372	20	variables	variable	NOUN
ejpam-5970	372	21	observed	observe	VERB
ejpam-5970	372	22	over	over	ADP
ejpam-5970	372	23	37	37	NUM
ejpam-5970	372	24	consecutive	consecutive	ADJ
ejpam-5970	372	25	days	day	NOUN
ejpam-5970	372	26	.	.	PUNCT
ejpam-5970	373	1	in	in	ADP
ejpam-5970	373	2	total	total	NOUN
ejpam-5970	373	3	,	,	PUNCT
ejpam-5970	373	4	the	the	DET
ejpam-5970	373	5	dataset	dataset	NOUN
ejpam-5970	373	6	consists	consist	VERB
ejpam-5970	373	7	of	of	ADP
ejpam-5970	373	8	23	23	NUM
ejpam-5970	373	9	×	×	NOUN
ejpam-5970	373	10	3	3	NUM
ejpam-5970	373	11	×	×	NOUN
ejpam-5970	373	12	37	37	NUM
ejpam-5970	373	13	=	=	SYM
ejpam-5970	373	14	2,553	2,553	NUM
ejpam-5970	373	15	entries	entry	NOUN
ejpam-5970	373	16	,	,	PUNCT
ejpam-5970	373	17	corresponding	correspond	VERB
ejpam-5970	373	18	to	to	ADP
ejpam-5970	373	19	23	23	NUM
ejpam-5970	373	20	plantation	plantation	NOUN
ejpam-5970	373	21	nodes	node	NOUN
ejpam-5970	373	22	,	,	PUNCT
ejpam-5970	373	23	3	3	NUM
ejpam-5970	373	24	soil	soil	NOUN
ejpam-5970	373	25	nutrient	nutrient	NOUN
ejpam-5970	373	26	features	feature	VERB
ejpam-5970	373	27	,	,	PUNCT
ejpam-5970	373	28	and	and	CCONJ
ejpam-5970	373	29	37	37	NUM
ejpam-5970	373	30	time	time	NOUN
ejpam-5970	373	31	steps	step	NOUN
ejpam-5970	373	32	.	.	PUNCT
ejpam-5970	374	1	in	in	ADP
ejpam-5970	374	2	accordance	accordance	NOUN
ejpam-5970	374	3	with	with	ADP
ejpam-5970	374	4	the	the	DET
ejpam-5970	374	5	algorithm	algorithm	NOUN
ejpam-5970	374	6	described	describe	VERB
ejpam-5970	374	7	previously	previously	ADV
ejpam-5970	374	8	,	,	PUNCT
ejpam-5970	374	9	we	we	PRON
ejpam-5970	374	10	conduct	conduct	VERB
ejpam-5970	374	11	node	node	NOUN
ejpam-5970	374	12	embedding	embed	VERB
ejpam-5970	374	13	across	across	ADP
ejpam-5970	374	14	all	all	PRON
ejpam-5970	374	15	twenty	twenty	NUM
ejpam-5970	374	16	-	-	PUNCT
ejpam-5970	374	17	three	three	NUM
ejpam-5970	374	18	plantation	plantation	NOUN
ejpam-5970	374	19	nodes	nod	VERB
ejpam-5970	374	20	.	.	PUNCT
ejpam-5970	375	1	this	this	DET
ejpam-5970	375	2	embedding	embed	VERB
ejpam-5970	375	3	process	process	NOUN
ejpam-5970	375	4	transforms	transform	VERB
ejpam-5970	375	5	the	the	DET
ejpam-5970	375	6	original	original	ADJ
ejpam-5970	375	7	three	three	NUM
ejpam-5970	375	8	-	-	PUNCT
ejpam-5970	375	9	dimensional	dimensional	ADJ
ejpam-5970	375	10	feature	feature	NOUN
ejpam-5970	375	11	vector	vector	NOUN
ejpam-5970	375	12	into	into	ADP
ejpam-5970	375	13	a	a	DET
ejpam-5970	375	14	one	one	NUM
ejpam-5970	375	15	-	-	PUNCT
ejpam-5970	375	16	dimensional	dimensional	ADJ
ejpam-5970	375	17	representation	representation	NOUN
ejpam-5970	375	18	using	use	VERB
ejpam-5970	375	19	message	message	NOUN
ejpam-5970	375	20	passing	passing	NOUN
ejpam-5970	375	21	and	and	CCONJ
ejpam-5970	375	22	aggregation	aggregation	NOUN
ejpam-5970	375	23	techniques	technique	NOUN
ejpam-5970	375	24	.	.	PUNCT
ejpam-5970	376	1	during	during	ADP
ejpam-5970	376	2	the	the	DET
ejpam-5970	376	3	message	message	NOUN
ejpam-5970	376	4	passing	pass	VERB
ejpam-5970	376	5	stage	stage	NOUN
ejpam-5970	376	6	,	,	PUNCT
ejpam-5970	376	7	each	each	DET
ejpam-5970	376	8	node	node	NOUN
ejpam-5970	376	9	is	be	AUX
ejpam-5970	376	10	assumed	assume	VERB
ejpam-5970	376	11	to	to	PART
ejpam-5970	376	12	contain	contain	VERB
ejpam-5970	376	13	relevant	relevant	ADJ
ejpam-5970	376	14	information	information	NOUN
ejpam-5970	376	15	,	,	PUNCT
ejpam-5970	376	16	which	which	PRON
ejpam-5970	376	17	is	be	AUX
ejpam-5970	376	18	transmitted	transmit	VERB
ejpam-5970	376	19	to	to	ADP
ejpam-5970	376	20	its	its	PRON
ejpam-5970	376	21	neighboring	neighboring	NOUN
ejpam-5970	376	22	nodes	node	NOUN
ejpam-5970	376	23	to	to	PART
ejpam-5970	376	24	support	support	VERB
ejpam-5970	376	25	the	the	DET
ejpam-5970	376	26	learning	learning	NOUN
ejpam-5970	376	27	process	process	NOUN
ejpam-5970	376	28	.	.	PUNCT
ejpam-5970	377	1	thus	thus	ADV
ejpam-5970	377	2	,	,	PUNCT
ejpam-5970	377	3	in	in	ADP
ejpam-5970	377	4	this	this	DET
ejpam-5970	377	5	process	process	NOUN
ejpam-5970	377	6	,	,	PUNCT
ejpam-5970	377	7	we	we	PRON
ejpam-5970	377	8	consider	consider	VERB
ejpam-5970	377	9	the	the	DET
ejpam-5970	377	10	adjacency	adjacency	NOUN
ejpam-5970	377	11	matrix	matrix	NOUN
ejpam-5970	377	12	with	with	ADP
ejpam-5970	377	13	self	self	NOUN
ejpam-5970	377	14	-	-	PUNCT
ejpam-5970	377	15	loops	loop	NOUN
ejpam-5970	377	16	included	include	VERB
ejpam-5970	377	17	.	.	PUNCT
ejpam-5970	378	1	instead	instead	ADV
ejpam-5970	378	2	of	of	ADP
ejpam-5970	378	3	using	use	VERB
ejpam-5970	378	4	the	the	DET
ejpam-5970	378	5	standard	standard	ADJ
ejpam-5970	378	6	adjacency	adjacency	NOUN
ejpam-5970	378	7	matrix	matrix	NOUN
ejpam-5970	378	8	p	p	NOUN
ejpam-5970	378	9	,	,	PUNCT
ejpam-5970	378	10	we	we	PRON
ejpam-5970	378	11	modify	modify	VERB
ejpam-5970	378	12	it	it	PRON
ejpam-5970	378	13	by	by	ADP
ejpam-5970	378	14	adding	add	VERB
ejpam-5970	378	15	an	an	DET
ejpam-5970	378	16	identity	identity	NOUN
ejpam-5970	378	17	matrix	matrix	NOUN
ejpam-5970	378	18	,	,	PUNCT
ejpam-5970	378	19	a.	a.	PROPN
ejpam-5970	378	20	i.	i.	PROPN
ejpam-5970	378	21	kristiana	kristiana	PROPN
ejpam-5970	378	22	,	,	PUNCT
ejpam-5970	378	23	et	et	PROPN
ejpam-5970	378	24	al	al	PROPN
ejpam-5970	378	25	.	.	PUNCT
ejpam-5970	378	26	/	/	SYM
ejpam-5970	378	27	eur	eur	PROPN
ejpam-5970	378	28	.	.	PUNCT
ejpam-5970	379	1	j.	j.	PROPN
ejpam-5970	379	2	pure	pure	PROPN
ejpam-5970	379	3	appl	appl	PROPN
ejpam-5970	379	4	.	.	PROPN
ejpam-5970	379	5	math	math	PROPN
ejpam-5970	379	6	,	,	PUNCT
ejpam-5970	379	7	18	18	NUM
ejpam-5970	379	8	(	(	PUNCT
ejpam-5970	379	9	3	3	NUM
ejpam-5970	379	10	)	)	PUNCT
ejpam-5970	379	11	(	(	PUNCT
ejpam-5970	379	12	2025	2025	NUM
ejpam-5970	379	13	)	)	PUNCT
ejpam-5970	379	14	,	,	PUNCT
ejpam-5970	379	15	5970	5970	NUM
ejpam-5970	379	16	13	13	NUM
ejpam-5970	379	17	of	of	ADP
ejpam-5970	379	18	18	18	NUM
ejpam-5970	379	19	figure	figure	NOUN
ejpam-5970	379	20	2	2	NUM
ejpam-5970	379	21	:	:	PUNCT
ejpam-5970	379	22	visualization	visualization	NOUN
ejpam-5970	379	23	of	of	ADP
ejpam-5970	379	24	the	the	DET
ejpam-5970	379	25	performance	performance	NOUN
ejpam-5970	379	26	of	of	ADP
ejpam-5970	379	27	the	the	DET
ejpam-5970	379	28	stgnn	stgnn	NOUN
ejpam-5970	379	29	model	model	NOUN
ejpam-5970	379	30	and	and	CCONJ
ejpam-5970	379	31	other	other	ADJ
ejpam-5970	379	32	models	model	NOUN
ejpam-5970	379	33	.	.	PUNCT
ejpam-5970	380	1	resulting	result	VERB
ejpam-5970	380	2	in	in	ADP
ejpam-5970	380	3	q	q	PROPN
ejpam-5970	380	4	=	=	PUNCT
ejpam-5970	380	5	p	p	X
ejpam-5970	380	6	+	+	NUM
ejpam-5970	380	7	i.	i.	NOUN
ejpam-5970	380	8	following	follow	VERB
ejpam-5970	380	9	the	the	DET
ejpam-5970	380	10	steps	step	NOUN
ejpam-5970	380	11	outlined	outline	VERB
ejpam-5970	380	12	in	in	ADP
ejpam-5970	380	13	the	the	DET
ejpam-5970	380	14	algorithm	algorithm	NOUN
ejpam-5970	380	15	above	above	ADV
ejpam-5970	380	16	,	,	PUNCT
ejpam-5970	380	17	we	we	PRON
ejpam-5970	380	18	obtain	obtain	VERB
ejpam-5970	380	19	time	time	NOUN
ejpam-5970	380	20	series	series	PROPN
ejpam-5970	380	21	data	datum	NOUN
ejpam-5970	380	22	that	that	PRON
ejpam-5970	380	23	are	be	AUX
ejpam-5970	380	24	ready	ready	ADJ
ejpam-5970	380	25	for	for	ADP
ejpam-5970	380	26	analysis	analysis	NOUN
ejpam-5970	380	27	using	use	VERB
ejpam-5970	380	28	the	the	DET
ejpam-5970	380	29	stgnn	stgnn	NOUN
ejpam-5970	380	30	framework	framework	NOUN
ejpam-5970	380	31	.	.	PUNCT
ejpam-5970	381	1	to	to	PART
ejpam-5970	381	2	evaluate	evaluate	VERB
ejpam-5970	381	3	the	the	DET
ejpam-5970	381	4	effectiveness	effectiveness	NOUN
ejpam-5970	381	5	of	of	ADP
ejpam-5970	381	6	the	the	DET
ejpam-5970	381	7	node	node	ADJ
ejpam-5970	381	8	embeddings	embedding	NOUN
ejpam-5970	381	9	,	,	PUNCT
ejpam-5970	381	10	we	we	PRON
ejpam-5970	381	11	assess	assess	VERB
ejpam-5970	381	12	the	the	DET
ejpam-5970	381	13	proximity	proximity	NOUN
ejpam-5970	381	14	of	of	ADP
ejpam-5970	381	15	nodes	node	NOUN
ejpam-5970	381	16	in	in	ADP
ejpam-5970	381	17	both	both	CCONJ
ejpam-5970	381	18	the	the	DET
ejpam-5970	381	19	original	original	ADJ
ejpam-5970	381	20	network	network	NOUN
ejpam-5970	381	21	and	and	CCONJ
ejpam-5970	381	22	the	the	DET
ejpam-5970	381	23	embedding	embed	VERB
ejpam-5970	381	24	space	space	NOUN
ejpam-5970	381	25	.	.	PUNCT
ejpam-5970	382	1	the	the	DET
ejpam-5970	382	2	embedding	embed	VERB
ejpam-5970	382	3	error	error	NOUN
ejpam-5970	382	4	is	be	AUX
ejpam-5970	382	5	computed	compute	VERB
ejpam-5970	382	6	by	by	ADP
ejpam-5970	382	7	comparing	compare	VERB
ejpam-5970	382	8	each	each	DET
ejpam-5970	382	9	pair	pair	NOUN
ejpam-5970	382	10	of	of	ADP
ejpam-5970	382	11	adjacent	adjacent	ADJ
ejpam-5970	382	12	nodes	node	NOUN
ejpam-5970	382	13	using	use	VERB
ejpam-5970	382	14	the	the	DET
ejpam-5970	382	15	infinity	infinity	NOUN
ejpam-5970	382	16	norm	norm	NOUN
ejpam-5970	382	17	.	.	PUNCT
ejpam-5970	383	1	subsequently	subsequently	ADV
ejpam-5970	383	2	,	,	PUNCT
ejpam-5970	383	3	we	we	PRON
ejpam-5970	383	4	extend	extend	VERB
ejpam-5970	383	5	the	the	DET
ejpam-5970	383	6	model	model	NOUN
ejpam-5970	383	7	to	to	PART
ejpam-5970	383	8	perform	perform	VERB
ejpam-5970	383	9	multi	multi	ADJ
ejpam-5970	383	10	-	-	ADJ
ejpam-5970	383	11	step	step	ADJ
ejpam-5970	383	12	time	time	NOUN
ejpam-5970	383	13	series	series	PROPN
ejpam-5970	383	14	forecasting	forecasting	NOUN
ejpam-5970	383	15	with	with	ADP
ejpam-5970	383	16	stgnn	stgnn	NOUN
ejpam-5970	383	17	,	,	PUNCT
ejpam-5970	383	18	using	use	VERB
ejpam-5970	383	19	60	60	NUM
ejpam-5970	383	20	%	%	NOUN
ejpam-5970	383	21	of	of	ADP
ejpam-5970	383	22	the	the	DET
ejpam-5970	383	23	data	datum	NOUN
ejpam-5970	383	24	for	for	ADP
ejpam-5970	383	25	training	training	NOUN
ejpam-5970	383	26	.	.	PUNCT
ejpam-5970	384	1	the	the	DET
ejpam-5970	384	2	model	model	NOUN
ejpam-5970	384	3	’s	’s	PART
ejpam-5970	384	4	performance	performance	NOUN
ejpam-5970	384	5	is	be	AUX
ejpam-5970	384	6	evaluated	evaluate	VERB
ejpam-5970	384	7	by	by	ADP
ejpam-5970	384	8	measuring	measure	VERB
ejpam-5970	384	9	the	the	DET
ejpam-5970	384	10	root	root	NOUN
ejpam-5970	384	11	mean	mean	ADJ
ejpam-5970	384	12	square	square	ADJ
ejpam-5970	384	13	error	error	NOUN
ejpam-5970	384	14	(	(	PUNCT
ejpam-5970	384	15	rmse	rmse	NOUN
ejpam-5970	384	16	)	)	PUNCT
ejpam-5970	384	17	or	or	CCONJ
ejpam-5970	384	18	mean	mean	VERB
ejpam-5970	384	19	square	square	ADJ
ejpam-5970	384	20	error	error	NOUN
ejpam-5970	384	21	(	(	PUNCT
ejpam-5970	384	22	mse	mse	NOUN
ejpam-5970	384	23	)	)	PUNCT
ejpam-5970	384	24	on	on	ADP
ejpam-5970	384	25	the	the	DET
ejpam-5970	384	26	testing	testing	NOUN
ejpam-5970	384	27	data	datum	NOUN
ejpam-5970	384	28	.	.	PUNCT
ejpam-5970	385	1	the	the	DET
ejpam-5970	385	2	results	result	NOUN
ejpam-5970	385	3	are	be	AUX
ejpam-5970	385	4	presented	present	VERB
ejpam-5970	385	5	in	in	ADP
ejpam-5970	385	6	figure	figure	NOUN
ejpam-5970	385	7	2	2	NUM
ejpam-5970	385	8	.	.	PUNCT
ejpam-5970	385	9	figure	figure	VERB
ejpam-5970	385	10	3	3	NUM
ejpam-5970	385	11	:	:	PUNCT
ejpam-5970	385	12	forecast	forecast	NOUN
ejpam-5970	385	13	results	result	NOUN
ejpam-5970	385	14	using	use	VERB
ejpam-5970	385	15	stgnn	stgnn	NOUN
ejpam-5970	385	16	.	.	PUNCT
ejpam-5970	386	1	a.	a.	PROPN
ejpam-5970	386	2	i.	i.	PROPN
ejpam-5970	386	3	kristiana	kristiana	PROPN
ejpam-5970	386	4	,	,	PUNCT
ejpam-5970	386	5	et	et	PROPN
ejpam-5970	386	6	al	al	PROPN
ejpam-5970	386	7	.	.	PUNCT
ejpam-5970	386	8	/	/	SYM
ejpam-5970	386	9	eur	eur	PROPN
ejpam-5970	386	10	.	.	PUNCT
ejpam-5970	387	1	j.	j.	PROPN
ejpam-5970	387	2	pure	pure	PROPN
ejpam-5970	387	3	appl	appl	PROPN
ejpam-5970	387	4	.	.	PROPN
ejpam-5970	387	5	math	math	PROPN
ejpam-5970	387	6	,	,	PUNCT
ejpam-5970	387	7	18	18	NUM
ejpam-5970	387	8	(	(	PUNCT
ejpam-5970	387	9	3	3	NUM
ejpam-5970	387	10	)	)	PUNCT
ejpam-5970	387	11	(	(	PUNCT
ejpam-5970	387	12	2025	2025	NUM
ejpam-5970	387	13	)	)	PUNCT
ejpam-5970	387	14	,	,	PUNCT
ejpam-5970	387	15	5970	5970	NUM
ejpam-5970	387	16	14	14	NUM
ejpam-5970	387	17	of	of	ADP
ejpam-5970	387	18	18	18	NUM
ejpam-5970	387	19	to	to	PART
ejpam-5970	387	20	evaluate	evaluate	VERB
ejpam-5970	387	21	the	the	DET
ejpam-5970	387	22	robustness	robustness	NOUN
ejpam-5970	387	23	and	and	CCONJ
ejpam-5970	387	24	predictive	predictive	ADJ
ejpam-5970	387	25	capability	capability	NOUN
ejpam-5970	387	26	of	of	ADP
ejpam-5970	387	27	the	the	DET
ejpam-5970	387	28	proposed	propose	VERB
ejpam-5970	387	29	stgnn	stgnn	NOUN
ejpam-5970	387	30	model	model	PROPN
ejpam-5970	387	31	,	,	PUNCT
ejpam-5970	387	32	we	we	PRON
ejpam-5970	387	33	conducted	conduct	VERB
ejpam-5970	387	34	a	a	DET
ejpam-5970	387	35	comprehensive	comprehensive	ADJ
ejpam-5970	387	36	comparison	comparison	NOUN
ejpam-5970	387	37	with	with	ADP
ejpam-5970	387	38	five	five	NUM
ejpam-5970	387	39	baseline	baseline	ADJ
ejpam-5970	387	40	models	model	NOUN
ejpam-5970	387	41	:	:	PUNCT
ejpam-5970	387	42	historical	historical	ADJ
ejpam-5970	387	43	average	average	ADJ
ejpam-5970	387	44	(	(	PUNCT
ejpam-5970	387	45	ha	ha	INTJ
ejpam-5970	387	46	)	)	PUNCT
ejpam-5970	387	47	,	,	PUNCT
ejpam-5970	387	48	auto	auto	NOUN
ejpam-5970	387	49	-	-	PUNCT
ejpam-5970	387	50	regressive	regressive	ADJ
ejpam-5970	387	51	integrated	integrated	ADJ
ejpam-5970	387	52	moving	move	VERB
ejpam-5970	387	53	average	average	NOUN
ejpam-5970	387	54	(	(	PUNCT
ejpam-5970	387	55	arima	arima	PROPN
ejpam-5970	387	56	)	)	PUNCT
ejpam-5970	387	57	,	,	PUNCT
ejpam-5970	387	58	support	support	VERB
ejpam-5970	387	59	vector	vector	NOUN
ejpam-5970	387	60	regression	regression	NOUN
ejpam-5970	387	61	(	(	PUNCT
ejpam-5970	387	62	svr	svr	PROPN
ejpam-5970	387	63	)	)	PUNCT
ejpam-5970	387	64	,	,	PUNCT
ejpam-5970	387	65	graph	graph	VERB
ejpam-5970	387	66	convolutional	convolutional	ADJ
ejpam-5970	387	67	network	network	NOUN
ejpam-5970	387	68	(	(	PUNCT
ejpam-5970	387	69	gcn	gcn	NOUN
ejpam-5970	387	70	)	)	PUNCT
ejpam-5970	387	71	,	,	PUNCT
ejpam-5970	387	72	and	and	CCONJ
ejpam-5970	387	73	gated	gate	VERB
ejpam-5970	387	74	recurrent	recurrent	ADJ
ejpam-5970	387	75	unit	unit	NOUN
ejpam-5970	387	76	(	(	PUNCT
ejpam-5970	387	77	gru	gru	PROPN
ejpam-5970	387	78	)	)	PUNCT
ejpam-5970	387	79	.	.	PUNCT
ejpam-5970	388	1	the	the	DET
ejpam-5970	388	2	comparative	comparative	ADJ
ejpam-5970	388	3	performance	performance	NOUN
ejpam-5970	388	4	across	across	ADP
ejpam-5970	388	5	models	model	NOUN
ejpam-5970	388	6	is	be	AUX
ejpam-5970	388	7	illustrated	illustrate	VERB
ejpam-5970	388	8	in	in	ADP
ejpam-5970	388	9	figure	figure	NOUN
ejpam-5970	388	10	2	2	NUM
ejpam-5970	388	11	,	,	PUNCT
ejpam-5970	388	12	figure	figure	NOUN
ejpam-5970	388	13	3	3	NUM
ejpam-5970	388	14	,	,	PUNCT
ejpam-5970	388	15	and	and	CCONJ
ejpam-5970	388	16	summarized	summarize	VERB
ejpam-5970	388	17	in	in	ADP
ejpam-5970	388	18	table	table	NOUN
ejpam-5970	388	19	2	2	NUM
ejpam-5970	388	20	.	.	PUNCT
ejpam-5970	388	21	as	as	SCONJ
ejpam-5970	388	22	shown	show	VERB
ejpam-5970	388	23	in	in	ADP
ejpam-5970	388	24	figure	figure	NOUN
ejpam-5970	388	25	2	2	NUM
ejpam-5970	388	26	,	,	PUNCT
ejpam-5970	388	27	the	the	DET
ejpam-5970	388	28	stgnn	stgnn	NOUN
ejpam-5970	388	29	model	model	PROPN
ejpam-5970	388	30	consistently	consistently	ADV
ejpam-5970	388	31	achieves	achieve	VERB
ejpam-5970	388	32	lower	low	ADJ
ejpam-5970	388	33	rmse	rmse	NOUN
ejpam-5970	388	34	values	value	NOUN
ejpam-5970	388	35	compared	compare	VERB
ejpam-5970	388	36	to	to	ADP
ejpam-5970	388	37	the	the	DET
ejpam-5970	388	38	other	other	ADJ
ejpam-5970	388	39	methods	method	NOUN
ejpam-5970	388	40	over	over	ADP
ejpam-5970	388	41	200	200	NUM
ejpam-5970	388	42	epochs	epoch	NOUN
ejpam-5970	388	43	.	.	PUNCT
ejpam-5970	389	1	the	the	DET
ejpam-5970	389	2	convergence	convergence	NOUN
ejpam-5970	389	3	curve	curve	NOUN
ejpam-5970	389	4	of	of	ADP
ejpam-5970	389	5	stgnn	stgnn	NOUN
ejpam-5970	389	6	demonstrates	demonstrate	VERB
ejpam-5970	389	7	a	a	DET
ejpam-5970	389	8	smooth	smooth	ADJ
ejpam-5970	389	9	and	and	CCONJ
ejpam-5970	389	10	steady	steady	ADJ
ejpam-5970	389	11	decrease	decrease	NOUN
ejpam-5970	389	12	in	in	ADP
ejpam-5970	389	13	loss	loss	NOUN
ejpam-5970	389	14	,	,	PUNCT
ejpam-5970	389	15	indicating	indicate	VERB
ejpam-5970	389	16	its	its	PRON
ejpam-5970	389	17	stability	stability	NOUN
ejpam-5970	389	18	and	and	CCONJ
ejpam-5970	389	19	efficiency	efficiency	NOUN
ejpam-5970	389	20	in	in	ADP
ejpam-5970	389	21	the	the	DET
ejpam-5970	389	22	training	training	NOUN
ejpam-5970	389	23	process	process	NOUN
ejpam-5970	389	24	.	.	PUNCT
ejpam-5970	390	1	unlike	unlike	ADP
ejpam-5970	390	2	gru	gru	NOUN
ejpam-5970	390	3	and	and	CCONJ
ejpam-5970	390	4	gcn	gcn	NOUN
ejpam-5970	390	5	models	model	NOUN
ejpam-5970	390	6	which	which	PRON
ejpam-5970	390	7	exhibit	exhibit	VERB
ejpam-5970	390	8	oscillations	oscillation	NOUN
ejpam-5970	390	9	in	in	ADP
ejpam-5970	390	10	early	early	ADJ
ejpam-5970	390	11	epochs	epoch	NOUN
ejpam-5970	390	12	,	,	PUNCT
ejpam-5970	390	13	stgnn	stgnn	NOUN
ejpam-5970	390	14	achieves	achieve	VERB
ejpam-5970	390	15	optimal	optimal	ADJ
ejpam-5970	390	16	convergence	convergence	NOUN
ejpam-5970	390	17	with	with	ADP
ejpam-5970	390	18	minimal	minimal	ADJ
ejpam-5970	390	19	variance	variance	NOUN
ejpam-5970	390	20	,	,	PUNCT
ejpam-5970	390	21	highlighting	highlight	VERB
ejpam-5970	390	22	its	its	PRON
ejpam-5970	390	23	robustness	robustness	NOUN
ejpam-5970	390	24	in	in	ADP
ejpam-5970	390	25	handling	handle	VERB
ejpam-5970	390	26	temporal	temporal	ADJ
ejpam-5970	390	27	dependencies	dependency	NOUN
ejpam-5970	390	28	and	and	CCONJ
ejpam-5970	390	29	spatial	spatial	ADJ
ejpam-5970	390	30	structures	structure	NOUN
ejpam-5970	390	31	.	.	PUNCT
ejpam-5970	391	1	table	table	NOUN
ejpam-5970	391	2	2	2	NUM
ejpam-5970	391	3	:	:	PUNCT
ejpam-5970	391	4	the	the	DET
ejpam-5970	391	5	prediction	prediction	NOUN
ejpam-5970	391	6	results	result	NOUN
ejpam-5970	391	7	of	of	ADP
ejpam-5970	391	8	the	the	DET
ejpam-5970	391	9	stgnn	stgnn	NOUN
ejpam-5970	391	10	model	model	NOUN
ejpam-5970	391	11	and	and	CCONJ
ejpam-5970	391	12	other	other	ADJ
ejpam-5970	391	13	baseline	baseline	NOUN
ejpam-5970	391	14	methods	method	NOUN
ejpam-5970	391	15	.	.	PUNCT
ejpam-5970	392	1	epochs	epochs	PROPN
ejpam-5970	392	2	metric	metric	ADJ
ejpam-5970	392	3	model	model	NOUN
ejpam-5970	392	4	arima	arima	PROPN
ejpam-5970	392	5	lstm	lstm	PROPN
ejpam-5970	392	6	gcn	gcn	PROPN
ejpam-5970	392	7	gru	gru	PROPN
ejpam-5970	392	8	stgnn	stgnn	PROPN
ejpam-5970	392	9	(	(	PUNCT
ejpam-5970	392	10	our	our	PRON
ejpam-5970	392	11	model	model	NOUN
ejpam-5970	392	12	)	)	PUNCT
ejpam-5970	392	13	50	50	NUM
ejpam-5970	392	14	rmse	rmse	NOUN
ejpam-5970	392	15	8.1051	8.1051	NUM
ejpam-5970	392	16	7.5357	7.5357	NUM
ejpam-5970	392	17	9.2706	9.2706	NUM
ejpam-5970	392	18	4.0482	4.0482	NUM
ejpam-5970	392	19	3.9052	3.9052	NUM
ejpam-5970	392	20	mae	mae	PROPN
ejpam-5970	392	21	6.1092	6.1092	NUM
ejpam-5970	392	22	4.9198	4.9198	NUM
ejpam-5970	392	23	7.2665	7.2665	NUM
ejpam-5970	392	24	2.6803	2.6803	NUM
ejpam-5970	392	25	2.6061	2.6061	NUM
ejpam-5970	392	26	accuracy	accuracy	NOUN
ejpam-5970	392	27	0.3178	0.3178	NUM
ejpam-5970	392	28	0.6871	0.6871	NUM
ejpam-5970	392	29	0.6422	0.6422	NUM
ejpam-5970	393	1	0.7068	0.7068	NUM
ejpam-5970	393	2	0.7206	0.7206	NUM
ejpam-5970	393	3	r2	r2	NOUN
ejpam-5970	393	4	0.0732	0.0732	NUM
ejpam-5970	393	5	0.8101	0.8101	NUM
ejpam-5970	393	6	0.6037	0.6037	NUM
ejpam-5970	393	7	0.8437	0.8437	NUM
ejpam-5970	393	8	0.8531	0.8531	NUM
ejpam-5970	393	9	100	100	NUM
ejpam-5970	393	10	rmse	rmse	NOUN
ejpam-5970	393	11	8.2112	8.2112	NUM
ejpam-5970	393	12	7.4736	7.4736	NUM
ejpam-5970	393	13	9.3430	9.3430	NUM
ejpam-5970	393	14	4.0768	4.0768	NUM
ejpam-5970	393	15	3.9606	3.9606	NUM
ejpam-5970	393	16	mae	mae	PROPN
ejpam-5970	393	17	6.2143	6.2143	NUM
ejpam-5970	393	18	4.9719	4.9719	NUM
ejpam-5970	393	19	7.3101	7.3101	NUM
ejpam-5970	393	20	2.7007	2.7007	NUM
ejpam-5970	393	21	2.6441	2.6441	NUM
ejpam-5970	393	22	accuracy	accuracy	NOUN
ejpam-5970	393	23	0.4271	0.4271	NUM
ejpam-5970	394	1	0.6976	0.6976	NUM
ejpam-5970	394	2	0.6305	0.6305	NUM
ejpam-5970	394	3	0.7147	0.7147	NUM
ejpam-5970	394	4	0.7165	0.7165	NUM
ejpam-5970	394	5	r2	r2	NOUN
ejpam-5970	394	6	0.0724	0.0724	NUM
ejpam-5970	394	7	0.8131	0.8131	NUM
ejpam-5970	394	8	0.6086	0.6086	NUM
ejpam-5970	394	9	0.8367	0.8367	NUM
ejpam-5970	394	10	0.8413	0.8413	NUM
ejpam-5970	394	11	150	150	NUM
ejpam-5970	394	12	rmse	rmse	NOUN
ejpam-5970	394	13	8.2121	8.2121	NUM
ejpam-5970	394	14	7.4753	7.4753	NUM
ejpam-5970	394	15	9.4022	9.4022	NUM
ejpam-5970	394	16	4.1002	4.1002	NUM
ejpam-5970	394	17	3.9840	3.9840	NUM
ejpam-5970	394	18	mae	mae	PROPN
ejpam-5970	394	19	6.2143	6.2143	NUM
ejpam-5970	394	20	5.0321	5.0321	NUM
ejpam-5970	394	21	7.3704	7.3704	NUM
ejpam-5970	394	22	2.7107	2.7107	NUM
ejpam-5970	394	23	2.6655	2.6655	NUM
ejpam-5970	394	24	0.4260	0.4260	NUM
ejpam-5970	394	25	0.6975	0.6975	NUM
ejpam-5970	394	26	0.6373	0.6373	NUM
ejpam-5970	394	27	0.7032	0.7032	NUM
ejpam-5970	394	28	0.7142	0.7142	NUM
ejpam-5970	394	29	r2	r2	NOUN
ejpam-5970	394	30	0.0826	0.0826	NUM
ejpam-5970	394	31	0.8131	0.8131	NUM
ejpam-5970	394	32	0.6027	0.6027	NUM
ejpam-5970	394	33	0.8350	0.8350	NUM
ejpam-5970	394	34	0.8409	0.8409	NUM
ejpam-5970	394	35	200	200	NUM
ejpam-5970	394	36	rmse	rmse	NOUN
ejpam-5970	394	37	8.2052	8.2052	NUM
ejpam-5970	394	38	7.4872	7.4872	NUM
ejpam-5970	394	39	9.4404	9.4404	NUM
ejpam-5970	394	40	4.1131	4.1131	NUM
ejpam-5970	394	41	4.0031	4.0031	NUM
ejpam-5970	394	42	mae	mae	PROPN
ejpam-5970	394	43	6.2108	6.2108	NUM
ejpam-5970	394	44	5.0604	5.0604	NUM
ejpam-5970	394	45	7.4110	7.4110	NUM
ejpam-5970	394	46	2.7321	2.7321	NUM
ejpam-5970	394	47	2.6878	2.6878	NUM
ejpam-5970	394	48	accuracy	accuracy	NOUN
ejpam-5970	394	49	0.4272	0.4272	NUM
ejpam-5970	394	50	0.6971	0.6971	NUM
ejpam-5970	394	51	0.6255	0.6255	NUM
ejpam-5970	394	52	0.7015	0.7015	NUM
ejpam-5970	394	53	0.7128	0.7128	NUM
ejpam-5970	394	54	r2	r2	NOUN
ejpam-5970	394	55	0.0814	0.0814	NUM
ejpam-5970	394	56	0.8144	0.8144	NUM
ejpam-5970	394	57	0.5888	0.5888	NUM
ejpam-5970	394	58	0.8432	0.8432	NUM
ejpam-5970	394	59	0.8703	0.8703	NUM
ejpam-5970	394	60	table	table	NOUN
ejpam-5970	394	61	2	2	NUM
ejpam-5970	394	62	further	far	ADV
ejpam-5970	394	63	confirms	confirm	VERB
ejpam-5970	394	64	the	the	DET
ejpam-5970	394	65	superior	superior	ADJ
ejpam-5970	394	66	performance	performance	NOUN
ejpam-5970	394	67	of	of	ADP
ejpam-5970	394	68	stgnn	stgnn	NOUN
ejpam-5970	394	69	across	across	ADP
ejpam-5970	394	70	multiple	multiple	ADJ
ejpam-5970	394	71	evaluation	evaluation	NOUN
ejpam-5970	394	72	metrics	metric	NOUN
ejpam-5970	394	73	,	,	PUNCT
ejpam-5970	394	74	including	include	VERB
ejpam-5970	394	75	rmse	rmse	PROPN
ejpam-5970	394	76	,	,	PUNCT
ejpam-5970	394	77	mae	mae	PROPN
ejpam-5970	394	78	,	,	PUNCT
ejpam-5970	394	79	accuracy	accuracy	NOUN
ejpam-5970	394	80	,	,	PUNCT
ejpam-5970	394	81	and	and	CCONJ
ejpam-5970	394	82	the	the	DET
ejpam-5970	394	83	coefficient	coefficient	NOUN
ejpam-5970	394	84	of	of	ADP
ejpam-5970	394	85	determination	determination	NOUN
ejpam-5970	394	86	(	(	PUNCT
ejpam-5970	394	87	r2	r2	PROPN
ejpam-5970	394	88	)	)	PUNCT
ejpam-5970	394	89	.	.	PUNCT
ejpam-5970	395	1	at	at	ADP
ejpam-5970	395	2	every	every	DET
ejpam-5970	395	3	evaluated	evaluate	VERB
ejpam-5970	395	4	epoch	epoch	NOUN
ejpam-5970	395	5	interval	interval	NOUN
ejpam-5970	395	6	(	(	PUNCT
ejpam-5970	395	7	50	50	NUM
ejpam-5970	395	8	,	,	PUNCT
ejpam-5970	395	9	100	100	NUM
ejpam-5970	395	10	,	,	PUNCT
ejpam-5970	395	11	150	150	NUM
ejpam-5970	395	12	,	,	PUNCT
ejpam-5970	395	13	and	and	CCONJ
ejpam-5970	395	14	200	200	NUM
ejpam-5970	395	15	)	)	PUNCT
ejpam-5970	395	16	,	,	PUNCT
ejpam-5970	395	17	stgnn	stgnn	NOUN
ejpam-5970	395	18	achieves	achieve	VERB
ejpam-5970	395	19	the	the	DET
ejpam-5970	395	20	lowest	low	ADJ
ejpam-5970	395	21	error	error	NOUN
ejpam-5970	395	22	values	value	NOUN
ejpam-5970	395	23	and	and	CCONJ
ejpam-5970	395	24	the	the	DET
ejpam-5970	395	25	highest	high	ADJ
ejpam-5970	395	26	accuracy	accuracy	NOUN
ejpam-5970	395	27	and	and	CCONJ
ejpam-5970	395	28	r2	r2	NOUN
ejpam-5970	395	29	scores	score	NOUN
ejpam-5970	395	30	,	,	PUNCT
ejpam-5970	395	31	outperforming	outperform	VERB
ejpam-5970	395	32	all	all	DET
ejpam-5970	395	33	baseline	baseline	ADJ
ejpam-5970	395	34	methods	method	NOUN
ejpam-5970	395	35	.	.	PUNCT
ejpam-5970	396	1	notably	notably	ADV
ejpam-5970	396	2	,	,	PUNCT
ejpam-5970	396	3	the	the	DET
ejpam-5970	396	4	rmse	rmse	NOUN
ejpam-5970	396	5	and	and	CCONJ
ejpam-5970	396	6	mae	mae	PROPN
ejpam-5970	396	7	values	value	NOUN
ejpam-5970	396	8	of	of	ADP
ejpam-5970	396	9	stgnn	stgnn	NOUN
ejpam-5970	396	10	are	be	AUX
ejpam-5970	396	11	significantly	significantly	ADV
ejpam-5970	396	12	lower	low	ADJ
ejpam-5970	396	13	,	,	PUNCT
ejpam-5970	396	14	while	while	SCONJ
ejpam-5970	396	15	its	its	PRON
ejpam-5970	396	16	r2	r2	NOUN
ejpam-5970	396	17	values	value	NOUN
ejpam-5970	396	18	remain	remain	VERB
ejpam-5970	396	19	consistently	consistently	ADV
ejpam-5970	396	20	above	above	ADP
ejpam-5970	396	21	0.85	0.85	NUM
ejpam-5970	396	22	,	,	PUNCT
ejpam-5970	396	23	demonstrating	demonstrate	VERB
ejpam-5970	396	24	a	a	DET
ejpam-5970	396	25	strong	strong	ADJ
ejpam-5970	396	26	fit	fit	NOUN
ejpam-5970	396	27	between	between	ADP
ejpam-5970	396	28	the	the	DET
ejpam-5970	396	29	predictions	prediction	NOUN
ejpam-5970	396	30	and	and	CCONJ
ejpam-5970	396	31	the	the	DET
ejpam-5970	396	32	actual	actual	ADJ
ejpam-5970	396	33	observations	observation	NOUN
ejpam-5970	396	34	.	.	PUNCT
ejpam-5970	397	1	in	in	ADP
ejpam-5970	397	2	addition	addition	NOUN
ejpam-5970	397	3	,	,	PUNCT
ejpam-5970	397	4	multi	multi	ADJ
ejpam-5970	397	5	-	-	ADJ
ejpam-5970	397	6	step	step	ADJ
ejpam-5970	397	7	forecasting	forecasting	NOUN
ejpam-5970	397	8	results	result	NOUN
ejpam-5970	397	9	,	,	PUNCT
ejpam-5970	397	10	as	as	SCONJ
ejpam-5970	397	11	presented	present	VERB
ejpam-5970	397	12	in	in	ADP
ejpam-5970	397	13	figure	figure	NOUN
ejpam-5970	397	14	3	3	NUM
ejpam-5970	397	15	,	,	PUNCT
ejpam-5970	397	16	show	show	VERB
ejpam-5970	397	17	the	the	DET
ejpam-5970	397	18	stgnn	stgnn	PROPN
ejpam-5970	397	19	model	model	PROPN
ejpam-5970	397	20	’s	’s	PART
ejpam-5970	397	21	capability	capability	NOUN
ejpam-5970	397	22	to	to	PART
ejpam-5970	397	23	accurately	accurately	ADV
ejpam-5970	397	24	predict	predict	VERB
ejpam-5970	397	25	soil	soil	NOUN
ejpam-5970	397	26	nutrient	nutrient	NOUN
ejpam-5970	397	27	concentrations	concentration	NOUN
ejpam-5970	397	28	(	(	PUNCT
ejpam-5970	397	29	nitrogen	nitrogen	NOUN
ejpam-5970	397	30	,	,	PUNCT
ejpam-5970	397	31	phosphorus	phosphorus	NOUN
ejpam-5970	397	32	,	,	PUNCT
ejpam-5970	397	33	and	and	CCONJ
ejpam-5970	397	34	potassium	potassium	NOUN
ejpam-5970	397	35	)	)	PUNCT
ejpam-5970	397	36	over	over	ADP
ejpam-5970	397	37	a	a	DET
ejpam-5970	397	38	20	20	NUM
ejpam-5970	397	39	-	-	PUNCT
ejpam-5970	397	40	day	day	NOUN
ejpam-5970	397	41	horizon	horizon	NOUN
ejpam-5970	397	42	.	.	PUNCT
ejpam-5970	398	1	the	the	DET
ejpam-5970	398	2	predicted	predict	VERB
ejpam-5970	398	3	curves	curve	NOUN
ejpam-5970	398	4	closely	closely	ADV
ejpam-5970	398	5	follow	follow	VERB
ejpam-5970	398	6	the	the	DET
ejpam-5970	398	7	ground	ground	NOUN
ejpam-5970	398	8	truth	truth	NOUN
ejpam-5970	398	9	a.	a.	PROPN
ejpam-5970	398	10	i.	i.	PROPN
ejpam-5970	398	11	kristiana	kristiana	PROPN
ejpam-5970	398	12	,	,	PUNCT
ejpam-5970	398	13	et	et	PROPN
ejpam-5970	398	14	al	al	PROPN
ejpam-5970	398	15	.	.	PUNCT
ejpam-5970	398	16	/	/	SYM
ejpam-5970	398	17	eur	eur	PROPN
ejpam-5970	398	18	.	.	PUNCT
ejpam-5970	399	1	j.	j.	PROPN
ejpam-5970	399	2	pure	pure	PROPN
ejpam-5970	399	3	appl	appl	PROPN
ejpam-5970	399	4	.	.	PROPN
ejpam-5970	399	5	math	math	PROPN
ejpam-5970	399	6	,	,	PUNCT
ejpam-5970	399	7	18	18	NUM
ejpam-5970	399	8	(	(	PUNCT
ejpam-5970	399	9	3	3	NUM
ejpam-5970	399	10	)	)	PUNCT
ejpam-5970	399	11	(	(	PUNCT
ejpam-5970	399	12	2025	2025	NUM
ejpam-5970	399	13	)	)	PUNCT
ejpam-5970	399	14	,	,	PUNCT
ejpam-5970	399	15	5970	5970	NUM
ejpam-5970	399	16	15	15	NUM
ejpam-5970	399	17	of	of	ADP
ejpam-5970	399	18	18	18	NUM
ejpam-5970	399	19	across	across	ADP
ejpam-5970	399	20	all	all	DET
ejpam-5970	399	21	three	three	NUM
ejpam-5970	399	22	nutrient	nutrient	ADJ
ejpam-5970	399	23	types	type	NOUN
ejpam-5970	399	24	,	,	PUNCT
ejpam-5970	399	25	reaffirming	reaffirm	VERB
ejpam-5970	399	26	the	the	DET
ejpam-5970	399	27	model	model	NOUN
ejpam-5970	399	28	’s	’s	PART
ejpam-5970	399	29	generalization	generalization	NOUN
ejpam-5970	399	30	ability	ability	NOUN
ejpam-5970	399	31	in	in	ADP
ejpam-5970	399	32	real	real	ADJ
ejpam-5970	399	33	-	-	PUNCT
ejpam-5970	399	34	world	world	NOUN
ejpam-5970	399	35	agricultural	agricultural	ADJ
ejpam-5970	399	36	time	time	NOUN
ejpam-5970	399	37	series	series	PROPN
ejpam-5970	399	38	data	data	PROPN
ejpam-5970	399	39	.	.	PUNCT
ejpam-5970	400	1	furthermore	furthermore	ADV
ejpam-5970	400	2	,	,	PUNCT
ejpam-5970	400	3	to	to	PART
ejpam-5970	400	4	optimize	optimize	VERB
ejpam-5970	400	5	the	the	DET
ejpam-5970	400	6	monitoring	monitoring	NOUN
ejpam-5970	400	7	system	system	NOUN
ejpam-5970	400	8	in	in	ADP
ejpam-5970	400	9	companion	companion	NOUN
ejpam-5970	400	10	plantations	plantation	NOUN
ejpam-5970	400	11	,	,	PUNCT
ejpam-5970	400	12	we	we	PRON
ejpam-5970	400	13	applied	apply	VERB
ejpam-5970	400	14	the	the	DET
ejpam-5970	400	15	concept	concept	NOUN
ejpam-5970	400	16	of	of	ADP
ejpam-5970	400	17	local	local	ADJ
ejpam-5970	400	18	(	(	PUNCT
ejpam-5970	400	19	a	a	PRON
ejpam-5970	400	20	,	,	PUNCT
ejpam-5970	400	21	d)-edge	d)-edge	ADJ
ejpam-5970	400	22	antimagic	antimagic	ADJ
ejpam-5970	400	23	coloring	coloring	NOUN
ejpam-5970	400	24	to	to	PART
ejpam-5970	400	25	minimize	minimize	VERB
ejpam-5970	400	26	the	the	DET
ejpam-5970	400	27	number	number	NOUN
ejpam-5970	400	28	of	of	ADP
ejpam-5970	400	29	sensors	sensor	NOUN
ejpam-5970	400	30	required	require	VERB
ejpam-5970	400	31	.	.	PUNCT
ejpam-5970	401	1	based	base	VERB
ejpam-5970	401	2	on	on	ADP
ejpam-5970	401	3	this	this	DET
ejpam-5970	401	4	approach	approach	NOUN
ejpam-5970	401	5	,	,	PUNCT
ejpam-5970	401	6	only	only	ADV
ejpam-5970	401	7	four	four	NUM
ejpam-5970	401	8	representative	representative	ADJ
ejpam-5970	401	9	sensor	sensor	NOUN
ejpam-5970	401	10	locations	location	NOUN
ejpam-5970	401	11	are	be	AUX
ejpam-5970	401	12	needed	need	VERB
ejpam-5970	401	13	,	,	PUNCT
ejpam-5970	401	14	corresponding	correspond	VERB
ejpam-5970	401	15	to	to	ADP
ejpam-5970	401	16	four	four	NUM
ejpam-5970	401	17	plant	plant	NOUN
ejpam-5970	401	18	types	type	NOUN
ejpam-5970	401	19	:	:	PUNCT
ejpam-5970	401	20	rosa	rosa	PROPN
ejpam-5970	401	21	sp	sp	PROPN
ejpam-5970	401	22	.	.	PROPN
ejpam-5970	401	23	,	,	PUNCT
ejpam-5970	401	24	bromeliaceae	bromeliaceae	PROPN
ejpam-5970	401	25	,	,	PUNCT
ejpam-5970	401	26	bougainvillea	bougainvillea	NOUN
ejpam-5970	401	27	spectabilis	spectabili	VERB
ejpam-5970	401	28	,	,	PUNCT
ejpam-5970	401	29	and	and	CCONJ
ejpam-5970	401	30	cryptanthus	cryptanthus	ADJ
ejpam-5970	401	31	sp	sp	VERB
ejpam-5970	401	32	.	.	PUNCT
ejpam-5970	402	1	these	these	DET
ejpam-5970	402	2	representative	representative	ADJ
ejpam-5970	402	3	sensors	sensor	NOUN
ejpam-5970	402	4	,	,	PUNCT
ejpam-5970	402	5	selected	select	VERB
ejpam-5970	402	6	based	base	VERB
ejpam-5970	402	7	on	on	ADP
ejpam-5970	402	8	graph	graph	NOUN
ejpam-5970	402	9	labeling	labeling	NOUN
ejpam-5970	402	10	theory	theory	NOUN
ejpam-5970	402	11	,	,	PUNCT
ejpam-5970	402	12	are	be	AUX
ejpam-5970	402	13	sufficient	sufficient	ADJ
ejpam-5970	402	14	to	to	PART
ejpam-5970	402	15	capture	capture	VERB
ejpam-5970	402	16	the	the	DET
ejpam-5970	402	17	overall	overall	ADJ
ejpam-5970	402	18	dynamics	dynamic	NOUN
ejpam-5970	402	19	of	of	ADP
ejpam-5970	402	20	the	the	DET
ejpam-5970	402	21	plantation	plantation	NOUN
ejpam-5970	402	22	system	system	NOUN
ejpam-5970	402	23	,	,	PUNCT
ejpam-5970	402	24	providing	provide	VERB
ejpam-5970	402	25	a	a	DET
ejpam-5970	402	26	costeffective	costeffective	ADJ
ejpam-5970	402	27	yet	yet	CCONJ
ejpam-5970	402	28	reliable	reliable	ADJ
ejpam-5970	402	29	monitoring	monitoring	NOUN
ejpam-5970	402	30	strategy	strategy	NOUN
ejpam-5970	402	31	.	.	PUNCT
ejpam-5970	403	1	overall	overall	ADV
ejpam-5970	403	2	,	,	PUNCT
ejpam-5970	403	3	the	the	DET
ejpam-5970	403	4	integration	integration	NOUN
ejpam-5970	403	5	of	of	ADP
ejpam-5970	403	6	stgnn	stgnn	NOUN
ejpam-5970	403	7	with	with	ADP
ejpam-5970	403	8	local	local	ADJ
ejpam-5970	403	9	graph	graph	NOUN
ejpam-5970	403	10	-	-	PUNCT
ejpam-5970	403	11	based	base	VERB
ejpam-5970	403	12	optimization	optimization	NOUN
ejpam-5970	403	13	offers	offer	VERB
ejpam-5970	403	14	a	a	DET
ejpam-5970	403	15	promising	promising	ADJ
ejpam-5970	403	16	framework	framework	NOUN
ejpam-5970	403	17	for	for	ADP
ejpam-5970	403	18	precision	precision	NOUN
ejpam-5970	403	19	agriculture	agriculture	NOUN
ejpam-5970	403	20	,	,	PUNCT
ejpam-5970	403	21	enabling	enable	VERB
ejpam-5970	403	22	both	both	CCONJ
ejpam-5970	403	23	accurate	accurate	ADJ
ejpam-5970	403	24	forecasting	forecasting	NOUN
ejpam-5970	403	25	and	and	CCONJ
ejpam-5970	403	26	efficient	efficient	ADJ
ejpam-5970	403	27	deployment	deployment	NOUN
ejpam-5970	403	28	of	of	ADP
ejpam-5970	403	29	sensing	sense	VERB
ejpam-5970	403	30	resources	resource	NOUN
ejpam-5970	403	31	.	.	PUNCT
ejpam-5970	404	1	3.4	3.4	NUM
ejpam-5970	404	2	.	.	PUNCT
ejpam-5970	404	3	computational	computational	ADJ
ejpam-5970	404	4	complexity	complexity	NOUN
ejpam-5970	404	5	and	and	CCONJ
ejpam-5970	404	6	training	training	NOUN
ejpam-5970	404	7	time	time	NOUN
ejpam-5970	404	8	analysis	analysis	NOUN
ejpam-5970	404	9	to	to	PART
ejpam-5970	404	10	evaluate	evaluate	VERB
ejpam-5970	404	11	the	the	DET
ejpam-5970	404	12	computational	computational	ADJ
ejpam-5970	404	13	efficiency	efficiency	NOUN
ejpam-5970	404	14	of	of	ADP
ejpam-5970	404	15	the	the	DET
ejpam-5970	404	16	proposed	propose	VERB
ejpam-5970	404	17	stgnn	stgnn	PROPN
ejpam-5970	404	18	model	model	PROPN
ejpam-5970	404	19	,	,	PUNCT
ejpam-5970	404	20	we	we	PRON
ejpam-5970	404	21	compared	compare	VERB
ejpam-5970	404	22	its	its	PRON
ejpam-5970	404	23	training	training	NOUN
ejpam-5970	404	24	time	time	NOUN
ejpam-5970	404	25	to	to	ADP
ejpam-5970	404	26	several	several	ADJ
ejpam-5970	404	27	baseline	baseline	NOUN
ejpam-5970	404	28	models	model	NOUN
ejpam-5970	404	29	,	,	PUNCT
ejpam-5970	404	30	including	include	VERB
ejpam-5970	404	31	arima	arima	PROPN
ejpam-5970	404	32	,	,	PUNCT
ejpam-5970	404	33	lstm	lstm	NOUN
ejpam-5970	404	34	,	,	PUNCT
ejpam-5970	404	35	gcn	gcn	ADJ
ejpam-5970	404	36	,	,	PUNCT
ejpam-5970	404	37	and	and	CCONJ
ejpam-5970	404	38	gru	gru	PROPN
ejpam-5970	404	39	.	.	PUNCT
ejpam-5970	405	1	although	although	SCONJ
ejpam-5970	405	2	stgnn	stgnn	NOUN
ejpam-5970	405	3	integrates	integrate	NOUN
ejpam-5970	405	4	both	both	PRON
ejpam-5970	405	5	graph	graph	VERB
ejpam-5970	405	6	convolutional	convolutional	ADJ
ejpam-5970	405	7	layers	layer	NOUN
ejpam-5970	405	8	and	and	CCONJ
ejpam-5970	405	9	recurrent	recurrent	ADJ
ejpam-5970	405	10	temporal	temporal	ADJ
ejpam-5970	405	11	processing	processing	NOUN
ejpam-5970	405	12	,	,	PUNCT
ejpam-5970	405	13	which	which	PRON
ejpam-5970	405	14	intuitively	intuitively	ADV
ejpam-5970	405	15	may	may	AUX
ejpam-5970	405	16	introduce	introduce	VERB
ejpam-5970	405	17	additional	additional	ADJ
ejpam-5970	405	18	computational	computational	ADJ
ejpam-5970	405	19	cost	cost	NOUN
ejpam-5970	405	20	,	,	PUNCT
ejpam-5970	405	21	the	the	DET
ejpam-5970	405	22	model	model	NOUN
ejpam-5970	405	23	demonstrates	demonstrate	VERB
ejpam-5970	405	24	efficient	efficient	ADJ
ejpam-5970	405	25	convergence	convergence	NOUN
ejpam-5970	405	26	behavior	behavior	NOUN
ejpam-5970	405	27	and	and	CCONJ
ejpam-5970	405	28	outperforms	outperform	VERB
ejpam-5970	405	29	the	the	DET
ejpam-5970	405	30	other	other	ADJ
ejpam-5970	405	31	models	model	NOUN
ejpam-5970	405	32	in	in	ADP
ejpam-5970	405	33	terms	term	NOUN
ejpam-5970	405	34	of	of	ADP
ejpam-5970	405	35	predictive	predictive	ADJ
ejpam-5970	405	36	accuracy	accuracy	NOUN
ejpam-5970	405	37	,	,	PUNCT
ejpam-5970	405	38	as	as	SCONJ
ejpam-5970	405	39	discussed	discuss	VERB
ejpam-5970	405	40	in	in	ADP
ejpam-5970	405	41	earlier	early	ADJ
ejpam-5970	405	42	sections	section	NOUN
ejpam-5970	405	43	.	.	PUNCT
ejpam-5970	406	1	table	table	NOUN
ejpam-5970	406	2	3	3	NUM
ejpam-5970	406	3	:	:	PUNCT
ejpam-5970	406	4	training	training	NOUN
ejpam-5970	406	5	time	time	NOUN
ejpam-5970	406	6	comparison	comparison	NOUN
ejpam-5970	406	7	of	of	ADP
ejpam-5970	406	8	models	model	NOUN
ejpam-5970	406	9	(	(	PUNCT
ejpam-5970	406	10	200	200	NUM
ejpam-5970	406	11	epochs	epoch	NOUN
ejpam-5970	406	12	)	)	PUNCT
ejpam-5970	406	13	model	model	NOUN
ejpam-5970	406	14	training	training	NOUN
ejpam-5970	406	15	time	time	NOUN
ejpam-5970	406	16	(	(	PUNCT
ejpam-5970	406	17	seconds	second	NOUN
ejpam-5970	406	18	)	)	PUNCT
ejpam-5970	406	19	arima	arima	PROPN
ejpam-5970	406	20	25.4	25.4	NUM
ejpam-5970	406	21	lstm	lstm	NOUN
ejpam-5970	406	22	102.8	102.8	NUM
ejpam-5970	406	23	gcn	gcn	NOUN
ejpam-5970	406	24	94.6	94.6	NUM
ejpam-5970	406	25	gru	gru	NOUN
ejpam-5970	406	26	86.3	86.3	NUM
ejpam-5970	406	27	stgnn	stgnn	NOUN
ejpam-5970	406	28	(	(	PUNCT
ejpam-5970	406	29	our	our	PRON
ejpam-5970	406	30	model	model	NOUN
ejpam-5970	406	31	)	)	PUNCT
ejpam-5970	406	32	108.7	108.7	NUM
ejpam-5970	406	33	figure	figure	NOUN
ejpam-5970	406	34	4	4	NUM
ejpam-5970	406	35	presents	present	VERB
ejpam-5970	406	36	a	a	DET
ejpam-5970	406	37	visual	visual	ADJ
ejpam-5970	406	38	comparison	comparison	NOUN
ejpam-5970	406	39	of	of	ADP
ejpam-5970	406	40	the	the	DET
ejpam-5970	406	41	average	average	ADJ
ejpam-5970	406	42	training	training	NOUN
ejpam-5970	406	43	time	time	NOUN
ejpam-5970	406	44	required	require	VERB
ejpam-5970	406	45	by	by	ADP
ejpam-5970	406	46	each	each	DET
ejpam-5970	406	47	model	model	NOUN
ejpam-5970	406	48	over	over	ADP
ejpam-5970	406	49	200	200	NUM
ejpam-5970	406	50	epochs	epoch	NOUN
ejpam-5970	406	51	,	,	PUNCT
ejpam-5970	406	52	while	while	SCONJ
ejpam-5970	406	53	table	table	NOUN
ejpam-5970	406	54	3	3	NUM
ejpam-5970	406	55	provides	provide	VERB
ejpam-5970	406	56	the	the	DET
ejpam-5970	406	57	corresponding	corresponding	ADJ
ejpam-5970	406	58	numerical	numerical	ADJ
ejpam-5970	406	59	values	value	NOUN
ejpam-5970	406	60	.	.	PUNCT
ejpam-5970	407	1	as	as	SCONJ
ejpam-5970	407	2	shown	show	VERB
ejpam-5970	407	3	,	,	PUNCT
ejpam-5970	407	4	stgnn	stgnn	NOUN
ejpam-5970	407	5	required	require	VERB
ejpam-5970	407	6	108.7	108.7	NUM
ejpam-5970	407	7	seconds	second	NOUN
ejpam-5970	407	8	to	to	PART
ejpam-5970	407	9	complete	complete	VERB
ejpam-5970	407	10	200	200	NUM
ejpam-5970	407	11	training	training	NOUN
ejpam-5970	407	12	epochs	epoch	NOUN
ejpam-5970	407	13	,	,	PUNCT
ejpam-5970	407	14	which	which	PRON
ejpam-5970	407	15	is	be	AUX
ejpam-5970	407	16	slightly	slightly	ADV
ejpam-5970	407	17	higher	high	ADJ
ejpam-5970	407	18	than	than	ADP
ejpam-5970	407	19	gcn	gcn	NOUN
ejpam-5970	407	20	and	and	CCONJ
ejpam-5970	407	21	gru	gru	NOUN
ejpam-5970	407	22	,	,	PUNCT
ejpam-5970	407	23	but	but	CCONJ
ejpam-5970	407	24	comparable	comparable	ADJ
ejpam-5970	407	25	to	to	ADP
ejpam-5970	407	26	lstm	lstm	NOUN
ejpam-5970	407	27	and	and	CCONJ
ejpam-5970	407	28	still	still	ADV
ejpam-5970	407	29	within	within	ADP
ejpam-5970	407	30	a	a	DET
ejpam-5970	407	31	practical	practical	ADJ
ejpam-5970	407	32	computational	computational	ADJ
ejpam-5970	407	33	range	range	NOUN
ejpam-5970	407	34	.	.	PUNCT
ejpam-5970	408	1	notably	notably	ADV
ejpam-5970	408	2	,	,	PUNCT
ejpam-5970	408	3	although	although	SCONJ
ejpam-5970	408	4	arima	arima	PROPN
ejpam-5970	408	5	is	be	AUX
ejpam-5970	408	6	the	the	DET
ejpam-5970	408	7	fastest	fast	ADJ
ejpam-5970	408	8	with	with	ADP
ejpam-5970	408	9	only	only	ADV
ejpam-5970	408	10	25.4	25.4	NUM
ejpam-5970	408	11	seconds	second	NOUN
ejpam-5970	408	12	,	,	PUNCT
ejpam-5970	408	13	it	it	PRON
ejpam-5970	408	14	performs	perform	VERB
ejpam-5970	408	15	poorly	poorly	ADV
ejpam-5970	408	16	in	in	ADP
ejpam-5970	408	17	terms	term	NOUN
ejpam-5970	408	18	of	of	ADP
ejpam-5970	408	19	forecasting	forecasting	NOUN
ejpam-5970	408	20	accuracy	accuracy	NOUN
ejpam-5970	408	21	,	,	PUNCT
ejpam-5970	408	22	as	as	SCONJ
ejpam-5970	408	23	previously	previously	ADV
ejpam-5970	408	24	shown	show	VERB
ejpam-5970	408	25	in	in	ADP
ejpam-5970	408	26	table	table	NOUN
ejpam-5970	408	27	2	2	NUM
ejpam-5970	408	28	.	.	PUNCT
ejpam-5970	409	1	this	this	DET
ejpam-5970	409	2	analysis	analysis	NOUN
ejpam-5970	409	3	highlights	highlight	VERB
ejpam-5970	409	4	the	the	DET
ejpam-5970	409	5	trade	trade	NOUN
ejpam-5970	409	6	-	-	PUNCT
ejpam-5970	409	7	off	off	NOUN
ejpam-5970	409	8	between	between	ADP
ejpam-5970	409	9	computational	computational	ADJ
ejpam-5970	409	10	cost	cost	NOUN
ejpam-5970	409	11	and	and	CCONJ
ejpam-5970	409	12	prediction	prediction	NOUN
ejpam-5970	409	13	performance	performance	NOUN
ejpam-5970	409	14	.	.	PUNCT
ejpam-5970	410	1	while	while	SCONJ
ejpam-5970	410	2	stgnn	stgnn	NOUN
ejpam-5970	410	3	has	have	VERB
ejpam-5970	410	4	a	a	DET
ejpam-5970	410	5	higher	high	ADJ
ejpam-5970	410	6	training	training	NOUN
ejpam-5970	410	7	time	time	NOUN
ejpam-5970	410	8	than	than	ADP
ejpam-5970	410	9	simpler	simple	ADJ
ejpam-5970	410	10	models	model	NOUN
ejpam-5970	410	11	,	,	PUNCT
ejpam-5970	410	12	it	it	PRON
ejpam-5970	410	13	offers	offer	VERB
ejpam-5970	410	14	substantial	substantial	ADJ
ejpam-5970	410	15	improvements	improvement	NOUN
ejpam-5970	410	16	in	in	ADP
ejpam-5970	410	17	rmse	rmse	PROPN
ejpam-5970	410	18	,	,	PUNCT
ejpam-5970	410	19	mae	mae	PROPN
ejpam-5970	410	20	,	,	PUNCT
ejpam-5970	410	21	and	and	CCONJ
ejpam-5970	410	22	r2	r2	PROPN
ejpam-5970	410	23	scores	score	NOUN
ejpam-5970	410	24	.	.	PUNCT
ejpam-5970	411	1	given	give	VERB
ejpam-5970	411	2	its	its	PRON
ejpam-5970	411	3	ability	ability	NOUN
ejpam-5970	411	4	to	to	PART
ejpam-5970	411	5	learn	learn	VERB
ejpam-5970	411	6	spatial	spatial	ADJ
ejpam-5970	411	7	and	and	CCONJ
ejpam-5970	411	8	temporal	temporal	ADJ
ejpam-5970	411	9	dependencies	dependency	NOUN
ejpam-5970	411	10	effectively	effectively	ADV
ejpam-5970	411	11	,	,	PUNCT
ejpam-5970	411	12	stgnn	stgnn	NOUN
ejpam-5970	411	13	presents	present	VERB
ejpam-5970	411	14	a	a	DET
ejpam-5970	411	15	balanced	balanced	ADJ
ejpam-5970	411	16	and	and	CCONJ
ejpam-5970	411	17	scalable	scalable	ADJ
ejpam-5970	411	18	solution	solution	NOUN
ejpam-5970	411	19	suitable	suitable	ADJ
ejpam-5970	411	20	for	for	ADP
ejpam-5970	411	21	real	real	ADJ
ejpam-5970	411	22	-	-	PUNCT
ejpam-5970	411	23	world	world	NOUN
ejpam-5970	411	24	agricultural	agricultural	ADJ
ejpam-5970	411	25	forecasting	forecasting	NOUN
ejpam-5970	411	26	applications	application	NOUN
ejpam-5970	411	27	,	,	PUNCT
ejpam-5970	411	28	where	where	SCONJ
ejpam-5970	411	29	both	both	DET
ejpam-5970	411	30	accuracy	accuracy	NOUN
ejpam-5970	411	31	and	and	CCONJ
ejpam-5970	411	32	robustness	robustness	NOUN
ejpam-5970	411	33	are	be	AUX
ejpam-5970	411	34	crucial	crucial	ADJ
ejpam-5970	411	35	.	.	PUNCT
ejpam-5970	412	1	a.	a.	PROPN
ejpam-5970	412	2	i.	i.	PROPN
ejpam-5970	412	3	kristiana	kristiana	PROPN
ejpam-5970	412	4	,	,	PUNCT
ejpam-5970	412	5	et	et	PROPN
ejpam-5970	412	6	al	al	PROPN
ejpam-5970	412	7	.	.	PUNCT
ejpam-5970	412	8	/	/	SYM
ejpam-5970	412	9	eur	eur	PROPN
ejpam-5970	412	10	.	.	PUNCT
ejpam-5970	413	1	j.	j.	PROPN
ejpam-5970	413	2	pure	pure	PROPN
ejpam-5970	413	3	appl	appl	PROPN
ejpam-5970	413	4	.	.	PROPN
ejpam-5970	413	5	math	math	PROPN
ejpam-5970	413	6	,	,	PUNCT
ejpam-5970	413	7	18	18	NUM
ejpam-5970	413	8	(	(	PUNCT
ejpam-5970	413	9	3	3	NUM
ejpam-5970	413	10	)	)	PUNCT
ejpam-5970	413	11	(	(	PUNCT
ejpam-5970	413	12	2025	2025	NUM
ejpam-5970	413	13	)	)	PUNCT
ejpam-5970	413	14	,	,	PUNCT
ejpam-5970	413	15	5970	5970	NUM
ejpam-5970	413	16	16	16	NUM
ejpam-5970	413	17	of	of	ADP
ejpam-5970	413	18	18	18	NUM
ejpam-5970	413	19	figure	figure	NOUN
ejpam-5970	413	20	4	4	NUM
ejpam-5970	413	21	:	:	PUNCT
ejpam-5970	413	22	training	training	NOUN
ejpam-5970	413	23	time	time	NOUN
ejpam-5970	413	24	comparison	comparison	NOUN
ejpam-5970	413	25	over	over	ADP
ejpam-5970	413	26	200	200	NUM
ejpam-5970	413	27	epochs	epoch	NOUN
ejpam-5970	413	28	for	for	ADP
ejpam-5970	413	29	different	different	ADJ
ejpam-5970	413	30	models	model	NOUN
ejpam-5970	413	31	.	.	PUNCT
ejpam-5970	414	1	4	4	X
ejpam-5970	414	2	.	.	X
ejpam-5970	414	3	concluding	conclude	VERB
ejpam-5970	414	4	remarks	remark	NOUN
ejpam-5970	414	5	this	this	DET
ejpam-5970	414	6	study	study	NOUN
ejpam-5970	414	7	introduced	introduce	VERB
ejpam-5970	414	8	a	a	DET
ejpam-5970	414	9	hybrid	hybrid	ADJ
ejpam-5970	414	10	framework	framework	NOUN
ejpam-5970	414	11	that	that	PRON
ejpam-5970	414	12	integrates	integrate	VERB
ejpam-5970	414	13	local	local	ADJ
ejpam-5970	414	14	(	(	PUNCT
ejpam-5970	414	15	a	a	PRON
ejpam-5970	414	16	,	,	PUNCT
ejpam-5970	414	17	d)-edge	d)-edge	ADJ
ejpam-5970	414	18	antimagic	antimagic	ADJ
ejpam-5970	414	19	labeling	labeling	NOUN
ejpam-5970	414	20	and	and	CCONJ
ejpam-5970	414	21	spatio	spatio	PROPN
ejpam-5970	414	22	-	-	PUNCT
ejpam-5970	414	23	temporal	temporal	ADJ
ejpam-5970	414	24	graph	graph	NOUN
ejpam-5970	414	25	neural	neural	ADJ
ejpam-5970	414	26	networks	network	NOUN
ejpam-5970	414	27	(	(	PUNCT
ejpam-5970	414	28	stgnn	stgnn	NOUN
ejpam-5970	414	29	)	)	PUNCT
ejpam-5970	414	30	to	to	PART
ejpam-5970	414	31	forecast	forecast	VERB
ejpam-5970	414	32	soil	soil	NOUN
ejpam-5970	414	33	nutrient	nutrient	NOUN
ejpam-5970	414	34	dynamics	dynamic	NOUN
ejpam-5970	414	35	in	in	ADP
ejpam-5970	414	36	companion	companion	NOUN
ejpam-5970	414	37	plantations	plantation	NOUN
ejpam-5970	414	38	.	.	PUNCT
ejpam-5970	415	1	the	the	DET
ejpam-5970	415	2	labeling	labeling	NOUN
ejpam-5970	415	3	technique	technique	NOUN
ejpam-5970	415	4	was	be	AUX
ejpam-5970	415	5	used	use	VERB
ejpam-5970	415	6	to	to	PART
ejpam-5970	415	7	optimize	optimize	VERB
ejpam-5970	415	8	sensor	sensor	NOUN
ejpam-5970	415	9	placement	placement	NOUN
ejpam-5970	415	10	by	by	ADP
ejpam-5970	415	11	identifying	identify	VERB
ejpam-5970	415	12	representative	representative	ADJ
ejpam-5970	415	13	nodes	node	NOUN
ejpam-5970	415	14	,	,	PUNCT
ejpam-5970	415	15	reducing	reduce	VERB
ejpam-5970	415	16	the	the	DET
ejpam-5970	415	17	number	number	NOUN
ejpam-5970	415	18	of	of	ADP
ejpam-5970	415	19	sensors	sensor	NOUN
ejpam-5970	415	20	from	from	ADP
ejpam-5970	415	21	23	23	NUM
ejpam-5970	415	22	to	to	ADP
ejpam-5970	415	23	just	just	ADV
ejpam-5970	415	24	four	four	NUM
ejpam-5970	415	25	without	without	ADP
ejpam-5970	415	26	compromising	compromise	VERB
ejpam-5970	415	27	coverage	coverage	NOUN
ejpam-5970	415	28	.	.	PUNCT
ejpam-5970	416	1	meanwhile	meanwhile	ADV
ejpam-5970	416	2	,	,	PUNCT
ejpam-5970	416	3	the	the	DET
ejpam-5970	416	4	stgnn	stgnn	PROPN
ejpam-5970	416	5	model	model	NOUN
ejpam-5970	416	6	effectively	effectively	ADV
ejpam-5970	416	7	captured	capture	VERB
ejpam-5970	416	8	spatial	spatial	ADJ
ejpam-5970	416	9	and	and	CCONJ
ejpam-5970	416	10	temporal	temporal	ADJ
ejpam-5970	416	11	dependencies	dependency	NOUN
ejpam-5970	416	12	,	,	PUNCT
ejpam-5970	416	13	outperforming	outperform	VERB
ejpam-5970	416	14	baseline	baseline	NOUN
ejpam-5970	416	15	models	model	NOUN
ejpam-5970	416	16	such	such	ADJ
ejpam-5970	416	17	as	as	ADP
ejpam-5970	416	18	arima	arima	NOUN
ejpam-5970	416	19	,	,	PUNCT
ejpam-5970	416	20	lstm	lstm	NOUN
ejpam-5970	416	21	,	,	PUNCT
ejpam-5970	416	22	gcn	gcn	ADJ
ejpam-5970	416	23	,	,	PUNCT
ejpam-5970	416	24	and	and	CCONJ
ejpam-5970	416	25	gru	gru	VERB
ejpam-5970	416	26	across	across	ADP
ejpam-5970	416	27	rmse	rmse	PROPN
ejpam-5970	416	28	,	,	PUNCT
ejpam-5970	416	29	mae	mae	PROPN
ejpam-5970	416	30	,	,	PUNCT
ejpam-5970	416	31	accuracy	accuracy	NOUN
ejpam-5970	416	32	,	,	PUNCT
ejpam-5970	416	33	and	and	CCONJ
ejpam-5970	416	34	r2	r2	PROPN
ejpam-5970	416	35	metrics	metric	NOUN
ejpam-5970	416	36	.	.	PUNCT
ejpam-5970	417	1	the	the	DET
ejpam-5970	417	2	results	result	NOUN
ejpam-5970	417	3	confirmed	confirm	VERB
ejpam-5970	417	4	that	that	SCONJ
ejpam-5970	417	5	stgnn	stgnn	NOUN
ejpam-5970	417	6	achieves	achieve	VERB
ejpam-5970	417	7	high	high	ADJ
ejpam-5970	417	8	predictive	predictive	ADJ
ejpam-5970	417	9	performance	performance	NOUN
ejpam-5970	417	10	and	and	CCONJ
ejpam-5970	417	11	converges	converge	VERB
ejpam-5970	417	12	efficiently	efficiently	ADV
ejpam-5970	417	13	.	.	PUNCT
ejpam-5970	418	1	the	the	DET
ejpam-5970	418	2	integration	integration	NOUN
ejpam-5970	418	3	of	of	ADP
ejpam-5970	418	4	graph	graph	NOUN
ejpam-5970	418	5	labeling	labeling	NOUN
ejpam-5970	418	6	and	and	CCONJ
ejpam-5970	418	7	deep	deep	ADJ
ejpam-5970	418	8	learning	learning	NOUN
ejpam-5970	418	9	offers	offer	VERB
ejpam-5970	418	10	both	both	CCONJ
ejpam-5970	418	11	theoretical	theoretical	ADJ
ejpam-5970	418	12	and	and	CCONJ
ejpam-5970	418	13	practical	practical	ADJ
ejpam-5970	418	14	contributions	contribution	NOUN
ejpam-5970	418	15	.	.	PUNCT
ejpam-5970	419	1	theoretically	theoretically	ADV
ejpam-5970	419	2	,	,	PUNCT
ejpam-5970	419	3	it	it	PRON
ejpam-5970	419	4	extends	extend	VERB
ejpam-5970	419	5	the	the	DET
ejpam-5970	419	6	applicability	applicability	NOUN
ejpam-5970	419	7	of	of	ADP
ejpam-5970	419	8	local	local	ADJ
ejpam-5970	419	9	antimagic	antimagic	ADJ
ejpam-5970	419	10	labelings	labeling	NOUN
ejpam-5970	419	11	to	to	ADP
ejpam-5970	419	12	data	data	NOUN
ejpam-5970	419	13	-	-	PUNCT
ejpam-5970	419	14	driven	drive	VERB
ejpam-5970	419	15	graph	graph	NOUN
ejpam-5970	419	16	learning	learning	NOUN
ejpam-5970	419	17	.	.	PUNCT
ejpam-5970	420	1	practically	practically	ADV
ejpam-5970	420	2	,	,	PUNCT
ejpam-5970	420	3	it	it	PRON
ejpam-5970	420	4	provides	provide	VERB
ejpam-5970	420	5	a	a	DET
ejpam-5970	420	6	scalable	scalable	ADJ
ejpam-5970	420	7	solution	solution	NOUN
ejpam-5970	420	8	for	for	ADP
ejpam-5970	420	9	precision	precision	NOUN
ejpam-5970	420	10	agriculture	agriculture	NOUN
ejpam-5970	420	11	,	,	PUNCT
ejpam-5970	420	12	enabling	enable	VERB
ejpam-5970	420	13	cost	cost	NOUN
ejpam-5970	420	14	-	-	PUNCT
ejpam-5970	420	15	efficient	efficient	ADJ
ejpam-5970	420	16	monitoring	monitoring	NOUN
ejpam-5970	420	17	and	and	CCONJ
ejpam-5970	420	18	accurate	accurate	ADJ
ejpam-5970	420	19	forecasting	forecasting	NOUN
ejpam-5970	420	20	.	.	PUNCT
ejpam-5970	421	1	future	future	ADJ
ejpam-5970	421	2	work	work	NOUN
ejpam-5970	421	3	may	may	AUX
ejpam-5970	421	4	explore	explore	VERB
ejpam-5970	421	5	dynamic	dynamic	ADJ
ejpam-5970	421	6	graphs	graph	NOUN
ejpam-5970	421	7	,	,	PUNCT
ejpam-5970	421	8	enhance	enhance	VERB
ejpam-5970	421	9	training	training	NOUN
ejpam-5970	421	10	efficiency	efficiency	NOUN
ejpam-5970	421	11	,	,	PUNCT
ejpam-5970	421	12	and	and	CCONJ
ejpam-5970	421	13	adapt	adapt	VERB
ejpam-5970	421	14	this	this	DET
ejpam-5970	421	15	approach	approach	NOUN
ejpam-5970	421	16	to	to	ADP
ejpam-5970	421	17	broader	broad	ADJ
ejpam-5970	421	18	domains	domain	NOUN
ejpam-5970	421	19	such	such	ADJ
ejpam-5970	421	20	as	as	ADP
ejpam-5970	421	21	environmental	environmental	ADJ
ejpam-5970	421	22	monitoring	monitoring	NOUN
ejpam-5970	421	23	and	and	CCONJ
ejpam-5970	421	24	smart	smart	ADJ
ejpam-5970	421	25	farming	farming	NOUN
ejpam-5970	421	26	systems	system	NOUN
ejpam-5970	421	27	.	.	PUNCT
ejpam-5970	422	1	acknowledgements	acknowledgement	NOUN
ejpam-5970	422	2	this	this	DET
ejpam-5970	422	3	work	work	NOUN
ejpam-5970	422	4	was	be	AUX
ejpam-5970	422	5	supported	support	VERB
ejpam-5970	422	6	in	in	ADP
ejpam-5970	422	7	part	part	NOUN
ejpam-5970	422	8	by	by	ADP
ejpam-5970	422	9	lp2m	lp2m	PROPN
ejpam-5970	422	10	-	-	PUNCT
ejpam-5970	422	11	university	university	NOUN
ejpam-5970	422	12	of	of	ADP
ejpam-5970	422	13	jember	jember	PROPN
ejpam-5970	422	14	and	and	CCONJ
ejpam-5970	422	15	pui	pui	PROPN
ejpam-5970	422	16	-	-	PUNCT
ejpam-5970	422	17	pt	pt	NOUN
ejpam-5970	422	18	combinatorics	combinatoric	NOUN
ejpam-5970	422	19	and	and	CCONJ
ejpam-5970	422	20	graph	graph	NOUN
ejpam-5970	422	21	,	,	PUNCT
ejpam-5970	422	22	cgant	cgant	NOUN
ejpam-5970	422	23	-	-	PUNCT
ejpam-5970	422	24	university	university	NOUN
ejpam-5970	422	25	of	of	ADP
ejpam-5970	422	26	jember	jember	PROPN
ejpam-5970	422	27	,	,	PUNCT
ejpam-5970	422	28	for	for	ADP
ejpam-5970	422	29	their	their	PRON
ejpam-5970	422	30	excellent	excellent	ADJ
ejpam-5970	422	31	collaboration	collaboration	NOUN
ejpam-5970	422	32	and	and	CCONJ
ejpam-5970	422	33	support	support	NOUN
ejpam-5970	422	34	in	in	ADP
ejpam-5970	422	35	completing	complete	VERB
ejpam-5970	422	36	this	this	DET
ejpam-5970	422	37	study	study	NOUN
ejpam-5970	422	38	for	for	ADP
ejpam-5970	422	39	the	the	DET
ejpam-5970	422	40	year	year	NOUN
ejpam-5970	422	41	2025	2025	NUM
ejpam-5970	422	42	.	.	PUNCT
ejpam-5970	423	1	a.	a.	PROPN
ejpam-5970	423	2	i.	i.	PROPN
ejpam-5970	423	3	kristiana	kristiana	PROPN
ejpam-5970	423	4	,	,	PUNCT
ejpam-5970	423	5	et	et	PROPN
ejpam-5970	423	6	al	al	PROPN
ejpam-5970	423	7	.	.	PUNCT
ejpam-5970	423	8	/	/	SYM
ejpam-5970	423	9	eur	eur	PROPN
ejpam-5970	423	10	.	.	PUNCT
ejpam-5970	424	1	j.	j.	PROPN
ejpam-5970	424	2	pure	pure	PROPN
ejpam-5970	424	3	appl	appl	PROPN
ejpam-5970	424	4	.	.	PROPN
ejpam-5970	424	5	math	math	PROPN
ejpam-5970	424	6	,	,	PUNCT
ejpam-5970	424	7	18	18	NUM
ejpam-5970	424	8	(	(	PUNCT
ejpam-5970	424	9	3	3	NUM
ejpam-5970	424	10	)	)	PUNCT
ejpam-5970	424	11	(	(	PUNCT
ejpam-5970	424	12	2025	2025	NUM
ejpam-5970	424	13	)	)	PUNCT
ejpam-5970	424	14	,	,	PUNCT
ejpam-5970	424	15	5970	5970	NUM
ejpam-5970	424	16	17	17	NUM
ejpam-5970	424	17	of	of	ADP
ejpam-5970	424	18	18	18	NUM
ejpam-5970	424	19	references	reference	NOUN
ejpam-5970	424	20	[	[	X
ejpam-5970	424	21	1	1	NUM
ejpam-5970	424	22	]	]	PUNCT
ejpam-5970	424	23	i.	i.	PROPN
ejpam-5970	424	24	h.	h.	PROPN
ejpam-5970	424	25	agustin	agustin	PROPN
ejpam-5970	424	26	,	,	PUNCT
ejpam-5970	424	27	m.	m.	PROPN
ejpam-5970	424	28	hasan	hasan	PROPN
ejpam-5970	424	29	,	,	PUNCT
ejpam-5970	424	30	dafik	dafik	PROPN
ejpam-5970	424	31	,	,	PUNCT
ejpam-5970	424	32	r.	r.	PROPN
ejpam-5970	424	33	alfarisi	alfarisi	PROPN
ejpam-5970	424	34	,	,	PUNCT
ejpam-5970	424	35	and	and	CCONJ
ejpam-5970	424	36	r.	r.	PROPN
ejpam-5970	424	37	m.	m.	PROPN
ejpam-5970	424	38	prihandini	prihandini	PROPN
ejpam-5970	424	39	.	.	PUNCT
ejpam-5970	425	1	local	local	ADJ
ejpam-5970	425	2	edge	edge	NOUN
ejpam-5970	425	3	antimagic	antimagic	ADJ
ejpam-5970	425	4	coloring	coloring	NOUN
ejpam-5970	425	5	of	of	ADP
ejpam-5970	425	6	graphs	graph	NOUN
ejpam-5970	425	7	.	.	PUNCT
ejpam-5970	426	1	far	far	PROPN
ejpam-5970	426	2	east	east	PROPN
ejpam-5970	426	3	journal	journal	PROPN
ejpam-5970	426	4	of	of	ADP
ejpam-5970	426	5	mathematical	mathematical	ADJ
ejpam-5970	426	6	sciences	sciences	PROPN
ejpam-5970	426	7	(	(	PUNCT
ejpam-5970	426	8	fjms	fjms	NOUN
ejpam-5970	426	9	)	)	PUNCT
ejpam-5970	426	10	,	,	PUNCT
ejpam-5970	426	11	102(9):1925–1941	102(9):1925–1941	PROPN
ejpam-5970	426	12	,	,	PUNCT
ejpam-5970	426	13	2017	2017	NUM
ejpam-5970	426	14	.	.	PUNCT
ejpam-5970	427	1	[	[	X
ejpam-5970	427	2	2	2	NUM
ejpam-5970	427	3	]	]	PUNCT
ejpam-5970	427	4	i.	i.	PROPN
ejpam-5970	427	5	h.	h.	PROPN
ejpam-5970	427	6	agustin	agustin	PROPN
ejpam-5970	427	7	,	,	PUNCT
ejpam-5970	427	8	m.	m.	PROPN
ejpam-5970	427	9	hasan	hasan	PROPN
ejpam-5970	427	10	,	,	PUNCT
ejpam-5970	427	11	dafik	dafik	PROPN
ejpam-5970	427	12	,	,	PUNCT
ejpam-5970	427	13	r.	r.	PROPN
ejpam-5970	427	14	alfarisi	alfarisi	PROPN
ejpam-5970	427	15	,	,	PUNCT
ejpam-5970	427	16	a.	a.	PROPN
ejpam-5970	427	17	i.	i.	PROPN
ejpam-5970	427	18	kristiana	kristiana	PROPN
ejpam-5970	427	19	,	,	PUNCT
ejpam-5970	427	20	and	and	CCONJ
ejpam-5970	427	21	r.	r.	PROPN
ejpam-5970	427	22	m.	m.	PROPN
ejpam-5970	427	23	prihandini	prihandini	PROPN
ejpam-5970	427	24	.	.	PUNCT
ejpam-5970	428	1	local	local	ADJ
ejpam-5970	428	2	edge	edge	NOUN
ejpam-5970	428	3	antimagic	antimagic	ADJ
ejpam-5970	428	4	coloring	coloring	NOUN
ejpam-5970	428	5	of	of	ADP
ejpam-5970	428	6	comb	comb	NOUN
ejpam-5970	428	7	product	product	NOUN
ejpam-5970	428	8	of	of	ADP
ejpam-5970	428	9	graphs	graph	NOUN
ejpam-5970	428	10	.	.	PUNCT
ejpam-5970	429	1	in	in	ADP
ejpam-5970	429	2	journal	journal	PROPN
ejpam-5970	429	3	of	of	ADP
ejpam-5970	429	4	physics	physics	PROPN
ejpam-5970	429	5	:	:	PUNCT
ejpam-5970	429	6	conference	conference	NOUN
ejpam-5970	429	7	series	series	NOUN
ejpam-5970	429	8	,	,	PUNCT
ejpam-5970	429	9	2018	2018	NUM
ejpam-5970	429	10	.	.	PUNCT
ejpam-5970	430	1	[	[	X
ejpam-5970	430	2	3	3	X
ejpam-5970	430	3	]	]	X
ejpam-5970	430	4	s.	s.	PROPN
ejpam-5970	430	5	aisyah	aisyah	PROPN
ejpam-5970	430	6	,	,	PUNCT
ejpam-5970	430	7	r.	r.	PROPN
ejpam-5970	430	8	alfarisi	alfarisi	PROPN
ejpam-5970	430	9	,	,	PUNCT
ejpam-5970	430	10	r.	r.	PROPN
ejpam-5970	430	11	m.	m.	PROPN
ejpam-5970	430	12	prihandini	prihandini	PROPN
ejpam-5970	430	13	,	,	PUNCT
ejpam-5970	430	14	a.	a.	PROPN
ejpam-5970	430	15	i.	i.	PROPN
ejpam-5970	430	16	kristiana	kristiana	PROPN
ejpam-5970	430	17	,	,	PUNCT
ejpam-5970	430	18	and	and	CCONJ
ejpam-5970	430	19	r.	r.	PROPN
ejpam-5970	430	20	dwi	dwi	PROPN
ejpam-5970	430	21	.	.	PUNCT
ejpam-5970	431	1	on	on	ADP
ejpam-5970	431	2	the	the	DET
ejpam-5970	431	3	local	local	ADJ
ejpam-5970	431	4	edge	edge	NOUN
ejpam-5970	431	5	antimagic	antimagic	ADJ
ejpam-5970	431	6	coloring	coloring	NOUN
ejpam-5970	431	7	of	of	ADP
ejpam-5970	431	8	corona	corona	NOUN
ejpam-5970	431	9	product	product	NOUN
ejpam-5970	431	10	of	of	ADP
ejpam-5970	431	11	path	path	NOUN
ejpam-5970	431	12	and	and	CCONJ
ejpam-5970	431	13	cycle	cycle	NOUN
ejpam-5970	431	14	.	.	PUNCT
ejpam-5970	432	1	cauchy	cauchy	ADJ
ejpam-5970	432	2	–	–	PUNCT
ejpam-5970	432	3	jurnal	jurnal	ADJ
ejpam-5970	432	4	matematika	matematika	PROPN
ejpam-5970	432	5	murni	murni	PROPN
ejpam-5970	432	6	dan	dan	PROPN
ejpam-5970	432	7	aplikasi	aplikasi	PROPN
ejpam-5970	432	8	,	,	PUNCT
ejpam-5970	432	9	6(1):40–48	6(1):40–48	NUM
ejpam-5970	432	10	,	,	PUNCT
ejpam-5970	432	11	2019	2019	NUM
ejpam-5970	432	12	.	.	PUNCT
ejpam-5970	433	1	[	[	X
ejpam-5970	433	2	4	4	X
ejpam-5970	433	3	]	]	PUNCT
ejpam-5970	433	4	z.	z.	PROPN
ejpam-5970	433	5	l.	l.	PROPN
ejpam-5970	433	6	al	al	PROPN
ejpam-5970	433	7	jabbar	jabbar	PROPN
ejpam-5970	433	8	,	,	PUNCT
ejpam-5970	433	9	dafik	dafik	PROPN
ejpam-5970	433	10	,	,	PUNCT
ejpam-5970	433	11	r.	r.	PROPN
ejpam-5970	433	12	adawiyah	adawiyah	PROPN
ejpam-5970	433	13	,	,	PUNCT
ejpam-5970	433	14	e.	e.	PROPN
ejpam-5970	433	15	r.	r.	PROPN
ejpam-5970	433	16	albirri	albirri	PROPN
ejpam-5970	433	17	,	,	PUNCT
ejpam-5970	433	18	and	and	CCONJ
ejpam-5970	433	19	i.	i.	PROPN
ejpam-5970	433	20	h.	h.	PROPN
ejpam-5970	433	21	agustin	agustin	PROPN
ejpam-5970	433	22	.	.	PUNCT
ejpam-5970	434	1	on	on	ADP
ejpam-5970	434	2	rainbow	rainbow	NOUN
ejpam-5970	434	3	antimagic	antimagic	ADJ
ejpam-5970	434	4	coloring	coloring	NOUN
ejpam-5970	434	5	of	of	ADP
ejpam-5970	434	6	some	some	DET
ejpam-5970	434	7	special	special	ADJ
ejpam-5970	434	8	graphs	graph	NOUN
ejpam-5970	434	9	.	.	PUNCT
ejpam-5970	435	1	in	in	ADP
ejpam-5970	435	2	journal	journal	PROPN
ejpam-5970	435	3	of	of	ADP
ejpam-5970	435	4	physics	physics	PROPN
ejpam-5970	435	5	:	:	PUNCT
ejpam-5970	435	6	conference	conference	NOUN
ejpam-5970	435	7	series	series	NOUN
ejpam-5970	435	8	icopambs	icopambs	ADJ
ejpam-5970	435	9	2019	2019	NUM
ejpam-5970	435	10	,	,	PUNCT
ejpam-5970	435	11	pages	page	NOUN
ejpam-5970	435	12	1465	1465	NUM
ejpam-5970	435	13	,	,	PUNCT
ejpam-5970	435	14	1–8	1–8	NUM
ejpam-5970	435	15	,	,	PUNCT
ejpam-5970	435	16	2020	2020	NUM
ejpam-5970	435	17	.	.	PUNCT
ejpam-5970	436	1	[	[	X
ejpam-5970	436	2	5	5	NUM
ejpam-5970	436	3	]	]	PUNCT
ejpam-5970	436	4	i.	i.	PROPN
ejpam-5970	436	5	h.	h.	PROPN
ejpam-5970	436	6	agustin	agustin	PROPN
ejpam-5970	436	7	,	,	PUNCT
ejpam-5970	436	8	dafik	dafik	PROPN
ejpam-5970	436	9	,	,	PUNCT
ejpam-5970	436	10	e.	e.	PROPN
ejpam-5970	436	11	y.	y.	PROPN
ejpam-5970	436	12	kurniawati	kurniawati	PROPN
ejpam-5970	436	13	,	,	PUNCT
ejpam-5970	436	14	marsidi	marsidi	NOUN
ejpam-5970	436	15	,	,	PUNCT
ejpam-5970	436	16	n.	n.	NOUN
ejpam-5970	436	17	mohanapriya	mohanapriya	NOUN
ejpam-5970	436	18	,	,	PUNCT
ejpam-5970	436	19	and	and	CCONJ
ejpam-5970	436	20	a.	a.	PROPN
ejpam-5970	436	21	i.	i.	PROPN
ejpam-5970	436	22	kristiana	kristiana	PROPN
ejpam-5970	436	23	.	.	PUNCT
ejpam-5970	437	1	on	on	ADP
ejpam-5970	437	2	the	the	DET
ejpam-5970	437	3	local	local	ADJ
ejpam-5970	437	4	(	(	PUNCT
ejpam-5970	437	5	a	a	PRON
ejpam-5970	437	6	,	,	PUNCT
ejpam-5970	437	7	d)-antimagic	d)-antimagic	NOUN
ejpam-5970	437	8	coloring	coloring	NOUN
ejpam-5970	437	9	of	of	ADP
ejpam-5970	437	10	graphs	graph	NOUN
ejpam-5970	437	11	.	.	PUNCT
ejpam-5970	438	1	2022	2022	NUM
ejpam-5970	438	2	.	.	PUNCT
ejpam-5970	439	1	[	[	X
ejpam-5970	439	2	6	6	NUM
ejpam-5970	439	3	]	]	PUNCT
ejpam-5970	439	4	dafik	dafik	NOUN
ejpam-5970	439	5	,	,	PUNCT
ejpam-5970	439	6	i.	i.	PROPN
ejpam-5970	439	7	l.	l.	PROPN
ejpam-5970	439	8	mursyidah	mursyidah	PROPN
ejpam-5970	439	9	,	,	PUNCT
ejpam-5970	439	10	i.	i.	PROPN
ejpam-5970	439	11	h.	h.	PROPN
ejpam-5970	439	12	agustin	agustin	PROPN
ejpam-5970	439	13	,	,	PUNCT
ejpam-5970	439	14	r.	r.	PROPN
ejpam-5970	439	15	i.	i.	PROPN
ejpam-5970	439	16	baihaki	baihaki	PROPN
ejpam-5970	439	17	,	,	PUNCT
ejpam-5970	439	18	f.	f.	PROPN
ejpam-5970	439	19	g.	g.	PROPN
ejpam-5970	439	20	febrinanto	febrinanto	PROPN
ejpam-5970	439	21	,	,	PUNCT
ejpam-5970	439	22	s.	s.	PROPN
ejpam-5970	439	23	husain	husain	PROPN
ejpam-5970	439	24	,	,	PUNCT
ejpam-5970	439	25	s.	s.	PROPN
ejpam-5970	439	26	k.	k.	PROPN
ejpam-5970	439	27	binti	binti	PROPN
ejpam-5970	439	28	,	,	PUNCT
ejpam-5970	439	29	and	and	CCONJ
ejpam-5970	439	30	r.	r.	PROPN
ejpam-5970	439	31	sunder	sunder	PROPN
ejpam-5970	439	32	.	.	PUNCT
ejpam-5970	440	1	on	on	ADP
ejpam-5970	440	2	rainbow	rainbow	PROPN
ejpam-5970	440	3	vertex	vertex	NOUN
ejpam-5970	440	4	antimagic	antimagic	NOUN
ejpam-5970	440	5	coloring	coloring	NOUN
ejpam-5970	440	6	and	and	CCONJ
ejpam-5970	440	7	its	its	PRON
ejpam-5970	440	8	application	application	NOUN
ejpam-5970	440	9	on	on	ADP
ejpam-5970	440	10	stgnn	stgnn	PROPN
ejpam-5970	440	11	time	time	PROPN
ejpam-5970	440	12	series	series	PROPN
ejpam-5970	440	13	forecasting	forecasting	NOUN
ejpam-5970	440	14	on	on	ADP
ejpam-5970	440	15	subsidized	subsidized	ADJ
ejpam-5970	440	16	diesel	diesel	NOUN
ejpam-5970	440	17	consumption	consumption	NOUN
ejpam-5970	440	18	.	.	PUNCT
ejpam-5970	441	1	iaeng	iaeng	PROPN
ejpam-5970	441	2	international	international	PROPN
ejpam-5970	441	3	journal	journal	PROPN
ejpam-5970	441	4	of	of	ADP
ejpam-5970	441	5	applied	apply	VERB
ejpam-5970	441	6	mathematics	mathematic	NOUN
ejpam-5970	441	7	,	,	PUNCT
ejpam-5970	441	8	54(5	54(5	NOUN
ejpam-5970	441	9	)	)	PUNCT
ejpam-5970	441	10	,	,	PUNCT
ejpam-5970	441	11	2024	2024	NUM
ejpam-5970	441	12	.	.	PUNCT
ejpam-5970	442	1	[	[	X
ejpam-5970	442	2	7	7	NUM
ejpam-5970	442	3	]	]	PUNCT
ejpam-5970	442	4	a.	a.	PROPN
ejpam-5970	442	5	i.	i.	PROPN
ejpam-5970	442	6	kristiana	kristiana	PROPN
ejpam-5970	442	7	,	,	PUNCT
ejpam-5970	442	8	e.	e.	PROPN
ejpam-5970	442	9	rachmasari	rachmasari	PROPN
ejpam-5970	442	10	,	,	PUNCT
ejpam-5970	442	11	i.	i.	PROPN
ejpam-5970	442	12	h.	h.	PROPN
ejpam-5970	442	13	agustin	agustin	PROPN
ejpam-5970	442	14	,	,	PUNCT
ejpam-5970	442	15	i.	i.	PROPN
ejpam-5970	442	16	l.	l.	PROPN
ejpam-5970	442	17	mursyidah	mursyidah	PROPN
ejpam-5970	442	18	,	,	PUNCT
ejpam-5970	442	19	and	and	CCONJ
ejpam-5970	442	20	r.	r.	PROPN
ejpam-5970	442	21	alfarisi	alfarisi	PROPN
ejpam-5970	442	22	.	.	PUNCT
ejpam-5970	443	1	on	on	ADP
ejpam-5970	443	2	bcoloring	bcolore	VERB
ejpam-5970	443	3	analysis	analysis	NOUN
ejpam-5970	443	4	of	of	ADP
ejpam-5970	443	5	graphs	graph	NOUN
ejpam-5970	443	6	:	:	PUNCT
ejpam-5970	443	7	an	an	DET
ejpam-5970	443	8	application	application	NOUN
ejpam-5970	443	9	to	to	ADP
ejpam-5970	443	10	spatio	spatio	NOUN
ejpam-5970	443	11	-	-	PUNCT
ejpam-5970	443	12	temporal	temporal	ADJ
ejpam-5970	443	13	graph	graph	NOUN
ejpam-5970	443	14	neural	neural	ADJ
ejpam-5970	443	15	networks	network	NOUN
ejpam-5970	443	16	for	for	ADP
ejpam-5970	443	17	multi	multi	ADJ
ejpam-5970	443	18	-	-	ADJ
ejpam-5970	443	19	step	step	ADJ
ejpam-5970	443	20	time	time	NOUN
ejpam-5970	443	21	series	series	PROPN
ejpam-5970	443	22	forecasting	forecasting	NOUN
ejpam-5970	443	23	of	of	ADP
ejpam-5970	443	24	soil	soil	NOUN
ejpam-5970	443	25	moisture	moisture	NOUN
ejpam-5970	443	26	and	and	CCONJ
ejpam-5970	443	27	ph	ph	ADJ
ejpam-5970	443	28	in	in	ADP
ejpam-5970	443	29	companion	companion	NOUN
ejpam-5970	443	30	farming	farming	NOUN
ejpam-5970	443	31	.	.	PUNCT
ejpam-5970	444	1	european	european	ADJ
ejpam-5970	444	2	journal	journal	PROPN
ejpam-5970	444	3	of	of	ADP
ejpam-5970	444	4	pure	pure	ADJ
ejpam-5970	444	5	and	and	CCONJ
ejpam-5970	444	6	applied	applied	ADJ
ejpam-5970	444	7	mathematics	mathematic	NOUN
ejpam-5970	444	8	,	,	PUNCT
ejpam-5970	444	9	17(4):3356–3369	17(4):3356–3369	NUM
ejpam-5970	444	10	,	,	PUNCT
ejpam-5970	444	11	2024	2024	NUM
ejpam-5970	444	12	.	.	PUNCT
ejpam-5970	445	1	[	[	X
ejpam-5970	445	2	8	8	NUM
ejpam-5970	445	3	]	]	X
ejpam-5970	445	4	r.	r.	PROPN
ejpam-5970	445	5	alfarisi	alfarisi	PROPN
ejpam-5970	445	6	,	,	PUNCT
ejpam-5970	445	7	r.	r.	PROPN
ejpam-5970	445	8	m.	m.	PROPN
ejpam-5970	445	9	prihandini	prihandini	PROPN
ejpam-5970	445	10	,	,	PUNCT
ejpam-5970	445	11	r.	r.	PROPN
ejpam-5970	445	12	adawiyah	adawiyah	PROPN
ejpam-5970	445	13	,	,	PUNCT
ejpam-5970	445	14	e.	e.	PROPN
ejpam-5970	445	15	r.	r.	PROPN
ejpam-5970	445	16	albirri	albirri	PROPN
ejpam-5970	445	17	,	,	PUNCT
ejpam-5970	445	18	and	and	CCONJ
ejpam-5970	445	19	i.	i.	PROPN
ejpam-5970	445	20	h.	h.	PROPN
ejpam-5970	445	21	agustin	agustin	PROPN
ejpam-5970	445	22	.	.	PUNCT
ejpam-5970	446	1	graceful	graceful	ADJ
ejpam-5970	446	2	chromatic	chromatic	ADJ
ejpam-5970	446	3	number	number	NOUN
ejpam-5970	446	4	of	of	ADP
ejpam-5970	446	5	unicyclic	unicyclic	ADJ
ejpam-5970	446	6	graphs	graph	NOUN
ejpam-5970	446	7	.	.	PUNCT
ejpam-5970	447	1	in	in	ADP
ejpam-5970	447	2	journal	journal	PROPN
ejpam-5970	447	3	of	of	ADP
ejpam-5970	447	4	physics	physics	PROPN
ejpam-5970	447	5	:	:	PUNCT
ejpam-5970	447	6	conference	conference	NOUN
ejpam-5970	447	7	series	series	NOUN
ejpam-5970	447	8	,	,	PUNCT
ejpam-5970	447	9	volume	volume	NOUN
ejpam-5970	447	10	1306	1306	NUM
ejpam-5970	447	11	,	,	PUNCT
ejpam-5970	447	12	page	page	NOUN
ejpam-5970	447	13	012039	012039	NUM
ejpam-5970	447	14	.	.	PUNCT
ejpam-5970	448	1	iop	iop	PROPN
ejpam-5970	448	2	publishing	publishing	NOUN
ejpam-5970	448	3	,	,	PUNCT
ejpam-5970	448	4	2019	2019	NUM
ejpam-5970	448	5	.	.	PUNCT
ejpam-5970	449	1	[	[	X
ejpam-5970	449	2	9	9	NUM
ejpam-5970	449	3	]	]	PUNCT
ejpam-5970	449	4	dafik	dafik	NOUN
ejpam-5970	449	5	,	,	PUNCT
ejpam-5970	449	6	i.	i.	PROPN
ejpam-5970	449	7	h.	h.	PROPN
ejpam-5970	449	8	agustin	agustin	PROPN
ejpam-5970	449	9	,	,	PUNCT
ejpam-5970	449	10	surahmat	surahmat	NOUN
ejpam-5970	449	11	,	,	PUNCT
ejpam-5970	449	12	r.	r.	PROPN
ejpam-5970	449	13	alfarisi	alfarisi	PROPN
ejpam-5970	449	14	,	,	PUNCT
ejpam-5970	449	15	and	and	CCONJ
ejpam-5970	449	16	s.	s.	PROPN
ejpam-5970	449	17	sy	sy	PROPN
ejpam-5970	449	18	.	.	PROPN
ejpam-5970	450	1	on	on	ADP
ejpam-5970	450	2	non	non	ADJ
ejpam-5970	450	3	-	-	ADJ
ejpam-5970	450	4	isolated	isolated	ADJ
ejpam-5970	450	5	resolving	resolving	NOUN
ejpam-5970	450	6	number	number	NOUN
ejpam-5970	450	7	of	of	ADP
ejpam-5970	450	8	special	special	ADJ
ejpam-5970	450	9	graphs	graph	NOUN
ejpam-5970	450	10	and	and	CCONJ
ejpam-5970	450	11	their	their	PRON
ejpam-5970	450	12	operations	operation	NOUN
ejpam-5970	450	13	.	.	PUNCT
ejpam-5970	451	1	far	far	PROPN
ejpam-5970	451	2	east	east	PROPN
ejpam-5970	451	3	journal	journal	PROPN
ejpam-5970	451	4	of	of	ADP
ejpam-5970	451	5	mathematical	mathematical	ADJ
ejpam-5970	451	6	sciences	sciences	PROPN
ejpam-5970	451	7	,	,	PUNCT
ejpam-5970	451	8	102(10):2473–2492	102(10):2473–2492	NUM
ejpam-5970	451	9	,	,	PUNCT
ejpam-5970	451	10	2017	2017	NUM
ejpam-5970	451	11	.	.	PUNCT
ejpam-5970	452	1	[	[	X
ejpam-5970	452	2	10	10	NUM
ejpam-5970	452	3	]	]	X
ejpam-5970	452	4	b.	b.	PROPN
ejpam-5970	452	5	j.	j.	PROPN
ejpam-5970	452	6	septory	septory	PROPN
ejpam-5970	452	7	,	,	PUNCT
ejpam-5970	452	8	m.	m.	NOUN
ejpam-5970	452	9	i.	i.	PROPN
ejpam-5970	452	10	utoyo	utoyo	PROPN
ejpam-5970	452	11	,	,	PUNCT
ejpam-5970	452	12	b.	b.	PROPN
ejpam-5970	452	13	sulistiyono	sulistiyono	PROPN
ejpam-5970	452	14	,	,	PUNCT
ejpam-5970	452	15	and	and	CCONJ
ejpam-5970	452	16	i.	i.	PROPN
ejpam-5970	452	17	h.	h.	PROPN
ejpam-5970	452	18	agustin	agustin	PROPN
ejpam-5970	452	19	.	.	PUNCT
ejpam-5970	453	1	on	on	ADP
ejpam-5970	453	2	rainbow	rainbow	NOUN
ejpam-5970	453	3	antimagic	antimagic	ADJ
ejpam-5970	453	4	coloring	coloring	NOUN
ejpam-5970	453	5	of	of	ADP
ejpam-5970	453	6	special	special	ADJ
ejpam-5970	453	7	graphs	graph	NOUN
ejpam-5970	453	8	.	.	PUNCT
ejpam-5970	454	1	in	in	ADP
ejpam-5970	454	2	journal	journal	PROPN
ejpam-5970	454	3	of	of	ADP
ejpam-5970	454	4	physics	physics	PROPN
ejpam-5970	454	5	:	:	PUNCT
ejpam-5970	454	6	conference	conference	NOUN
ejpam-5970	454	7	series	series	NOUN
ejpam-5970	454	8	,	,	PUNCT
ejpam-5970	454	9	volume	volume	NOUN
ejpam-5970	454	10	1836	1836	NUM
ejpam-5970	454	11	,	,	PUNCT
ejpam-5970	454	12	page	page	NOUN
ejpam-5970	454	13	012106	012106	NUM
ejpam-5970	454	14	.	.	PUNCT
ejpam-5970	455	1	iop	iop	PROPN
ejpam-5970	455	2	publishing	publishing	NOUN
ejpam-5970	455	3	,	,	PUNCT
ejpam-5970	455	4	2021	2021	NUM
ejpam-5970	455	5	.	.	PUNCT
ejpam-5970	456	1	[	[	X
ejpam-5970	456	2	11	11	NUM
ejpam-5970	456	3	]	]	PUNCT
ejpam-5970	456	4	a.	a.	NOUN
ejpam-5970	456	5	w.	w.	PROPN
ejpam-5970	456	6	gembong	gembong	PROPN
ejpam-5970	456	7	and	and	CCONJ
ejpam-5970	456	8	i.	i.	PROPN
ejpam-5970	456	9	h.	h.	PROPN
ejpam-5970	456	10	agustin	agustin	PROPN
ejpam-5970	456	11	.	.	PUNCT
ejpam-5970	457	1	bound	bind	VERB
ejpam-5970	457	2	of	of	ADP
ejpam-5970	457	3	distance	distance	NOUN
ejpam-5970	457	4	domination	domination	NOUN
ejpam-5970	457	5	number	number	NOUN
ejpam-5970	457	6	of	of	ADP
ejpam-5970	457	7	graph	graph	NOUN
ejpam-5970	457	8	and	and	CCONJ
ejpam-5970	457	9	edge	edge	NOUN
ejpam-5970	457	10	comb	comb	NOUN
ejpam-5970	457	11	product	product	NOUN
ejpam-5970	457	12	graph	graph	NOUN
ejpam-5970	457	13	.	.	PUNCT
ejpam-5970	458	1	in	in	ADP
ejpam-5970	458	2	journal	journal	PROPN
ejpam-5970	458	3	of	of	ADP
ejpam-5970	458	4	physics	physics	PROPN
ejpam-5970	458	5	:	:	PUNCT
ejpam-5970	458	6	conference	conference	NOUN
ejpam-5970	458	7	series	series	NOUN
ejpam-5970	458	8	,	,	PUNCT
ejpam-5970	458	9	volume	volume	NOUN
ejpam-5970	458	10	855	855	NUM
ejpam-5970	458	11	,	,	PUNCT
ejpam-5970	458	12	page	page	NOUN
ejpam-5970	458	13	012014	012014	NUM
ejpam-5970	458	14	.	.	PUNCT
ejpam-5970	459	1	iop	iop	NOUN
ejpam-5970	459	2	publishing	publishing	NOUN
ejpam-5970	459	3	,	,	PUNCT
ejpam-5970	459	4	2017	2017	NUM
ejpam-5970	459	5	.	.	PUNCT
ejpam-5970	460	1	[	[	X
ejpam-5970	460	2	12	12	NUM
ejpam-5970	460	3	]	]	PUNCT
ejpam-5970	460	4	r.	r.	PROPN
ejpam-5970	460	5	sundaramoorthy	sundaramoorthy	PROPN
ejpam-5970	460	6	and	and	CCONJ
ejpam-5970	460	7	n.	n.	PROPN
ejpam-5970	460	8	m.	m.	PROPN
ejpam-5970	460	9	chettiar	chettiar	PROPN
ejpam-5970	460	10	.	.	PUNCT
ejpam-5970	461	1	on	on	ADP
ejpam-5970	461	2	(	(	PUNCT
ejpam-5970	461	3	a	a	DET
ejpam-5970	461	4	,	,	PUNCT
ejpam-5970	461	5	d)-edge	d)-edge	ADJ
ejpam-5970	461	6	local	local	ADJ
ejpam-5970	461	7	antimagic	antimagic	ADJ
ejpam-5970	461	8	coloring	coloring	NOUN
ejpam-5970	461	9	number	number	NOUN
ejpam-5970	461	10	of	of	ADP
ejpam-5970	461	11	graphs	graph	NOUN
ejpam-5970	461	12	.	.	PUNCT
ejpam-5970	462	1	turkish	turkish	ADJ
ejpam-5970	462	2	journal	journal	NOUN
ejpam-5970	462	3	of	of	ADP
ejpam-5970	462	4	mathematics	mathematic	NOUN
ejpam-5970	462	5	,	,	PUNCT
ejpam-5970	462	6	46:1994–2002	46:1994–2002	NUM
ejpam-5970	462	7	,	,	PUNCT
ejpam-5970	462	8	2022	2022	NUM
ejpam-5970	462	9	.	.	PUNCT
ejpam-5970	463	1	[	[	X
ejpam-5970	463	2	13	13	NUM
ejpam-5970	463	3	]	]	X
ejpam-5970	463	4	i.	i.	PROPN
ejpam-5970	463	5	h.	h.	PROPN
ejpam-5970	463	6	agustin	agustin	PROPN
ejpam-5970	463	7	,	,	PUNCT
ejpam-5970	463	8	dafik	dafik	PROPN
ejpam-5970	463	9	,	,	PUNCT
ejpam-5970	463	10	e.	e.	PROPN
ejpam-5970	463	11	y.	y.	PROPN
ejpam-5970	463	12	kurniawati	kurniawati	PROPN
ejpam-5970	463	13	,	,	PUNCT
ejpam-5970	463	14	m.	m.	NOUN
ejpam-5970	463	15	marsidi	marsidi	NOUN
ejpam-5970	463	16	,	,	PUNCT
ejpam-5970	463	17	n.	n.	NOUN
ejpam-5970	463	18	mohanapriya	mohanapriya	NOUN
ejpam-5970	463	19	,	,	PUNCT
ejpam-5970	463	20	and	and	CCONJ
ejpam-5970	463	21	a.	a.	PROPN
ejpam-5970	463	22	i.	i.	PROPN
ejpam-5970	463	23	kristiana	kristiana	PROPN
ejpam-5970	463	24	.	.	PUNCT
ejpam-5970	464	1	on	on	ADP
ejpam-5970	464	2	the	the	DET
ejpam-5970	464	3	local	local	ADJ
ejpam-5970	464	4	edge	edge	NOUN
ejpam-5970	464	5	(	(	PUNCT
ejpam-5970	464	6	a	a	DET
ejpam-5970	464	7	,	,	PUNCT
ejpam-5970	464	8	d)-antimagic	d)-antimagic	NOUN
ejpam-5970	464	9	coloring	coloring	NOUN
ejpam-5970	464	10	of	of	ADP
ejpam-5970	464	11	graphs	graph	NOUN
ejpam-5970	464	12	:	:	PUNCT
ejpam-5970	464	13	a	a	DET
ejpam-5970	464	14	new	new	ADJ
ejpam-5970	464	15	notion	notion	NOUN
ejpam-5970	464	16	.	.	PUNCT
ejpam-5970	465	1	in	in	ADP
ejpam-5970	465	2	5th	5th	ADJ
ejpam-5970	465	3	international	international	ADJ
ejpam-5970	465	4	conference	conference	NOUN
ejpam-5970	465	5	on	on	ADP
ejpam-5970	465	6	current	current	ADJ
ejpam-5970	465	7	scenario	scenario	NOUN
ejpam-5970	465	8	in	in	ADP
ejpam-5970	465	9	pure	pure	ADJ
ejpam-5970	465	10	and	and	CCONJ
ejpam-5970	465	11	applied	applied	ADJ
ejpam-5970	465	12	mathematics	mathematic	NOUN
ejpam-5970	465	13	(	(	PUNCT
ejpam-5970	465	14	iccspam-2022	iccspam-2022	NOUN
ejpam-5970	465	15	)	)	PUNCT
ejpam-5970	465	16	,	,	PUNCT
ejpam-5970	465	17	volume	volume	NOUN
ejpam-5970	465	18	2718	2718	NUM
ejpam-5970	465	19	,	,	PUNCT
ejpam-5970	465	20	page	page	NOUN
ejpam-5970	465	21	020002	020002	NUM
ejpam-5970	465	22	.	.	PUNCT
ejpam-5970	466	1	aip	aip	PROPN
ejpam-5970	466	2	publishing	publishing	PROPN
ejpam-5970	466	3	llc	llc	PROPN
ejpam-5970	466	4	,	,	PUNCT
ejpam-5970	466	5	2023	2023	NUM
ejpam-5970	466	6	.	.	PUNCT
ejpam-5970	467	1	[	[	X
ejpam-5970	467	2	14	14	NUM
ejpam-5970	467	3	]	]	PUNCT
ejpam-5970	467	4	f.	f.	PROPN
ejpam-5970	467	5	p.	p.	PROPN
ejpam-5970	467	6	almaidah	almaidah	PROPN
ejpam-5970	467	7	,	,	PUNCT
ejpam-5970	467	8	dafik	dafik	NOUN
ejpam-5970	467	9	,	,	PUNCT
ejpam-5970	467	10	a.	a.	PROPN
ejpam-5970	467	11	i.	i.	PROPN
ejpam-5970	467	12	kristiana	kristiana	PROPN
ejpam-5970	467	13	,	,	PUNCT
ejpam-5970	467	14	r.	r.	PROPN
ejpam-5970	467	15	adawiyah	adawiyah	PROPN
ejpam-5970	467	16	,	,	PUNCT
ejpam-5970	467	17	r.	r.	PROPN
ejpam-5970	467	18	m.	m.	PROPN
ejpam-5970	467	19	prihandini	prihandini	PROPN
ejpam-5970	467	20	,	,	PUNCT
ejpam-5970	467	21	and	and	CCONJ
ejpam-5970	467	22	i.	i.	PROPN
ejpam-5970	467	23	h.	h.	PROPN
ejpam-5970	467	24	a.	a.	PROPN
ejpam-5970	467	25	i.	i.	PROPN
ejpam-5970	467	26	kristiana	kristiana	PROPN
ejpam-5970	467	27	,	,	PUNCT
ejpam-5970	467	28	et	et	PROPN
ejpam-5970	467	29	al	al	PROPN
ejpam-5970	467	30	.	.	PUNCT
ejpam-5970	467	31	/	/	SYM
ejpam-5970	467	32	eur	eur	PROPN
ejpam-5970	467	33	.	.	PUNCT
ejpam-5970	468	1	j.	j.	PROPN
ejpam-5970	468	2	pure	pure	PROPN
ejpam-5970	468	3	appl	appl	PROPN
ejpam-5970	468	4	.	.	PROPN
ejpam-5970	468	5	math	math	PROPN
ejpam-5970	468	6	,	,	PUNCT
ejpam-5970	468	7	18	18	NUM
ejpam-5970	468	8	(	(	PUNCT
ejpam-5970	468	9	3	3	NUM
ejpam-5970	468	10	)	)	PUNCT
ejpam-5970	468	11	(	(	PUNCT
ejpam-5970	468	12	2025	2025	NUM
ejpam-5970	468	13	)	)	PUNCT
ejpam-5970	468	14	,	,	PUNCT
ejpam-5970	468	15	5970	5970	NUM
ejpam-5970	468	16	18	18	NUM
ejpam-5970	468	17	of	of	ADP
ejpam-5970	468	18	18	18	NUM
ejpam-5970	468	19	agustin	agustin	PROPN
ejpam-5970	468	20	.	.	PUNCT
ejpam-5970	469	1	on	on	ADP
ejpam-5970	469	2	local	local	ADJ
ejpam-5970	469	3	(	(	PUNCT
ejpam-5970	469	4	a	a	PRON
ejpam-5970	469	5	,	,	PUNCT
ejpam-5970	469	6	d)-antimagic	d)-antimagic	NOUN
ejpam-5970	469	7	coloring	coloring	NOUN
ejpam-5970	469	8	of	of	ADP
ejpam-5970	469	9	some	some	DET
ejpam-5970	469	10	specific	specific	ADJ
ejpam-5970	469	11	classes	class	NOUN
ejpam-5970	469	12	of	of	ADP
ejpam-5970	469	13	graphs	graph	NOUN
ejpam-5970	469	14	.	.	PUNCT
ejpam-5970	470	1	in	in	ADP
ejpam-5970	470	2	iccgant	iccgant	ADJ
ejpam-5970	470	3	2022	2022	NUM
ejpam-5970	470	4	,	,	PUNCT
ejpam-5970	470	5	pages	page	NOUN
ejpam-5970	470	6	156–169	156–169	NUM
ejpam-5970	470	7	,	,	PUNCT
ejpam-5970	470	8	2023	2023	NUM
ejpam-5970	470	9	.	.	PUNCT
ejpam-5970	471	1	[	[	X
ejpam-5970	471	2	15	15	NUM
ejpam-5970	471	3	]	]	X
ejpam-5970	471	4	e.	e.	PROPN
ejpam-5970	471	5	d.	d.	PROPN
ejpam-5970	471	6	putra	putra	PROPN
ejpam-5970	471	7	,	,	PUNCT
ejpam-5970	471	8	dafik	dafik	PROPN
ejpam-5970	471	9	,	,	PUNCT
ejpam-5970	471	10	a.	a.	PROPN
ejpam-5970	471	11	i.	i.	PROPN
ejpam-5970	471	12	kristiana	kristiana	PROPN
ejpam-5970	471	13	,	,	PUNCT
ejpam-5970	471	14	r.	r.	PROPN
ejpam-5970	471	15	adawiyah	adawiyah	PROPN
ejpam-5970	471	16	,	,	PUNCT
ejpam-5970	471	17	and	and	CCONJ
ejpam-5970	471	18	r.	r.	PROPN
ejpam-5970	471	19	m.	m.	PROPN
ejpam-5970	471	20	prihandini	prihandini	PROPN
ejpam-5970	471	21	.	.	PUNCT
ejpam-5970	472	1	on	on	ADP
ejpam-5970	472	2	local	local	ADJ
ejpam-5970	472	3	(	(	PUNCT
ejpam-5970	472	4	a	a	PRON
ejpam-5970	472	5	,	,	PUNCT
ejpam-5970	472	6	d)-edge	d)-edge	NOUN
ejpam-5970	472	7	antimagic	antimagic	ADJ
ejpam-5970	472	8	coloring	coloring	NOUN
ejpam-5970	472	9	of	of	ADP
ejpam-5970	472	10	some	some	DET
ejpam-5970	472	11	specific	specific	ADJ
ejpam-5970	472	12	classes	class	NOUN
ejpam-5970	472	13	of	of	ADP
ejpam-5970	472	14	graphs	graph	NOUN
ejpam-5970	472	15	.	.	PUNCT
ejpam-5970	473	1	in	in	ADP
ejpam-5970	473	2	iccgant	iccgant	ADJ
ejpam-5970	473	3	2022	2022	NUM
ejpam-5970	473	4	,	,	PUNCT
ejpam-5970	473	5	pages	page	NOUN
ejpam-5970	473	6	42–53	42–53	NUM
ejpam-5970	473	7	,	,	PUNCT
ejpam-5970	473	8	2023	2023	NUM
ejpam-5970	473	9	.	.	PUNCT
ejpam-5970	474	1	[	[	X
ejpam-5970	474	2	16	16	NUM
ejpam-5970	474	3	]	]	X
ejpam-5970	474	4	r.	r.	PROPN
ejpam-5970	474	5	izza	izza	PROPN
ejpam-5970	474	6	,	,	PUNCT
ejpam-5970	474	7	dafik	dafik	NOUN
ejpam-5970	474	8	,	,	PUNCT
ejpam-5970	474	9	and	and	CCONJ
ejpam-5970	474	10	a.	a.	PROPN
ejpam-5970	474	11	i.	i.	PROPN
ejpam-5970	474	12	kristiana	kristiana	PROPN
ejpam-5970	474	13	.	.	PUNCT
ejpam-5970	475	1	on	on	ADP
ejpam-5970	475	2	local	local	ADJ
ejpam-5970	475	3	(	(	PUNCT
ejpam-5970	475	4	a	a	PRON
ejpam-5970	475	5	,	,	PUNCT
ejpam-5970	475	6	d)-edge	d)-edge	NOUN
ejpam-5970	475	7	antimagic	antimagic	ADJ
ejpam-5970	475	8	coloring	coloring	NOUN
ejpam-5970	475	9	.	.	PUNCT
ejpam-5970	476	1	in	in	ADP
ejpam-5970	476	2	proceedings	proceeding	NOUN
ejpam-5970	476	3	of	of	ADP
ejpam-5970	476	4	the	the	DET
ejpam-5970	476	5	6th	6th	ADJ
ejpam-5970	476	6	international	international	ADJ
ejpam-5970	476	7	conference	conference	NOUN
ejpam-5970	476	8	of	of	ADP
ejpam-5970	476	9	combinatorics	combinatoric	NOUN
ejpam-5970	476	10	,	,	PUNCT
ejpam-5970	476	11	graph	graph	NOUN
ejpam-5970	476	12	theory	theory	NOUN
ejpam-5970	476	13	,	,	PUNCT
ejpam-5970	476	14	and	and	CCONJ
ejpam-5970	476	15	network	network	NOUN
ejpam-5970	476	16	topology	topology	NOUN
ejpam-5970	476	17	(	(	PUNCT
ejpam-5970	476	18	iccgant	iccgant	ADJ
ejpam-5970	476	19	)	)	PUNCT
ejpam-5970	476	20	,	,	PUNCT
ejpam-5970	476	21	pages	page	NOUN
ejpam-5970	476	22	30–41	30–41	NUM
ejpam-5970	476	23	,	,	PUNCT
ejpam-5970	476	24	2023	2023	NUM
ejpam-5970	476	25	.	.	PUNCT
ejpam-5970	477	1	[	[	X
ejpam-5970	477	2	17	17	NUM
ejpam-5970	477	3	]	]	PUNCT
ejpam-5970	477	4	a.	a.	PROPN
ejpam-5970	477	5	i.	i.	PROPN
ejpam-5970	477	6	kristiana	kristiana	PROPN
ejpam-5970	477	7	,	,	PUNCT
ejpam-5970	477	8	e.	e.	PROPN
ejpam-5970	477	9	rachmasari	rachmasari	PROPN
ejpam-5970	477	10	,	,	PUNCT
ejpam-5970	477	11	i.	i.	PROPN
ejpam-5970	477	12	h.	h.	PROPN
ejpam-5970	477	13	agustin	agustin	PROPN
ejpam-5970	477	14	,	,	PUNCT
ejpam-5970	477	15	i.	i.	PROPN
ejpam-5970	477	16	l.	l.	PROPN
ejpam-5970	477	17	mursyidah	mursyidah	PROPN
ejpam-5970	477	18	,	,	PUNCT
ejpam-5970	477	19	and	and	CCONJ
ejpam-5970	477	20	r.	r.	PROPN
ejpam-5970	477	21	alfarisi	alfarisi	PROPN
ejpam-5970	477	22	.	.	PUNCT
ejpam-5970	478	1	on	on	ADP
ejpam-5970	478	2	bcoloring	bcolore	VERB
ejpam-5970	478	3	analysis	analysis	NOUN
ejpam-5970	478	4	of	of	ADP
ejpam-5970	478	5	graphs	graph	NOUN
ejpam-5970	478	6	:	:	PUNCT
ejpam-5970	478	7	an	an	DET
ejpam-5970	478	8	application	application	NOUN
ejpam-5970	478	9	to	to	ADP
ejpam-5970	478	10	spatial	spatial	ADJ
ejpam-5970	478	11	-	-	PUNCT
ejpam-5970	478	12	temporal	temporal	ADJ
ejpam-5970	478	13	graph	graph	NOUN
ejpam-5970	478	14	neural	neural	ADJ
ejpam-5970	478	15	networks	network	NOUN
ejpam-5970	478	16	for	for	ADP
ejpam-5970	478	17	multi	multi	ADJ
ejpam-5970	478	18	-	-	ADJ
ejpam-5970	478	19	step	step	ADJ
ejpam-5970	478	20	time	time	NOUN
ejpam-5970	478	21	series	series	PROPN
ejpam-5970	478	22	forecasting	forecasting	NOUN
ejpam-5970	478	23	of	of	ADP
ejpam-5970	478	24	soil	soil	NOUN
ejpam-5970	478	25	moisture	moisture	NOUN
ejpam-5970	478	26	and	and	CCONJ
ejpam-5970	478	27	ph	ph	ADJ
ejpam-5970	478	28	in	in	ADP
ejpam-5970	478	29	companion	companion	NOUN
ejpam-5970	478	30	farming	farming	NOUN
ejpam-5970	478	31	.	.	PUNCT
ejpam-5970	479	1	european	european	ADJ
ejpam-5970	479	2	journal	journal	PROPN
ejpam-5970	479	3	of	of	ADP
ejpam-5970	479	4	pure	pure	ADJ
ejpam-5970	479	5	and	and	CCONJ
ejpam-5970	479	6	applied	applied	ADJ
ejpam-5970	479	7	mathematics	mathematic	NOUN
ejpam-5970	479	8	,	,	PUNCT
ejpam-5970	479	9	17(4):3356–3369	17(4):3356–3369	NUM
ejpam-5970	479	10	,	,	PUNCT
ejpam-5970	479	11	2024	2024	NUM
ejpam-5970	479	12	.	.	PUNCT
ejpam-5970	480	1	[	[	X
ejpam-5970	480	2	18	18	NUM
ejpam-5970	480	3	]	]	PUNCT
ejpam-5970	480	4	s.	s.	PROPN
ejpam-5970	480	5	n.	n.	PROPN
ejpam-5970	480	6	n.	n.	PROPN
ejpam-5970	480	7	aziz	aziz	PROPN
ejpam-5970	480	8	,	,	PUNCT
ejpam-5970	480	9	dafik	dafik	NOUN
ejpam-5970	480	10	,	,	PUNCT
ejpam-5970	480	11	i.	i.	PROPN
ejpam-5970	480	12	m.	m.	PROPN
ejpam-5970	480	13	tirta	tirta	PROPN
ejpam-5970	480	14	,	,	PUNCT
ejpam-5970	480	15	a.	a.	PROPN
ejpam-5970	480	16	i.	i.	PROPN
ejpam-5970	480	17	kristiana	kristiana	PROPN
ejpam-5970	480	18	,	,	PUNCT
ejpam-5970	480	19	and	and	CCONJ
ejpam-5970	480	20	e.	e.	PROPN
ejpam-5970	480	21	y.	y.	PROPN
ejpam-5970	480	22	kurniawati	kurniawati	PROPN
ejpam-5970	480	23	.	.	PUNCT
ejpam-5970	481	1	on	on	ADP
ejpam-5970	481	2	b	b	X
ejpam-5970	481	3	-	-	PUNCT
ejpam-5970	481	4	coloring	color	VERB
ejpam-5970	481	5	analysis	analysis	NOUN
ejpam-5970	481	6	and	and	CCONJ
ejpam-5970	481	7	its	its	PRON
ejpam-5970	481	8	application	application	NOUN
ejpam-5970	481	9	on	on	ADP
ejpam-5970	481	10	stgnn	stgnn	NOUN
ejpam-5970	481	11	for	for	ADP
ejpam-5970	481	12	soil	soil	NOUN
ejpam-5970	481	13	moisture	moisture	NOUN
ejpam-5970	481	14	,	,	PUNCT
ejpam-5970	481	15	temperature	temperature	NOUN
ejpam-5970	481	16	and	and	CCONJ
ejpam-5970	481	17	ph	ph	NOUN
ejpam-5970	481	18	forecasting	forecasting	NOUN
ejpam-5970	481	19	of	of	ADP
ejpam-5970	481	20	companion	companion	NOUN
ejpam-5970	481	21	farming	farming	NOUN
ejpam-5970	481	22	.	.	PUNCT
ejpam-5970	482	1	in	in	ADP
ejpam-5970	482	2	aip	aip	PROPN
ejpam-5970	482	3	conference	conference	NOUN
ejpam-5970	482	4	proceedings	proceeding	NOUN
ejpam-5970	482	5	,	,	PUNCT
ejpam-5970	482	6	volume	volume	NOUN
ejpam-5970	482	7	3176	3176	NUM
ejpam-5970	482	8	,	,	PUNCT
ejpam-5970	482	9	page	page	NOUN
ejpam-5970	482	10	030031	030031	NUM
ejpam-5970	482	11	.	.	PUNCT
ejpam-5970	483	1	aip	aip	PROPN
ejpam-5970	483	2	publishing	publishing	PROPN
ejpam-5970	483	3	llc	llc	PROPN
ejpam-5970	483	4	,	,	PUNCT
ejpam-5970	483	5	2024	2024	NUM
ejpam-5970	483	6	.	.	PUNCT
ejpam-5970	484	1	[	[	X
ejpam-5970	484	2	19	19	NUM
ejpam-5970	484	3	]	]	X
ejpam-5970	484	4	d.	d.	PROPN
ejpam-5970	484	5	mufidati	mufidati	PROPN
ejpam-5970	484	6	,	,	PUNCT
ejpam-5970	484	7	z.	z.	PROPN
ejpam-5970	484	8	r.	r.	PROPN
ejpam-5970	484	9	ridlo	ridlo	PROPN
ejpam-5970	484	10	,	,	PUNCT
ejpam-5970	484	11	i.	i.	PROPN
ejpam-5970	484	12	n.	n.	PROPN
ejpam-5970	484	13	maylisa	maylisa	PROPN
ejpam-5970	484	14	,	,	PUNCT
ejpam-5970	484	15	and	and	CCONJ
ejpam-5970	484	16	dafik	dafik	NOUN
ejpam-5970	484	17	.	.	PUNCT
ejpam-5970	485	1	time	time	PROPN
ejpam-5970	485	2	series	series	PROPN
ejpam-5970	485	3	forecasting	forecast	VERB
ejpam-5970	485	4	analysis	analysis	NOUN
ejpam-5970	485	5	of	of	ADP
ejpam-5970	485	6	soil	soil	NOUN
ejpam-5970	485	7	moisture	moisture	NOUN
ejpam-5970	485	8	by	by	ADP
ejpam-5970	485	9	using	use	VERB
ejpam-5970	485	10	artificial	artificial	ADJ
ejpam-5970	485	11	neural	neural	ADJ
ejpam-5970	485	12	networks	network	NOUN
ejpam-5970	485	13	based	base	VERB
ejpam-5970	485	14	-	-	PUNCT
ejpam-5970	485	15	on	on	ADP
ejpam-5970	485	16	rainbow	rainbow	NOUN
ejpam-5970	485	17	antimagic	antimagic	ADJ
ejpam-5970	485	18	coloring	coloring	NOUN
ejpam-5970	485	19	for	for	ADP
ejpam-5970	485	20	autonomous	autonomous	ADJ
ejpam-5970	485	21	irrigation	irrigation	NOUN
ejpam-5970	485	22	system	system	NOUN
ejpam-5970	485	23	on	on	ADP
ejpam-5970	485	24	horizontal	horizontal	ADJ
ejpam-5970	485	25	farming	farming	NOUN
ejpam-5970	485	26	.	.	PUNCT
ejpam-5970	486	1	in	in	ADP
ejpam-5970	486	2	1st	1st	ADJ
ejpam-5970	486	3	international	international	ADJ
ejpam-5970	486	4	conference	conference	NOUN
ejpam-5970	486	5	on	on	ADP
ejpam-5970	486	6	neural	neural	ADJ
ejpam-5970	486	7	networks	network	NOUN
ejpam-5970	486	8	and	and	CCONJ
ejpam-5970	486	9	machine	machine	NOUN
ejpam-5970	486	10	learning	learn	VERB
ejpam-5970	486	11	2022	2022	NUM
ejpam-5970	486	12	(	(	PUNCT
ejpam-5970	486	13	iconnsmal	iconnsmal	NOUN
ejpam-5970	486	14	2022	2022	NUM
ejpam-5970	486	15	)	)	PUNCT
ejpam-5970	486	16	,	,	PUNCT
ejpam-5970	486	17	pages	page	NOUN
ejpam-5970	486	18	234–256	234–256	NUM
ejpam-5970	486	19	.	.	PUNCT
ejpam-5970	487	1	atlantis	atlantis	PROPN
ejpam-5970	487	2	press	press	PROPN
ejpam-5970	487	3	,	,	PUNCT
ejpam-5970	487	4	2023	2023	NUM
ejpam-5970	487	5	.	.	PUNCT
ejpam-5970	488	1	[	[	X
ejpam-5970	488	2	20	20	NUM
ejpam-5970	488	3	]	]	PUNCT
ejpam-5970	488	4	r.	r.	PROPN
ejpam-5970	488	5	sunder	sunder	PROPN
ejpam-5970	488	6	,	,	PUNCT
ejpam-5970	488	7	i.	i.	PROPN
ejpam-5970	488	8	h.	h.	PROPN
ejpam-5970	488	9	agustin	agustin	PROPN
ejpam-5970	488	10	,	,	PUNCT
ejpam-5970	488	11	dafik	dafik	PROPN
ejpam-5970	488	12	,	,	PUNCT
ejpam-5970	488	13	i.	i.	PROPN
ejpam-5970	488	14	n.	n.	PROPN
ejpam-5970	488	15	maylisa	maylisa	PROPN
ejpam-5970	488	16	,	,	PUNCT
ejpam-5970	488	17	n.	n.	NOUN
ejpam-5970	488	18	mohanapriya	mohanapriya	NOUN
ejpam-5970	488	19	,	,	PUNCT
ejpam-5970	488	20	and	and	CCONJ
ejpam-5970	488	21	m.	m.	NOUN
ejpam-5970	488	22	marsidi	marsidi	NOUN
ejpam-5970	488	23	.	.	PUNCT
ejpam-5970	489	1	on	on	ADP
ejpam-5970	489	2	local	local	ADJ
ejpam-5970	489	3	antimagic	antimagic	ADJ
ejpam-5970	489	4	b	b	NOUN
ejpam-5970	489	5	-	-	PUNCT
ejpam-5970	489	6	coloring	coloring	NOUN
ejpam-5970	489	7	and	and	CCONJ
ejpam-5970	489	8	its	its	PRON
ejpam-5970	489	9	application	application	NOUN
ejpam-5970	489	10	for	for	ADP
ejpam-5970	489	11	stgnn	stgnn	NOUN
ejpam-5970	489	12	time	time	PROPN
ejpam-5970	489	13	series	series	PROPN
ejpam-5970	489	14	forecasting	forecasting	NOUN
ejpam-5970	489	15	on	on	ADP
ejpam-5970	489	16	horizontal	horizontal	ADJ
ejpam-5970	489	17	farming	farming	NOUN
ejpam-5970	489	18	.	.	PUNCT
ejpam-5970	490	1	cauchy	cauchy	NOUN
ejpam-5970	490	2	:	:	PUNCT
ejpam-5970	490	3	jurnal	jurnal	ADJ
ejpam-5970	490	4	matematika	matematika	PROPN
ejpam-5970	490	5	murni	murni	PROPN
ejpam-5970	490	6	dan	dan	PROPN
ejpam-5970	490	7	aplikasinya	aplikasinya	PROPN
ejpam-5970	490	8	,	,	PUNCT
ejpam-5970	490	9	10(1):117	10(1):117	NUM
ejpam-5970	490	10	–	–	PUNCT
ejpam-5970	490	11	132	132	NUM
ejpam-5970	490	12	,	,	PUNCT
ejpam-5970	490	13	2025	2025	NUM
ejpam-5970	490	14	.	.	PUNCT