id	sid	tid	token	lemma	pos
ejpam-4722	1	1	european	european	PROPN
ejpam-4722	1	2	journal	journal	PROPN
ejpam-4722	1	3	of	of	ADP
ejpam-4722	1	4	pure	pure	ADJ
ejpam-4722	1	5	and	and	CCONJ
ejpam-4722	1	6	applied	apply	VERB
ejpam-4722	1	7	mathematics	mathematic	NOUN
ejpam-4722	1	8	vol	vol	NOUN
ejpam-4722	1	9	.	.	PUNCT
ejpam-4722	2	1	16	16	NUM
ejpam-4722	2	2	,	,	PUNCT
ejpam-4722	2	3	no	no	INTJ
ejpam-4722	2	4	.	.	NOUN
ejpam-4722	2	5	3	3	NUM
ejpam-4722	2	6	,	,	PUNCT
ejpam-4722	2	7	2023	2023	NUM
ejpam-4722	2	8	,	,	PUNCT
ejpam-4722	2	9	1794	1794	NUM
ejpam-4722	2	10	-	-	SYM
ejpam-4722	2	11	1808	1808	NUM
ejpam-4722	2	12	issn	issn	PROPN
ejpam-4722	2	13	1307	1307	NUM
ejpam-4722	2	14	-	-	SYM
ejpam-4722	2	15	5543	5543	NUM
ejpam-4722	2	16	–	–	PUNCT
ejpam-4722	2	17	ejpam.com	ejpam.com	X
ejpam-4722	2	18	published	publish	VERB
ejpam-4722	2	19	by	by	ADP
ejpam-4722	2	20	new	new	PROPN
ejpam-4722	2	21	york	york	PROPN
ejpam-4722	2	22	business	business	PROPN
ejpam-4722	2	23	global	global	PROPN
ejpam-4722	2	24	on	on	ADP
ejpam-4722	2	25	weighted	weight	VERB
ejpam-4722	2	26	vertex	vertex	NOUN
ejpam-4722	2	27	and	and	CCONJ
ejpam-4722	2	28	edge	edge	VERB
ejpam-4722	2	29	mostar	mostar	PROPN
ejpam-4722	2	30	index	index	NOUN
ejpam-4722	2	31	for	for	ADP
ejpam-4722	2	32	trees	tree	NOUN
ejpam-4722	2	33	and	and	CCONJ
ejpam-4722	2	34	cacti	cacti	NOUN
ejpam-4722	2	35	with	with	ADP
ejpam-4722	2	36	fixed	fix	VERB
ejpam-4722	2	37	parameter	parameter	NOUN
ejpam-4722	2	38	farwa	farwa	NOUN
ejpam-4722	2	39	asmat1,∗	asmat1,∗	NOUN
ejpam-4722	2	40	,	,	PUNCT
ejpam-4722	2	41	humaira	humaira	PROPN
ejpam-4722	2	42	asmat2	asmat2	PROPN
ejpam-4722	2	43	,	,	PUNCT
ejpam-4722	2	44	sameh	sameh	NOUN
ejpam-4722	2	45	askar3	askar3	NOUN
ejpam-4722	2	46	,	,	PUNCT
ejpam-4722	2	47	hijaz	hijaz	PROPN
ejpam-4722	2	48	ahamd4,6,7	ahamd4,6,7	PROPN
ejpam-4722	2	49	,	,	PUNCT
ejpam-4722	2	50	muhammad	muhammad	PROPN
ejpam-4722	2	51	ijaz	ijaz	PROPN
ejpam-4722	2	52	khan5	khan5	PROPN
ejpam-4722	2	53	1,5	1,5	NUM
ejpam-4722	2	54	school	school	NOUN
ejpam-4722	2	55	of	of	ADP
ejpam-4722	2	56	mathematical	mathematical	ADJ
ejpam-4722	2	57	sciences	science	NOUN
ejpam-4722	2	58	,	,	PUNCT
ejpam-4722	2	59	peking	peking	NOUN
ejpam-4722	2	60	university	university	NOUN
ejpam-4722	2	61	,	,	PUNCT
ejpam-4722	2	62	beijing	beijing	PROPN
ejpam-4722	2	63	100871	100871	NUM
ejpam-4722	2	64	,	,	PUNCT
ejpam-4722	2	65	p.r	p.r	PROPN
ejpam-4722	2	66	.	.	PROPN
ejpam-4722	2	67	china	china	PROPN
ejpam-4722	2	68	2	2	PROPN
ejpam-4722	2	69	department	department	NOUN
ejpam-4722	2	70	of	of	ADP
ejpam-4722	2	71	mathematics	mathematic	NOUN
ejpam-4722	2	72	and	and	CCONJ
ejpam-4722	2	73	statistics	statistic	NOUN
ejpam-4722	2	74	,	,	PUNCT
ejpam-4722	2	75	university	university	NOUN
ejpam-4722	2	76	of	of	ADP
ejpam-4722	2	77	lahore	lahore	PROPN
ejpam-4722	2	78	,	,	PUNCT
ejpam-4722	2	79	pakistan	pakistan	PROPN
ejpam-4722	2	80	3	3	NUM
ejpam-4722	2	81	department	department	NOUN
ejpam-4722	2	82	of	of	ADP
ejpam-4722	2	83	statistics	statistic	NOUN
ejpam-4722	2	84	and	and	CCONJ
ejpam-4722	2	85	operations	operation	NOUN
ejpam-4722	2	86	research	research	NOUN
ejpam-4722	2	87	,	,	PUNCT
ejpam-4722	2	88	college	college	NOUN
ejpam-4722	2	89	of	of	ADP
ejpam-4722	2	90	science	science	NOUN
ejpam-4722	2	91	,	,	PUNCT
ejpam-4722	2	92	king	king	PROPN
ejpam-4722	2	93	saud	saud	PROPN
ejpam-4722	2	94	university	university	PROPN
ejpam-4722	2	95	,	,	PUNCT
ejpam-4722	2	96	p.o	p.o	PROPN
ejpam-4722	2	97	.	.	PROPN
ejpam-4722	2	98	box	box	PROPN
ejpam-4722	2	99	2455	2455	NUM
ejpam-4722	2	100	,	,	PUNCT
ejpam-4722	2	101	riyadh	riyadh	PROPN
ejpam-4722	2	102	11451	11451	NUM
ejpam-4722	2	103	,	,	PUNCT
ejpam-4722	2	104	saudi	saudi	PROPN
ejpam-4722	2	105	arabia	arabia	PROPN
ejpam-4722	2	106	4	4	NUM
ejpam-4722	2	107	section	section	NOUN
ejpam-4722	2	108	of	of	ADP
ejpam-4722	2	109	mathematics	mathematic	NOUN
ejpam-4722	2	110	,	,	PUNCT
ejpam-4722	2	111	international	international	ADJ
ejpam-4722	2	112	telematic	telematic	ADJ
ejpam-4722	2	113	university	university	NOUN
ejpam-4722	2	114	uninettuno	uninettuno	NOUN
ejpam-4722	2	115	,	,	PUNCT
ejpam-4722	2	116	corso	corso	PROPN
ejpam-4722	2	117	vittorio	vittorio	PROPN
ejpam-4722	2	118	emanuele	emanuele	PROPN
ejpam-4722	2	119	-	-	PUNCT
ejpam-4722	2	120	ii	ii	PROPN
ejpam-4722	2	121	,	,	PUNCT
ejpam-4722	2	122	39,00186	39,00186	NUM
ejpam-4722	2	123	roma	roma	PROPN
ejpam-4722	2	124	,	,	PUNCT
ejpam-4722	2	125	italy	italy	PROPN
ejpam-4722	2	126	5	5	NUM
ejpam-4722	2	127	department	department	PROPN
ejpam-4722	2	128	of	of	ADP
ejpam-4722	2	129	mechanical	mechanical	ADJ
ejpam-4722	2	130	engineering	engineering	NOUN
ejpam-4722	2	131	,	,	PUNCT
ejpam-4722	2	132	lebanese	lebanese	ADJ
ejpam-4722	2	133	american	american	PROPN
ejpam-4722	2	134	university	university	PROPN
ejpam-4722	2	135	,	,	PUNCT
ejpam-4722	2	136	beirut	beirut	PROPN
ejpam-4722	2	137	,	,	PUNCT
ejpam-4722	2	138	lebanon	lebanon	PROPN
ejpam-4722	2	139	6	6	NUM
ejpam-4722	2	140	near	near	ADP
ejpam-4722	2	141	east	east	PROPN
ejpam-4722	2	142	university	university	PROPN
ejpam-4722	2	143	,	,	PUNCT
ejpam-4722	2	144	operational	operational	ADJ
ejpam-4722	2	145	research	research	NOUN
ejpam-4722	2	146	center	center	NOUN
ejpam-4722	2	147	in	in	ADP
ejpam-4722	2	148	healthcare	healthcare	PROPN
ejpam-4722	2	149	,	,	PUNCT
ejpam-4722	2	150	nicosia	nicosia	PROPN
ejpam-4722	2	151	99138	99138	NUM
ejpam-4722	2	152	,	,	PUNCT
ejpam-4722	2	153	trnc	trnc	PROPN
ejpam-4722	2	154	mersin	mersin	PROPN
ejpam-4722	2	155	10	10	NUM
ejpam-4722	2	156	,	,	PUNCT
ejpam-4722	2	157	turkey	turkey	PROPN
ejpam-4722	2	158	7	7	NUM
ejpam-4722	2	159	department	department	NOUN
ejpam-4722	2	160	of	of	ADP
ejpam-4722	2	161	computer	computer	NOUN
ejpam-4722	2	162	science	science	NOUN
ejpam-4722	2	163	and	and	CCONJ
ejpam-4722	2	164	mathematics	mathematic	NOUN
ejpam-4722	2	165	,	,	PUNCT
ejpam-4722	2	166	lebanese	lebanese	ADJ
ejpam-4722	2	167	american	american	PROPN
ejpam-4722	2	168	university	university	PROPN
ejpam-4722	2	169	,	,	PUNCT
ejpam-4722	2	170	beirut	beirut	PROPN
ejpam-4722	2	171	,	,	PUNCT
ejpam-4722	2	172	lebanon	lebanon	PROPN
ejpam-4722	2	173	abstract	abstract	NOUN
ejpam-4722	2	174	.	.	PUNCT
ejpam-4722	3	1	it	it	PRON
ejpam-4722	3	2	was	be	AUX
ejpam-4722	3	3	introduced	introduce	VERB
ejpam-4722	3	4	by	by	ADP
ejpam-4722	3	5	došlić	došlić	PROPN
ejpam-4722	3	6	and	and	CCONJ
ejpam-4722	3	7	ivica	ivica	PROPN
ejpam-4722	3	8	et	et	PROPN
ejpam-4722	3	9	al	al	PROPN
ejpam-4722	3	10	.	.	PUNCT
ejpam-4722	4	1	(	(	PUNCT
ejpam-4722	4	2	journal	journal	NOUN
ejpam-4722	4	3	of	of	ADP
ejpam-4722	4	4	mathematical	mathematical	ADJ
ejpam-4722	4	5	chemistry	chemistry	NOUN
ejpam-4722	4	6	,	,	PUNCT
ejpam-4722	4	7	56(10	56(10	NUM
ejpam-4722	4	8	)	)	PUNCT
ejpam-4722	4	9	(	(	PUNCT
ejpam-4722	4	10	2018	2018	NUM
ejpam-4722	4	11	):	):	PUNCT
ejpam-4722	4	12	2995–3013	2995–3013	NUM
ejpam-4722	4	13	)	)	PUNCT
ejpam-4722	4	14	,	,	PUNCT
ejpam-4722	4	15	as	as	ADP
ejpam-4722	4	16	an	an	DET
ejpam-4722	4	17	innovative	innovative	ADJ
ejpam-4722	4	18	graph	graph	NOUN
ejpam-4722	4	19	-	-	PUNCT
ejpam-4722	4	20	theoretic	theoretic	NOUN
ejpam-4722	4	21	topological	topological	ADJ
ejpam-4722	4	22	identifier	identifier	NOUN
ejpam-4722	4	23	,	,	PUNCT
ejpam-4722	4	24	the	the	DET
ejpam-4722	4	25	mostar	mostar	PROPN
ejpam-4722	4	26	index	index	NOUN
ejpam-4722	4	27	is	be	AUX
ejpam-4722	4	28	significant	significant	ADJ
ejpam-4722	4	29	in	in	ADP
ejpam-4722	4	30	simulating	simulate	VERB
ejpam-4722	4	31	compounds	compound	VERB
ejpam-4722	4	32	thermodynamic	thermodynamic	ADJ
ejpam-4722	4	33	properties	property	NOUN
ejpam-4722	4	34	in	in	ADP
ejpam-4722	4	35	simulations	simulation	NOUN
ejpam-4722	4	36	,	,	PUNCT
ejpam-4722	4	37	which	which	PRON
ejpam-4722	4	38	is	be	AUX
ejpam-4722	4	39	defined	define	VERB
ejpam-4722	4	40	as	as	ADP
ejpam-4722	4	41	sum	sum	NOUN
ejpam-4722	4	42	of	of	ADP
ejpam-4722	4	43	absolute	absolute	ADJ
ejpam-4722	4	44	values	value	NOUN
ejpam-4722	4	45	of	of	ADP
ejpam-4722	4	46	the	the	DET
ejpam-4722	4	47	differences	difference	NOUN
ejpam-4722	4	48	among	among	ADP
ejpam-4722	4	49	nu(e|ω	nu(e|ω	NUM
ejpam-4722	4	50	)	)	PUNCT
ejpam-4722	4	51	and	and	CCONJ
ejpam-4722	4	52	nv(e|ω	nv(e|ω	NOUN
ejpam-4722	4	53	)	)	PUNCT
ejpam-4722	4	54	over	over	ADP
ejpam-4722	4	55	all	all	DET
ejpam-4722	4	56	lines	line	NOUN
ejpam-4722	4	57	e	e	X
ejpam-4722	4	58	=	=	PUNCT
ejpam-4722	4	59	uv	uv	PROPN
ejpam-4722	4	60	∈	∈	PROPN
ejpam-4722	4	61	ω	ω	PROPN
ejpam-4722	4	62	,	,	PUNCT
ejpam-4722	4	63	where	where	SCONJ
ejpam-4722	4	64	nu(e|ω	nu(e|ω	NUM
ejpam-4722	4	65	)	)	PUNCT
ejpam-4722	4	66	(	(	PUNCT
ejpam-4722	4	67	resp	resp	NOUN
ejpam-4722	4	68	.	.	PUNCT
ejpam-4722	5	1	nv(e|ω	nv(e|ω	NUM
ejpam-4722	5	2	)	)	PUNCT
ejpam-4722	5	3	)	)	PUNCT
ejpam-4722	5	4	is	be	AUX
ejpam-4722	5	5	the	the	DET
ejpam-4722	5	6	collection	collection	NOUN
ejpam-4722	5	7	of	of	ADP
ejpam-4722	5	8	vertices	vertex	NOUN
ejpam-4722	5	9	of	of	ADP
ejpam-4722	5	10	ω	ω	NOUN
ejpam-4722	5	11	closer	close	ADV
ejpam-4722	5	12	to	to	ADP
ejpam-4722	5	13	vertex	vertex	NOUN
ejpam-4722	5	14	u	u	NOUN
ejpam-4722	5	15	(	(	PUNCT
ejpam-4722	5	16	resp	resp	NOUN
ejpam-4722	5	17	.	.	PUNCT
ejpam-4722	6	1	v	v	X
ejpam-4722	6	2	)	)	PUNCT
ejpam-4722	6	3	than	than	ADP
ejpam-4722	6	4	to	to	PART
ejpam-4722	6	5	vertex	vertex	VERB
ejpam-4722	6	6	v	v	NOUN
ejpam-4722	6	7	(	(	PUNCT
ejpam-4722	6	8	resp	resp	NOUN
ejpam-4722	6	9	.	.	PUNCT
ejpam-4722	7	1	u	u	NOUN
ejpam-4722	7	2	)	)	PUNCT
ejpam-4722	7	3	.	.	PUNCT
ejpam-4722	8	1	let	let	VERB
ejpam-4722	8	2	c(n	c(n	PROPN
ejpam-4722	8	3	,	,	PUNCT
ejpam-4722	8	4	k	k	NOUN
ejpam-4722	8	5	)	)	PUNCT
ejpam-4722	8	6	be	be	VERB
ejpam-4722	8	7	the	the	DET
ejpam-4722	8	8	set	set	NOUN
ejpam-4722	8	9	of	of	ADP
ejpam-4722	8	10	all	all	DET
ejpam-4722	8	11	n	n	CCONJ
ejpam-4722	8	12	-	-	PUNCT
ejpam-4722	8	13	vertex	vertex	NOUN
ejpam-4722	8	14	cactus	cactus	NOUN
ejpam-4722	8	15	graphs	graph	NOUN
ejpam-4722	8	16	with	with	ADP
ejpam-4722	8	17	exactly	exactly	ADV
ejpam-4722	8	18	k	k	PROPN
ejpam-4722	8	19	cycles	cycle	NOUN
ejpam-4722	8	20	and	and	CCONJ
ejpam-4722	8	21	t	t	PROPN
ejpam-4722	8	22	(	(	PUNCT
ejpam-4722	8	23	n	n	CCONJ
ejpam-4722	8	24	,	,	PUNCT
ejpam-4722	8	25	d	d	X
ejpam-4722	8	26	)	)	PUNCT
ejpam-4722	8	27	be	be	VERB
ejpam-4722	8	28	the	the	DET
ejpam-4722	8	29	set	set	NOUN
ejpam-4722	8	30	of	of	ADP
ejpam-4722	8	31	all	all	DET
ejpam-4722	8	32	n	n	CCONJ
ejpam-4722	8	33	-	-	PUNCT
ejpam-4722	8	34	vertex	vertex	NOUN
ejpam-4722	8	35	tree	tree	NOUN
ejpam-4722	8	36	graphs	graph	NOUN
ejpam-4722	8	37	with	with	ADP
ejpam-4722	8	38	diameter	diameter	NOUN
ejpam-4722	8	39	d.	d.	PROPN
ejpam-4722	9	1	it	it	PRON
ejpam-4722	9	2	is	be	AUX
ejpam-4722	9	3	said	say	VERB
ejpam-4722	9	4	that	that	SCONJ
ejpam-4722	9	5	a	a	DET
ejpam-4722	9	6	cactus	cactus	NOUN
ejpam-4722	9	7	is	be	AUX
ejpam-4722	9	8	a	a	DET
ejpam-4722	9	9	connected	connected	ADJ
ejpam-4722	9	10	graph	graph	NOUN
ejpam-4722	9	11	with	with	ADP
ejpam-4722	9	12	blocks	block	NOUN
ejpam-4722	9	13	that	that	PRON
ejpam-4722	9	14	comprise	comprise	NOUN
ejpam-4722	9	15	of	of	ADP
ejpam-4722	9	16	either	either	CCONJ
ejpam-4722	9	17	cycles	cycle	NOUN
ejpam-4722	9	18	or	or	CCONJ
ejpam-4722	9	19	edges	edge	NOUN
ejpam-4722	9	20	.	.	PUNCT
ejpam-4722	10	1	beginning	begin	VERB
ejpam-4722	10	2	with	with	ADP
ejpam-4722	10	3	the	the	DET
ejpam-4722	10	4	weighted	weight	VERB
ejpam-4722	10	5	mostar	mostar	PROPN
ejpam-4722	10	6	index	index	NOUN
ejpam-4722	10	7	of	of	ADP
ejpam-4722	10	8	graphs	graph	NOUN
ejpam-4722	10	9	,	,	PUNCT
ejpam-4722	10	10	we	we	PRON
ejpam-4722	10	11	developed	develop	VERB
ejpam-4722	10	12	certain	certain	ADJ
ejpam-4722	10	13	transformations	transformation	NOUN
ejpam-4722	10	14	that	that	SCONJ
ejpam-4722	10	15	either	either	CCONJ
ejpam-4722	10	16	increase	increase	VERB
ejpam-4722	10	17	or	or	CCONJ
ejpam-4722	10	18	decrease	decrease	VERB
ejpam-4722	10	19	the	the	DET
ejpam-4722	10	20	index	index	NOUN
ejpam-4722	10	21	.	.	PUNCT
ejpam-4722	11	1	to	to	PART
ejpam-4722	11	2	advance	advance	VERB
ejpam-4722	11	3	this	this	DET
ejpam-4722	11	4	analysis	analysis	NOUN
ejpam-4722	11	5	,	,	PUNCT
ejpam-4722	11	6	we	we	PRON
ejpam-4722	11	7	determine	determine	VERB
ejpam-4722	11	8	the	the	DET
ejpam-4722	11	9	extreme	extreme	ADJ
ejpam-4722	11	10	graphs	graph	NOUN
ejpam-4722	11	11	where	where	SCONJ
ejpam-4722	11	12	the	the	DET
ejpam-4722	11	13	maximum	maximum	ADJ
ejpam-4722	11	14	and	and	CCONJ
ejpam-4722	11	15	minimum	minimum	ADJ
ejpam-4722	11	16	values	value	NOUN
ejpam-4722	11	17	of	of	ADP
ejpam-4722	11	18	the	the	DET
ejpam-4722	11	19	weighted	weight	VERB
ejpam-4722	11	20	edge	edge	NOUN
ejpam-4722	11	21	mostar	mostar	PROPN
ejpam-4722	11	22	index	index	NOUN
ejpam-4722	11	23	are	be	AUX
ejpam-4722	11	24	accomplished	accomplish	VERB
ejpam-4722	11	25	.	.	PUNCT
ejpam-4722	12	1	moreover	moreover	ADV
ejpam-4722	12	2	,	,	PUNCT
ejpam-4722	12	3	we	we	PRON
ejpam-4722	12	4	compute	compute	VERB
ejpam-4722	12	5	the	the	DET
ejpam-4722	12	6	maximum	maximum	ADJ
ejpam-4722	12	7	weighted	weight	VERB
ejpam-4722	12	8	vertex	vertex	NOUN
ejpam-4722	12	9	mostar	mostar	PROPN
ejpam-4722	12	10	invariant	invariant	PROPN
ejpam-4722	12	11	for	for	ADP
ejpam-4722	12	12	trees	tree	NOUN
ejpam-4722	12	13	with	with	ADP
ejpam-4722	12	14	order	order	NOUN
ejpam-4722	12	15	n	n	NOUN
ejpam-4722	12	16	and	and	CCONJ
ejpam-4722	12	17	fixed	fix	VERB
ejpam-4722	12	18	diameter	diameter	NOUN
ejpam-4722	12	19	d.	d.	PROPN
ejpam-4722	12	20	2020	2020	NUM
ejpam-4722	12	21	mathematics	mathematics	PROPN
ejpam-4722	12	22	subject	subject	NOUN
ejpam-4722	12	23	classifications	classification	NOUN
ejpam-4722	12	24	:	:	PUNCT
ejpam-4722	12	25	05c05	05c05	NUM
ejpam-4722	12	26	,	,	PUNCT
ejpam-4722	12	27	05c35	05c35	NUM
ejpam-4722	12	28	,	,	PUNCT
ejpam-4722	12	29	05c12	05c12	NOUN
ejpam-4722	12	30	,	,	PUNCT
ejpam-4722	12	31	05c92	05c92	X
ejpam-4722	13	1	key	key	ADJ
ejpam-4722	13	2	words	word	NOUN
ejpam-4722	13	3	and	and	CCONJ
ejpam-4722	13	4	phrases	phrase	NOUN
ejpam-4722	13	5	:	:	PUNCT
ejpam-4722	13	6	weighted	weight	VERB
ejpam-4722	13	7	mostar	mostar	PROPN
ejpam-4722	13	8	index	index	PROPN
ejpam-4722	13	9	,	,	PUNCT
ejpam-4722	13	10	trees	tree	NOUN
ejpam-4722	13	11	,	,	PUNCT
ejpam-4722	13	12	diameter	diameter	NOUN
ejpam-4722	13	13	,	,	PUNCT
ejpam-4722	13	14	extremal	extremal	ADJ
ejpam-4722	13	15	values	value	NOUN
ejpam-4722	13	16	,	,	PUNCT
ejpam-4722	13	17	cactus	cactus	NOUN
ejpam-4722	13	18	graphs	graph	NOUN
ejpam-4722	13	19	∗corresponding	∗corresponde	VERB
ejpam-4722	13	20	author	author	NOUN
ejpam-4722	13	21	.	.	PUNCT
ejpam-4722	14	1	doi	doi	NOUN
ejpam-4722	14	2	:	:	PUNCT
ejpam-4722	14	3	https://doi.org/10.29020/nybg.ejpam.v16i3.4722	https://doi.org/10.29020/nybg.ejpam.v16i3.4722	ADJ
ejpam-4722	14	4	email	email	NOUN
ejpam-4722	14	5	addresses	address	NOUN
ejpam-4722	14	6	:	:	PUNCT
ejpam-4722	14	7	farwaasmat@pku.edu.cn	farwaasmat@pku.edu.cn	PROPN
ejpam-4722	14	8	(	(	PUNCT
ejpam-4722	14	9	f.	f.	PROPN
ejpam-4722	14	10	asmat	asmat	PROPN
ejpam-4722	14	11	)	)	PUNCT
ejpam-4722	14	12	,	,	PUNCT
ejpam-4722	14	13	humairaasmat17@gmail.com	humairaasmat17@gmail.com	PROPN
ejpam-4722	14	14	(	(	PUNCT
ejpam-4722	14	15	h.	h.	PROPN
ejpam-4722	14	16	asmat	asmat	PROPN
ejpam-4722	14	17	)	)	PUNCT
ejpam-4722	14	18	,	,	PUNCT
ejpam-4722	14	19	saskar@ksu.edu.sa	saskar@ksu.edu.sa	PROPN
ejpam-4722	14	20	(	(	PUNCT
ejpam-4722	14	21	s.	s.	PROPN
ejpam-4722	14	22	askar	askar	PROPN
ejpam-4722	14	23	)	)	PUNCT
ejpam-4722	14	24	,	,	PUNCT
ejpam-4722	14	25	ahmad.hijaz@uninettuno.it	ahmad.hijaz@uninettuno.it	NOUN
ejpam-4722	14	26	(	(	PUNCT
ejpam-4722	14	27	h.	h.	PROPN
ejpam-4722	14	28	ahmad	ahmad	PROPN
ejpam-4722	14	29	)	)	PUNCT
ejpam-4722	14	30	,	,	PUNCT
ejpam-4722	14	31	hmikhan@math.qau.edu.pk	hmikhan@math.qau.edu.pk	PROPN
ejpam-4722	14	32	(	(	PUNCT
ejpam-4722	14	33	m.	m.	PROPN
ejpam-4722	14	34	i.	i.	PROPN
ejpam-4722	14	35	khan	khan	PROPN
ejpam-4722	14	36	)	)	PUNCT
ejpam-4722	14	37	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4722	14	38	1794	1794	NUM
ejpam-4722	15	1	©	©	ADP
ejpam-4722	15	2	2023	2023	NUM
ejpam-4722	15	3	ejpam	ejpam	NOUN
ejpam-4722	15	4	all	all	DET
ejpam-4722	15	5	rights	right	NOUN
ejpam-4722	15	6	reserved	reserve	VERB
ejpam-4722	15	7	.	.	PUNCT
ejpam-4722	16	1	f.	f.	PROPN
ejpam-4722	16	2	asmat	asmat	PROPN
ejpam-4722	16	3	et	et	PROPN
ejpam-4722	16	4	al	al	PROPN
ejpam-4722	16	5	.	.	PUNCT
ejpam-4722	16	6	/	/	SYM
ejpam-4722	16	7	eur	eur	PROPN
ejpam-4722	16	8	.	.	PUNCT
ejpam-4722	17	1	j.	j.	PROPN
ejpam-4722	17	2	pure	pure	PROPN
ejpam-4722	17	3	appl	appl	PROPN
ejpam-4722	17	4	.	.	PROPN
ejpam-4722	17	5	math	math	PROPN
ejpam-4722	17	6	,	,	PUNCT
ejpam-4722	17	7	16	16	NUM
ejpam-4722	17	8	(	(	PUNCT
ejpam-4722	17	9	3	3	NUM
ejpam-4722	17	10	)	)	PUNCT
ejpam-4722	17	11	(	(	PUNCT
ejpam-4722	17	12	2023	2023	NUM
ejpam-4722	17	13	)	)	PUNCT
ejpam-4722	17	14	,	,	PUNCT
ejpam-4722	17	15	1794	1794	NUM
ejpam-4722	17	16	-	-	SYM
ejpam-4722	17	17	1808	1808	NUM
ejpam-4722	17	18	1795	1795	NUM
ejpam-4722	17	19	1	1	NUM
ejpam-4722	17	20	.	.	PUNCT
ejpam-4722	18	1	introduction	introduction	NOUN
ejpam-4722	18	2	graph	graph	NOUN
ejpam-4722	18	3	theory	theory	NOUN
ejpam-4722	18	4	is	be	AUX
ejpam-4722	18	5	a	a	DET
ejpam-4722	18	6	subfield	subfield	NOUN
ejpam-4722	18	7	of	of	ADP
ejpam-4722	18	8	mathematics	mathematic	NOUN
ejpam-4722	18	9	that	that	PRON
ejpam-4722	18	10	studies	study	VERB
ejpam-4722	18	11	the	the	DET
ejpam-4722	18	12	properties	property	NOUN
ejpam-4722	18	13	of	of	ADP
ejpam-4722	18	14	graphs	graph	NOUN
ejpam-4722	18	15	.	.	PUNCT
ejpam-4722	19	1	it	it	PRON
ejpam-4722	19	2	is	be	AUX
ejpam-4722	19	3	currently	currently	ADV
ejpam-4722	19	4	being	be	AUX
ejpam-4722	19	5	applied	apply	VERB
ejpam-4722	19	6	in	in	ADP
ejpam-4722	19	7	a	a	DET
ejpam-4722	19	8	variety	variety	NOUN
ejpam-4722	19	9	of	of	ADP
ejpam-4722	19	10	scientific	scientific	ADJ
ejpam-4722	19	11	disciplines	discipline	NOUN
ejpam-4722	19	12	including	include	VERB
ejpam-4722	19	13	chemistry	chemistry	NOUN
ejpam-4722	19	14	,	,	PUNCT
ejpam-4722	19	15	engineering	engineering	NOUN
ejpam-4722	19	16	,	,	PUNCT
ejpam-4722	19	17	and	and	CCONJ
ejpam-4722	19	18	physics	physics	NOUN
ejpam-4722	19	19	.	.	PUNCT
ejpam-4722	20	1	graph	graph	NOUN
ejpam-4722	20	2	theory	theory	NOUN
ejpam-4722	20	3	can	can	AUX
ejpam-4722	20	4	be	be	AUX
ejpam-4722	20	5	used	use	VERB
ejpam-4722	20	6	to	to	PART
ejpam-4722	20	7	model	model	VERB
ejpam-4722	20	8	and	and	CCONJ
ejpam-4722	20	9	study	study	VERB
ejpam-4722	20	10	various	various	ADJ
ejpam-4722	20	11	problems	problem	NOUN
ejpam-4722	20	12	and	and	CCONJ
ejpam-4722	20	13	phenomena	phenomenon	NOUN
ejpam-4722	20	14	in	in	ADP
ejpam-4722	20	15	mathematics	mathematic	NOUN
ejpam-4722	20	16	,	,	PUNCT
ejpam-4722	20	17	computer	computer	NOUN
ejpam-4722	20	18	science	science	NOUN
ejpam-4722	20	19	,	,	PUNCT
ejpam-4722	20	20	biology	biology	NOUN
ejpam-4722	20	21	,	,	PUNCT
ejpam-4722	20	22	sociology	sociology	NOUN
ejpam-4722	20	23	,	,	PUNCT
ejpam-4722	20	24	and	and	CCONJ
ejpam-4722	20	25	operations	operation	NOUN
ejpam-4722	20	26	research	research	NOUN
ejpam-4722	20	27	.	.	PUNCT
ejpam-4722	21	1	one	one	NUM
ejpam-4722	21	2	of	of	ADP
ejpam-4722	21	3	the	the	DET
ejpam-4722	21	4	tools	tool	NOUN
ejpam-4722	21	5	that	that	PRON
ejpam-4722	21	6	graph	graph	NOUN
ejpam-4722	21	7	theory	theory	NOUN
ejpam-4722	21	8	provides	provide	VERB
ejpam-4722	21	9	is	be	AUX
ejpam-4722	21	10	the	the	DET
ejpam-4722	21	11	concept	concept	NOUN
ejpam-4722	21	12	of	of	ADP
ejpam-4722	21	13	topological	topological	ADJ
ejpam-4722	21	14	descriptors	descriptor	NOUN
ejpam-4722	21	15	,	,	PUNCT
ejpam-4722	21	16	which	which	PRON
ejpam-4722	21	17	are	be	AUX
ejpam-4722	21	18	numerical	numerical	ADJ
ejpam-4722	21	19	values	value	NOUN
ejpam-4722	21	20	that	that	PRON
ejpam-4722	21	21	capture	capture	VERB
ejpam-4722	21	22	some	some	DET
ejpam-4722	21	23	aspects	aspect	NOUN
ejpam-4722	21	24	of	of	ADP
ejpam-4722	21	25	the	the	DET
ejpam-4722	21	26	structure	structure	NOUN
ejpam-4722	21	27	and	and	CCONJ
ejpam-4722	21	28	properties	property	NOUN
ejpam-4722	21	29	of	of	ADP
ejpam-4722	21	30	graphs	graph	NOUN
ejpam-4722	21	31	.	.	PUNCT
ejpam-4722	22	1	quantitative	quantitative	ADJ
ejpam-4722	22	2	structure	structure	NOUN
ejpam-4722	22	3	-	-	PUNCT
ejpam-4722	22	4	property/	property/	NUM
ejpam-4722	22	5	quantitative	quantitative	ADJ
ejpam-4722	22	6	structure	structure	NOUN
ejpam-4722	22	7	-	-	PUNCT
ejpam-4722	22	8	activity	activity	NOUN
ejpam-4722	22	9	relationship	relationship	NOUN
ejpam-4722	22	10	(	(	PUNCT
ejpam-4722	22	11	qspr	qspr	NOUN
ejpam-4722	22	12	/	/	SYM
ejpam-4722	22	13	qsar	qsar	NOUN
ejpam-4722	22	14	)	)	PUNCT
ejpam-4722	22	15	schemes	scheme	NOUN
ejpam-4722	22	16	are	be	AUX
ejpam-4722	22	17	utilized	utilize	VERB
ejpam-4722	22	18	as	as	ADP
ejpam-4722	22	19	regression	regression	NOUN
ejpam-4722	22	20	models	model	NOUN
ejpam-4722	22	21	in	in	ADP
ejpam-4722	22	22	reticular	reticular	ADJ
ejpam-4722	22	23	chemistry	chemistry	NOUN
ejpam-4722	22	24	to	to	PART
ejpam-4722	22	25	correlate	correlate	VERB
ejpam-4722	22	26	with	with	ADP
ejpam-4722	22	27	various	various	ADJ
ejpam-4722	22	28	of	of	ADP
ejpam-4722	22	29	biological	biological	ADJ
ejpam-4722	22	30	and	and	CCONJ
ejpam-4722	22	31	physicochemical	physicochemical	ADJ
ejpam-4722	22	32	activities	activity	NOUN
ejpam-4722	22	33	.	.	PUNCT
ejpam-4722	23	1	harold	harold	PROPN
ejpam-4722	23	2	wiener	wiener	PROPN
ejpam-4722	24	1	[	[	X
ejpam-4722	24	2	31	31	NUM
ejpam-4722	24	3	]	]	PUNCT
ejpam-4722	24	4	pioneered	pioneer	VERB
ejpam-4722	24	5	a	a	DET
ejpam-4722	24	6	novel	novel	ADJ
ejpam-4722	24	7	way	way	NOUN
ejpam-4722	24	8	to	to	PART
ejpam-4722	24	9	estimate	estimate	VERB
ejpam-4722	24	10	the	the	DET
ejpam-4722	24	11	boiling	boiling	NOUN
ejpam-4722	24	12	point	point	NOUN
ejpam-4722	24	13	of	of	ADP
ejpam-4722	24	14	alkanes	alkane	NOUN
ejpam-4722	24	15	from	from	ADP
ejpam-4722	24	16	their	their	PRON
ejpam-4722	24	17	molecular	molecular	ADJ
ejpam-4722	24	18	shape	shape	NOUN
ejpam-4722	24	19	.	.	PUNCT
ejpam-4722	25	1	he	he	PRON
ejpam-4722	25	2	converted	convert	VERB
ejpam-4722	25	3	the	the	DET
ejpam-4722	25	4	chemical	chemical	NOUN
ejpam-4722	25	5	structure	structure	NOUN
ejpam-4722	25	6	into	into	ADP
ejpam-4722	25	7	a	a	DET
ejpam-4722	25	8	single	single	ADJ
ejpam-4722	25	9	number	number	NOUN
ejpam-4722	25	10	that	that	PRON
ejpam-4722	25	11	reflected	reflect	VERB
ejpam-4722	25	12	its	its	PRON
ejpam-4722	25	13	characteristics	characteristic	NOUN
ejpam-4722	25	14	.	.	PUNCT
ejpam-4722	26	1	this	this	DET
ejpam-4722	26	2	number	number	NOUN
ejpam-4722	26	3	,	,	PUNCT
ejpam-4722	26	4	called	call	VERB
ejpam-4722	26	5	a	a	DET
ejpam-4722	26	6	topological	topological	ADJ
ejpam-4722	26	7	descriptor	descriptor	NOUN
ejpam-4722	26	8	or	or	CCONJ
ejpam-4722	26	9	index	index	NOUN
ejpam-4722	26	10	,	,	PUNCT
ejpam-4722	26	11	was	be	AUX
ejpam-4722	26	12	obtained	obtain	VERB
ejpam-4722	26	13	from	from	ADP
ejpam-4722	26	14	a	a	DET
ejpam-4722	26	15	chemical	chemical	NOUN
ejpam-4722	26	16	graph	graph	NOUN
ejpam-4722	26	17	,	,	PUNCT
ejpam-4722	26	18	a	a	DET
ejpam-4722	26	19	simplified	simplified	ADJ
ejpam-4722	26	20	representation	representation	NOUN
ejpam-4722	26	21	of	of	ADP
ejpam-4722	26	22	an	an	DET
ejpam-4722	26	23	organic	organic	ADJ
ejpam-4722	26	24	molecule	molecule	NOUN
ejpam-4722	26	25	as	as	ADP
ejpam-4722	26	26	a	a	DET
ejpam-4722	26	27	network	network	NOUN
ejpam-4722	26	28	of	of	ADP
ejpam-4722	26	29	atoms	atom	NOUN
ejpam-4722	26	30	and	and	CCONJ
ejpam-4722	26	31	bonds	bond	NOUN
ejpam-4722	26	32	.	.	PUNCT
ejpam-4722	27	1	this	this	DET
ejpam-4722	27	2	technique	technique	NOUN
ejpam-4722	27	3	also	also	ADV
ejpam-4722	27	4	enables	enable	VERB
ejpam-4722	27	5	us	we	PRON
ejpam-4722	27	6	to	to	PART
ejpam-4722	27	7	model	model	VERB
ejpam-4722	27	8	many	many	ADJ
ejpam-4722	27	9	other	other	ADJ
ejpam-4722	27	10	properties	property	NOUN
ejpam-4722	27	11	of	of	ADP
ejpam-4722	27	12	molecules	molecule	NOUN
ejpam-4722	27	13	,	,	PUNCT
ejpam-4722	27	14	such	such	ADJ
ejpam-4722	27	15	as	as	ADP
ejpam-4722	27	16	their	their	PRON
ejpam-4722	27	17	behavior	behavior	NOUN
ejpam-4722	27	18	under	under	ADP
ejpam-4722	27	19	extreme	extreme	ADJ
ejpam-4722	27	20	conditions	condition	NOUN
ejpam-4722	27	21	,	,	PUNCT
ejpam-4722	27	22	their	their	PRON
ejpam-4722	27	23	energy	energy	NOUN
ejpam-4722	27	24	release	release	NOUN
ejpam-4722	27	25	or	or	CCONJ
ejpam-4722	27	26	absorption	absorption	NOUN
ejpam-4722	27	27	,	,	PUNCT
ejpam-4722	27	28	and	and	CCONJ
ejpam-4722	27	29	their	their	PRON
ejpam-4722	27	30	interaction	interaction	NOUN
ejpam-4722	27	31	with	with	ADP
ejpam-4722	27	32	living	living	NOUN
ejpam-4722	27	33	systems	system	NOUN
ejpam-4722	27	34	[	[	X
ejpam-4722	27	35	4	4	NUM
ejpam-4722	27	36	,	,	PUNCT
ejpam-4722	27	37	35	35	NUM
ejpam-4722	27	38	]	]	PUNCT
ejpam-4722	27	39	.	.	PUNCT
ejpam-4722	28	1	in	in	ADP
ejpam-4722	28	2	this	this	DET
ejpam-4722	28	3	study	study	NOUN
ejpam-4722	28	4	,	,	PUNCT
ejpam-4722	28	5	we	we	PRON
ejpam-4722	28	6	apply	apply	VERB
ejpam-4722	28	7	topological	topological	ADJ
ejpam-4722	28	8	descriptors	descriptor	NOUN
ejpam-4722	28	9	to	to	PART
ejpam-4722	28	10	develop	develop	VERB
ejpam-4722	28	11	robust	robust	ADJ
ejpam-4722	28	12	regression	regression	NOUN
ejpam-4722	28	13	models	model	NOUN
ejpam-4722	28	14	for	for	ADP
ejpam-4722	28	15	these	these	DET
ejpam-4722	28	16	properties	property	NOUN
ejpam-4722	28	17	.	.	PUNCT
ejpam-4722	29	1	topological	topological	ADJ
ejpam-4722	29	2	descriptors	descriptor	NOUN
ejpam-4722	29	3	play	play	VERB
ejpam-4722	29	4	a	a	DET
ejpam-4722	29	5	crucial	crucial	ADJ
ejpam-4722	29	6	role	role	NOUN
ejpam-4722	29	7	in	in	ADP
ejpam-4722	29	8	the	the	DET
ejpam-4722	29	9	definitional	definitional	ADJ
ejpam-4722	29	10	work	work	NOUN
ejpam-4722	29	11	done	do	VERB
ejpam-4722	29	12	in	in	ADP
ejpam-4722	29	13	the	the	DET
ejpam-4722	29	14	chemical	chemical	NOUN
ejpam-4722	29	15	sciences	sciences	PROPN
ejpam-4722	29	16	,	,	PUNCT
ejpam-4722	29	17	mathematical	mathematical	ADJ
ejpam-4722	29	18	chemistry	chemistry	NOUN
ejpam-4722	29	19	,	,	PUNCT
ejpam-4722	29	20	chemical	chemical	NOUN
ejpam-4722	29	21	graph	graph	NOUN
ejpam-4722	29	22	theory	theory	NOUN
ejpam-4722	29	23	,	,	PUNCT
ejpam-4722	29	24	and	and	CCONJ
ejpam-4722	29	25	pharmaceutical	pharmaceutical	NOUN
ejpam-4722	29	26	science	science	NOUN
ejpam-4722	29	27	;	;	PUNCT
ejpam-4722	29	28	for	for	ADP
ejpam-4722	29	29	example	example	NOUN
ejpam-4722	29	30	,	,	PUNCT
ejpam-4722	29	31	topological	topological	ADJ
ejpam-4722	29	32	indices	index	NOUN
ejpam-4722	29	33	for	for	ADP
ejpam-4722	29	34	bond	bond	NOUN
ejpam-4722	29	35	connectivity	connectivity	NOUN
ejpam-4722	29	36	are	be	AUX
ejpam-4722	29	37	used	use	VERB
ejpam-4722	29	38	to	to	PART
ejpam-4722	29	39	quantify	quantify	VERB
ejpam-4722	29	40	properties	property	NOUN
ejpam-4722	29	41	like	like	ADP
ejpam-4722	29	42	branching	branch	VERB
ejpam-4722	29	43	,	,	PUNCT
ejpam-4722	29	44	compactness	compactness	NOUN
ejpam-4722	29	45	,	,	PUNCT
ejpam-4722	29	46	centrality	centrality	NOUN
ejpam-4722	29	47	,	,	PUNCT
ejpam-4722	29	48	regularity	regularity	NOUN
ejpam-4722	29	49	,	,	PUNCT
ejpam-4722	29	50	variability	variability	NOUN
ejpam-4722	29	51	,	,	PUNCT
ejpam-4722	29	52	bioactivity	bioactivity	NOUN
ejpam-4722	29	53	,	,	PUNCT
ejpam-4722	29	54	etc	etc	X
ejpam-4722	30	1	[	[	X
ejpam-4722	30	2	27	27	NUM
ejpam-4722	30	3	]	]	PUNCT
ejpam-4722	30	4	.	.	PUNCT
ejpam-4722	31	1	there	there	PRON
ejpam-4722	31	2	are	be	VERB
ejpam-4722	31	3	remarkable	remarkable	ADJ
ejpam-4722	31	4	subclasses	subclass	NOUN
ejpam-4722	31	5	of	of	ADP
ejpam-4722	31	6	indices	index	NOUN
ejpam-4722	31	7	known	know	VERB
ejpam-4722	31	8	as	as	ADP
ejpam-4722	31	9	vertex	vertex	NOUN
ejpam-4722	31	10	and	and	CCONJ
ejpam-4722	31	11	edge	edge	NOUN
ejpam-4722	31	12	bond	bond	NOUN
ejpam-4722	31	13	-	-	PUNCT
ejpam-4722	31	14	additive	additive	ADJ
ejpam-4722	31	15	indices	index	NOUN
ejpam-4722	31	16	or	or	CCONJ
ejpam-4722	31	17	degree	degree	NOUN
ejpam-4722	31	18	based	base	VERB
ejpam-4722	31	19	indices	index	NOUN
ejpam-4722	31	20	that	that	PRON
ejpam-4722	31	21	attempt	attempt	VERB
ejpam-4722	31	22	to	to	PART
ejpam-4722	31	23	capture	capture	VERB
ejpam-4722	31	24	some	some	DET
ejpam-4722	31	25	valuable	valuable	ADJ
ejpam-4722	31	26	aspects	aspect	NOUN
ejpam-4722	31	27	of	of	ADP
ejpam-4722	31	28	complete	complete	ADJ
ejpam-4722	31	29	graphs	graph	NOUN
ejpam-4722	31	30	by	by	ADP
ejpam-4722	31	31	adding	add	VERB
ejpam-4722	31	32	up	up	ADP
ejpam-4722	31	33	the	the	DET
ejpam-4722	31	34	contributions	contribution	NOUN
ejpam-4722	31	35	of	of	ADP
ejpam-4722	31	36	individual	individual	ADJ
ejpam-4722	31	37	vertices	vertex	NOUN
ejpam-4722	31	38	and/or	and/or	CCONJ
ejpam-4722	31	39	edges	edge	NOUN
ejpam-4722	31	40	.	.	PUNCT
ejpam-4722	32	1	it	it	PRON
ejpam-4722	32	2	garnered	garner	VERB
ejpam-4722	32	3	a	a	DET
ejpam-4722	32	4	lot	lot	NOUN
ejpam-4722	32	5	of	of	ADP
ejpam-4722	32	6	interest	interest	NOUN
ejpam-4722	32	7	in	in	ADP
ejpam-4722	32	8	the	the	DET
ejpam-4722	32	9	context	context	NOUN
ejpam-4722	32	10	of	of	ADP
ejpam-4722	32	11	complex	complex	ADJ
ejpam-4722	32	12	networks	network	NOUN
ejpam-4722	32	13	and	and	CCONJ
ejpam-4722	32	14	in	in	ADP
ejpam-4722	32	15	more	more	ADV
ejpam-4722	32	16	traditional	traditional	ADJ
ejpam-4722	32	17	chemical	chemical	NOUN
ejpam-4722	32	18	graph	graph	NOUN
ejpam-4722	32	19	theory	theory	NOUN
ejpam-4722	32	20	applications	application	NOUN
ejpam-4722	32	21	.	.	PUNCT
ejpam-4722	33	1	a	a	DET
ejpam-4722	33	2	distance	distance	NOUN
ejpam-4722	33	3	based	base	VERB
ejpam-4722	33	4	index	index	NOUN
ejpam-4722	33	5	is	be	AUX
ejpam-4722	33	6	a	a	DET
ejpam-4722	33	7	invariant	invariant	NOUN
ejpam-4722	33	8	based	base	VERB
ejpam-4722	33	9	on	on	ADP
ejpam-4722	33	10	the	the	DET
ejpam-4722	33	11	distance	distance	NOUN
ejpam-4722	33	12	between	between	ADP
ejpam-4722	33	13	the	the	DET
ejpam-4722	33	14	vertices	vertex	NOUN
ejpam-4722	33	15	or	or	CCONJ
ejpam-4722	33	16	edges	edge	NOUN
ejpam-4722	33	17	of	of	ADP
ejpam-4722	33	18	any	any	DET
ejpam-4722	33	19	graph	graph	NOUN
ejpam-4722	33	20	[	[	X
ejpam-4722	33	21	20	20	NUM
ejpam-4722	33	22	]	]	PUNCT
ejpam-4722	33	23	.	.	PUNCT
ejpam-4722	34	1	wiener	wiener	NOUN
ejpam-4722	35	1	[	[	X
ejpam-4722	35	2	32	32	NUM
ejpam-4722	35	3	]	]	PUNCT
ejpam-4722	35	4	introduced	introduce	VERB
ejpam-4722	35	5	the	the	DET
ejpam-4722	35	6	first	first	ADJ
ejpam-4722	35	7	graph	graph	NOUN
ejpam-4722	35	8	index	index	NOUN
ejpam-4722	35	9	based	base	VERB
ejpam-4722	35	10	on	on	ADP
ejpam-4722	35	11	distance	distance	NOUN
ejpam-4722	35	12	between	between	ADP
ejpam-4722	35	13	vertices	vertex	NOUN
ejpam-4722	35	14	of	of	ADP
ejpam-4722	35	15	a	a	DET
ejpam-4722	35	16	graph	graph	NOUN
ejpam-4722	35	17	,	,	PUNCT
ejpam-4722	35	18	which	which	PRON
ejpam-4722	35	19	is	be	AUX
ejpam-4722	35	20	described	describe	VERB
ejpam-4722	35	21	as	as	ADP
ejpam-4722	35	22	w	w	PROPN
ejpam-4722	35	23	(	(	PUNCT
ejpam-4722	35	24	ω	ω	NOUN
ejpam-4722	35	25	)	)	PUNCT
ejpam-4722	35	26	=	=	SYM
ejpam-4722	35	27	∑	∑	PUNCT
ejpam-4722	35	28	u	u	PROPN
ejpam-4722	35	29	,	,	PUNCT
ejpam-4722	35	30	v∈v	v∈v	NOUN
ejpam-4722	35	31	(	(	PUNCT
ejpam-4722	35	32	ω	ω	NOUN
ejpam-4722	35	33	)	)	PUNCT
ejpam-4722	35	34	dω(u	dω(u	PUNCT
ejpam-4722	35	35	,	,	PUNCT
ejpam-4722	35	36	v	v	NOUN
ejpam-4722	35	37	)	)	PUNCT
ejpam-4722	35	38	,	,	PUNCT
ejpam-4722	35	39	where	where	SCONJ
ejpam-4722	35	40	dω(u	dω(u	PUNCT
ejpam-4722	35	41	,	,	PUNCT
ejpam-4722	35	42	v	v	NOUN
ejpam-4722	35	43	)	)	PUNCT
ejpam-4722	35	44	represents	represent	VERB
ejpam-4722	35	45	the	the	DET
ejpam-4722	35	46	shortest	short	ADJ
ejpam-4722	35	47	distance	distance	NOUN
ejpam-4722	35	48	between	between	ADP
ejpam-4722	35	49	u	u	NOUN
ejpam-4722	35	50	and	and	CCONJ
ejpam-4722	35	51	v.	v.	ADP
ejpam-4722	35	52	many	many	ADJ
ejpam-4722	35	53	researchers	researcher	NOUN
ejpam-4722	35	54	have	have	AUX
ejpam-4722	35	55	been	be	AUX
ejpam-4722	35	56	exclusively	exclusively	ADV
ejpam-4722	35	57	studied	study	VERB
ejpam-4722	35	58	the	the	DET
ejpam-4722	35	59	wiener	wiener	NOUN
ejpam-4722	35	60	index	index	NOUN
ejpam-4722	35	61	and	and	CCONJ
ejpam-4722	35	62	mostly	mostly	ADV
ejpam-4722	35	63	characterize	characterize	VERB
ejpam-4722	35	64	the	the	DET
ejpam-4722	35	65	sharp	sharp	ADV
ejpam-4722	35	66	lower	low	ADJ
ejpam-4722	35	67	and	and	CCONJ
ejpam-4722	35	68	upper	upper	ADJ
ejpam-4722	35	69	bounds	bound	NOUN
ejpam-4722	35	70	for	for	ADP
ejpam-4722	35	71	different	different	ADJ
ejpam-4722	35	72	graph	graph	NOUN
ejpam-4722	35	73	families	family	NOUN
ejpam-4722	35	74	which	which	PRON
ejpam-4722	35	75	can	can	AUX
ejpam-4722	35	76	be	be	AUX
ejpam-4722	35	77	read	read	VERB
ejpam-4722	35	78	in	in	ADP
ejpam-4722	35	79	[	[	X
ejpam-4722	35	80	5	5	NUM
ejpam-4722	35	81	,	,	PUNCT
ejpam-4722	35	82	8	8	NUM
ejpam-4722	35	83	,	,	PUNCT
ejpam-4722	35	84	10	10	NUM
ejpam-4722	35	85	,	,	PUNCT
ejpam-4722	35	86	33	33	NUM
ejpam-4722	35	87	]	]	PUNCT
ejpam-4722	35	88	and	and	CCONJ
ejpam-4722	35	89	then	then	ADV
ejpam-4722	35	90	research	research	NOUN
ejpam-4722	35	91	extend	extend	NOUN
ejpam-4722	35	92	to	to	PART
ejpam-4722	35	93	discover	discover	VERB
ejpam-4722	35	94	the	the	DET
ejpam-4722	35	95	new	new	ADJ
ejpam-4722	35	96	form	form	NOUN
ejpam-4722	35	97	of	of	ADP
ejpam-4722	35	98	wiener	wiener	NOUN
ejpam-4722	35	99	index	index	NOUN
ejpam-4722	35	100	named	name	VERB
ejpam-4722	35	101	polarity	polarity	NOUN
ejpam-4722	35	102	index	index	NOUN
ejpam-4722	35	103	wp	wp	PROPN
ejpam-4722	35	104	(	(	PUNCT
ejpam-4722	35	105	ω	ω	NOUN
ejpam-4722	35	106	)	)	PUNCT
ejpam-4722	35	107	,	,	PUNCT
ejpam-4722	35	108	which	which	PRON
ejpam-4722	35	109	is	be	AUX
ejpam-4722	35	110	restricted	restrict	VERB
ejpam-4722	35	111	to	to	PART
ejpam-4722	35	112	distance	distance	NOUN
ejpam-4722	35	113	3	3	NUM
ejpam-4722	35	114	among	among	ADP
ejpam-4722	35	115	all	all	DET
ejpam-4722	35	116	unordered	unordered	ADJ
ejpam-4722	35	117	pairs	pair	NOUN
ejpam-4722	35	118	of	of	ADP
ejpam-4722	35	119	vertices	vertex	NOUN
ejpam-4722	35	120	in	in	ADP
ejpam-4722	35	121	ω	ω	PROPN
ejpam-4722	35	122	.	.	PUNCT
ejpam-4722	36	1	the	the	DET
ejpam-4722	36	2	applications	application	NOUN
ejpam-4722	36	3	and	and	CCONJ
ejpam-4722	36	4	detailed	detailed	ADJ
ejpam-4722	36	5	classification	classification	NOUN
ejpam-4722	36	6	of	of	ADP
ejpam-4722	36	7	wiener	wiener	NOUN
ejpam-4722	36	8	polarity	polarity	NOUN
ejpam-4722	36	9	index	index	NOUN
ejpam-4722	36	10	have	have	AUX
ejpam-4722	36	11	been	be	AUX
ejpam-4722	36	12	discussed	discuss	VERB
ejpam-4722	36	13	in	in	ADP
ejpam-4722	36	14	[	[	X
ejpam-4722	36	15	18	18	NUM
ejpam-4722	36	16	,	,	PUNCT
ejpam-4722	36	17	22	22	NUM
ejpam-4722	36	18	]	]	PUNCT
ejpam-4722	36	19	.	.	PUNCT
ejpam-4722	37	1	consider	consider	VERB
ejpam-4722	37	2	an	an	DET
ejpam-4722	37	3	edge	edge	NOUN
ejpam-4722	37	4	e	e	NOUN
ejpam-4722	37	5	=	=	PUNCT
ejpam-4722	37	6	uv	uv	PROPN
ejpam-4722	37	7	∈	∈	PROPN
ejpam-4722	37	8	ω	ω	NOUN
ejpam-4722	37	9	and	and	CCONJ
ejpam-4722	37	10	the	the	DET
ejpam-4722	37	11	following	follow	VERB
ejpam-4722	37	12	three	three	NUM
ejpam-4722	37	13	sets	set	NOUN
ejpam-4722	37	14	defined	define	VERB
ejpam-4722	37	15	as	as	ADP
ejpam-4722	37	16	nu(e	nu(e	NOUN
ejpam-4722	37	17	)	)	PUNCT
ejpam-4722	37	18	=	=	SYM
ejpam-4722	38	1	{	{	PUNCT
ejpam-4722	38	2	k	k	X
ejpam-4722	38	3	∈	∈	PROPN
ejpam-4722	38	4	vω	vω	ADP
ejpam-4722	38	5	:	:	PUNCT
ejpam-4722	38	6	d(u	d(u	PROPN
ejpam-4722	38	7	,	,	PUNCT
ejpam-4722	38	8	k	k	NOUN
ejpam-4722	38	9	)	)	PUNCT
ejpam-4722	38	10	<	<	X
ejpam-4722	39	1	d(v	d(v	PROPN
ejpam-4722	39	2	,	,	PUNCT
ejpam-4722	39	3	k	k	NOUN
ejpam-4722	39	4	)	)	PUNCT
ejpam-4722	39	5	}	}	PUNCT
ejpam-4722	39	6	,	,	PUNCT
ejpam-4722	39	7	nv(e	nv(e	NOUN
ejpam-4722	39	8	)	)	PUNCT
ejpam-4722	39	9	=	=	PRON
ejpam-4722	39	10	{	{	PUNCT
ejpam-4722	39	11	k	k	X
ejpam-4722	39	12	∈	∈	PROPN
ejpam-4722	39	13	vω	vω	NOUN
ejpam-4722	39	14	:	:	PUNCT
ejpam-4722	39	15	d(v	d(v	ADJ
ejpam-4722	39	16	,	,	PUNCT
ejpam-4722	39	17	k	k	NOUN
ejpam-4722	39	18	)	)	PUNCT
ejpam-4722	39	19	<	<	X
ejpam-4722	39	20	d(u	d(u	PROPN
ejpam-4722	39	21	,	,	PUNCT
ejpam-4722	39	22	k	k	NOUN
ejpam-4722	39	23	)	)	PUNCT
ejpam-4722	39	24	}	}	PUNCT
ejpam-4722	39	25	,	,	PUNCT
ejpam-4722	39	26	no(e	no(e	X
ejpam-4722	39	27	)	)	PUNCT
ejpam-4722	39	28	=	=	PRON
ejpam-4722	39	29	{	{	PUNCT
ejpam-4722	39	30	k	k	X
ejpam-4722	39	31	∈	∈	PROPN
ejpam-4722	40	1	vω	vω	ADP
ejpam-4722	40	2	:	:	PUNCT
ejpam-4722	40	3	d(u	d(u	PROPN
ejpam-4722	40	4	,	,	PUNCT
ejpam-4722	40	5	k	k	NOUN
ejpam-4722	40	6	)	)	PUNCT
ejpam-4722	40	7	=	=	SYM
ejpam-4722	41	1	d(v	d(v	PROPN
ejpam-4722	41	2	,	,	PUNCT
ejpam-4722	41	3	k	k	NOUN
ejpam-4722	41	4	)	)	PUNCT
ejpam-4722	41	5	}	}	PUNCT
ejpam-4722	41	6	.	.	PUNCT
ejpam-4722	42	1	thus	thus	ADV
ejpam-4722	42	2	,	,	PUNCT
ejpam-4722	42	3	the	the	DET
ejpam-4722	42	4	divisions	division	NOUN
ejpam-4722	42	5	of	of	ADP
ejpam-4722	42	6	nodes	node	NOUN
ejpam-4722	42	7	in	in	ADP
ejpam-4722	42	8	ω	ω	PROPN
ejpam-4722	42	9	with	with	ADP
ejpam-4722	42	10	respect	respect	NOUN
ejpam-4722	42	11	to	to	ADP
ejpam-4722	42	12	edge	edge	NOUN
ejpam-4722	42	13	e	e	NOUN
ejpam-4722	42	14	are	be	AUX
ejpam-4722	42	15	represented	represent	VERB
ejpam-4722	42	16	by	by	ADP
ejpam-4722	42	17	f.	f.	PROPN
ejpam-4722	42	18	asmat	asmat	PROPN
ejpam-4722	42	19	et	et	PROPN
ejpam-4722	42	20	al	al	PROPN
ejpam-4722	42	21	.	.	PUNCT
ejpam-4722	42	22	/	/	SYM
ejpam-4722	42	23	eur	eur	PROPN
ejpam-4722	42	24	.	.	PUNCT
ejpam-4722	43	1	j.	j.	PROPN
ejpam-4722	43	2	pure	pure	PROPN
ejpam-4722	43	3	appl	appl	PROPN
ejpam-4722	43	4	.	.	PROPN
ejpam-4722	43	5	math	math	PROPN
ejpam-4722	43	6	,	,	PUNCT
ejpam-4722	43	7	16	16	NUM
ejpam-4722	43	8	(	(	PUNCT
ejpam-4722	43	9	3	3	NUM
ejpam-4722	43	10	)	)	PUNCT
ejpam-4722	43	11	(	(	PUNCT
ejpam-4722	43	12	2023	2023	NUM
ejpam-4722	43	13	)	)	PUNCT
ejpam-4722	43	14	,	,	PUNCT
ejpam-4722	43	15	1794	1794	NUM
ejpam-4722	43	16	-	-	SYM
ejpam-4722	43	17	1808	1808	NUM
ejpam-4722	43	18	1796	1796	NUM
ejpam-4722	44	1	[	[	X
ejpam-4722	44	2	nu(e	nu(e	NOUN
ejpam-4722	44	3	)	)	PUNCT
ejpam-4722	44	4	,	,	PUNCT
ejpam-4722	44	5	nv(e	nv(e	NOUN
ejpam-4722	44	6	)	)	PUNCT
ejpam-4722	44	7	,	,	PUNCT
ejpam-4722	44	8	no(e	no(e	X
ejpam-4722	44	9	)	)	PUNCT
ejpam-4722	44	10	]	]	PUNCT
ejpam-4722	44	11	.	.	PUNCT
ejpam-4722	45	1	the	the	DET
ejpam-4722	45	2	collection	collection	NOUN
ejpam-4722	45	3	of	of	ADP
ejpam-4722	45	4	vertices	vertex	NOUN
ejpam-4722	45	5	in	in	ADP
ejpam-4722	45	6	nu(e	nu(e	NOUN
ejpam-4722	45	7	)	)	PUNCT
ejpam-4722	45	8	,	,	PUNCT
ejpam-4722	45	9	nv(e	nv(e	NOUN
ejpam-4722	45	10	)	)	PUNCT
ejpam-4722	45	11	and	and	CCONJ
ejpam-4722	45	12	no(e	no(e	NOUN
ejpam-4722	45	13	)	)	PUNCT
ejpam-4722	45	14	are	be	AUX
ejpam-4722	45	15	symbolized	symbolize	VERB
ejpam-4722	45	16	by	by	ADP
ejpam-4722	45	17	nu(e|ω	nu(e|ω	NOUN
ejpam-4722	45	18	)	)	PUNCT
ejpam-4722	45	19	,	,	PUNCT
ejpam-4722	45	20	nv(e|ω	nv(e|ω	NOUN
ejpam-4722	45	21	)	)	PUNCT
ejpam-4722	45	22	,	,	PUNCT
ejpam-4722	45	23	and	and	CCONJ
ejpam-4722	45	24	no(e|ω	no(e|ω	NUM
ejpam-4722	45	25	)	)	PUNCT
ejpam-4722	45	26	,	,	PUNCT
ejpam-4722	45	27	respectively	respectively	ADV
ejpam-4722	45	28	.	.	PUNCT
ejpam-4722	46	1	the	the	DET
ejpam-4722	46	2	mathematical	mathematical	ADJ
ejpam-4722	46	3	term	term	NOUN
ejpam-4722	46	4	of	of	ADP
ejpam-4722	46	5	wiener	wiener	NOUN
ejpam-4722	46	6	index	index	NOUN
ejpam-4722	46	7	is	be	AUX
ejpam-4722	46	8	explained	explain	VERB
ejpam-4722	46	9	as	as	SCONJ
ejpam-4722	46	10	follows	follow	VERB
ejpam-4722	46	11	[	[	X
ejpam-4722	46	12	3	3	NUM
ejpam-4722	46	13	]	]	PUNCT
ejpam-4722	46	14	,	,	PUNCT
ejpam-4722	46	15	we(ω	we(ω	X
ejpam-4722	46	16	)	)	PUNCT
ejpam-4722	47	1	=	=	PUNCT
ejpam-4722	47	2	∑	∑	PUNCT
ejpam-4722	47	3	uv∈e(ω	uv∈e(ω	NUM
ejpam-4722	47	4	)	)	PUNCT
ejpam-4722	47	5	nu(e|ω)nv(e|ω	nu(e|ω)nv(e|ω	PROPN
ejpam-4722	47	6	)	)	PUNCT
ejpam-4722	47	7	,	,	PUNCT
ejpam-4722	47	8	where	where	SCONJ
ejpam-4722	47	9	all	all	DET
ejpam-4722	47	10	right	right	ADJ
ejpam-4722	47	11	-	-	PUNCT
ejpam-4722	47	12	hand	hand	NOUN
ejpam-4722	47	13	side	side	NOUN
ejpam-4722	47	14	sums	sum	NOUN
ejpam-4722	47	15	have	have	VERB
ejpam-4722	47	16	n	n	ADV
ejpam-4722	47	17	−	−	PROPN
ejpam-4722	47	18	1	1	NUM
ejpam-4722	47	19	,	,	PUNCT
ejpam-4722	47	20	and	and	CCONJ
ejpam-4722	47	21	their	their	PRON
ejpam-4722	47	22	individual	individual	ADJ
ejpam-4722	47	23	values	value	NOUN
ejpam-4722	47	24	can	can	AUX
ejpam-4722	47	25	be	be	AUX
ejpam-4722	47	26	roughly	roughly	ADV
ejpam-4722	47	27	estimated	estimate	VERB
ejpam-4722	47	28	.	.	PUNCT
ejpam-4722	48	1	mostar	mostar	PROPN
ejpam-4722	48	2	index	index	PROPN
ejpam-4722	48	3	was	be	AUX
ejpam-4722	48	4	recently	recently	ADV
ejpam-4722	48	5	introduced	introduce	VERB
ejpam-4722	48	6	by	by	ADP
ejpam-4722	48	7	doslić	doslić	PROPN
ejpam-4722	48	8	et	et	PROPN
ejpam-4722	48	9	al	al	PROPN
ejpam-4722	48	10	.	.	PUNCT
ejpam-4722	49	1	(	(	PUNCT
ejpam-4722	49	2	journal	journal	NOUN
ejpam-4722	49	3	of	of	ADP
ejpam-4722	49	4	mathematical	mathematical	ADJ
ejpam-4722	49	5	chemistry	chemistry	NOUN
ejpam-4722	49	6	,	,	PUNCT
ejpam-4722	49	7	56(10	56(10	NUM
ejpam-4722	49	8	)	)	PUNCT
ejpam-4722	49	9	(	(	PUNCT
ejpam-4722	49	10	2018	2018	NUM
ejpam-4722	49	11	):	):	PUNCT
ejpam-4722	49	12	2995–3013	2995–3013	NUM
ejpam-4722	49	13	)	)	PUNCT
ejpam-4722	49	14	,	,	PUNCT
ejpam-4722	49	15	which	which	PRON
ejpam-4722	49	16	is	be	AUX
ejpam-4722	49	17	defined	define	VERB
ejpam-4722	49	18	as	as	ADP
ejpam-4722	49	19	mov(ω	mov(ω	PROPN
ejpam-4722	49	20	)	)	PUNCT
ejpam-4722	49	21	=	=	SYM
ejpam-4722	50	1	∑	∑	PUNCT
ejpam-4722	50	2	uv∈e(ω	uv∈e(ω	NUM
ejpam-4722	50	3	)	)	PUNCT
ejpam-4722	50	4	|nu(e|ω)−	|nu(e|ω)−	NOUN
ejpam-4722	50	5	nv(e|ω)|	nv(e|ω)|	ADV
ejpam-4722	50	6	,	,	PUNCT
ejpam-4722	50	7	where	where	SCONJ
ejpam-4722	50	8	nu(e|ω	nu(e|ω	NUM
ejpam-4722	50	9	)	)	PUNCT
ejpam-4722	50	10	(	(	PUNCT
ejpam-4722	50	11	resp	resp	NOUN
ejpam-4722	50	12	.	.	PUNCT
ejpam-4722	51	1	nv(e|ω	nv(e|ω	NUM
ejpam-4722	51	2	)	)	PUNCT
ejpam-4722	51	3	)	)	PUNCT
ejpam-4722	51	4	is	be	AUX
ejpam-4722	51	5	the	the	DET
ejpam-4722	51	6	collection	collection	NOUN
ejpam-4722	51	7	of	of	ADP
ejpam-4722	51	8	vertices	vertex	NOUN
ejpam-4722	51	9	of	of	ADP
ejpam-4722	51	10	ω	ω	NOUN
ejpam-4722	51	11	closer	close	ADV
ejpam-4722	51	12	to	to	ADP
ejpam-4722	51	13	vertex	vertex	NOUN
ejpam-4722	51	14	u	u	NOUN
ejpam-4722	51	15	(	(	PUNCT
ejpam-4722	51	16	resp	resp	NOUN
ejpam-4722	51	17	.	.	PUNCT
ejpam-4722	52	1	v	v	X
ejpam-4722	52	2	)	)	PUNCT
ejpam-4722	52	3	than	than	ADP
ejpam-4722	52	4	to	to	PART
ejpam-4722	52	5	vertex	vertex	VERB
ejpam-4722	52	6	v	v	NOUN
ejpam-4722	52	7	(	(	PUNCT
ejpam-4722	52	8	resp	resp	NOUN
ejpam-4722	52	9	.	.	PUNCT
ejpam-4722	53	1	u	u	NOUN
ejpam-4722	53	2	)	)	PUNCT
ejpam-4722	53	3	.	.	PUNCT
ejpam-4722	54	1	arockiaraj	arockiaraj	PROPN
ejpam-4722	54	2	and	and	CCONJ
ejpam-4722	54	3	clement	clement	PROPN
ejpam-4722	54	4	,	,	PUNCT
ejpam-4722	54	5	et	et	PROPN
ejpam-4722	54	6	al	al	PROPN
ejpam-4722	54	7	.	.	PUNCT
ejpam-4722	55	1	(	(	PUNCT
ejpam-4722	55	2	sar	sar	NOUN
ejpam-4722	55	3	and	and	CCONJ
ejpam-4722	55	4	qsar	qsar	VERB
ejpam-4722	55	5	in	in	ADP
ejpam-4722	55	6	environmental	environmental	ADJ
ejpam-4722	55	7	research	research	NOUN
ejpam-4722	55	8	,	,	PUNCT
ejpam-4722	55	9	31(3	31(3	NUM
ejpam-4722	55	10	)	)	PUNCT
ejpam-4722	55	11	(	(	PUNCT
ejpam-4722	55	12	2020	2020	NUM
ejpam-4722	55	13	):	):	PUNCT
ejpam-4722	55	14	187–208	187–208	NUM
ejpam-4722	55	15	)	)	PUNCT
ejpam-4722	55	16	have	have	AUX
ejpam-4722	55	17	recently	recently	ADV
ejpam-4722	55	18	proposed	propose	VERB
ejpam-4722	55	19	two	two	NUM
ejpam-4722	55	20	new	new	ADJ
ejpam-4722	55	21	topological	topological	ADJ
ejpam-4722	55	22	indices	index	NOUN
ejpam-4722	55	23	in	in	ADP
ejpam-4722	55	24	this	this	DET
ejpam-4722	55	25	vein	vein	NOUN
ejpam-4722	55	26	,	,	PUNCT
ejpam-4722	55	27	the	the	DET
ejpam-4722	55	28	weighted	weight	VERB
ejpam-4722	55	29	edge	edge	NOUN
ejpam-4722	55	30	mostar	mostar	PROPN
ejpam-4722	55	31	index	index	NOUN
ejpam-4722	55	32	and	and	CCONJ
ejpam-4722	55	33	the	the	DET
ejpam-4722	55	34	weighted	weight	VERB
ejpam-4722	55	35	vertex	vertex	PROPN
ejpam-4722	55	36	mostar	mostar	PROPN
ejpam-4722	55	37	index	index	PROPN
ejpam-4722	55	38	,	,	PUNCT
ejpam-4722	55	39	which	which	PRON
ejpam-4722	55	40	are	be	AUX
ejpam-4722	55	41	defined	define	VERB
ejpam-4722	55	42	as	as	ADP
ejpam-4722	55	43	mowv	mowv	NOUN
ejpam-4722	55	44	(	(	PUNCT
ejpam-4722	55	45	ω	ω	NOUN
ejpam-4722	55	46	)	)	PUNCT
ejpam-4722	55	47	=	=	SYM
ejpam-4722	56	1	∑	∑	PUNCT
ejpam-4722	56	2	uv∈e(ω	uv∈e(ω	NUM
ejpam-4722	56	3	)	)	PUNCT
ejpam-4722	56	4	(	(	PUNCT
ejpam-4722	56	5	dω(u	dω(u	PUNCT
ejpam-4722	56	6	)	)	PUNCT
ejpam-4722	56	7	+	+	CCONJ
ejpam-4722	56	8	dω(v))|nu(e|ω)−	dω(v))|nu(e|ω)−	PROPN
ejpam-4722	56	9	nv(e|ω)|	nv(e|ω)|	ADV
ejpam-4722	56	10	,	,	PUNCT
ejpam-4722	56	11	mowe	mowe	NOUN
ejpam-4722	56	12	(	(	PUNCT
ejpam-4722	56	13	ω	ω	NOUN
ejpam-4722	56	14	)	)	PUNCT
ejpam-4722	56	15	=	=	SYM
ejpam-4722	56	16	∑	∑	PUNCT
ejpam-4722	56	17	uv∈e(ω	uv∈e(ω	NUM
ejpam-4722	56	18	)	)	PUNCT
ejpam-4722	56	19	(	(	PUNCT
ejpam-4722	56	20	dω(u	dω(u	PUNCT
ejpam-4722	56	21	)	)	PUNCT
ejpam-4722	56	22	+	+	CCONJ
ejpam-4722	56	23	dω(v))|mu(e|ω)−mv(e|ω)|	dω(v))|mu(e|ω)−mv(e|ω)|	X
ejpam-4722	56	24	,	,	PUNCT
ejpam-4722	56	25	where	where	SCONJ
ejpam-4722	56	26	mu(e|ω	mu(e|ω	X
ejpam-4722	56	27	)	)	PUNCT
ejpam-4722	56	28	(	(	PUNCT
ejpam-4722	56	29	resp	resp	NOUN
ejpam-4722	56	30	.	.	PUNCT
ejpam-4722	56	31	mv(e|ω	mv(e|ω	NUM
ejpam-4722	56	32	)	)	PUNCT
ejpam-4722	56	33	)	)	PUNCT
ejpam-4722	56	34	is	be	AUX
ejpam-4722	56	35	the	the	DET
ejpam-4722	56	36	collection	collection	NOUN
ejpam-4722	56	37	of	of	ADP
ejpam-4722	56	38	edges	edge	NOUN
ejpam-4722	56	39	of	of	ADP
ejpam-4722	56	40	ω	ω	NOUN
ejpam-4722	56	41	closer	close	ADV
ejpam-4722	56	42	to	to	ADP
ejpam-4722	56	43	vertex	vertex	NOUN
ejpam-4722	56	44	u	u	NOUN
ejpam-4722	56	45	(	(	PUNCT
ejpam-4722	56	46	resp	resp	NOUN
ejpam-4722	56	47	.	.	PUNCT
ejpam-4722	57	1	v	v	X
ejpam-4722	57	2	)	)	PUNCT
ejpam-4722	57	3	than	than	ADP
ejpam-4722	57	4	to	to	PART
ejpam-4722	57	5	vertex	vertex	VERB
ejpam-4722	57	6	v	v	NOUN
ejpam-4722	57	7	(	(	PUNCT
ejpam-4722	57	8	resp	resp	NOUN
ejpam-4722	57	9	.	.	PUNCT
ejpam-4722	58	1	u	u	NOUN
ejpam-4722	58	2	)	)	PUNCT
ejpam-4722	58	3	.	.	PUNCT
ejpam-4722	59	1	many	many	ADJ
ejpam-4722	59	2	researchers	researcher	NOUN
ejpam-4722	59	3	have	have	AUX
ejpam-4722	59	4	been	be	AUX
ejpam-4722	59	5	extensively	extensively	ADV
ejpam-4722	59	6	worked	work	VERB
ejpam-4722	59	7	on	on	ADP
ejpam-4722	59	8	different	different	ADJ
ejpam-4722	59	9	distance	distance	NOUN
ejpam-4722	59	10	based	base	VERB
ejpam-4722	59	11	indices	index	NOUN
ejpam-4722	59	12	,	,	PUNCT
ejpam-4722	59	13	see	see	VERB
ejpam-4722	59	14	[	[	X
ejpam-4722	59	15	1	1	NUM
ejpam-4722	59	16	,	,	PUNCT
ejpam-4722	59	17	6	6	NUM
ejpam-4722	59	18	,	,	PUNCT
ejpam-4722	59	19	11	11	NUM
ejpam-4722	59	20	,	,	PUNCT
ejpam-4722	59	21	16	16	NUM
ejpam-4722	59	22	,	,	PUNCT
ejpam-4722	59	23	17	17	NUM
ejpam-4722	59	24	,	,	PUNCT
ejpam-4722	59	25	36	36	NUM
ejpam-4722	59	26	]	]	PUNCT
ejpam-4722	59	27	.	.	PUNCT
ejpam-4722	60	1	motivated	motivate	VERB
ejpam-4722	60	2	by	by	ADP
ejpam-4722	60	3	the	the	DET
ejpam-4722	60	4	success	success	NOUN
ejpam-4722	60	5	of	of	ADP
ejpam-4722	60	6	previous	previous	ADJ
ejpam-4722	60	7	research	research	NOUN
ejpam-4722	60	8	,	,	PUNCT
ejpam-4722	60	9	došlić	došlić	PROPN
ejpam-4722	60	10	and	and	CCONJ
ejpam-4722	60	11	ivica	ivica	PROPN
ejpam-4722	60	12	et	et	PROPN
ejpam-4722	60	13	al	al	PROPN
ejpam-4722	60	14	.	.	PROPN
ejpam-4722	61	1	recently	recently	ADV
ejpam-4722	61	2	introduced	introduce	VERB
ejpam-4722	61	3	mostar	mostar	PROPN
ejpam-4722	61	4	invariant	invariant	PROPN
ejpam-4722	61	5	(	(	PUNCT
ejpam-4722	61	6	journal	journal	NOUN
ejpam-4722	61	7	of	of	ADP
ejpam-4722	61	8	mathematical	mathematical	ADJ
ejpam-4722	61	9	chemistry	chemistry	NOUN
ejpam-4722	61	10	,	,	PUNCT
ejpam-4722	61	11	56(10	56(10	NUM
ejpam-4722	61	12	)	)	PUNCT
ejpam-4722	61	13	(	(	PUNCT
ejpam-4722	61	14	2018	2018	NUM
ejpam-4722	61	15	):	):	PUNCT
ejpam-4722	61	16	2995–3013	2995–3013	NUM
ejpam-4722	61	17	)	)	PUNCT
ejpam-4722	61	18	,	,	PUNCT
ejpam-4722	61	19	which	which	PRON
ejpam-4722	61	20	belongs	belong	VERB
ejpam-4722	61	21	to	to	ADP
ejpam-4722	61	22	bond	bond	NOUN
ejpam-4722	61	23	-	-	PUNCT
ejpam-4722	61	24	additive	additive	ADJ
ejpam-4722	61	25	indices	index	NOUN
ejpam-4722	61	26	as	as	SCONJ
ejpam-4722	61	27	they	they	PRON
ejpam-4722	61	28	capture	capture	VERB
ejpam-4722	61	29	the	the	DET
ejpam-4722	61	30	relevant	relevant	ADJ
ejpam-4722	61	31	properties	property	NOUN
ejpam-4722	61	32	of	of	ADP
ejpam-4722	61	33	a	a	DET
ejpam-4722	61	34	graph	graph	NOUN
ejpam-4722	61	35	.	.	PUNCT
ejpam-4722	62	1	many	many	ADJ
ejpam-4722	62	2	research	research	NOUN
ejpam-4722	62	3	works	work	NOUN
ejpam-4722	62	4	have	have	AUX
ejpam-4722	62	5	been	be	AUX
ejpam-4722	62	6	done	do	VERB
ejpam-4722	62	7	on	on	ADP
ejpam-4722	62	8	mostar	mostar	PROPN
ejpam-4722	62	9	index	index	PROPN
ejpam-4722	62	10	,	,	PUNCT
ejpam-4722	62	11	read	read	VERB
ejpam-4722	62	12	[	[	X
ejpam-4722	62	13	13	13	NUM
ejpam-4722	62	14	,	,	PUNCT
ejpam-4722	62	15	14	14	NUM
ejpam-4722	62	16	,	,	PUNCT
ejpam-4722	62	17	23	23	NUM
ejpam-4722	62	18	,	,	PUNCT
ejpam-4722	62	19	25	25	NUM
ejpam-4722	62	20	]	]	PUNCT
ejpam-4722	62	21	.	.	PUNCT
ejpam-4722	63	1	a	a	DET
ejpam-4722	63	2	graph	graph	NOUN
ejpam-4722	63	3	is	be	AUX
ejpam-4722	63	4	said	say	VERB
ejpam-4722	63	5	to	to	PART
ejpam-4722	63	6	be	be	AUX
ejpam-4722	63	7	cactus	cactus	ADJ
ejpam-4722	63	8	if	if	SCONJ
ejpam-4722	63	9	all	all	PRON
ejpam-4722	63	10	of	of	ADP
ejpam-4722	63	11	its	its	PRON
ejpam-4722	63	12	vertices	vertex	NOUN
ejpam-4722	63	13	must	must	AUX
ejpam-4722	63	14	be	be	AUX
ejpam-4722	63	15	either	either	CCONJ
ejpam-4722	63	16	edges	edge	NOUN
ejpam-4722	63	17	or	or	CCONJ
ejpam-4722	63	18	cycles	cycle	NOUN
ejpam-4722	63	19	,	,	PUNCT
ejpam-4722	63	20	and	and	CCONJ
ejpam-4722	63	21	no	no	DET
ejpam-4722	63	22	two	two	NUM
ejpam-4722	63	23	cycles	cycle	NOUN
ejpam-4722	63	24	can	can	AUX
ejpam-4722	63	25	share	share	VERB
ejpam-4722	63	26	more	more	ADJ
ejpam-4722	63	27	than	than	ADP
ejpam-4722	63	28	one	one	NUM
ejpam-4722	63	29	vertex	vertex	NOUN
ejpam-4722	63	30	.	.	PUNCT
ejpam-4722	64	1	readers	reader	NOUN
ejpam-4722	64	2	can	can	AUX
ejpam-4722	64	3	read	read	VERB
ejpam-4722	64	4	many	many	ADJ
ejpam-4722	64	5	works	work	NOUN
ejpam-4722	64	6	on	on	ADP
ejpam-4722	64	7	cactus	cactus	NOUN
ejpam-4722	64	8	graph	graph	NOUN
ejpam-4722	64	9	herein	herein	NOUN
ejpam-4722	64	10	[	[	PUNCT
ejpam-4722	64	11	9	9	NUM
ejpam-4722	64	12	,	,	PUNCT
ejpam-4722	64	13	21	21	NUM
ejpam-4722	64	14	,	,	PUNCT
ejpam-4722	64	15	28–30	28–30	PROPN
ejpam-4722	64	16	]	]	PUNCT
ejpam-4722	64	17	.	.	PUNCT
ejpam-4722	65	1	extremal	extremal	ADJ
ejpam-4722	65	2	bicyclic	bicyclic	NOUN
ejpam-4722	65	3	graphs	graph	NOUN
ejpam-4722	65	4	were	be	AUX
ejpam-4722	65	5	obtained	obtain	VERB
ejpam-4722	65	6	by	by	ADP
ejpam-4722	65	7	tepeh	tepeh	NOUN
ejpam-4722	65	8	with	with	ADP
ejpam-4722	65	9	respect	respect	NOUN
ejpam-4722	65	10	to	to	ADP
ejpam-4722	65	11	the	the	DET
ejpam-4722	65	12	mostar	mostar	PROPN
ejpam-4722	65	13	index	index	NOUN
ejpam-4722	65	14	[	[	X
ejpam-4722	65	15	26	26	NUM
ejpam-4722	65	16	]	]	PUNCT
ejpam-4722	65	17	,	,	PUNCT
ejpam-4722	65	18	while	while	SCONJ
ejpam-4722	65	19	extremal	extremal	ADJ
ejpam-4722	65	20	catacondensed	catacondensed	ADJ
ejpam-4722	65	21	benzenoids	benzenoid	NOUN
ejpam-4722	65	22	were	be	AUX
ejpam-4722	65	23	established	establish	VERB
ejpam-4722	65	24	by	by	ADP
ejpam-4722	65	25	deng	deng	PROPN
ejpam-4722	66	1	[	[	X
ejpam-4722	66	2	12	12	NUM
ejpam-4722	66	3	]	]	PUNCT
ejpam-4722	66	4	.	.	PUNCT
ejpam-4722	67	1	there	there	PRON
ejpam-4722	67	2	are	be	VERB
ejpam-4722	67	3	a	a	DET
ejpam-4722	67	4	number	number	NOUN
ejpam-4722	67	5	of	of	ADP
ejpam-4722	67	6	different	different	ADJ
ejpam-4722	67	7	conclusions	conclusion	NOUN
ejpam-4722	67	8	and	and	CCONJ
ejpam-4722	67	9	points	point	NOUN
ejpam-4722	67	10	of	of	ADP
ejpam-4722	67	11	view	view	NOUN
ejpam-4722	67	12	that	that	PRON
ejpam-4722	67	13	can	can	AUX
ejpam-4722	67	14	be	be	AUX
ejpam-4722	67	15	drawn	draw	VERB
ejpam-4722	67	16	from	from	ADP
ejpam-4722	67	17	the	the	DET
ejpam-4722	67	18	mostar	mostar	PROPN
ejpam-4722	67	19	index	index	PROPN
ejpam-4722	67	20	,	,	PUNCT
ejpam-4722	67	21	which	which	PRON
ejpam-4722	67	22	are	be	AUX
ejpam-4722	67	23	all	all	PRON
ejpam-4722	67	24	explained	explain	VERB
ejpam-4722	67	25	by	by	ADP
ejpam-4722	67	26	ali	ali	PROPN
ejpam-4722	67	27	[	[	X
ejpam-4722	67	28	2	2	NUM
ejpam-4722	67	29	]	]	PUNCT
ejpam-4722	67	30	.	.	PUNCT
ejpam-4722	68	1	imran	imran	PROPN
ejpam-4722	68	2	et	et	PROPN
ejpam-4722	68	3	al	al	PROPN
ejpam-4722	68	4	.	.	PROPN
ejpam-4722	68	5	,	,	PUNCT
ejpam-4722	69	1	[	[	X
ejpam-4722	69	2	19	19	NUM
ejpam-4722	69	3	]	]	PUNCT
ejpam-4722	69	4	computed	compute	VERB
ejpam-4722	69	5	weighted	weight	VERB
ejpam-4722	69	6	mostar	mostar	PROPN
ejpam-4722	69	7	invariants	invariant	NOUN
ejpam-4722	69	8	of	of	ADP
ejpam-4722	69	9	phthalocyanines	phthalocyanine	NOUN
ejpam-4722	69	10	,	,	PUNCT
ejpam-4722	69	11	triazine	triazine	NOUN
ejpam-4722	69	12	-	-	PUNCT
ejpam-4722	69	13	based	base	VERB
ejpam-4722	69	14	and	and	CCONJ
ejpam-4722	69	15	nanostar	nanostar	ADJ
ejpam-4722	69	16	dendrimers	dendrimer	NOUN
ejpam-4722	69	17	.	.	PUNCT
ejpam-4722	70	1	brezovnik	brezovnik	VERB
ejpam-4722	71	1	[	[	X
ejpam-4722	71	2	7	7	NUM
ejpam-4722	71	3	]	]	PUNCT
ejpam-4722	71	4	studied	study	VERB
ejpam-4722	71	5	szeged	szeged	PROPN
ejpam-4722	71	6	and	and	CCONJ
ejpam-4722	71	7	mostar	mostar	PROPN
ejpam-4722	71	8	root	root	NOUN
ejpam-4722	71	9	-	-	PUNCT
ejpam-4722	71	10	indices	index	NOUN
ejpam-4722	71	11	of	of	ADP
ejpam-4722	71	12	graphs	graph	NOUN
ejpam-4722	71	13	.	.	PUNCT
ejpam-4722	72	1	consider	consider	VERB
ejpam-4722	72	2	c(n	c(n	PROPN
ejpam-4722	72	3	,	,	PUNCT
ejpam-4722	72	4	k	k	PROPN
ejpam-4722	72	5	)	)	PUNCT
ejpam-4722	72	6	,	,	PUNCT
ejpam-4722	72	7	the	the	DET
ejpam-4722	72	8	collection	collection	NOUN
ejpam-4722	72	9	of	of	ADP
ejpam-4722	72	10	all	all	DET
ejpam-4722	72	11	cactus	cactus	NOUN
ejpam-4722	72	12	graphs	graph	NOUN
ejpam-4722	72	13	with	with	ADP
ejpam-4722	72	14	n	n	ADP
ejpam-4722	72	15	vertices	vertex	NOUN
ejpam-4722	72	16	and	and	CCONJ
ejpam-4722	72	17	k	k	PROPN
ejpam-4722	72	18	cycles	cycle	NOUN
ejpam-4722	72	19	.	.	PUNCT
ejpam-4722	73	1	inspired	inspire	VERB
ejpam-4722	73	2	by	by	ADP
ejpam-4722	73	3	the	the	DET
ejpam-4722	73	4	existing	exist	VERB
ejpam-4722	73	5	literature	literature	NOUN
ejpam-4722	73	6	on	on	ADP
ejpam-4722	73	7	cactus	cactus	NOUN
ejpam-4722	73	8	graphs	graph	NOUN
ejpam-4722	73	9	and	and	CCONJ
ejpam-4722	73	10	weighted	weight	VERB
ejpam-4722	73	11	edge	edge	PROPN
ejpam-4722	73	12	mostar	mostar	PROPN
ejpam-4722	73	13	index	index	PROPN
ejpam-4722	73	14	,	,	PUNCT
ejpam-4722	73	15	we	we	PRON
ejpam-4722	73	16	extend	extend	VERB
ejpam-4722	73	17	the	the	DET
ejpam-4722	73	18	previous	previous	ADJ
ejpam-4722	73	19	results	result	NOUN
ejpam-4722	73	20	to	to	ADP
ejpam-4722	73	21	a	a	DET
ejpam-4722	73	22	more	more	ADV
ejpam-4722	73	23	general	general	ADJ
ejpam-4722	73	24	setting	setting	NOUN
ejpam-4722	73	25	by	by	ADP
ejpam-4722	73	26	using	use	VERB
ejpam-4722	73	27	the	the	DET
ejpam-4722	73	28	extremal	extremal	ADJ
ejpam-4722	73	29	graphs	graph	NOUN
ejpam-4722	73	30	as	as	ADP
ejpam-4722	73	31	an	an	DET
ejpam-4722	73	32	illustrative	illustrative	ADJ
ejpam-4722	73	33	example	example	NOUN
ejpam-4722	73	34	.	.	PUNCT
ejpam-4722	74	1	we	we	PRON
ejpam-4722	74	2	then	then	ADV
ejpam-4722	74	3	establish	establish	VERB
ejpam-4722	74	4	an	an	DET
ejpam-4722	74	5	upper	upper	ADJ
ejpam-4722	74	6	bound	bind	VERB
ejpam-4722	74	7	for	for	ADP
ejpam-4722	74	8	the	the	DET
ejpam-4722	74	9	weighted	weight	VERB
ejpam-4722	74	10	edge	edge	NOUN
ejpam-4722	74	11	mostar	mostar	PROPN
ejpam-4722	74	12	f.	f.	PROPN
ejpam-4722	74	13	asmat	asmat	PROPN
ejpam-4722	74	14	et	et	PROPN
ejpam-4722	74	15	al	al	PROPN
ejpam-4722	74	16	.	.	PUNCT
ejpam-4722	74	17	/	/	SYM
ejpam-4722	74	18	eur	eur	PROPN
ejpam-4722	74	19	.	.	PUNCT
ejpam-4722	75	1	j.	j.	PROPN
ejpam-4722	75	2	pure	pure	PROPN
ejpam-4722	75	3	appl	appl	PROPN
ejpam-4722	75	4	.	.	PROPN
ejpam-4722	75	5	math	math	PROPN
ejpam-4722	75	6	,	,	PUNCT
ejpam-4722	75	7	16	16	NUM
ejpam-4722	75	8	(	(	PUNCT
ejpam-4722	75	9	3	3	NUM
ejpam-4722	75	10	)	)	PUNCT
ejpam-4722	75	11	(	(	PUNCT
ejpam-4722	75	12	2023	2023	NUM
ejpam-4722	75	13	)	)	PUNCT
ejpam-4722	75	14	,	,	PUNCT
ejpam-4722	75	15	1794	1794	NUM
ejpam-4722	75	16	-	-	SYM
ejpam-4722	75	17	1808	1808	NUM
ejpam-4722	75	18	1797	1797	NUM
ejpam-4722	75	19	index	index	NOUN
ejpam-4722	76	1	and	and	CCONJ
ejpam-4722	76	2	identify	identify	VERB
ejpam-4722	76	3	the	the	DET
ejpam-4722	76	4	extremal	extremal	ADJ
ejpam-4722	76	5	graph	graph	NOUN
ejpam-4722	76	6	among	among	ADP
ejpam-4722	76	7	all	all	DET
ejpam-4722	76	8	the	the	DET
ejpam-4722	76	9	graphs	graph	NOUN
ejpam-4722	76	10	in	in	ADP
ejpam-4722	76	11	c(n	c(n	PROPN
ejpam-4722	76	12	,	,	PUNCT
ejpam-4722	76	13	k	k	NOUN
ejpam-4722	76	14	)	)	PUNCT
ejpam-4722	76	15	.	.	PUNCT
ejpam-4722	77	1	let	let	VERB
ejpam-4722	77	2	t	t	PROPN
ejpam-4722	77	3	(	(	PUNCT
ejpam-4722	77	4	n	n	X
ejpam-4722	77	5	,	,	PUNCT
ejpam-4722	77	6	d	d	X
ejpam-4722	77	7	)	)	PUNCT
ejpam-4722	77	8	denote	denote	VERB
ejpam-4722	77	9	the	the	DET
ejpam-4722	77	10	set	set	NOUN
ejpam-4722	77	11	of	of	ADP
ejpam-4722	77	12	tree	tree	NOUN
ejpam-4722	77	13	graphs	graph	NOUN
ejpam-4722	77	14	with	with	ADP
ejpam-4722	77	15	n	n	ADP
ejpam-4722	77	16	vertices	vertex	NOUN
ejpam-4722	77	17	and	and	CCONJ
ejpam-4722	77	18	diameter	diameter	NOUN
ejpam-4722	77	19	d.	d.	PROPN
ejpam-4722	77	20	let	let	VERB
ejpam-4722	77	21	t	t	PROPN
ejpam-4722	77	22	(	(	PUNCT
ejpam-4722	77	23	̂n	̂n	ADJ
ejpam-4722	77	24	,	,	PUNCT
ejpam-4722	77	25	d	d	NOUN
ejpam-4722	77	26	)	)	PUNCT
ejpam-4722	77	27	∈	∈	PROPN
ejpam-4722	77	28	t	t	PROPN
ejpam-4722	77	29	(	(	PUNCT
ejpam-4722	77	30	n	n	X
ejpam-4722	77	31	,	,	PUNCT
ejpam-4722	77	32	d	d	X
ejpam-4722	77	33	)	)	PUNCT
ejpam-4722	77	34	be	be	AUX
ejpam-4722	77	35	the	the	DET
ejpam-4722	77	36	special	special	ADJ
ejpam-4722	77	37	tree	tree	NOUN
ejpam-4722	77	38	graph	graph	NOUN
ejpam-4722	77	39	with	with	ADP
ejpam-4722	77	40	diameter	diameter	NOUN
ejpam-4722	77	41	d	d	NOUN
ejpam-4722	77	42	and	and	CCONJ
ejpam-4722	78	1	n	n	CCONJ
ejpam-4722	78	2	−	−	PROPN
ejpam-4722	79	1	d	d	SYM
ejpam-4722	79	2	−	−	PROPN
ejpam-4722	79	3	1	1	NUM
ejpam-4722	79	4	pendent	pendent	NOUN
ejpam-4722	79	5	vertices	vertex	NOUN
ejpam-4722	79	6	attached	attach	VERB
ejpam-4722	79	7	to	to	ADP
ejpam-4722	79	8	a	a	DET
ejpam-4722	79	9	fixed	fix	VERB
ejpam-4722	79	10	vertex	vertex	NOUN
ejpam-4722	79	11	.	.	PUNCT
ejpam-4722	80	1	finally	finally	ADV
ejpam-4722	80	2	,	,	PUNCT
ejpam-4722	80	3	we	we	PRON
ejpam-4722	80	4	determine	determine	VERB
ejpam-4722	80	5	the	the	DET
ejpam-4722	80	6	maximum	maximum	ADJ
ejpam-4722	80	7	value	value	NOUN
ejpam-4722	80	8	of	of	ADP
ejpam-4722	80	9	the	the	DET
ejpam-4722	80	10	weighted	weight	VERB
ejpam-4722	80	11	vertex	vertex	NOUN
ejpam-4722	80	12	mostar	mostar	PROPN
ejpam-4722	80	13	index	index	PROPN
ejpam-4722	80	14	over	over	ADP
ejpam-4722	80	15	all	all	DET
ejpam-4722	80	16	the	the	DET
ejpam-4722	80	17	tree	tree	NOUN
ejpam-4722	80	18	graphs	graph	NOUN
ejpam-4722	80	19	.	.	PUNCT
ejpam-4722	81	1	2	2	X
ejpam-4722	81	2	.	.	X
ejpam-4722	81	3	preliminaries	preliminary	NOUN
ejpam-4722	81	4	results	result	NOUN
ejpam-4722	81	5	and	and	CCONJ
ejpam-4722	81	6	notations	notation	NOUN
ejpam-4722	81	7	here	here	ADV
ejpam-4722	81	8	,	,	PUNCT
ejpam-4722	81	9	we	we	PRON
ejpam-4722	81	10	only	only	ADV
ejpam-4722	81	11	deal	deal	VERB
ejpam-4722	81	12	with	with	ADP
ejpam-4722	81	13	simple	simple	ADJ
ejpam-4722	81	14	finite	finite	ADJ
ejpam-4722	81	15	connected	connect	VERB
ejpam-4722	81	16	graphs	graph	NOUN
ejpam-4722	81	17	.	.	PUNCT
ejpam-4722	82	1	other	other	ADJ
ejpam-4722	82	2	notations	notation	NOUN
ejpam-4722	82	3	can	can	AUX
ejpam-4722	82	4	be	be	AUX
ejpam-4722	82	5	studied	study	VERB
ejpam-4722	82	6	in	in	ADP
ejpam-4722	82	7	[	[	X
ejpam-4722	82	8	15	15	NUM
ejpam-4722	82	9	]	]	PUNCT
ejpam-4722	82	10	.	.	PUNCT
ejpam-4722	83	1	let	let	VERB
ejpam-4722	83	2	ω	ω	PRON
ejpam-4722	83	3	be	be	AUX
ejpam-4722	83	4	a	a	DET
ejpam-4722	83	5	connected	connected	ADJ
ejpam-4722	83	6	graph	graph	NOUN
ejpam-4722	83	7	comprises	comprise	VERB
ejpam-4722	83	8	vertex	vertex	NOUN
ejpam-4722	83	9	set	set	VERB
ejpam-4722	83	10	v	v	PROPN
ejpam-4722	83	11	(	(	PUNCT
ejpam-4722	83	12	ω	ω	NOUN
ejpam-4722	83	13	)	)	PUNCT
ejpam-4722	83	14	and	and	CCONJ
ejpam-4722	83	15	edge	edge	NOUN
ejpam-4722	83	16	set	set	VERB
ejpam-4722	83	17	e(ω	e(ω	PROPN
ejpam-4722	83	18	)	)	PUNCT
ejpam-4722	83	19	.	.	PUNCT
ejpam-4722	84	1	for	for	ADP
ejpam-4722	84	2	an	an	DET
ejpam-4722	84	3	edge	edge	NOUN
ejpam-4722	84	4	uv	uv	NOUN
ejpam-4722	84	5	∈	∈	NOUN
ejpam-4722	84	6	e(ω	e(ω	PROPN
ejpam-4722	84	7	)	)	PUNCT
ejpam-4722	84	8	,	,	PUNCT
ejpam-4722	84	9	the	the	DET
ejpam-4722	84	10	graph	graph	NOUN
ejpam-4722	84	11	ω	ω	PROPN
ejpam-4722	84	12	−	−	NOUN
ejpam-4722	84	13	uv	uv	NOUN
ejpam-4722	84	14	is	be	AUX
ejpam-4722	84	15	obtained	obtain	VERB
ejpam-4722	84	16	by	by	ADP
ejpam-4722	84	17	removing	remove	VERB
ejpam-4722	84	18	uv	uv	PROPN
ejpam-4722	84	19	∈	∈	PROPN
ejpam-4722	84	20	e(ω	e(ω	PROPN
ejpam-4722	84	21	)	)	PUNCT
ejpam-4722	84	22	from	from	ADP
ejpam-4722	84	23	ω	ω	PROPN
ejpam-4722	84	24	.	.	PUNCT
ejpam-4722	85	1	for	for	ADP
ejpam-4722	85	2	any	any	DET
ejpam-4722	85	3	vertex	vertex	NOUN
ejpam-4722	85	4	u	u	NOUN
ejpam-4722	85	5	∈	∈	PROPN
ejpam-4722	85	6	v	v	PROPN
ejpam-4722	85	7	(	(	PUNCT
ejpam-4722	85	8	ω	ω	NOUN
ejpam-4722	85	9	)	)	PUNCT
ejpam-4722	85	10	,	,	PUNCT
ejpam-4722	85	11	let	let	AUX
ejpam-4722	85	12	nu(ω	nu(ω	PUNCT
ejpam-4722	85	13	)	)	PUNCT
ejpam-4722	85	14	represents	represent	VERB
ejpam-4722	85	15	the	the	DET
ejpam-4722	85	16	number	number	NOUN
ejpam-4722	85	17	of	of	ADP
ejpam-4722	85	18	edges	edge	NOUN
ejpam-4722	85	19	incidents	incident	NOUN
ejpam-4722	85	20	to	to	ADP
ejpam-4722	85	21	u	u	NOUN
ejpam-4722	85	22	in	in	ADP
ejpam-4722	85	23	ω	ω	PROPN
ejpam-4722	85	24	and	and	CCONJ
ejpam-4722	85	25	dω(u	dω(u	PUNCT
ejpam-4722	85	26	)	)	PUNCT
ejpam-4722	85	27	=	=	SYM
ejpam-4722	85	28	|nu(ω)|	|nu(ω)|	PROPN
ejpam-4722	85	29	represents	represent	VERB
ejpam-4722	85	30	the	the	DET
ejpam-4722	85	31	degree	degree	NOUN
ejpam-4722	85	32	of	of	ADP
ejpam-4722	85	33	u.	u.	NOUN
ejpam-4722	85	34	a	a	DET
ejpam-4722	85	35	vertex	vertex	NOUN
ejpam-4722	85	36	with	with	ADP
ejpam-4722	85	37	exactly	exactly	ADV
ejpam-4722	85	38	one	one	NUM
ejpam-4722	85	39	degree	degree	NOUN
ejpam-4722	85	40	is	be	AUX
ejpam-4722	85	41	called	call	VERB
ejpam-4722	85	42	pendant	pendant	ADJ
ejpam-4722	85	43	.	.	PUNCT
ejpam-4722	86	1	a	a	DET
ejpam-4722	86	2	cut	cut	ADJ
ejpam-4722	86	3	vertex	vertex	NOUN
ejpam-4722	86	4	of	of	ADP
ejpam-4722	86	5	a	a	DET
ejpam-4722	86	6	graph	graph	NOUN
ejpam-4722	86	7	is	be	AUX
ejpam-4722	86	8	any	any	DET
ejpam-4722	86	9	vertex	vertex	NOUN
ejpam-4722	86	10	that	that	PRON
ejpam-4722	86	11	when	when	SCONJ
ejpam-4722	86	12	it	it	PRON
ejpam-4722	86	13	removed	remove	VERB
ejpam-4722	86	14	the	the	DET
ejpam-4722	86	15	number	number	NOUN
ejpam-4722	86	16	of	of	ADP
ejpam-4722	86	17	connected	connected	ADJ
ejpam-4722	86	18	components	component	NOUN
ejpam-4722	86	19	of	of	ADP
ejpam-4722	86	20	this	this	DET
ejpam-4722	86	21	graph	graph	NOUN
ejpam-4722	86	22	increases	increase	NOUN
ejpam-4722	86	23	.	.	PUNCT
ejpam-4722	87	1	similarly	similarly	ADV
ejpam-4722	87	2	,	,	PUNCT
ejpam-4722	87	3	an	an	DET
ejpam-4722	87	4	edge	edge	NOUN
ejpam-4722	87	5	is	be	AUX
ejpam-4722	87	6	called	call	VERB
ejpam-4722	87	7	cut	cut	ADJ
ejpam-4722	87	8	edge	edge	NOUN
ejpam-4722	87	9	if	if	SCONJ
ejpam-4722	87	10	,	,	PUNCT
ejpam-4722	87	11	by	by	ADP
ejpam-4722	87	12	deleting	delete	VERB
ejpam-4722	87	13	that	that	DET
ejpam-4722	87	14	edge	edge	NOUN
ejpam-4722	87	15	,	,	PUNCT
ejpam-4722	87	16	the	the	DET
ejpam-4722	87	17	graph	graph	NOUN
ejpam-4722	87	18	is	be	AUX
ejpam-4722	87	19	converted	convert	VERB
ejpam-4722	87	20	into	into	ADP
ejpam-4722	87	21	exactly	exactly	ADV
ejpam-4722	87	22	two	two	NUM
ejpam-4722	87	23	components	component	NOUN
ejpam-4722	87	24	.	.	PUNCT
ejpam-4722	88	1	consider	consider	VERB
ejpam-4722	88	2	that	that	DET
ejpam-4722	88	3	pn	pn	PROPN
ejpam-4722	88	4	,	,	PUNCT
ejpam-4722	88	5	sn	sn	PROPN
ejpam-4722	88	6	,	,	PUNCT
ejpam-4722	88	7	cn	cn	PROPN
ejpam-4722	88	8	and	and	CCONJ
ejpam-4722	88	9	kn	kn	PROPN
ejpam-4722	88	10	the	the	DET
ejpam-4722	88	11	path	path	NOUN
ejpam-4722	88	12	,	,	PUNCT
ejpam-4722	88	13	star	star	NOUN
ejpam-4722	88	14	,	,	PUNCT
ejpam-4722	88	15	cycle	cycle	NOUN
ejpam-4722	88	16	,	,	PUNCT
ejpam-4722	88	17	and	and	CCONJ
ejpam-4722	88	18	complete	complete	ADJ
ejpam-4722	88	19	graph	graph	NOUN
ejpam-4722	88	20	with	with	ADP
ejpam-4722	88	21	n	n	ADP
ejpam-4722	88	22	vertices	vertex	NOUN
ejpam-4722	88	23	,	,	PUNCT
ejpam-4722	88	24	respectively	respectively	ADV
ejpam-4722	88	25	.	.	PUNCT
ejpam-4722	89	1	let	let	VERB
ejpam-4722	89	2	sn	sn	PROPN
ejpam-4722	89	3	be	be	AUX
ejpam-4722	89	4	the	the	DET
ejpam-4722	89	5	star	star	NOUN
ejpam-4722	89	6	of	of	ADP
ejpam-4722	89	7	order	order	NOUN
ejpam-4722	89	8	n.	n.	PROPN
ejpam-4722	89	9	denote	denote	NOUN
ejpam-4722	89	10	by	by	ADP
ejpam-4722	89	11	s∗n	s∗n	NUM
ejpam-4722	89	12	the	the	DET
ejpam-4722	89	13	graph	graph	NOUN
ejpam-4722	89	14	generated	generate	VERB
ejpam-4722	89	15	by	by	ADP
ejpam-4722	89	16	associating	associate	VERB
ejpam-4722	89	17	one	one	NUM
ejpam-4722	89	18	new	new	ADJ
ejpam-4722	89	19	edge	edge	NOUN
ejpam-4722	89	20	among	among	ADP
ejpam-4722	89	21	the	the	DET
ejpam-4722	89	22	leaves	leave	NOUN
ejpam-4722	89	23	of	of	ADP
ejpam-4722	89	24	the	the	DET
ejpam-4722	89	25	star	star	NOUN
ejpam-4722	89	26	sn	sn	PROPN
ejpam-4722	89	27	.	.	PUNCT
ejpam-4722	90	1	let	let	VERB
ejpam-4722	90	2	s∗,kn	s∗,kn	NOUN
ejpam-4722	90	3	be	be	AUX
ejpam-4722	90	4	the	the	DET
ejpam-4722	90	5	generated	generate	VERB
ejpam-4722	90	6	graph	graph	NOUN
ejpam-4722	90	7	of	of	ADP
ejpam-4722	90	8	order	order	NOUN
ejpam-4722	90	9	n	n	PRON
ejpam-4722	90	10	constructed	construct	VERB
ejpam-4722	90	11	by	by	ADP
ejpam-4722	90	12	associating	associate	VERB
ejpam-4722	90	13	k	k	PROPN
ejpam-4722	90	14	new	new	ADJ
ejpam-4722	90	15	edges	edge	NOUN
ejpam-4722	90	16	between	between	ADP
ejpam-4722	90	17	the	the	DET
ejpam-4722	90	18	leaves	leave	NOUN
ejpam-4722	90	19	in	in	ADP
ejpam-4722	90	20	a	a	DET
ejpam-4722	90	21	star	star	NOUN
ejpam-4722	90	22	sn	sn	NOUN
ejpam-4722	90	23	.	.	PUNCT
ejpam-4722	91	1	in	in	ADP
ejpam-4722	91	2	particular	particular	ADJ
ejpam-4722	91	3	,	,	PUNCT
ejpam-4722	91	4	s∗n	s∗n	NUM
ejpam-4722	91	5	is	be	AUX
ejpam-4722	91	6	just	just	ADV
ejpam-4722	91	7	s∗,1n	s∗,1n	PROPN
ejpam-4722	91	8	.	.	PUNCT
ejpam-4722	92	1	theorem	theorem	NOUN
ejpam-4722	92	2	1	1	NUM
ejpam-4722	92	3	.	.	PUNCT
ejpam-4722	93	1	[	[	X
ejpam-4722	93	2	34	34	NUM
ejpam-4722	93	3	]	]	PUNCT
ejpam-4722	93	4	let	let	VERB
ejpam-4722	93	5	ω	ω	NUM
ejpam-4722	93	6	∈	∈	PROPN
ejpam-4722	93	7	c(n	c(n	PROPN
ejpam-4722	93	8	,	,	PUNCT
ejpam-4722	93	9	k	k	NOUN
ejpam-4722	93	10	)	)	PUNCT
ejpam-4722	93	11	be	be	VERB
ejpam-4722	93	12	a	a	DET
ejpam-4722	93	13	connected	connected	ADJ
ejpam-4722	93	14	graph	graph	NOUN
ejpam-4722	93	15	.	.	PUNCT
ejpam-4722	94	1	then	then	ADV
ejpam-4722	94	2	(	(	PUNCT
ejpam-4722	94	3	i	i	NOUN
ejpam-4722	94	4	)	)	PUNCT
ejpam-4722	94	5	for	for	ADP
ejpam-4722	94	6	n	n	X
ejpam-4722	94	7	≥	≥	NOUN
ejpam-4722	94	8	10	10	NUM
ejpam-4722	94	9	and	and	CCONJ
ejpam-4722	94	10	n	n	CCONJ
ejpam-4722	94	11	<	<	X
ejpam-4722	94	12	4k	4k	X
ejpam-4722	94	13	then	then	ADV
ejpam-4722	94	14	moe(ω	moe(ω	PROPN
ejpam-4722	94	15	)	)	PUNCT
ejpam-4722	94	16	≤	≤	NOUN
ejpam-4722	95	1	2n2	2n2	NUM
ejpam-4722	95	2	−	−	NOUN
ejpam-4722	95	3	8n	8n	NOUN
ejpam-4722	95	4	+	+	CCONJ
ejpam-4722	95	5	(	(	PUNCT
ejpam-4722	95	6	24	24	NUM
ejpam-4722	95	7	−	−	NOUN
ejpam-4722	95	8	4n)k	4n)k	NUM
ejpam-4722	95	9	with	with	ADP
ejpam-4722	95	10	equality	equality	NOUN
ejpam-4722	95	11	if	if	SCONJ
ejpam-4722	95	12	and	and	CCONJ
ejpam-4722	95	13	only	only	ADV
ejpam-4722	95	14	if	if	SCONJ
ejpam-4722	95	15	ω	ω	PRON
ejpam-4722	95	16	∼=	∼=	PROPN
ejpam-4722	95	17	ωn(3	ωn(3	NUM
ejpam-4722	95	18	,	,	PUNCT
ejpam-4722	95	19	3	3	NUM
ejpam-4722	95	20	,	,	PUNCT
ejpam-4722	95	21	3	3	NUM
ejpam-4722	95	22	...	...	PUNCT
ejpam-4722	95	23	,	,	PUNCT
ejpam-4722	95	24	3︸	3︸	NUM
ejpam-4722	95	25	︷︷	︷︷	NOUN
ejpam-4722	95	26	︸	︸	ADP
ejpam-4722	95	27	4k−n	4k−n	NUM
ejpam-4722	95	28	,	,	PUNCT
ejpam-4722	95	29	4	4	NUM
ejpam-4722	95	30	,	,	PUNCT
ejpam-4722	95	31	4	4	NUM
ejpam-4722	95	32	,	,	PUNCT
ejpam-4722	95	33	4	4	NUM
ejpam-4722	95	34	,	,	PUNCT
ejpam-4722	95	35	...	...	PUNCT
ejpam-4722	95	36	,	,	PUNCT
ejpam-4722	95	37	4︸	4︸	NUM
ejpam-4722	95	38	︷︷	︷︷	PROPN
ejpam-4722	95	39	︸	︸	X
ejpam-4722	95	40	n−3k	n−3k	PROPN
ejpam-4722	95	41	)	)	PUNCT
ejpam-4722	95	42	.	.	PUNCT
ejpam-4722	96	1	(	(	PUNCT
ejpam-4722	96	2	ii	ii	NOUN
ejpam-4722	96	3	)	)	PUNCT
ejpam-4722	96	4	for	for	ADP
ejpam-4722	96	5	n	n	NUM
ejpam-4722	96	6	≥	≥	NOUN
ejpam-4722	96	7	10	10	NUM
ejpam-4722	96	8	and	and	CCONJ
ejpam-4722	96	9	n	n	PRON
ejpam-4722	96	10	≥	≥	NOUN
ejpam-4722	96	11	4k	4k	X
ejpam-4722	96	12	then	then	ADV
ejpam-4722	96	13	moe(ω	moe(ω	PROPN
ejpam-4722	96	14	)	)	PUNCT
ejpam-4722	96	15	≤	≤	NOUN
ejpam-4722	96	16	n2	n2	NOUN
ejpam-4722	96	17	−	−	PROPN
ejpam-4722	96	18	n	n	PRON
ejpam-4722	96	19	−	−	PROPN
ejpam-4722	96	20	12k	12k	NUM
ejpam-4722	96	21	with	with	ADP
ejpam-4722	96	22	equality	equality	NOUN
ejpam-4722	96	23	if	if	SCONJ
ejpam-4722	96	24	and	and	CCONJ
ejpam-4722	96	25	only	only	ADV
ejpam-4722	96	26	if	if	SCONJ
ejpam-4722	96	27	ω	ω	PROPN
ejpam-4722	96	28	∼=	∼=	ADP
ejpam-4722	96	29	ωn(4	ωn(4	PROPN
ejpam-4722	96	30	,	,	PUNCT
ejpam-4722	96	31	4	4	NUM
ejpam-4722	96	32	,	,	PUNCT
ejpam-4722	96	33	4	4	NUM
ejpam-4722	96	34	,	,	PUNCT
ejpam-4722	96	35	...	...	PUNCT
ejpam-4722	96	36	,	,	PUNCT
ejpam-4722	96	37	4	4	NUM
ejpam-4722	96	38	)	)	PUNCT
ejpam-4722	96	39	.	.	PUNCT
ejpam-4722	97	1	(	(	PUNCT
ejpam-4722	97	2	iii	iii	NOUN
ejpam-4722	97	3	)	)	PUNCT
ejpam-4722	97	4	for	for	ADP
ejpam-4722	97	5	n	n	NOUN
ejpam-4722	97	6	=	=	SYM
ejpam-4722	97	7	9	9	NUM
ejpam-4722	97	8	,	,	PUNCT
ejpam-4722	97	9	then	then	ADV
ejpam-4722	97	10	moe(ω	moe(ω	PROPN
ejpam-4722	97	11	)	)	PUNCT
ejpam-4722	97	12	≤	≤	NOUN
ejpam-4722	97	13	72−	72−	NUM
ejpam-4722	97	14	12k	12k	PROPN
ejpam-4722	97	15	with	with	ADP
ejpam-4722	97	16	equality	equality	NOUN
ejpam-4722	97	17	if	if	SCONJ
ejpam-4722	97	18	and	and	CCONJ
ejpam-4722	97	19	only	only	ADV
ejpam-4722	97	20	if	if	SCONJ
ejpam-4722	97	21	ω	ω	PRON
ejpam-4722	97	22	∼=	∼=	PROPN
ejpam-4722	97	23	ω9	ω9	NOUN
ejpam-4722	97	24	.	.	PUNCT
ejpam-4722	98	1	(	(	PUNCT
ejpam-4722	98	2	iv	iv	X
ejpam-4722	98	3	)	)	PUNCT
ejpam-4722	98	4	for	for	ADP
ejpam-4722	98	5	n	n	PRON
ejpam-4722	98	6	≤	≤	NOUN
ejpam-4722	98	7	9	9	NUM
ejpam-4722	98	8	,	,	PUNCT
ejpam-4722	98	9	then	then	ADV
ejpam-4722	98	10	moe(ω	moe(ω	PROPN
ejpam-4722	98	11	)	)	PUNCT
ejpam-4722	98	12	≤	≤	NOUN
ejpam-4722	98	13	n2	n2	NOUN
ejpam-4722	98	14	−	−	PROPN
ejpam-4722	98	15	n	n	CCONJ
ejpam-4722	98	16	−	−	PROPN
ejpam-4722	98	17	(	(	PUNCT
ejpam-4722	98	18	n	n	PROPN
ejpam-4722	98	19	+	+	CCONJ
ejpam-4722	98	20	3)k	3)k	NUM
ejpam-4722	98	21	with	with	ADP
ejpam-4722	98	22	equality	equality	NOUN
ejpam-4722	98	23	if	if	SCONJ
ejpam-4722	98	24	and	and	CCONJ
ejpam-4722	98	25	only	only	ADV
ejpam-4722	98	26	if	if	SCONJ
ejpam-4722	98	27	ω	ω	PRON
ejpam-4722	98	28	∼=	∼=	PROPN
ejpam-4722	98	29	ωn(3	ωn(3	NUM
ejpam-4722	98	30	,	,	PUNCT
ejpam-4722	98	31	3	3	NUM
ejpam-4722	98	32	,	,	PUNCT
ejpam-4722	98	33	3	3	NUM
ejpam-4722	98	34	,	,	PUNCT
ejpam-4722	98	35	...	...	PUNCT
ejpam-4722	98	36	,	,	PUNCT
ejpam-4722	98	37	3	3	NUM
ejpam-4722	98	38	)	)	PUNCT
ejpam-4722	98	39	.	.	PUNCT
ejpam-4722	99	1	the	the	DET
ejpam-4722	99	2	second	second	ADJ
ejpam-4722	99	3	maximum	maximum	ADJ
ejpam-4722	99	4	edge	edge	NOUN
ejpam-4722	99	5	mostar	mostar	PROPN
ejpam-4722	99	6	index	index	NOUN
ejpam-4722	99	7	for	for	ADP
ejpam-4722	99	8	c(n	c(n	PROPN
ejpam-4722	99	9	,	,	PUNCT
ejpam-4722	99	10	k	k	NOUN
ejpam-4722	99	11	)	)	PUNCT
ejpam-4722	99	12	with	with	ADP
ejpam-4722	99	13	the	the	DET
ejpam-4722	99	14	following	follow	VERB
ejpam-4722	99	15	given	give	VERB
ejpam-4722	99	16	conditions	condition	NOUN
ejpam-4722	99	17	determined	determine	VERB
ejpam-4722	99	18	by	by	ADP
ejpam-4722	99	19	liu	liu	PROPN
ejpam-4722	99	20	et	et	PROPN
ejpam-4722	99	21	al	al	PROPN
ejpam-4722	100	1	[	[	X
ejpam-4722	100	2	24	24	NUM
ejpam-4722	100	3	]	]	PUNCT
ejpam-4722	100	4	.	.	PUNCT
ejpam-4722	101	1	theorem	theorem	NOUN
ejpam-4722	101	2	2	2	NUM
ejpam-4722	101	3	.	.	PUNCT
ejpam-4722	102	1	[	[	X
ejpam-4722	102	2	34	34	NUM
ejpam-4722	102	3	]	]	PUNCT
ejpam-4722	102	4	let	let	VERB
ejpam-4722	102	5	ĉ(n	ĉ(n	NOUN
ejpam-4722	102	6	,	,	PUNCT
ejpam-4722	102	7	k	k	ADJ
ejpam-4722	102	8	)	)	PUNCT
ejpam-4722	102	9	∈	∈	PROPN
ejpam-4722	102	10	c(n	c(n	PROPN
ejpam-4722	102	11	,	,	PUNCT
ejpam-4722	102	12	k	k	NOUN
ejpam-4722	102	13	)	)	PUNCT
ejpam-4722	102	14	be	be	VERB
ejpam-4722	102	15	a	a	DET
ejpam-4722	102	16	connected	connected	ADJ
ejpam-4722	102	17	graph	graph	NOUN
ejpam-4722	102	18	achieving	achieve	VERB
ejpam-4722	102	19	maximum	maximum	ADJ
ejpam-4722	102	20	edge	edge	NOUN
ejpam-4722	102	21	mostar	mostar	PROPN
ejpam-4722	102	22	index	index	NOUN
ejpam-4722	102	23	for	for	ADP
ejpam-4722	102	24	n	n	NUM
ejpam-4722	102	25	≥	≥	NOUN
ejpam-4722	102	26	3k	3k	X
ejpam-4722	103	1	+	+	CCONJ
ejpam-4722	103	2	2	2	NUM
ejpam-4722	103	3	,	,	PUNCT
ejpam-4722	103	4	k	k	X
ejpam-4722	103	5	≥	≥	NUM
ejpam-4722	103	6	2	2	NUM
ejpam-4722	103	7	and	and	CCONJ
ejpam-4722	103	8	n	n	PRON
ejpam-4722	103	9	≥	≥	NOUN
ejpam-4722	103	10	9	9	NUM
ejpam-4722	103	11	,	,	PUNCT
ejpam-4722	103	12	k	k	NOUN
ejpam-4722	103	13	=	=	SYM
ejpam-4722	103	14	1	1	X
ejpam-4722	103	15	.	.	X
ejpam-4722	103	16	for	for	ADP
ejpam-4722	103	17	any	any	DET
ejpam-4722	103	18	ω	ω	PROPN
ejpam-4722	103	19	∈	∈	PROPN
ejpam-4722	103	20	c(n	c(n	PROPN
ejpam-4722	103	21	,	,	PUNCT
ejpam-4722	103	22	k	k	PROPN
ejpam-4722	103	23	)	)	PUNCT
ejpam-4722	103	24	,	,	PUNCT
ejpam-4722	103	25	we	we	PRON
ejpam-4722	103	26	have	have	VERB
ejpam-4722	103	27	moe(ω	moe(ω	NOUN
ejpam-4722	103	28	)	)	PUNCT
ejpam-4722	103	29	<	<	X
ejpam-4722	103	30	moe(ĉ(n	moe(ĉ(n	PROPN
ejpam-4722	103	31	,	,	PUNCT
ejpam-4722	103	32	k	k	NOUN
ejpam-4722	103	33	)	)	PUNCT
ejpam-4722	103	34	)	)	PUNCT
ejpam-4722	103	35	.	.	PUNCT
ejpam-4722	104	1	lemma	lemma	PROPN
ejpam-4722	104	2	1	1	NUM
ejpam-4722	104	3	.	.	PUNCT
ejpam-4722	105	1	[	[	X
ejpam-4722	105	2	2	2	X
ejpam-4722	105	3	]	]	PUNCT
ejpam-4722	105	4	suppose	suppose	VERB
ejpam-4722	105	5	that	that	SCONJ
ejpam-4722	105	6	ω	ω	PROPN
ejpam-4722	105	7	is	be	AUX
ejpam-4722	105	8	a	a	DET
ejpam-4722	105	9	connected	connected	ADJ
ejpam-4722	105	10	graph	graph	NOUN
ejpam-4722	105	11	and	and	CCONJ
ejpam-4722	105	12	k	k	PROPN
ejpam-4722	105	13	is	be	AUX
ejpam-4722	105	14	an	an	DET
ejpam-4722	105	15	induced	induced	ADJ
ejpam-4722	105	16	subgraph	subgraph	NOUN
ejpam-4722	105	17	of	of	ADP
ejpam-4722	105	18	ω	ω	NUM
ejpam-4722	105	19	such	such	ADJ
ejpam-4722	105	20	that	that	SCONJ
ejpam-4722	105	21	k	k	PROPN
ejpam-4722	105	22	is	be	AUX
ejpam-4722	105	23	a	a	DET
ejpam-4722	105	24	tree	tree	NOUN
ejpam-4722	105	25	and	and	CCONJ
ejpam-4722	105	26	connected	connect	VERB
ejpam-4722	105	27	with	with	ADP
ejpam-4722	105	28	ω	ω	NUM
ejpam-4722	105	29	by	by	ADP
ejpam-4722	105	30	cut	cut	NOUN
ejpam-4722	105	31	vertex	vertex	NOUN
ejpam-4722	105	32	u.	u.	NOUN
ejpam-4722	105	33	consider	consider	VERB
ejpam-4722	105	34	that	that	SCONJ
ejpam-4722	105	35	k	k	PROPN
ejpam-4722	105	36	transform	transform	VERB
ejpam-4722	105	37	f.	f.	PROPN
ejpam-4722	105	38	asmat	asmat	PROPN
ejpam-4722	105	39	et	et	PROPN
ejpam-4722	105	40	al	al	PROPN
ejpam-4722	105	41	.	.	PUNCT
ejpam-4722	105	42	/	/	SYM
ejpam-4722	105	43	eur	eur	PROPN
ejpam-4722	105	44	.	.	PUNCT
ejpam-4722	106	1	j.	j.	PROPN
ejpam-4722	106	2	pure	pure	PROPN
ejpam-4722	106	3	appl	appl	PROPN
ejpam-4722	106	4	.	.	PROPN
ejpam-4722	106	5	math	math	PROPN
ejpam-4722	106	6	,	,	PUNCT
ejpam-4722	106	7	16	16	NUM
ejpam-4722	106	8	(	(	PUNCT
ejpam-4722	106	9	3	3	NUM
ejpam-4722	106	10	)	)	PUNCT
ejpam-4722	106	11	(	(	PUNCT
ejpam-4722	106	12	2023	2023	NUM
ejpam-4722	106	13	)	)	PUNCT
ejpam-4722	106	14	,	,	PUNCT
ejpam-4722	106	15	1794	1794	NUM
ejpam-4722	106	16	-	-	SYM
ejpam-4722	106	17	1808	1808	NUM
ejpam-4722	106	18	1798	1798	NUM
ejpam-4722	106	19	to	to	PART
ejpam-4722	106	20	star	star	NOUN
ejpam-4722	106	21	graph	graph	NOUN
ejpam-4722	106	22	centered	center	VERB
ejpam-4722	106	23	at	at	ADP
ejpam-4722	106	24	u	u	NOUN
ejpam-4722	106	25	,	,	PUNCT
ejpam-4722	106	26	then	then	ADV
ejpam-4722	106	27	weighted	weight	VERB
ejpam-4722	106	28	vertex	vertex	NOUN
ejpam-4722	106	29	index	index	NOUN
ejpam-4722	106	30	mowv	mowv	NOUN
ejpam-4722	106	31	(	(	PUNCT
ejpam-4722	106	32	ω	ω	NOUN
ejpam-4722	106	33	)	)	PUNCT
ejpam-4722	106	34	increases	increase	NOUN
ejpam-4722	106	35	(	(	PUNCT
ejpam-4722	106	36	unless	unless	SCONJ
ejpam-4722	106	37	k	k	PROPN
ejpam-4722	106	38	is	be	AUX
ejpam-4722	106	39	already	already	ADV
ejpam-4722	106	40	such	such	DET
ejpam-4722	106	41	a	a	DET
ejpam-4722	106	42	star	star	NOUN
ejpam-4722	106	43	)	)	PUNCT
ejpam-4722	106	44	.	.	PUNCT
ejpam-4722	107	1	similarly	similarly	ADV
ejpam-4722	107	2	,	,	PUNCT
ejpam-4722	107	3	if	if	SCONJ
ejpam-4722	107	4	k	k	PROPN
ejpam-4722	107	5	transform	transform	VERB
ejpam-4722	107	6	to	to	ADP
ejpam-4722	107	7	path	path	NOUN
ejpam-4722	107	8	graph	graph	NOUN
ejpam-4722	107	9	with	with	ADP
ejpam-4722	107	10	end	end	NOUN
ejpam-4722	107	11	vertex	vertex	NOUN
ejpam-4722	107	12	u	u	NOUN
ejpam-4722	107	13	,	,	PUNCT
ejpam-4722	107	14	then	then	ADV
ejpam-4722	107	15	weighted	weight	VERB
ejpam-4722	107	16	vertex	vertex	NOUN
ejpam-4722	107	17	index	index	NOUN
ejpam-4722	107	18	mowv	mowv	NOUN
ejpam-4722	107	19	(	(	PUNCT
ejpam-4722	107	20	ω	ω	NOUN
ejpam-4722	107	21	)	)	PUNCT
ejpam-4722	107	22	decreases	decrease	NOUN
ejpam-4722	107	23	.	.	PUNCT
ejpam-4722	108	1	3	3	X
ejpam-4722	108	2	.	.	X
ejpam-4722	108	3	main	main	ADJ
ejpam-4722	108	4	results	result	NOUN
ejpam-4722	108	5	in	in	ADP
ejpam-4722	108	6	this	this	DET
ejpam-4722	108	7	section	section	NOUN
ejpam-4722	108	8	,	,	PUNCT
ejpam-4722	108	9	we	we	PRON
ejpam-4722	108	10	present	present	VERB
ejpam-4722	108	11	our	our	PRON
ejpam-4722	108	12	main	main	ADJ
ejpam-4722	108	13	results	result	NOUN
ejpam-4722	108	14	of	of	ADP
ejpam-4722	108	15	this	this	DET
ejpam-4722	108	16	paper	paper	NOUN
ejpam-4722	108	17	.	.	PUNCT
ejpam-4722	109	1	more	more	ADV
ejpam-4722	109	2	precisely	precisely	ADV
ejpam-4722	109	3	,	,	PUNCT
ejpam-4722	109	4	we	we	PRON
ejpam-4722	109	5	have	have	VERB
ejpam-4722	109	6	the	the	DET
ejpam-4722	109	7	following	follow	VERB
ejpam-4722	109	8	two	two	NUM
ejpam-4722	109	9	results	result	NOUN
ejpam-4722	109	10	.	.	PUNCT
ejpam-4722	110	1	theorem	theorem	NOUN
ejpam-4722	110	2	3	3	NUM
ejpam-4722	110	3	.	.	PUNCT
ejpam-4722	111	1	among	among	ADP
ejpam-4722	111	2	all	all	DET
ejpam-4722	111	3	the	the	DET
ejpam-4722	111	4	tree	tree	NOUN
ejpam-4722	111	5	graphs	graph	NOUN
ejpam-4722	111	6	in	in	ADP
ejpam-4722	111	7	t	t	PROPN
ejpam-4722	111	8	(	(	PUNCT
ejpam-4722	111	9	n	n	CCONJ
ejpam-4722	111	10	,	,	PUNCT
ejpam-4722	111	11	d	d	X
ejpam-4722	111	12	)	)	PUNCT
ejpam-4722	111	13	the	the	DET
ejpam-4722	111	14	t	t	PROPN
ejpam-4722	111	15	(	(	PUNCT
ejpam-4722	111	16	n̂	n̂	ADV
ejpam-4722	111	17	,	,	PUNCT
ejpam-4722	111	18	d	d	NOUN
ejpam-4722	111	19	)	)	PUNCT
ejpam-4722	111	20	,	,	PUNCT
ejpam-4722	111	21	for	for	ADP
ejpam-4722	111	22	n	n	PRON
ejpam-4722	112	1	≥	≥	NOUN
ejpam-4722	112	2	d	d	NOUN
ejpam-4722	112	3	+	+	CCONJ
ejpam-4722	112	4	1	1	NUM
ejpam-4722	112	5	and	and	CCONJ
ejpam-4722	112	6	d	d	NOUN
ejpam-4722	112	7	≥	≥	NUM
ejpam-4722	112	8	6	6	NUM
ejpam-4722	112	9	has	have	VERB
ejpam-4722	112	10	maximum	maximum	ADJ
ejpam-4722	112	11	weighted	weight	VERB
ejpam-4722	112	12	vertex	vertex	PROPN
ejpam-4722	112	13	mostar	mostar	PROPN
ejpam-4722	112	14	index	index	PROPN
ejpam-4722	112	15	.	.	PUNCT
ejpam-4722	113	1	thus	thus	ADV
ejpam-4722	113	2	for	for	ADP
ejpam-4722	113	3	any	any	DET
ejpam-4722	113	4	ω	ω	PROPN
ejpam-4722	113	5	∈	∈	PROPN
ejpam-4722	113	6	t	t	PROPN
ejpam-4722	113	7	(	(	PUNCT
ejpam-4722	113	8	n	n	X
ejpam-4722	113	9	,	,	PUNCT
ejpam-4722	113	10	d	d	PROPN
ejpam-4722	113	11	)	)	PUNCT
ejpam-4722	113	12	,	,	PUNCT
ejpam-4722	113	13	we	we	PRON
ejpam-4722	113	14	have	have	VERB
ejpam-4722	113	15	mowv	mowv	NOUN
ejpam-4722	113	16	(	(	PUNCT
ejpam-4722	113	17	ω	ω	NOUN
ejpam-4722	113	18	)	)	PUNCT
ejpam-4722	113	19	<	<	X
ejpam-4722	113	20	mowv	mowv	NOUN
ejpam-4722	113	21	(	(	PUNCT
ejpam-4722	113	22	t	t	PROPN
ejpam-4722	113	23	(	(	PUNCT
ejpam-4722	113	24	n̂	n̂	ADV
ejpam-4722	113	25	,	,	PUNCT
ejpam-4722	113	26	d	d	NOUN
ejpam-4722	113	27	)	)	PUNCT
ejpam-4722	113	28	)	)	PUNCT
ejpam-4722	114	1	we	we	PRON
ejpam-4722	114	2	have	have	AUX
ejpam-4722	114	3	following	follow	VERB
ejpam-4722	114	4	result	result	NOUN
ejpam-4722	114	5	by	by	ADP
ejpam-4722	114	6	using	use	VERB
ejpam-4722	114	7	theorem	theorem	ADJ
ejpam-4722	114	8	3	3	NUM
ejpam-4722	114	9	.	.	PUNCT
ejpam-4722	114	10	corollary	corollary	ADJ
ejpam-4722	114	11	1	1	NUM
ejpam-4722	114	12	.	.	PUNCT
ejpam-4722	115	1	let	let	VERB
ejpam-4722	115	2	ω	ω	NUM
ejpam-4722	115	3	∈	∈	PROPN
ejpam-4722	115	4	t	t	PROPN
ejpam-4722	115	5	(	(	PUNCT
ejpam-4722	115	6	n	n	X
ejpam-4722	115	7	,	,	PUNCT
ejpam-4722	115	8	d	d	X
ejpam-4722	115	9	)	)	PUNCT
ejpam-4722	115	10	be	be	VERB
ejpam-4722	115	11	the	the	DET
ejpam-4722	115	12	tree	tree	NOUN
ejpam-4722	115	13	graph	graph	NOUN
ejpam-4722	115	14	with	with	ADP
ejpam-4722	115	15	n	n	PRON
ejpam-4722	115	16	≥	≥	NUM
ejpam-4722	115	17	2	2	NUM
ejpam-4722	115	18	and	and	CCONJ
ejpam-4722	115	19	d	d	NOUN
ejpam-4722	115	20	≥	≥	NUM
ejpam-4722	115	21	2	2	NUM
ejpam-4722	115	22	,	,	PUNCT
ejpam-4722	115	23	then	then	ADV
ejpam-4722	115	24	we	we	PRON
ejpam-4722	115	25	have	have	VERB
ejpam-4722	115	26	the	the	DET
ejpam-4722	115	27	following	following	NOUN
ejpam-4722	115	28	.	.	PUNCT
ejpam-4722	116	1	mowv	mowv	NOUN
ejpam-4722	116	2	(	(	PUNCT
ejpam-4722	116	3	ω	ω	NOUN
ejpam-4722	116	4	)	)	PUNCT
ejpam-4722	116	5	=	=	SYM
ejpam-4722	117	1			PROPN
ejpam-4722	117	2	n3	n3	VERB
ejpam-4722	117	3	−	−	PROPN
ejpam-4722	117	4	3n2	3n2	NUM
ejpam-4722	118	1	+	+	NUM
ejpam-4722	118	2	2n	2n	NUM
ejpam-4722	118	3	n	n	PRON
ejpam-4722	118	4	≥	≥	NUM
ejpam-4722	118	5	d+	d+	PUNCT
ejpam-4722	118	6	1	1	NUM
ejpam-4722	118	7	,	,	PUNCT
ejpam-4722	118	8	d	d	NOUN
ejpam-4722	118	9	=	=	SYM
ejpam-4722	118	10	2	2	NUM
ejpam-4722	118	11	n3	n3	NOUN
ejpam-4722	118	12	−	−	PROPN
ejpam-4722	118	13	5n2	5n2	NUM
ejpam-4722	118	14	+	+	CCONJ
ejpam-4722	118	15	10n−	10n−	NUM
ejpam-4722	118	16	12	12	NUM
ejpam-4722	118	17	n	n	NUM
ejpam-4722	118	18	≥	≥	NOUN
ejpam-4722	118	19	d+	d+	PUNCT
ejpam-4722	118	20	1	1	NUM
ejpam-4722	118	21	,	,	PUNCT
ejpam-4722	118	22	d	d	NOUN
ejpam-4722	118	23	=	=	SYM
ejpam-4722	118	24	3	3	NUM
ejpam-4722	118	25	n3	n3	NOUN
ejpam-4722	118	26	−	−	PROPN
ejpam-4722	118	27	(	(	PUNCT
ejpam-4722	118	28	2m+	2m+	NUM
ejpam-4722	118	29	1)n2	1)n2	NUM
ejpam-4722	118	30	+	+	CCONJ
ejpam-4722	118	31	d2	d2	PROPN
ejpam-4722	118	32	+	+	PROPN
ejpam-4722	118	33	5d−	5d−	NUM
ejpam-4722	118	34	4−	4−	NUM
ejpam-4722	119	1	12(n−	12(n−	NUM
ejpam-4722	119	2	12	12	NUM
ejpam-4722	119	3	)	)	PUNCT
ejpam-4722	119	4	n	n	CCONJ
ejpam-4722	119	5	≥	≥	NOUN
ejpam-4722	119	6	d+	d+	PUNCT
ejpam-4722	119	7	1	1	X
ejpam-4722	119	8	,	,	PUNCT
ejpam-4722	119	9	m	m	VERB
ejpam-4722	119	10	≥	≥	NOUN
ejpam-4722	119	11	1	1	NUM
ejpam-4722	119	12	,	,	PUNCT
ejpam-4722	119	13	and	and	CCONJ
ejpam-4722	119	14	d	d	PRON
ejpam-4722	119	15	≥	≥	NUM
ejpam-4722	119	16	6	6	NUM
ejpam-4722	119	17	(	(	PUNCT
ejpam-4722	119	18	1	1	NUM
ejpam-4722	119	19	)	)	PUNCT
ejpam-4722	119	20	theorem	theorem	NOUN
ejpam-4722	119	21	4	4	NUM
ejpam-4722	119	22	.	.	X
ejpam-4722	120	1	for	for	ADP
ejpam-4722	120	2	any	any	DET
ejpam-4722	120	3	graph	graph	NOUN
ejpam-4722	120	4	ω	ω	NUM
ejpam-4722	120	5	∈	∈	PROPN
ejpam-4722	120	6	c(n	c(n	PROPN
ejpam-4722	120	7	,	,	PUNCT
ejpam-4722	120	8	k	k	NOUN
ejpam-4722	120	9	)	)	PUNCT
ejpam-4722	120	10	where	where	SCONJ
ejpam-4722	120	11	n	n	NUM
ejpam-4722	120	12	≥	≥	NOUN
ejpam-4722	120	13	2k	2k	NUM
ejpam-4722	120	14	+	+	CCONJ
ejpam-4722	120	15	1	1	NUM
ejpam-4722	120	16	,	,	PUNCT
ejpam-4722	120	17	mowe	mowe	NOUN
ejpam-4722	120	18	(	(	PUNCT
ejpam-4722	120	19	ω	ω	NOUN
ejpam-4722	120	20	)	)	PUNCT
ejpam-4722	120	21	≤	≤	NOUN
ejpam-4722	120	22	n3	n3	NOUN
ejpam-4722	120	23	+	+	CCONJ
ejpam-4722	120	24	(	(	PUNCT
ejpam-4722	120	25	k	k	PROPN
ejpam-4722	120	26	−	−	PROPN
ejpam-4722	120	27	4)n2	4)n2	NUM
ejpam-4722	121	1	+	+	CCONJ
ejpam-4722	121	2	(	(	PUNCT
ejpam-4722	121	3	−3k	−3k	PROPN
ejpam-4722	121	4	+	+	NUM
ejpam-4722	122	1	5)n−	5)n−	PROPN
ejpam-4722	122	2	(	(	PUNCT
ejpam-4722	122	3	2n+	2n+	NUM
ejpam-4722	122	4	4	4	NUM
ejpam-4722	122	5	)	)	PUNCT
ejpam-4722	122	6	,	,	PUNCT
ejpam-4722	122	7	∀n	∀n	NUM
ejpam-4722	122	8	≥	≥	NOUN
ejpam-4722	122	9	1	1	NUM
ejpam-4722	122	10	with	with	ADP
ejpam-4722	122	11	the	the	DET
ejpam-4722	122	12	equality	equality	NOUN
ejpam-4722	122	13	holds	hold	VERB
ejpam-4722	122	14	if	if	SCONJ
ejpam-4722	122	15	and	and	CCONJ
ejpam-4722	122	16	only	only	ADV
ejpam-4722	122	17	if	if	SCONJ
ejpam-4722	122	18	ω	ω	PRON
ejpam-4722	122	19	∼=	∼=	PROPN
ejpam-4722	122	20	s∗,kn	s∗,kn	NOUN
ejpam-4722	122	21	.	.	PUNCT
ejpam-4722	123	1	4	4	X
ejpam-4722	123	2	.	.	X
ejpam-4722	123	3	proof	proof	NOUN
ejpam-4722	123	4	of	of	ADP
ejpam-4722	123	5	main	main	ADJ
ejpam-4722	123	6	results	result	NOUN
ejpam-4722	123	7	first	first	ADV
ejpam-4722	123	8	of	of	ADP
ejpam-4722	123	9	all	all	PRON
ejpam-4722	123	10	,	,	PUNCT
ejpam-4722	123	11	some	some	DET
ejpam-4722	123	12	basic	basic	ADJ
ejpam-4722	123	13	lemmas	lemma	NOUN
ejpam-4722	123	14	are	be	AUX
ejpam-4722	123	15	proved	prove	VERB
ejpam-4722	123	16	so	so	SCONJ
ejpam-4722	123	17	that	that	SCONJ
ejpam-4722	123	18	the	the	DET
ejpam-4722	123	19	main	main	ADJ
ejpam-4722	123	20	result	result	NOUN
ejpam-4722	123	21	can	can	AUX
ejpam-4722	123	22	be	be	AUX
ejpam-4722	123	23	proved	prove	VERB
ejpam-4722	123	24	easily	easily	ADV
ejpam-4722	123	25	.	.	PUNCT
ejpam-4722	124	1	in	in	ADP
ejpam-4722	124	2	lemma	lemma	PROPN
ejpam-4722	124	3	2	2	NUM
ejpam-4722	124	4	,	,	PUNCT
ejpam-4722	124	5	we	we	PRON
ejpam-4722	124	6	establish	establish	VERB
ejpam-4722	124	7	a	a	DET
ejpam-4722	124	8	graph	graph	NOUN
ejpam-4722	124	9	ω2	ω2	ADJ
ejpam-4722	124	10	by	by	ADP
ejpam-4722	124	11	converting	convert	VERB
ejpam-4722	124	12	a	a	DET
ejpam-4722	124	13	cut	cut	ADJ
ejpam-4722	124	14	edge	edge	NOUN
ejpam-4722	124	15	uv	uv	NOUN
ejpam-4722	124	16	into	into	ADP
ejpam-4722	124	17	a	a	DET
ejpam-4722	124	18	pendent	pendent	ADJ
ejpam-4722	124	19	edge	edge	NOUN
ejpam-4722	124	20	uv	uv	NOUN
ejpam-4722	124	21	in	in	ADP
ejpam-4722	124	22	ω1	ω1	PROPN
ejpam-4722	124	23	,	,	PUNCT
ejpam-4722	124	24	such	such	ADJ
ejpam-4722	124	25	that	that	SCONJ
ejpam-4722	124	26	the	the	DET
ejpam-4722	124	27	new	new	ADJ
ejpam-4722	124	28	graph	graph	NOUN
ejpam-4722	124	29	ω2	ω2	NOUN
ejpam-4722	124	30	has	have	VERB
ejpam-4722	124	31	a	a	DET
ejpam-4722	124	32	greater	great	ADJ
ejpam-4722	124	33	weighted	weight	VERB
ejpam-4722	124	34	vertex	vertex	NOUN
ejpam-4722	124	35	mostar	mostar	PROPN
ejpam-4722	124	36	invariant	invariant	PROPN
ejpam-4722	124	37	.	.	PUNCT
ejpam-4722	125	1	lemma	lemma	PROPN
ejpam-4722	125	2	2	2	X
ejpam-4722	125	3	.	.	PUNCT
ejpam-4722	125	4	suppose	suppose	VERB
ejpam-4722	125	5	that	that	SCONJ
ejpam-4722	125	6	two	two	NUM
ejpam-4722	125	7	subgraphs	subgraphs	NOUN
ejpam-4722	125	8	t1	t1	NOUN
ejpam-4722	125	9	and	and	CCONJ
ejpam-4722	125	10	t2	t2	NOUN
ejpam-4722	125	11	such	such	ADJ
ejpam-4722	125	12	that	that	SCONJ
ejpam-4722	125	13	connected	connect	VERB
ejpam-4722	125	14	by	by	ADP
ejpam-4722	125	15	an	an	DET
ejpam-4722	125	16	edge	edge	NOUN
ejpam-4722	125	17	uv	uv	NOUN
ejpam-4722	125	18	,	,	PUNCT
ejpam-4722	125	19	where	where	SCONJ
ejpam-4722	125	20	u	u	PROPN
ejpam-4722	125	21	∈	∈	PROPN
ejpam-4722	125	22	v	v	ADP
ejpam-4722	125	23	(	(	PUNCT
ejpam-4722	125	24	t1	t1	NOUN
ejpam-4722	125	25	)	)	PUNCT
ejpam-4722	125	26	and	and	CCONJ
ejpam-4722	125	27	v	v	ADP
ejpam-4722	125	28	∈	∈	PROPN
ejpam-4722	125	29	v	v	NOUN
ejpam-4722	125	30	(	(	PUNCT
ejpam-4722	125	31	t2	t2	NOUN
ejpam-4722	125	32	)	)	PUNCT
ejpam-4722	125	33	,	,	PUNCT
ejpam-4722	125	34	and	and	CCONJ
ejpam-4722	125	35	acquired	acquire	VERB
ejpam-4722	125	36	the	the	DET
ejpam-4722	125	37	graph	graph	NOUN
ejpam-4722	125	38	ω1	ω1	PROPN
ejpam-4722	125	39	.	.	PUNCT
ejpam-4722	126	1	now	now	ADV
ejpam-4722	126	2	,	,	PUNCT
ejpam-4722	126	3	we	we	PRON
ejpam-4722	126	4	construct	construct	VERB
ejpam-4722	126	5	the	the	DET
ejpam-4722	126	6	new	new	ADJ
ejpam-4722	126	7	graph	graph	NOUN
ejpam-4722	126	8	ω2	ω2	ADJ
ejpam-4722	126	9	by	by	ADP
ejpam-4722	126	10	deleting	delete	VERB
ejpam-4722	126	11	the	the	DET
ejpam-4722	126	12	cut	cut	NOUN
ejpam-4722	126	13	edge	edge	NOUN
ejpam-4722	126	14	uv	uv	NOUN
ejpam-4722	126	15	and	and	CCONJ
ejpam-4722	126	16	associating	associate	VERB
ejpam-4722	126	17	a	a	DET
ejpam-4722	126	18	pendent	pendent	ADJ
ejpam-4722	126	19	edges	edge	NOUN
ejpam-4722	126	20	at	at	ADP
ejpam-4722	126	21	central	central	ADJ
ejpam-4722	126	22	vertex	vertex	NOUN
ejpam-4722	126	23	in	in	ADP
ejpam-4722	126	24	ω1	ω1	PROPN
ejpam-4722	126	25	.	.	PUNCT
ejpam-4722	127	1	then	then	ADV
ejpam-4722	127	2	mowv	mowv	NOUN
ejpam-4722	127	3	(	(	PUNCT
ejpam-4722	127	4	ω1	ω1	PROPN
ejpam-4722	127	5	)	)	PUNCT
ejpam-4722	127	6	<	<	X
ejpam-4722	127	7	mowv	mowv	NOUN
ejpam-4722	127	8	(	(	PUNCT
ejpam-4722	127	9	ω2	ω2	ADJ
ejpam-4722	127	10	)	)	PUNCT
ejpam-4722	127	11	.	.	PUNCT
ejpam-4722	128	1	proof	proof	NOUN
ejpam-4722	128	2	.	.	PUNCT
ejpam-4722	129	1	suppose	suppose	VERB
ejpam-4722	129	2	t1	t1	NOUN
ejpam-4722	129	3	and	and	CCONJ
ejpam-4722	129	4	t2	t2	NOUN
ejpam-4722	129	5	be	be	VERB
ejpam-4722	129	6	subgraphs	subgraph	NOUN
ejpam-4722	129	7	of	of	ADP
ejpam-4722	129	8	ω1	ω1	PROPN
ejpam-4722	129	9	.	.	PUNCT
ejpam-4722	130	1	by	by	ADP
ejpam-4722	130	2	construction	construction	NOUN
ejpam-4722	130	3	of	of	ADP
ejpam-4722	130	4	ω2	ω2	ADJ
ejpam-4722	130	5	,	,	PUNCT
ejpam-4722	130	6	the	the	DET
ejpam-4722	130	7	number	number	NOUN
ejpam-4722	130	8	of	of	ADP
ejpam-4722	130	9	closer	close	ADJ
ejpam-4722	130	10	vertices	vertex	NOUN
ejpam-4722	130	11	of	of	ADP
ejpam-4722	130	12	end	end	NOUN
ejpam-4722	130	13	vertices	vertex	NOUN
ejpam-4722	130	14	of	of	ADP
ejpam-4722	130	15	the	the	DET
ejpam-4722	130	16	fixed	fix	VERB
ejpam-4722	130	17	edge	edge	NOUN
ejpam-4722	130	18	of	of	ADP
ejpam-4722	130	19	t1	t1	NOUN
ejpam-4722	130	20	and	and	CCONJ
ejpam-4722	130	21	t2	t2	PROPN
ejpam-4722	130	22	in	in	ADP
ejpam-4722	130	23	ω1	ω1	PROPN
ejpam-4722	130	24	remains	remain	VERB
ejpam-4722	130	25	same	same	ADJ
ejpam-4722	130	26	in	in	ADP
ejpam-4722	130	27	ω2	ω2	ADJ
ejpam-4722	130	28	,	,	PUNCT
ejpam-4722	130	29	respectively	respectively	ADV
ejpam-4722	130	30	.	.	PUNCT
ejpam-4722	131	1	therefore	therefore	ADV
ejpam-4722	131	2	,	,	PUNCT
ejpam-4722	131	3	for	for	ADP
ejpam-4722	131	4	an	an	DET
ejpam-4722	131	5	edge	edge	NOUN
ejpam-4722	131	6	xy	xy	PROPN
ejpam-4722	131	7	∈	∈	PROPN
ejpam-4722	131	8	e(tm	e(tm	PROPN
ejpam-4722	131	9	)	)	PUNCT
ejpam-4722	131	10	for	for	ADP
ejpam-4722	131	11	m	m	PROPN
ejpam-4722	131	12	∈	∈	NOUN
ejpam-4722	131	13	{	{	PUNCT
ejpam-4722	131	14	1	1	NUM
ejpam-4722	131	15	,	,	PUNCT
ejpam-4722	131	16	2	2	NUM
ejpam-4722	131	17	}	}	PUNCT
ejpam-4722	131	18	,	,	PUNCT
ejpam-4722	131	19	we	we	PRON
ejpam-4722	131	20	have	have	VERB
ejpam-4722	131	21	nx(e|ω1)(x	nx(e|ω1)(x	NOUN
ejpam-4722	131	22	)	)	PUNCT
ejpam-4722	132	1	=	=	SYM
ejpam-4722	132	2	nx(e|ω2)(x	nx(e|ω2)(x	NOUN
ejpam-4722	132	3	)	)	PUNCT
ejpam-4722	132	4	and	and	CCONJ
ejpam-4722	132	5	ny(e|ω1)(y	ny(e|ω1)(y	NUM
ejpam-4722	132	6	)	)	PUNCT
ejpam-4722	133	1	=	=	PUNCT
ejpam-4722	133	2	ny(e|ω2)(y	ny(e|ω2)(y	ADJ
ejpam-4722	133	3	)	)	PUNCT
ejpam-4722	133	4	.	.	PUNCT
ejpam-4722	134	1	f.	f.	PROPN
ejpam-4722	134	2	asmat	asmat	PROPN
ejpam-4722	134	3	et	et	PROPN
ejpam-4722	134	4	al	al	PROPN
ejpam-4722	134	5	.	.	PUNCT
ejpam-4722	134	6	/	/	SYM
ejpam-4722	134	7	eur	eur	PROPN
ejpam-4722	134	8	.	.	PUNCT
ejpam-4722	135	1	j.	j.	PROPN
ejpam-4722	135	2	pure	pure	PROPN
ejpam-4722	135	3	appl	appl	PROPN
ejpam-4722	135	4	.	.	PROPN
ejpam-4722	135	5	math	math	PROPN
ejpam-4722	135	6	,	,	PUNCT
ejpam-4722	135	7	16	16	NUM
ejpam-4722	135	8	(	(	PUNCT
ejpam-4722	135	9	3	3	NUM
ejpam-4722	135	10	)	)	PUNCT
ejpam-4722	135	11	(	(	PUNCT
ejpam-4722	135	12	2023	2023	NUM
ejpam-4722	135	13	)	)	PUNCT
ejpam-4722	135	14	,	,	PUNCT
ejpam-4722	135	15	1794	1794	NUM
ejpam-4722	135	16	-	-	SYM
ejpam-4722	135	17	1808	1808	NUM
ejpam-4722	135	18	1799	1799	NUM
ejpam-4722	135	19	for	for	ADP
ejpam-4722	135	20	the	the	DET
ejpam-4722	135	21	cut	cut	NOUN
ejpam-4722	135	22	edge	edge	NOUN
ejpam-4722	135	23	uv	uv	NOUN
ejpam-4722	135	24	in	in	ADP
ejpam-4722	135	25	ω1	ω1	PROPN
ejpam-4722	135	26	,	,	PUNCT
ejpam-4722	135	27	we	we	PRON
ejpam-4722	135	28	have	have	AUX
ejpam-4722	135	29	nu(e|ω1)(u	nu(e|ω1)(u	VERB
ejpam-4722	135	30	)	)	PUNCT
ejpam-4722	135	31	=	=	SYM
ejpam-4722	135	32	nv(e|ω1)(v	nv(e|ω1)(v	X
ejpam-4722	135	33	)	)	PUNCT
ejpam-4722	136	1	=	=	SYM
ejpam-4722	136	2	|e(t1)|+1	|e(t1)|+1	NOUN
ejpam-4722	136	3	.	.	PUNCT
ejpam-4722	137	1	similarly	similarly	ADV
ejpam-4722	137	2	for	for	ADP
ejpam-4722	137	3	graph	graph	NOUN
ejpam-4722	137	4	ω2	ω2	ADJ
ejpam-4722	137	5	,	,	PUNCT
ejpam-4722	137	6	nu(e|ω2)(u	nu(e|ω2)(u	ADJ
ejpam-4722	137	7	)	)	PUNCT
ejpam-4722	138	1	=	=	PUNCT
ejpam-4722	138	2	|e(t1)|+	|e(t1)|+	PROPN
ejpam-4722	138	3	|e(t2|+	|e(t2|+	VERB
ejpam-4722	138	4	1	1	NUM
ejpam-4722	138	5	and	and	CCONJ
ejpam-4722	138	6	nv(e|ω2)(v	nv(e|ω2)(v	PROPN
ejpam-4722	138	7	)	)	PUNCT
ejpam-4722	139	1	=	=	SYM
ejpam-4722	139	2	1	1	X
ejpam-4722	139	3	.	.	PUNCT
ejpam-4722	139	4	by	by	ADP
ejpam-4722	139	5	using	use	VERB
ejpam-4722	139	6	the	the	DET
ejpam-4722	139	7	definition	definition	NOUN
ejpam-4722	139	8	of	of	ADP
ejpam-4722	139	9	weighted	weight	VERB
ejpam-4722	139	10	vertex	vertex	PROPN
ejpam-4722	139	11	mostar	mostar	PROPN
ejpam-4722	139	12	index	index	PROPN
ejpam-4722	139	13	,	,	PUNCT
ejpam-4722	139	14	we	we	PRON
ejpam-4722	139	15	have	have	VERB
ejpam-4722	139	16	mowv	mowv	NOUN
ejpam-4722	139	17	(	(	PUNCT
ejpam-4722	139	18	ω	ω	NOUN
ejpam-4722	139	19	)	)	PUNCT
ejpam-4722	139	20	=	=	PUNCT
ejpam-4722	139	21	∑	∑	PUNCT
ejpam-4722	139	22	e	e	X
ejpam-4722	139	23	=	=	NOUN
ejpam-4722	139	24	uv∈e(ω	uv∈e(ω	NUM
ejpam-4722	139	25	)	)	PUNCT
ejpam-4722	139	26	(	(	PUNCT
ejpam-4722	139	27	dω(u	dω(u	PUNCT
ejpam-4722	139	28	)	)	PUNCT
ejpam-4722	140	1	+	+	CCONJ
ejpam-4722	140	2	dω(v))|nu(e|ω)(v)−	dω(v))|nu(e|ω)(v)−	PROPN
ejpam-4722	140	3	nv(e|ω)(v)|	nv(e|ω)(v)|	NOUN
ejpam-4722	140	4	,	,	PUNCT
ejpam-4722	140	5	mowv	mowv	NOUN
ejpam-4722	140	6	(	(	PUNCT
ejpam-4722	140	7	ω1)−mowv	ω1)−mowv	X
ejpam-4722	140	8	(	(	PUNCT
ejpam-4722	140	9	ω2	ω2	ADJ
ejpam-4722	140	10	)	)	PUNCT
ejpam-4722	140	11	=	=	SYM
ejpam-4722	140	12	(	(	PUNCT
ejpam-4722	140	13	dω(u	dω(u	PUNCT
ejpam-4722	140	14	)	)	PUNCT
ejpam-4722	141	1	+	+	CCONJ
ejpam-4722	141	2	dω(v))|nu(e|ω1)(u)−	dω(v))|nu(e|ω1)(u)−	NOUN
ejpam-4722	141	3	nv(e|ω1)(u)|	nv(e|ω1)(u)|	NOUN
ejpam-4722	141	4	+	+	CCONJ
ejpam-4722	141	5	2∑	2∑	NUM
ejpam-4722	141	6	m=1	m=1	PUNCT
ejpam-4722	141	7	∑	∑	NOUN
ejpam-4722	141	8	xy∈e(t1	xy∈e(t1	PROPN
ejpam-4722	141	9	)	)	PUNCT
ejpam-4722	141	10	(	(	PUNCT
ejpam-4722	141	11	dω(x	dω(x	X
ejpam-4722	141	12	)	)	PUNCT
ejpam-4722	142	1	+	+	CCONJ
ejpam-4722	142	2	dω(y))|nx(e|ω1)(x)−	dω(y))|nx(e|ω1)(x)−	ADP
ejpam-4722	142	3	ny(e|ω1)(y)|	ny(e|ω1)(y)|	PROPN
ejpam-4722	142	4	−	−	PROPN
ejpam-4722	142	5	(	(	PUNCT
ejpam-4722	142	6	dω(u	dω(u	PUNCT
ejpam-4722	142	7	)	)	PUNCT
ejpam-4722	142	8	+	+	PUNCT
ejpam-4722	143	1	dω(v))|nu(e|ω2)(u)−	dω(v))|nu(e|ω2)(u)−	ADP
ejpam-4722	143	2	nv(e|ω2)(v)|	nv(e|ω2)(v)|	NOUN
ejpam-4722	143	3	−	−	PROPN
ejpam-4722	143	4	2∑	2∑	NUM
ejpam-4722	143	5	m=1	m=1	X
ejpam-4722	143	6	∑	∑	PUNCT
ejpam-4722	143	7	xy∈e(t2	xy∈e(t2	NUM
ejpam-4722	143	8	)	)	PUNCT
ejpam-4722	143	9	(	(	PUNCT
ejpam-4722	143	10	dω(x	dω(x	X
ejpam-4722	143	11	)	)	PUNCT
ejpam-4722	143	12	+	+	CCONJ
ejpam-4722	143	13	dω(y))|nx(e|ω2)(x)−	dω(y))|nx(e|ω2)(x)−	PROPN
ejpam-4722	143	14	ny(e|ω2)(y)|	ny(e|ω2)(y)|	ADV
ejpam-4722	143	15	,	,	PUNCT
ejpam-4722	143	16	=	=	SYM
ejpam-4722	143	17	|{e(t1	|{e(t1	PROPN
ejpam-4722	143	18	)	)	PUNCT
ejpam-4722	143	19	+	+	CCONJ
ejpam-4722	143	20	1	1	X
ejpam-4722	143	21	}	}	PUNCT
ejpam-4722	143	22	−	−	PROPN
ejpam-4722	143	23	{	{	PUNCT
ejpam-4722	143	24	e(t2	e(t2	NOUN
ejpam-4722	143	25	)	)	PUNCT
ejpam-4722	143	26	+	+	NUM
ejpam-4722	143	27	1}|+	1}|+	NUM
ejpam-4722	143	28	2∑	2∑	NUM
ejpam-4722	143	29	m=1	m=1	PUNCT
ejpam-4722	143	30	∑	∑	PROPN
ejpam-4722	143	31	xy∈e(t1	xy∈e(t1	PROPN
ejpam-4722	143	32	)	)	PUNCT
ejpam-4722	144	1	|nx(e|ω1(x)−	|nx(e|ω1(x)−	ADP
ejpam-4722	144	2	ny(e|ω1)(y)|	ny(e|ω1)(y)|	PROPN
ejpam-4722	144	3	−	−	PROPN
ejpam-4722	144	4	|{e(t1	|{e(t1	PROPN
ejpam-4722	144	5	)	)	PUNCT
ejpam-4722	144	6	+	+	NUM
ejpam-4722	144	7	e(t1	e(t1	NOUN
ejpam-4722	144	8	)	)	PUNCT
ejpam-4722	145	1	+	+	CCONJ
ejpam-4722	145	2	1	1	X
ejpam-4722	145	3	}	}	PUNCT
ejpam-4722	145	4	−	−	PROPN
ejpam-4722	145	5	{	{	PUNCT
ejpam-4722	145	6	1}|	1}|	NUM
ejpam-4722	145	7	−	−	PROPN
ejpam-4722	145	8	2∑	2∑	NUM
ejpam-4722	145	9	m=1	m=1	X
ejpam-4722	145	10	∑	∑	INTJ
ejpam-4722	145	11	xy∈e(t2	xy∈e(t2	PROPN
ejpam-4722	145	12	)	)	PUNCT
ejpam-4722	145	13	|nx(e|ω2)(x)−	|nx(e|ω2)(x)−	PROPN
ejpam-4722	145	14	ny(e|ω2)(y)|	ny(e|ω2)(y)|	ADV
ejpam-4722	145	15	,	,	PUNCT
ejpam-4722	145	16	=	=	SYM
ejpam-4722	145	17	−|e(t1)|	−|e(t1)|	PROPN
ejpam-4722	145	18	−	−	PROPN
ejpam-4722	145	19	|e(t2)|	|e(t2)|	PROPN
ejpam-4722	145	20	,	,	PUNCT
ejpam-4722	145	21	there	there	PRON
ejpam-4722	145	22	are	be	VERB
ejpam-4722	145	23	two	two	NUM
ejpam-4722	145	24	cases	case	NOUN
ejpam-4722	145	25	,	,	PUNCT
ejpam-4722	145	26	if	if	SCONJ
ejpam-4722	145	27	case	case	NOUN
ejpam-4722	145	28	1	1	NUM
ejpam-4722	145	29	.	.	X
ejpam-4722	146	1	|e(t1)|	|e(t1)|	NUM
ejpam-4722	146	2	≥	≥	NOUN
ejpam-4722	146	3	|e(t2)|	|e(t2)|	NOUN
ejpam-4722	146	4	,	,	PUNCT
ejpam-4722	146	5	then	then	ADV
ejpam-4722	146	6	−2|e(t2)|	−2|e(t2)|	VERB
ejpam-4722	146	7	<	<	X
ejpam-4722	146	8	0	0	NUM
ejpam-4722	146	9	,	,	PUNCT
ejpam-4722	146	10	case	case	NOUN
ejpam-4722	146	11	2	2	NUM
ejpam-4722	146	12	.	.	X
ejpam-4722	146	13	|e(t2)|	|e(t2)|	PROPN
ejpam-4722	146	14	≥	≥	NUM
ejpam-4722	146	15	|e(t1)|	|e(t1)|	NUM
ejpam-4722	146	16	,	,	PUNCT
ejpam-4722	146	17	then	then	ADV
ejpam-4722	146	18	−2|e(t1)|	−2|e(t1)|	PRON
ejpam-4722	146	19	<	<	X
ejpam-4722	146	20	0	0	NUM
ejpam-4722	146	21	,	,	PUNCT
ejpam-4722	146	22	in	in	ADP
ejpam-4722	146	23	each	each	DET
ejpam-4722	146	24	case	case	NOUN
ejpam-4722	146	25	,	,	PUNCT
ejpam-4722	146	26	mowv	mowv	NOUN
ejpam-4722	146	27	(	(	PUNCT
ejpam-4722	146	28	ω1)−mowv	ω1)−mowv	X
ejpam-4722	146	29	(	(	PUNCT
ejpam-4722	146	30	ω2	ω2	ADJ
ejpam-4722	146	31	)	)	PUNCT
ejpam-4722	146	32	<	<	X
ejpam-4722	146	33	0	0	NUM
ejpam-4722	146	34	,	,	PUNCT
ejpam-4722	146	35	which	which	PRON
ejpam-4722	146	36	shows	show	VERB
ejpam-4722	146	37	maximum	maximum	ADJ
ejpam-4722	146	38	weighted	weight	VERB
ejpam-4722	146	39	vertex	vertex	PROPN
ejpam-4722	146	40	moster	moster	PROPN
ejpam-4722	146	41	index	index	NOUN
ejpam-4722	146	42	.	.	PUNCT
ejpam-4722	147	1	this	this	PRON
ejpam-4722	147	2	completes	complete	VERB
ejpam-4722	147	3	the	the	DET
ejpam-4722	147	4	proof	proof	NOUN
ejpam-4722	147	5	.	.	PUNCT
ejpam-4722	148	1	further	far	ADV
ejpam-4722	148	2	,	,	PUNCT
ejpam-4722	148	3	we	we	PRON
ejpam-4722	148	4	deduce	deduce	VERB
ejpam-4722	148	5	new	new	ADJ
ejpam-4722	148	6	ω2	ω2	ADV
ejpam-4722	148	7	from	from	ADP
ejpam-4722	148	8	ω1	ω1	PROPN
ejpam-4722	148	9	moving	move	VERB
ejpam-4722	148	10	all	all	DET
ejpam-4722	148	11	the	the	DET
ejpam-4722	148	12	pendent	pendent	NOUN
ejpam-4722	148	13	vertices	vertex	NOUN
ejpam-4722	148	14	to	to	ADP
ejpam-4722	148	15	a	a	DET
ejpam-4722	148	16	central	central	ADJ
ejpam-4722	148	17	vertices	vertex	NOUN
ejpam-4722	148	18	such	such	ADJ
ejpam-4722	148	19	that	that	SCONJ
ejpam-4722	148	20	new	new	ADJ
ejpam-4722	148	21	graph	graph	NOUN
ejpam-4722	148	22	has	have	VERB
ejpam-4722	148	23	maximum	maximum	ADV
ejpam-4722	148	24	weighted	weight	VERB
ejpam-4722	148	25	vertex	vertex	PROPN
ejpam-4722	148	26	moster	moster	PROPN
ejpam-4722	148	27	index	index	PROPN
ejpam-4722	148	28	.	.	PUNCT
ejpam-4722	149	1	lemma	lemma	PROPN
ejpam-4722	149	2	3	3	X
ejpam-4722	149	3	.	.	PUNCT
ejpam-4722	150	1	let	let	VERB
ejpam-4722	150	2	t1	t1	NOUN
ejpam-4722	150	3	and	and	CCONJ
ejpam-4722	150	4	t2	t2	NOUN
ejpam-4722	150	5	be	be	VERB
ejpam-4722	150	6	two	two	NUM
ejpam-4722	150	7	subgraphs	subgraph	NOUN
ejpam-4722	150	8	constructed	construct	VERB
ejpam-4722	150	9	by	by	ADP
ejpam-4722	150	10	adjoining	adjoin	VERB
ejpam-4722	150	11	n	n	CCONJ
ejpam-4722	150	12	−	−	PROPN
ejpam-4722	151	1	d	d	SYM
ejpam-4722	151	2	−	−	PROPN
ejpam-4722	151	3	1	1	NUM
ejpam-4722	151	4	pendent	pendent	NOUN
ejpam-4722	151	5	vertices	vertex	NOUN
ejpam-4722	151	6	at	at	ADP
ejpam-4722	151	7	central	central	ADJ
ejpam-4722	151	8	vertices	vertex	NOUN
ejpam-4722	151	9	with	with	ADP
ejpam-4722	151	10	d	d	PROPN
ejpam-4722	151	11	(	(	PUNCT
ejpam-4722	151	12	with	with	ADP
ejpam-4722	151	13	even	even	ADV
ejpam-4722	151	14	diameter	diameter	NOUN
ejpam-4722	151	15	)	)	PUNCT
ejpam-4722	151	16	.	.	PUNCT
ejpam-4722	152	1	consider	consider	VERB
ejpam-4722	152	2	that	that	SCONJ
ejpam-4722	152	3	two	two	NUM
ejpam-4722	152	4	subgraphs	subgraph	NOUN
ejpam-4722	152	5	t1	t1	NOUN
ejpam-4722	152	6	and	and	CCONJ
ejpam-4722	152	7	t2	t2	NOUN
ejpam-4722	152	8	with	with	ADP
ejpam-4722	152	9	common	common	ADJ
ejpam-4722	152	10	ukvk	ukvk	NOUN
ejpam-4722	152	11	edge	edge	NOUN
ejpam-4722	152	12	between	between	ADP
ejpam-4722	152	13	them	they	PRON
ejpam-4722	152	14	,	,	PUNCT
ejpam-4722	152	15	presented	present	VERB
ejpam-4722	152	16	by	by	ADP
ejpam-4722	152	17	ω1	ω1	PROPN
ejpam-4722	152	18	.	.	PUNCT
ejpam-4722	152	19	now	now	ADV
ejpam-4722	152	20	construct	construct	VERB
ejpam-4722	152	21	ω2	ω2	ADV
ejpam-4722	152	22	from	from	ADP
ejpam-4722	152	23	ω1	ω1	PROPN
ejpam-4722	152	24	by	by	ADP
ejpam-4722	152	25	removing	remove	VERB
ejpam-4722	152	26	all	all	DET
ejpam-4722	152	27	pendent	pendent	ADJ
ejpam-4722	152	28	vertices	vertex	NOUN
ejpam-4722	152	29	and	and	CCONJ
ejpam-4722	152	30	ukvk	ukvk	NOUN
ejpam-4722	152	31	edge	edge	NOUN
ejpam-4722	152	32	to	to	ADP
ejpam-4722	152	33	central	central	ADJ
ejpam-4722	152	34	vertex	vertex	NOUN
ejpam-4722	152	35	.	.	PUNCT
ejpam-4722	153	1	then	then	ADV
ejpam-4722	153	2	mowv	mowv	NOUN
ejpam-4722	153	3	(	(	PUNCT
ejpam-4722	153	4	ω1	ω1	PROPN
ejpam-4722	153	5	)	)	PUNCT
ejpam-4722	153	6	<	<	X
ejpam-4722	153	7	mowv	mowv	NOUN
ejpam-4722	153	8	(	(	PUNCT
ejpam-4722	153	9	ω2	ω2	ADJ
ejpam-4722	153	10	)	)	PUNCT
ejpam-4722	153	11	.	.	PUNCT
ejpam-4722	154	1	proof	proof	NOUN
ejpam-4722	154	2	.	.	PUNCT
ejpam-4722	155	1	suppose	suppose	VERB
ejpam-4722	155	2	t1	t1	NOUN
ejpam-4722	155	3	and	and	CCONJ
ejpam-4722	155	4	t2	t2	NOUN
ejpam-4722	155	5	be	be	VERB
ejpam-4722	155	6	subgraphs	subgraph	NOUN
ejpam-4722	155	7	of	of	ADP
ejpam-4722	155	8	ω1	ω1	PROPN
ejpam-4722	155	9	.	.	PUNCT
ejpam-4722	156	1	by	by	ADP
ejpam-4722	156	2	construction	construction	NOUN
ejpam-4722	156	3	of	of	ADP
ejpam-4722	156	4	ω2	ω2	ADJ
ejpam-4722	156	5	,	,	PUNCT
ejpam-4722	156	6	the	the	DET
ejpam-4722	156	7	number	number	NOUN
ejpam-4722	156	8	of	of	ADP
ejpam-4722	156	9	closer	close	ADJ
ejpam-4722	156	10	vertices	vertex	NOUN
ejpam-4722	156	11	of	of	ADP
ejpam-4722	156	12	end	end	NOUN
ejpam-4722	156	13	vertices	vertex	NOUN
ejpam-4722	156	14	of	of	ADP
ejpam-4722	156	15	the	the	DET
ejpam-4722	156	16	fixed	fix	VERB
ejpam-4722	156	17	edge	edge	NOUN
ejpam-4722	156	18	of	of	ADP
ejpam-4722	156	19	t1	t1	NOUN
ejpam-4722	156	20	and	and	CCONJ
ejpam-4722	156	21	t2	t2	PROPN
ejpam-4722	156	22	in	in	ADP
ejpam-4722	156	23	ω1	ω1	PROPN
ejpam-4722	156	24	remains	remain	VERB
ejpam-4722	156	25	same	same	ADJ
ejpam-4722	156	26	in	in	ADP
ejpam-4722	156	27	ω2	ω2	ADJ
ejpam-4722	156	28	respectively	respectively	ADV
ejpam-4722	156	29	.	.	PUNCT
ejpam-4722	157	1	therefore	therefore	ADV
ejpam-4722	157	2	,	,	PUNCT
ejpam-4722	157	3	for	for	ADP
ejpam-4722	157	4	an	an	DET
ejpam-4722	157	5	edge	edge	NOUN
ejpam-4722	157	6	xy	xy	PROPN
ejpam-4722	157	7	∈	∈	PROPN
ejpam-4722	157	8	e(t	e(t	PROPN
ejpam-4722	157	9	)	)	PUNCT
ejpam-4722	157	10	,	,	PUNCT
ejpam-4722	157	11	nx(e|ω1)(x	nx(e|ω1)(x	PROPN
ejpam-4722	157	12	)	)	PUNCT
ejpam-4722	157	13	=	=	SYM
ejpam-4722	157	14	nx(e|ω2)(x	nx(e|ω2)(x	NOUN
ejpam-4722	157	15	)	)	PUNCT
ejpam-4722	157	16	and	and	CCONJ
ejpam-4722	157	17	ny(e|ω1)(y	ny(e|ω1)(y	NUM
ejpam-4722	157	18	)	)	PUNCT
ejpam-4722	158	1	=	=	PUNCT
ejpam-4722	158	2	ny(e|ω2)(y	ny(e|ω2)(y	ADJ
ejpam-4722	158	3	)	)	PUNCT
ejpam-4722	158	4	the	the	DET
ejpam-4722	158	5	cut	cut	NOUN
ejpam-4722	158	6	edge	edge	NOUN
ejpam-4722	158	7	ukvk	ukvk	NOUN
ejpam-4722	158	8	in	in	ADP
ejpam-4722	158	9	ω1	ω1	PROPN
ejpam-4722	158	10	follows	follow	VERB
ejpam-4722	158	11	as	as	ADP
ejpam-4722	158	12	,	,	PUNCT
ejpam-4722	158	13	f.	f.	PROPN
ejpam-4722	158	14	asmat	asmat	PROPN
ejpam-4722	158	15	et	et	PROPN
ejpam-4722	158	16	al	al	PROPN
ejpam-4722	158	17	.	.	PUNCT
ejpam-4722	158	18	/	/	SYM
ejpam-4722	158	19	eur	eur	PROPN
ejpam-4722	158	20	.	.	PUNCT
ejpam-4722	159	1	j.	j.	PROPN
ejpam-4722	159	2	pure	pure	PROPN
ejpam-4722	159	3	appl	appl	PROPN
ejpam-4722	159	4	.	.	PROPN
ejpam-4722	159	5	math	math	PROPN
ejpam-4722	159	6	,	,	PUNCT
ejpam-4722	159	7	16	16	NUM
ejpam-4722	159	8	(	(	PUNCT
ejpam-4722	159	9	3	3	NUM
ejpam-4722	159	10	)	)	PUNCT
ejpam-4722	159	11	(	(	PUNCT
ejpam-4722	159	12	2023	2023	NUM
ejpam-4722	159	13	)	)	PUNCT
ejpam-4722	159	14	,	,	PUNCT
ejpam-4722	159	15	1794	1794	NUM
ejpam-4722	159	16	-	-	SYM
ejpam-4722	159	17	1808	1808	NUM
ejpam-4722	159	18	1800	1800	NUM
ejpam-4722	159	19	case	case	NOUN
ejpam-4722	159	20	3	3	X
ejpam-4722	159	21	.	.	PUNCT
ejpam-4722	160	1	duk	duk	NOUN
ejpam-4722	160	2	=	=	NOUN
ejpam-4722	160	3	dvk	dvk	NOUN
ejpam-4722	160	4	=	=	SYM
ejpam-4722	160	5	(	(	PUNCT
ejpam-4722	160	6	n	n	CCONJ
ejpam-4722	160	7	−	−	PROPN
ejpam-4722	160	8	d	d	NOUN
ejpam-4722	160	9	)	)	PUNCT
ejpam-4722	161	1	+	+	NUM
ejpam-4722	161	2	1	1	NUM
ejpam-4722	161	3	,	,	PUNCT
ejpam-4722	161	4	and	and	CCONJ
ejpam-4722	161	5	nuk	nuk	PROPN
ejpam-4722	161	6	(	(	PUNCT
ejpam-4722	161	7	e|ω1)(uk	e|ω1)(uk	PROPN
ejpam-4722	161	8	)	)	PUNCT
ejpam-4722	161	9	=	=	PUNCT
ejpam-4722	162	1	[	[	X
ejpam-4722	162	2	e(t1	e(t1	X
ejpam-4722	162	3	)	)	PUNCT
ejpam-4722	163	1	+	+	CCONJ
ejpam-4722	163	2	2	2	NUM
ejpam-4722	163	3	,	,	PUNCT
ejpam-4722	163	4	nvk(e|ω1)(vk	nvk(e|ω1)(vk	NOUN
ejpam-4722	163	5	)	)	PUNCT
ejpam-4722	163	6	=	=	SYM
ejpam-4722	163	7	e(t2	e(t2	NOUN
ejpam-4722	163	8	)	)	PUNCT
ejpam-4722	164	1	+	+	CCONJ
ejpam-4722	164	2	2	2	X
ejpam-4722	164	3	.	.	X
ejpam-4722	164	4	furthermore	furthermore	ADV
ejpam-4722	164	5	,	,	PUNCT
ejpam-4722	164	6	pendent	pendent	ADJ
ejpam-4722	164	7	edges	edge	NOUN
ejpam-4722	164	8	at	at	ADP
ejpam-4722	164	9	central	central	ADJ
ejpam-4722	164	10	vertices	vertex	NOUN
ejpam-4722	164	11	in	in	ADP
ejpam-4722	164	12	ω1	ω1	PROPN
ejpam-4722	164	13	connected	connect	VERB
ejpam-4722	164	14	with	with	ADP
ejpam-4722	164	15	uk	uk	PROPN
ejpam-4722	164	16	are	be	AUX
ejpam-4722	164	17	following	follow	VERB
ejpam-4722	164	18	as	as	ADP
ejpam-4722	164	19	:	:	PUNCT
ejpam-4722	164	20	case	case	NOUN
ejpam-4722	164	21	4	4	NUM
ejpam-4722	164	22	.	.	PUNCT
ejpam-4722	164	23	duk	duk	NOUN
ejpam-4722	164	24	=	=	NOUN
ejpam-4722	164	25	dvk	dvk	NOUN
ejpam-4722	164	26	=	=	SYM
ejpam-4722	164	27	(	(	PUNCT
ejpam-4722	164	28	n−d)+1	n−d)+1	NOUN
ejpam-4722	164	29	,	,	PUNCT
ejpam-4722	164	30	and	and	CCONJ
ejpam-4722	164	31	nuk	nuk	PROPN
ejpam-4722	164	32	(	(	PUNCT
ejpam-4722	164	33	e|ω1)(uk	e|ω1)(uk	PROPN
ejpam-4722	164	34	)	)	PUNCT
ejpam-4722	164	35	=	=	SYM
ejpam-4722	164	36	nvk(e|ω1)(vk	nvk(e|ω1)(vk	NOUN
ejpam-4722	164	37	)	)	PUNCT
ejpam-4722	164	38	=	=	PUNCT
ejpam-4722	165	1	[	[	X
ejpam-4722	165	2	e(t	e(t	NOUN
ejpam-4722	165	3	)	)	PUNCT
ejpam-4722	166	1	+	+	NOUN
ejpam-4722	166	2	e(t	e(t	NOUN
ejpam-4722	166	3	)	)	PUNCT
ejpam-4722	166	4	]	]	X
ejpam-4722	166	5	+3	+3	ADJ
ejpam-4722	166	6	,	,	PUNCT
ejpam-4722	166	7	da∗k	da∗k	NOUN
ejpam-4722	166	8	=	=	SYM
ejpam-4722	166	9	db∗k	db∗k	NOUN
ejpam-4722	166	10	=	=	SYM
ejpam-4722	166	11	1	1	NUM
ejpam-4722	166	12	,	,	PUNCT
ejpam-4722	166	13	for	for	ADP
ejpam-4722	166	14	some	some	DET
ejpam-4722	166	15	1	1	NUM
ejpam-4722	166	16	≤	≤	NUM
ejpam-4722	166	17	k	k	X
ejpam-4722	166	18	≤	≤	ADJ
ejpam-4722	166	19	n−	n−	NOUN
ejpam-4722	166	20	d−	d−	PROPN
ejpam-4722	166	21	1	1	NUM
ejpam-4722	166	22	.	.	PUNCT
ejpam-4722	166	23	similarly	similarly	ADV
ejpam-4722	166	24	,	,	PUNCT
ejpam-4722	166	25	2n	2n	NUM
ejpam-4722	166	26	−	−	NOUN
ejpam-4722	166	27	2d	2d	NOUN
ejpam-4722	166	28	−	−	PROPN
ejpam-4722	166	29	1	1	NUM
ejpam-4722	166	30	pendent	pendent	NOUN
ejpam-4722	166	31	vertices	vertex	NOUN
ejpam-4722	166	32	at	at	ADP
ejpam-4722	166	33	central	central	ADJ
ejpam-4722	166	34	vertex	vertex	NOUN
ejpam-4722	166	35	in	in	ADP
ejpam-4722	166	36	ω2	ω2	ADJ
ejpam-4722	166	37	by	by	ADP
ejpam-4722	166	38	removing	remove	VERB
ejpam-4722	166	39	pendent	pendent	ADJ
ejpam-4722	166	40	vertices	vertex	NOUN
ejpam-4722	166	41	and	and	CCONJ
ejpam-4722	166	42	cut	cut	VERB
ejpam-4722	166	43	edge	edge	NOUN
ejpam-4722	166	44	from	from	ADP
ejpam-4722	166	45	ω1	ω1	PROPN
ejpam-4722	166	46	.	.	PUNCT
ejpam-4722	167	1	now	now	ADV
ejpam-4722	167	2	,	,	PUNCT
ejpam-4722	167	3	the	the	DET
ejpam-4722	167	4	pendent	pendent	NOUN
ejpam-4722	167	5	edges	edge	VERB
ejpam-4722	167	6	uv∗k	uv∗k	NOUN
ejpam-4722	167	7	,	,	PUNCT
ejpam-4722	167	8	where	where	SCONJ
ejpam-4722	167	9	1	1	NUM
ejpam-4722	167	10	≤	≤	NUM
ejpam-4722	167	11	k	k	X
ejpam-4722	167	12	≤	≤	ADJ
ejpam-4722	167	13	2n	2n	NUM
ejpam-4722	167	14	−	−	NOUN
ejpam-4722	167	15	2d	2d	NOUN
ejpam-4722	167	16	−	−	NOUN
ejpam-4722	167	17	1	1	NUM
ejpam-4722	167	18	at	at	ADP
ejpam-4722	167	19	central	central	ADJ
ejpam-4722	167	20	vertex	vertex	NOUN
ejpam-4722	167	21	of	of	ADP
ejpam-4722	167	22	ω2	ω2	PROPN
ejpam-4722	167	23	.	.	PUNCT
ejpam-4722	168	1	subcase	subcase	PROPN
ejpam-4722	168	2	1	1	NUM
ejpam-4722	168	3	.	.	PUNCT
ejpam-4722	168	4	nu(e|ω2)(u	nu(e|ω2)(u	ADJ
ejpam-4722	168	5	)	)	PUNCT
ejpam-4722	169	1	=	=	SYM
ejpam-4722	169	2	|e(t1	|e(t1	NOUN
ejpam-4722	169	3	)	)	PUNCT
ejpam-4722	170	1	+	+	CCONJ
ejpam-4722	170	2	2|	2|	NUM
ejpam-4722	170	3	,	,	PUNCT
ejpam-4722	170	4	and	and	CCONJ
ejpam-4722	170	5	nv∗k	nv∗k	NUM
ejpam-4722	170	6	(	(	PUNCT
ejpam-4722	170	7	e|ω2)(v	e|ω2)(v	X
ejpam-4722	170	8	∗	∗	X
ejpam-4722	170	9	k	k	NOUN
ejpam-4722	170	10	)	)	PUNCT
ejpam-4722	170	11	=	=	SYM
ejpam-4722	170	12	1	1	X
ejpam-4722	170	13	.	.	PUNCT
ejpam-4722	170	14	by	by	ADP
ejpam-4722	170	15	combining	combine	VERB
ejpam-4722	170	16	cases	case	NOUN
ejpam-4722	170	17	3,4	3,4	NUM
ejpam-4722	170	18	and	and	CCONJ
ejpam-4722	170	19	subcase	subcase	NOUN
ejpam-4722	170	20	1	1	NUM
ejpam-4722	170	21	,	,	PUNCT
ejpam-4722	170	22	and	and	CCONJ
ejpam-4722	170	23	employing	employ	VERB
ejpam-4722	170	24	definition	definition	NOUN
ejpam-4722	170	25	of	of	ADP
ejpam-4722	170	26	weighted	weight	VERB
ejpam-4722	170	27	vertex	vertex	PROPN
ejpam-4722	170	28	mostar	mostar	PROPN
ejpam-4722	170	29	index	index	PROPN
ejpam-4722	170	30	,	,	PUNCT
ejpam-4722	170	31	we	we	PRON
ejpam-4722	170	32	have	have	VERB
ejpam-4722	170	33	mowv	mowv	NOUN
ejpam-4722	170	34	(	(	PUNCT
ejpam-4722	170	35	ω1)−mowv	ω1)−mowv	X
ejpam-4722	170	36	(	(	PUNCT
ejpam-4722	170	37	ω2	ω2	ADJ
ejpam-4722	170	38	)	)	PUNCT
ejpam-4722	170	39	=	=	PUNCT
ejpam-4722	171	1	[	[	PUNCT
ejpam-4722	171	2	2∑	2∑	NUM
ejpam-4722	171	3	m=1	m=1	X
ejpam-4722	171	4	∑	∑	NOUN
ejpam-4722	171	5	xy∈e(t1	xy∈e(t1	PROPN
ejpam-4722	171	6	)	)	PUNCT
ejpam-4722	171	7	(	(	PUNCT
ejpam-4722	171	8	dω1(x	dω1(x	NOUN
ejpam-4722	171	9	)	)	PUNCT
ejpam-4722	172	1	+	+	CCONJ
ejpam-4722	172	2	dω1(y))|nx(e|ω1)(x)−	dω1(y))|nx(e|ω1)(x)−	PROPN
ejpam-4722	172	3	ny(e|ω1)(y)|	ny(e|ω1)(y)|	PROPN
ejpam-4722	172	4	+	+	CCONJ
ejpam-4722	172	5	n−d−1∑	n−d−1∑	PROPN
ejpam-4722	172	6	k=1	k=1	X
ejpam-4722	172	7	(	(	PUNCT
ejpam-4722	172	8	dω1(a	dω1(a	PROPN
ejpam-4722	172	9	∗	∗	PROPN
ejpam-4722	172	10	k	k	PROPN
ejpam-4722	172	11	)	)	PUNCT
ejpam-4722	173	1	+	+	CCONJ
ejpam-4722	173	2	dω1(uk))|na∗k	dω1(uk))|na∗k	ADJ
ejpam-4722	173	3	(	(	PUNCT
ejpam-4722	173	4	e|ω1)(a	e|ω1)(a	NOUN
ejpam-4722	173	5	∗	∗	PROPN
ejpam-4722	173	6	k)−	k)−	PROPN
ejpam-4722	173	7	nuk	nuk	PROPN
ejpam-4722	173	8	(	(	PUNCT
ejpam-4722	173	9	e|ω1)(uk)|	e|ω1)(uk)|	NOUN
ejpam-4722	173	10	+	+	CCONJ
ejpam-4722	173	11	n−d−1∑	n−d−1∑	PROPN
ejpam-4722	173	12	k=1	k=1	PROPN
ejpam-4722	173	13	(	(	PUNCT
ejpam-4722	173	14	dω1(b	dω1(b	PROPN
ejpam-4722	173	15	∗	∗	PROPN
ejpam-4722	173	16	k	k	NOUN
ejpam-4722	173	17	)	)	PUNCT
ejpam-4722	174	1	+	+	CCONJ
ejpam-4722	174	2	dω1(vk))|nb∗k	dω1(vk))|nb∗k	NOUN
ejpam-4722	174	3	(	(	PUNCT
ejpam-4722	174	4	e|ω1)(b	e|ω1)(b	NOUN
ejpam-4722	174	5	∗	∗	NOUN
ejpam-4722	174	6	k)−	k)−	PROPN
ejpam-4722	174	7	nvk(e|ω1)(vk)|	nvk(e|ω1)(vk)|	PROPN
ejpam-4722	174	8	]	]	PUNCT
ejpam-4722	174	9	−	−	PROPN
ejpam-4722	175	1	[	[	PUNCT
ejpam-4722	175	2	2∑	2∑	NUM
ejpam-4722	175	3	m=1	m=1	X
ejpam-4722	175	4	∑	∑	NOUN
ejpam-4722	175	5	xy∈e(t1	xy∈e(t1	PROPN
ejpam-4722	175	6	)	)	PUNCT
ejpam-4722	175	7	(	(	PUNCT
ejpam-4722	175	8	dω2(x	dω2(x	PROPN
ejpam-4722	175	9	)	)	PUNCT
ejpam-4722	175	10	+	+	CCONJ
ejpam-4722	176	1	dω2a(y))|nx(e|ω2)(x)−	dω2a(y))|nx(e|ω2)(x)−	PROPN
ejpam-4722	176	2	ny(e|ω2(y)|	ny(e|ω2(y)|	PROPN
ejpam-4722	176	3	−	−	PROPN
ejpam-4722	176	4	2n−2d−1∑	2n−2d−1∑	PROPN
ejpam-4722	176	5	k=1	k=1	PUNCT
ejpam-4722	176	6	(	(	PUNCT
ejpam-4722	176	7	dω2(u	dω2(u	NOUN
ejpam-4722	176	8	)	)	PUNCT
ejpam-4722	177	1	+	+	CCONJ
ejpam-4722	177	2	dω2(v	dω2(v	PROPN
ejpam-4722	177	3	∗	∗	NOUN
ejpam-4722	177	4	k))|nv∗k	k))|nv∗k	X
ejpam-4722	177	5	(	(	PUNCT
ejpam-4722	177	6	e|ω2)(v	e|ω2)(v	X
ejpam-4722	177	7	∗	∗	NOUN
ejpam-4722	177	8	k)−	k)−	PROPN
ejpam-4722	177	9	nu(e|ω2(u)|	nu(e|ω2(u)|	PROPN
ejpam-4722	177	10	]	]	PUNCT
ejpam-4722	177	11	,	,	PUNCT
ejpam-4722	177	12	≤	≤	X
ejpam-4722	177	13	[	[	PUNCT
ejpam-4722	177	14	{	{	PUNCT
ejpam-4722	177	15	(	(	PUNCT
ejpam-4722	177	16	n−	n−	NOUN
ejpam-4722	177	17	d	d	NOUN
ejpam-4722	177	18	)	)	PUNCT
ejpam-4722	178	1	+	+	CCONJ
ejpam-4722	178	2	2}(e(t1)−	2}(e(t1)−	NUM
ejpam-4722	178	3	e(t2)−	e(t2)−	ADJ
ejpam-4722	178	4	2	2	NUM
ejpam-4722	178	5	)	)	PUNCT
ejpam-4722	178	6	+	+	CCONJ
ejpam-4722	178	7	{	{	PUNCT
ejpam-4722	178	8	(	(	PUNCT
ejpam-4722	178	9	n−	n−	NOUN
ejpam-4722	178	10	d	d	NOUN
ejpam-4722	178	11	)	)	PUNCT
ejpam-4722	179	1	+	+	NUM
ejpam-4722	179	2	2}(e(t1	2}(e(t1	NUM
ejpam-4722	179	3	)	)	PUNCT
ejpam-4722	180	1	+	+	CCONJ
ejpam-4722	180	2	e(t2	e(t2	NOUN
ejpam-4722	180	3	)	)	PUNCT
ejpam-4722	180	4	+	+	CCONJ
ejpam-4722	180	5	1	1	NUM
ejpam-4722	180	6	)	)	PUNCT
ejpam-4722	180	7	]	]	PUNCT
ejpam-4722	180	8	,	,	PUNCT
ejpam-4722	180	9	=	=	PUNCT
ejpam-4722	180	10	[	[	PUNCT
ejpam-4722	180	11	{	{	PUNCT
ejpam-4722	180	12	(	(	PUNCT
ejpam-4722	180	13	n−	n−	NOUN
ejpam-4722	180	14	d	d	NOUN
ejpam-4722	180	15	)	)	PUNCT
ejpam-4722	181	1	+	+	CCONJ
ejpam-4722	181	2	2}(−1	2}(−1	NUM
ejpam-4722	181	3	)	)	PUNCT
ejpam-4722	181	4	]	]	PUNCT
ejpam-4722	181	5	,	,	PUNCT
ejpam-4722	181	6	<	<	X
ejpam-4722	181	7	0	0	NUM
ejpam-4722	181	8	it	it	PRON
ejpam-4722	181	9	shows	show	VERB
ejpam-4722	181	10	,	,	PUNCT
ejpam-4722	181	11	mowv	mowv	NOUN
ejpam-4722	181	12	(	(	PUNCT
ejpam-4722	181	13	ω1)−mowv	ω1)−mowv	X
ejpam-4722	181	14	(	(	PUNCT
ejpam-4722	181	15	ω2	ω2	ADJ
ejpam-4722	181	16	)	)	PUNCT
ejpam-4722	181	17	<	<	X
ejpam-4722	181	18	0	0	NUM
ejpam-4722	181	19	,	,	PUNCT
ejpam-4722	181	20	which	which	PRON
ejpam-4722	181	21	shows	show	VERB
ejpam-4722	181	22	proof	proof	NOUN
ejpam-4722	181	23	is	be	AUX
ejpam-4722	181	24	complete	complete	ADJ
ejpam-4722	181	25	.	.	PUNCT
ejpam-4722	182	1	corollary	corollary	ADJ
ejpam-4722	182	2	2	2	NUM
ejpam-4722	182	3	.	.	PUNCT
ejpam-4722	183	1	consider	consider	VERB
ejpam-4722	183	2	ω	ω	NUM
ejpam-4722	183	3	be	be	AUX
ejpam-4722	183	4	the	the	DET
ejpam-4722	183	5	graph	graph	NOUN
ejpam-4722	183	6	with	with	ADP
ejpam-4722	183	7	even	even	ADV
ejpam-4722	183	8	diameter	diameter	NOUN
ejpam-4722	183	9	and	and	CCONJ
ejpam-4722	183	10	t	t	PROPN
ejpam-4722	183	11	be	be	AUX
ejpam-4722	183	12	subgraph	subgraph	NOUN
ejpam-4722	183	13	of	of	ADP
ejpam-4722	183	14	ω	ω	PROPN
ejpam-4722	183	15	,	,	PUNCT
ejpam-4722	183	16	which	which	PRON
ejpam-4722	183	17	is	be	AUX
ejpam-4722	183	18	presented	present	VERB
ejpam-4722	183	19	by	by	ADP
ejpam-4722	183	20	ω1	ω1	PROPN
ejpam-4722	183	21	.	.	PROPN
ejpam-4722	183	22	to	to	PART
ejpam-4722	183	23	construct	construct	VERB
ejpam-4722	183	24	ω2	ω2	ADV
ejpam-4722	183	25	from	from	ADP
ejpam-4722	183	26	ω1	ω1	PROPN
ejpam-4722	183	27	,	,	PUNCT
ejpam-4722	183	28	remove	remove	VERB
ejpam-4722	183	29	both	both	DET
ejpam-4722	183	30	pendent	pendent	NOUN
ejpam-4722	183	31	vertices	vertex	NOUN
ejpam-4722	183	32	connected	connect	VERB
ejpam-4722	183	33	with	with	ADP
ejpam-4722	183	34	cut	cut	ADJ
ejpam-4722	183	35	edge	edge	NOUN
ejpam-4722	183	36	and	and	CCONJ
ejpam-4722	183	37	attach	attach	VERB
ejpam-4722	183	38	at	at	ADP
ejpam-4722	183	39	central	central	ADJ
ejpam-4722	183	40	vertex	vertex	NOUN
ejpam-4722	183	41	of	of	ADP
ejpam-4722	183	42	t	t	PROPN
ejpam-4722	183	43	.	.	PUNCT
ejpam-4722	184	1	then	then	ADV
ejpam-4722	184	2	mowv	mowv	NOUN
ejpam-4722	184	3	(	(	PUNCT
ejpam-4722	184	4	ω1	ω1	PROPN
ejpam-4722	184	5	)	)	PUNCT
ejpam-4722	184	6	<	<	X
ejpam-4722	184	7	mowv	mowv	NOUN
ejpam-4722	184	8	(	(	PUNCT
ejpam-4722	184	9	ω2	ω2	ADJ
ejpam-4722	184	10	)	)	PUNCT
ejpam-4722	184	11	f.	f.	PROPN
ejpam-4722	184	12	asmat	asmat	PROPN
ejpam-4722	184	13	et	et	PROPN
ejpam-4722	184	14	al	al	PROPN
ejpam-4722	184	15	.	.	PUNCT
ejpam-4722	184	16	/	/	SYM
ejpam-4722	184	17	eur	eur	PROPN
ejpam-4722	184	18	.	.	PUNCT
ejpam-4722	185	1	j.	j.	PROPN
ejpam-4722	185	2	pure	pure	PROPN
ejpam-4722	185	3	appl	appl	PROPN
ejpam-4722	185	4	.	.	PROPN
ejpam-4722	185	5	math	math	PROPN
ejpam-4722	185	6	,	,	PUNCT
ejpam-4722	185	7	16	16	NUM
ejpam-4722	185	8	(	(	PUNCT
ejpam-4722	185	9	3	3	NUM
ejpam-4722	185	10	)	)	PUNCT
ejpam-4722	185	11	(	(	PUNCT
ejpam-4722	185	12	2023	2023	NUM
ejpam-4722	185	13	)	)	PUNCT
ejpam-4722	185	14	,	,	PUNCT
ejpam-4722	185	15	1794	1794	NUM
ejpam-4722	185	16	-	-	SYM
ejpam-4722	185	17	1808	1808	NUM
ejpam-4722	185	18	1801	1801	NUM
ejpam-4722	185	19	proof	proof	NOUN
ejpam-4722	185	20	.	.	PUNCT
ejpam-4722	185	21	suppose	suppose	VERB
ejpam-4722	185	22	two	two	NUM
ejpam-4722	185	23	subgraphs	subgraph	NOUN
ejpam-4722	185	24	in	in	ADP
ejpam-4722	185	25	ω1	ω1	PROPN
ejpam-4722	185	26	say	say	VERB
ejpam-4722	185	27	,	,	PUNCT
ejpam-4722	185	28	t1	t1	NOUN
ejpam-4722	185	29	and	and	CCONJ
ejpam-4722	185	30	t2	t2	NOUN
ejpam-4722	185	31	.	.	PUNCT
ejpam-4722	186	1	by	by	ADP
ejpam-4722	186	2	construction	construction	NOUN
ejpam-4722	186	3	of	of	ADP
ejpam-4722	186	4	ω2	ω2	ADJ
ejpam-4722	186	5	,	,	PUNCT
ejpam-4722	186	6	the	the	DET
ejpam-4722	186	7	number	number	NOUN
ejpam-4722	186	8	of	of	ADP
ejpam-4722	186	9	closer	close	ADJ
ejpam-4722	186	10	vertices	vertex	NOUN
ejpam-4722	186	11	of	of	ADP
ejpam-4722	186	12	end	end	NOUN
ejpam-4722	186	13	vertices	vertex	NOUN
ejpam-4722	186	14	of	of	ADP
ejpam-4722	186	15	the	the	DET
ejpam-4722	186	16	fixed	fix	VERB
ejpam-4722	186	17	edge	edge	NOUN
ejpam-4722	186	18	of	of	ADP
ejpam-4722	186	19	t1	t1	NOUN
ejpam-4722	186	20	and	and	CCONJ
ejpam-4722	186	21	t2	t2	PROPN
ejpam-4722	186	22	in	in	ADP
ejpam-4722	186	23	ω1	ω1	PROPN
ejpam-4722	186	24	remains	remain	VERB
ejpam-4722	186	25	same	same	ADJ
ejpam-4722	186	26	in	in	ADP
ejpam-4722	186	27	ω2	ω2	ADJ
ejpam-4722	186	28	,	,	PUNCT
ejpam-4722	186	29	respectively	respectively	ADV
ejpam-4722	186	30	.	.	PUNCT
ejpam-4722	187	1	therefore	therefore	ADV
ejpam-4722	187	2	,	,	PUNCT
ejpam-4722	187	3	for	for	ADP
ejpam-4722	187	4	an	an	DET
ejpam-4722	187	5	edge	edge	NOUN
ejpam-4722	187	6	xy	xy	PROPN
ejpam-4722	187	7	∈	∈	PROPN
ejpam-4722	187	8	e(tr	e(tr	PROPN
ejpam-4722	187	9	)	)	PUNCT
ejpam-4722	187	10	,	,	PUNCT
ejpam-4722	187	11	where	where	SCONJ
ejpam-4722	187	12	r	r	NOUN
ejpam-4722	187	13	∈	∈	PROPN
ejpam-4722	187	14	{	{	PUNCT
ejpam-4722	187	15	1	1	NUM
ejpam-4722	187	16	,	,	PUNCT
ejpam-4722	187	17	2	2	NUM
ejpam-4722	187	18	}	}	PUNCT
ejpam-4722	187	19	we	we	PRON
ejpam-4722	187	20	have	have	VERB
ejpam-4722	187	21	nx(e|ω1)(x	nx(e|ω1)(x	NOUN
ejpam-4722	187	22	)	)	PUNCT
ejpam-4722	187	23	=	=	SYM
ejpam-4722	187	24	nx(e|ω2)(x	nx(e|ω2)(x	NOUN
ejpam-4722	187	25	)	)	PUNCT
ejpam-4722	187	26	and	and	CCONJ
ejpam-4722	187	27	ny(e|ω1)(y	ny(e|ω1)(y	NUM
ejpam-4722	187	28	)	)	PUNCT
ejpam-4722	187	29	=	=	PUNCT
ejpam-4722	188	1	ny(e|ω2)(y	ny(e|ω2)(y	ADJ
ejpam-4722	188	2	)	)	PUNCT
ejpam-4722	188	3	.	.	PUNCT
ejpam-4722	189	1	the	the	DET
ejpam-4722	189	2	number	number	NOUN
ejpam-4722	189	3	of	of	ADP
ejpam-4722	189	4	closed	closed	ADJ
ejpam-4722	189	5	vertices	vertex	NOUN
ejpam-4722	189	6	of	of	ADP
ejpam-4722	189	7	a	a	DET
ejpam-4722	189	8	fixed	fix	VERB
ejpam-4722	189	9	vertex	vertex	NOUN
ejpam-4722	189	10	of	of	ADP
ejpam-4722	189	11	t	t	PROPN
ejpam-4722	189	12	in	in	ADP
ejpam-4722	189	13	ω1	ω1	PROPN
ejpam-4722	189	14	is	be	AUX
ejpam-4722	189	15	d	d	NOUN
ejpam-4722	189	16	and	and	CCONJ
ejpam-4722	189	17	d−1	d−1	PROPN
ejpam-4722	189	18	in	in	ADP
ejpam-4722	189	19	ω2	ω2	NUM
ejpam-4722	189	20	.	.	PUNCT
ejpam-4722	190	1	the	the	DET
ejpam-4722	190	2	following	follow	VERB
ejpam-4722	190	3	case	case	NOUN
ejpam-4722	190	4	for	for	ADP
ejpam-4722	190	5	cut	cut	ADJ
ejpam-4722	190	6	edge	edge	NOUN
ejpam-4722	190	7	uv	uv	NOUN
ejpam-4722	190	8	∈	∈	PROPN
ejpam-4722	190	9	e(ω1	e(ω1	NOUN
ejpam-4722	190	10	)	)	PUNCT
ejpam-4722	190	11	.	.	PUNCT
ejpam-4722	191	1	case	case	NOUN
ejpam-4722	191	2	5	5	NUM
ejpam-4722	191	3	.	.	PUNCT
ejpam-4722	191	4	du	du	PROPN
ejpam-4722	191	5	=	=	PROPN
ejpam-4722	191	6	dv	dv	PROPN
ejpam-4722	191	7	=	=	PROPN
ejpam-4722	191	8	3	3	NUM
ejpam-4722	191	9	,	,	PUNCT
ejpam-4722	191	10	and	and	CCONJ
ejpam-4722	191	11	nu(e|ω1)(u	nu(e|ω1)(u	ADJ
ejpam-4722	191	12	)	)	PUNCT
ejpam-4722	191	13	=	=	SYM
ejpam-4722	191	14	e(t	e(t	NOUN
ejpam-4722	191	15	)	)	PUNCT
ejpam-4722	192	1	+	+	CCONJ
ejpam-4722	192	2	1	1	NUM
ejpam-4722	192	3	,	,	PUNCT
ejpam-4722	192	4	nv(e|ω1)(v	nv(e|ω1)(v	X
ejpam-4722	192	5	)	)	PUNCT
ejpam-4722	192	6	=	=	SYM
ejpam-4722	193	1	3	3	X
ejpam-4722	193	2	.	.	NOUN
ejpam-4722	193	3	similar	similar	ADJ
ejpam-4722	193	4	results	result	NOUN
ejpam-4722	193	5	for	for	ADP
ejpam-4722	193	6	pendent	pendent	NOUN
ejpam-4722	193	7	vertices	vertex	NOUN
ejpam-4722	193	8	adjoining	adjoin	VERB
ejpam-4722	193	9	at	at	ADP
ejpam-4722	193	10	vertex	vertex	NOUN
ejpam-4722	193	11	u.	u.	NOUN
ejpam-4722	193	12	case	case	NOUN
ejpam-4722	193	13	6	6	NUM
ejpam-4722	193	14	.	.	PUNCT
ejpam-4722	193	15	nv(e|ω1)(v	nv(e|ω1)(v	X
ejpam-4722	193	16	)	)	PUNCT
ejpam-4722	194	1	=	=	SYM
ejpam-4722	194	2	e(t	e(t	PROPN
ejpam-4722	194	3	)	)	PUNCT
ejpam-4722	195	1	+	+	CCONJ
ejpam-4722	195	2	3	3	NUM
ejpam-4722	195	3	,	,	PUNCT
ejpam-4722	195	4	and	and	CCONJ
ejpam-4722	195	5	nu∗	nu∗	ADV
ejpam-4722	195	6	1	1	NUM
ejpam-4722	195	7	(	(	PUNCT
ejpam-4722	195	8	e|ω1)(u	e|ω1)(u	NOUN
ejpam-4722	195	9	∗	∗	NOUN
ejpam-4722	195	10	1	1	NUM
ejpam-4722	195	11	)	)	PUNCT
ejpam-4722	195	12	=	=	PUNCT
ejpam-4722	195	13	nu∗	nu∗	ADJ
ejpam-4722	195	14	2	2	NUM
ejpam-4722	195	15	(	(	PUNCT
ejpam-4722	195	16	e|ω1)(u	e|ω1)(u	NOUN
ejpam-4722	195	17	∗	∗	NOUN
ejpam-4722	195	18	2	2	NUM
ejpam-4722	195	19	)	)	PUNCT
ejpam-4722	195	20	=	=	SYM
ejpam-4722	196	1	1	1	X
ejpam-4722	196	2	.	.	X
ejpam-4722	196	3	there	there	PRON
ejpam-4722	196	4	are	be	VERB
ejpam-4722	196	5	following	follow	VERB
ejpam-4722	196	6	cases	case	NOUN
ejpam-4722	196	7	in	in	ADP
ejpam-4722	196	8	ω2	ω2	ADJ
ejpam-4722	196	9	,	,	PUNCT
ejpam-4722	196	10	for	for	ADP
ejpam-4722	196	11	pendent	pendent	ADJ
ejpam-4722	196	12	edges	edge	NOUN
ejpam-4722	196	13	uv	uv	PROPN
ejpam-4722	196	14	∈	∈	PROPN
ejpam-4722	196	15	e(ω2	e(ω2	X
ejpam-4722	196	16	)	)	PUNCT
ejpam-4722	196	17	.	.	PUNCT
ejpam-4722	197	1	case	case	NOUN
ejpam-4722	197	2	7	7	X
ejpam-4722	197	3	.	.	PUNCT
ejpam-4722	197	4	du	du	PROPN
ejpam-4722	197	5	=	=	SYM
ejpam-4722	197	6	3	3	PROPN
ejpam-4722	197	7	,	,	PUNCT
ejpam-4722	197	8	dv	dv	PROPN
ejpam-4722	197	9	=	=	PROPN
ejpam-4722	197	10	du∗	du∗	PROPN
ejpam-4722	197	11	2	2	NUM
ejpam-4722	197	12	=	=	SYM
ejpam-4722	197	13	du∗	du∗	NOUN
ejpam-4722	197	14	1	1	NUM
ejpam-4722	197	15	=	=	SYM
ejpam-4722	197	16	1	1	NUM
ejpam-4722	197	17	.	.	PUNCT
ejpam-4722	197	18	case	case	NOUN
ejpam-4722	197	19	8	8	NUM
ejpam-4722	197	20	.	.	PUNCT
ejpam-4722	197	21	nu(e|ω2)(u	nu(e|ω2)(u	ADJ
ejpam-4722	197	22	)	)	PUNCT
ejpam-4722	198	1	=	=	SYM
ejpam-4722	198	2	e(t	e(t	PROPN
ejpam-4722	198	3	)	)	PUNCT
ejpam-4722	199	1	+	+	CCONJ
ejpam-4722	199	2	3	3	NUM
ejpam-4722	199	3	,	,	PUNCT
ejpam-4722	199	4	and	and	CCONJ
ejpam-4722	199	5	nv(e|ω2)(v	nv(e|ω2)(v	PROPN
ejpam-4722	199	6	)	)	PUNCT
ejpam-4722	200	1	=	=	SYM
ejpam-4722	200	2	nu∗	nu∗	ADJ
ejpam-4722	200	3	1	1	NUM
ejpam-4722	200	4	(	(	PUNCT
ejpam-4722	200	5	e|ω2)(u	e|ω2)(u	ADJ
ejpam-4722	200	6	∗	∗	NOUN
ejpam-4722	200	7	1	1	NUM
ejpam-4722	200	8	)	)	PUNCT
ejpam-4722	200	9	=	=	SYM
ejpam-4722	200	10	nu∗	nu∗	ADJ
ejpam-4722	200	11	2	2	NUM
ejpam-4722	200	12	(	(	PUNCT
ejpam-4722	200	13	e|ω2)(u	e|ω2)(u	ADJ
ejpam-4722	200	14	∗	∗	NOUN
ejpam-4722	200	15	2	2	NUM
ejpam-4722	200	16	)	)	PUNCT
ejpam-4722	200	17	=	=	SYM
ejpam-4722	200	18	1	1	X
ejpam-4722	200	19	.	.	PUNCT
ejpam-4722	200	20	by	by	ADP
ejpam-4722	200	21	combining	combine	VERB
ejpam-4722	200	22	cases	case	NOUN
ejpam-4722	200	23	5	5	NUM
ejpam-4722	200	24	,	,	PUNCT
ejpam-4722	200	25	6	6	NUM
ejpam-4722	200	26	,	,	PUNCT
ejpam-4722	200	27	7	7	NUM
ejpam-4722	200	28	and	and	CCONJ
ejpam-4722	200	29	8	8	NUM
ejpam-4722	200	30	,	,	PUNCT
ejpam-4722	200	31	and	and	CCONJ
ejpam-4722	200	32	employing	employ	VERB
ejpam-4722	200	33	definition	definition	NOUN
ejpam-4722	200	34	of	of	ADP
ejpam-4722	200	35	weighted	weight	VERB
ejpam-4722	200	36	vertex	vertex	PROPN
ejpam-4722	200	37	mostar	mostar	PROPN
ejpam-4722	200	38	index	index	PROPN
ejpam-4722	200	39	,	,	PUNCT
ejpam-4722	200	40	we	we	PRON
ejpam-4722	200	41	have	have	VERB
ejpam-4722	200	42	,	,	PUNCT
ejpam-4722	200	43	mowv	mowv	NOUN
ejpam-4722	200	44	(	(	PUNCT
ejpam-4722	200	45	ω1)−mowv	ω1)−mowv	X
ejpam-4722	200	46	(	(	PUNCT
ejpam-4722	200	47	ω2	ω2	ADJ
ejpam-4722	200	48	)	)	PUNCT
ejpam-4722	200	49	=	=	PUNCT
ejpam-4722	201	1	[	[	PUNCT
ejpam-4722	201	2	2∑	2∑	NUM
ejpam-4722	201	3	m=1	m=1	X
ejpam-4722	201	4	∑	∑	NOUN
ejpam-4722	201	5	xy∈e(t1	xy∈e(t1	PROPN
ejpam-4722	201	6	)	)	PUNCT
ejpam-4722	201	7	(	(	PUNCT
ejpam-4722	201	8	dω1(x	dω1(x	NOUN
ejpam-4722	201	9	)	)	PUNCT
ejpam-4722	202	1	+	+	CCONJ
ejpam-4722	203	1	dω1(y))|nx(e|ω1)(x)−	dω1(y))|nx(e|ω1)(x)−	PROPN
ejpam-4722	203	2	ny(e|ω1)(y)|	ny(e|ω1)(y)|	PROPN
ejpam-4722	203	3	+	+	CCONJ
ejpam-4722	203	4	(	(	PUNCT
ejpam-4722	203	5	dω1(u	dω1(u	PROPN
ejpam-4722	203	6	)	)	PUNCT
ejpam-4722	203	7	+	+	NUM
ejpam-4722	203	8	dω1(v))|nv(e|ω1)(v)−	dω1(v))|nv(e|ω1)(v)−	PROPN
ejpam-4722	203	9	nu(e|ω1)(u)|	nu(e|ω1)(u)|	NOUN
ejpam-4722	204	1	+	+	CCONJ
ejpam-4722	204	2	(	(	PUNCT
ejpam-4722	204	3	dω1(u	dω1(u	PROPN
ejpam-4722	204	4	∗	∗	NOUN
ejpam-4722	204	5	1	1	NUM
ejpam-4722	204	6	)	)	PUNCT
ejpam-4722	204	7	+	+	CCONJ
ejpam-4722	204	8	dω1(v))|nu∗	dω1(v))|nu∗	NOUN
ejpam-4722	204	9	1	1	NUM
ejpam-4722	204	10	(	(	PUNCT
ejpam-4722	204	11	e|ω1)(u	e|ω1)(u	ADJ
ejpam-4722	204	12	∗	∗	NOUN
ejpam-4722	204	13	1)−	1)−	PROPN
ejpam-4722	204	14	nv(e|ω1)(v)|	nv(e|ω1)(v)|	NOUN
ejpam-4722	204	15	+	+	CCONJ
ejpam-4722	204	16	(	(	PUNCT
ejpam-4722	204	17	dω1(u	dω1(u	PROPN
ejpam-4722	204	18	∗	∗	NOUN
ejpam-4722	204	19	2	2	NUM
ejpam-4722	204	20	)	)	PUNCT
ejpam-4722	204	21	+	+	CCONJ
ejpam-4722	204	22	dω1(v))|nu∗	dω1(v))|nu∗	NOUN
ejpam-4722	204	23	2	2	NUM
ejpam-4722	204	24	(	(	PUNCT
ejpam-4722	204	25	e|ω1)(u	e|ω1)(u	NOUN
ejpam-4722	204	26	∗	∗	NOUN
ejpam-4722	204	27	2)−	2)−	NUM
ejpam-4722	204	28	nv(e|ω1)(v)|	nv(e|ω1)(v)|	PROPN
ejpam-4722	204	29	−	−	PROPN
ejpam-4722	204	30	(	(	PUNCT
ejpam-4722	204	31	dω2(v	dω2(v	PROPN
ejpam-4722	204	32	)	)	PUNCT
ejpam-4722	204	33	+	+	CCONJ
ejpam-4722	204	34	dω2(u))|nv(e|ω2)(v)−	dω2(u))|nv(e|ω2)(v)−	PROPN
ejpam-4722	204	35	nu(e|ω2)(u)|	nu(e|ω2)(u)|	ADV
ejpam-4722	204	36	−	−	PROPN
ejpam-4722	204	37	(	(	PUNCT
ejpam-4722	204	38	dω2(u	dω2(u	PROPN
ejpam-4722	204	39	∗	∗	NOUN
ejpam-4722	204	40	1	1	NUM
ejpam-4722	204	41	)	)	PUNCT
ejpam-4722	205	1	+	+	CCONJ
ejpam-4722	205	2	dω2(u))|nu∗	dω2(u))|nu∗	NOUN
ejpam-4722	205	3	1	1	NUM
ejpam-4722	205	4	(	(	PUNCT
ejpam-4722	205	5	e|ω2)(u	e|ω2)(u	ADJ
ejpam-4722	205	6	∗	∗	NOUN
ejpam-4722	205	7	1)−	1)−	PROPN
ejpam-4722	205	8	nu(e|ω2)(u)|	nu(e|ω2)(u)|	NOUN
ejpam-4722	205	9	−	−	PROPN
ejpam-4722	205	10	(	(	PUNCT
ejpam-4722	205	11	dω2(u	dω2(u	NOUN
ejpam-4722	205	12	∗	∗	NOUN
ejpam-4722	205	13	2	2	NUM
ejpam-4722	205	14	)	)	PUNCT
ejpam-4722	205	15	+	+	CCONJ
ejpam-4722	205	16	dω2(u))|nu∗	dω2(u))|nu∗	NOUN
ejpam-4722	205	17	2	2	NUM
ejpam-4722	205	18	(	(	PUNCT
ejpam-4722	205	19	e|ω2)(u	e|ω2)(u	ADJ
ejpam-4722	205	20	∗	∗	NOUN
ejpam-4722	205	21	2)−	2)−	NUM
ejpam-4722	206	1	nu(e|ω2)(u)|	nu(e|ω2)(u)|	NOUN
ejpam-4722	206	2	−	−	NOUN
ejpam-4722	206	3	2∑	2∑	NUM
ejpam-4722	206	4	r=1	r=1	NOUN
ejpam-4722	206	5	∑	∑	PUNCT
ejpam-4722	206	6	xy∈e(t2	xy∈e(t2	PROPN
ejpam-4722	206	7	)	)	PUNCT
ejpam-4722	206	8	(	(	PUNCT
ejpam-4722	206	9	dω2(x	dω2(x	PROPN
ejpam-4722	206	10	)	)	PUNCT
ejpam-4722	206	11	+	+	CCONJ
ejpam-4722	207	1	dω2(y))|nx(e|ω2)(x)−	dω2(y))|nx(e|ω2)(x)−	PROPN
ejpam-4722	207	2	ny(e|ω2)(y)|	ny(e|ω2)(y)|	ADV
ejpam-4722	207	3	]	]	PUNCT
ejpam-4722	207	4	,	,	PUNCT
ejpam-4722	207	5	=	=	PUNCT
ejpam-4722	207	6	[	[	PUNCT
ejpam-4722	207	7	(	(	PUNCT
ejpam-4722	207	8	3	3	NUM
ejpam-4722	207	9	+	+	SYM
ejpam-4722	207	10	3)(|3−	3)(|3−	NUM
ejpam-4722	207	11	|e(t	|e(t	PROPN
ejpam-4722	207	12	)	)	PUNCT
ejpam-4722	207	13	|	|	ADV
ejpam-4722	207	14	−	−	PROPN
ejpam-4722	207	15	1|	1|	NUM
ejpam-4722	207	16	)	)	PUNCT
ejpam-4722	208	1	+	+	CCONJ
ejpam-4722	208	2	(	(	PUNCT
ejpam-4722	208	3	3	3	NUM
ejpam-4722	208	4	+	+	SYM
ejpam-4722	208	5	1)(|1−	1)(|1−	NUM
ejpam-4722	208	6	|e(t	|e(t	PROPN
ejpam-4722	208	7	)	)	PUNCT
ejpam-4722	208	8	|	|	ADV
ejpam-4722	208	9	−	−	NOUN
ejpam-4722	208	10	3|	3|	NUM
ejpam-4722	208	11	)	)	PUNCT
ejpam-4722	209	1	+	+	CCONJ
ejpam-4722	209	2	(	(	PUNCT
ejpam-4722	209	3	3	3	NUM
ejpam-4722	209	4	+	+	SYM
ejpam-4722	209	5	1)(|1−	1)(|1−	NUM
ejpam-4722	209	6	|e(t	|e(t	PROPN
ejpam-4722	209	7	)	)	PUNCT
ejpam-4722	209	8	|	|	ADV
ejpam-4722	209	9	−	−	NOUN
ejpam-4722	209	10	3|	3|	NUM
ejpam-4722	209	11	)	)	PUNCT
ejpam-4722	209	12	−	−	PROPN
ejpam-4722	210	1	(	(	PUNCT
ejpam-4722	210	2	3	3	NUM
ejpam-4722	210	3	+	+	SYM
ejpam-4722	210	4	1)(|1−	1)(|1−	NUM
ejpam-4722	210	5	|e(t	|e(t	PROPN
ejpam-4722	210	6	)	)	PUNCT
ejpam-4722	210	7	|	|	ADV
ejpam-4722	210	8	−	−	PROPN
ejpam-4722	210	9	3|)−	3|)−	PROPN
ejpam-4722	210	10	(	(	PUNCT
ejpam-4722	210	11	3	3	NUM
ejpam-4722	210	12	+	+	SYM
ejpam-4722	210	13	1)(|1−	1)(|1−	NUM
ejpam-4722	210	14	|e(t	|e(t	PROPN
ejpam-4722	210	15	)	)	PUNCT
ejpam-4722	210	16	|	|	ADV
ejpam-4722	210	17	−	−	PROPN
ejpam-4722	210	18	3|)−	3|)−	PROPN
ejpam-4722	210	19	(	(	PUNCT
ejpam-4722	210	20	3	3	NUM
ejpam-4722	210	21	+	+	SYM
ejpam-4722	210	22	1)(|1−	1)(|1−	NUM
ejpam-4722	210	23	|e(t	|e(t	PROPN
ejpam-4722	210	24	)	)	PUNCT
ejpam-4722	210	25	|	|	ADV
ejpam-4722	210	26	−	−	NOUN
ejpam-4722	210	27	3|	3|	NUM
ejpam-4722	210	28	)	)	PUNCT
ejpam-4722	210	29	]	]	PUNCT
ejpam-4722	210	30	,	,	PUNCT
ejpam-4722	210	31	≤	≤	ADJ
ejpam-4722	210	32	−6|e(t	−6|e(t	NOUN
ejpam-4722	210	33	)	)	PUNCT
ejpam-4722	210	34	|+	|+	PROPN
ejpam-4722	210	35	4|e(t	4|e(t	NOUN
ejpam-4722	210	36	)	)	PUNCT
ejpam-4722	210	37	|+	|+	NOUN
ejpam-4722	210	38	20	20	NUM
ejpam-4722	210	39	,	,	PUNCT
ejpam-4722	210	40	<	<	X
ejpam-4722	210	41	0	0	X
ejpam-4722	210	42	it	it	PRON
ejpam-4722	210	43	shows	show	VERB
ejpam-4722	210	44	,	,	PUNCT
ejpam-4722	210	45	mowv	mowv	NOUN
ejpam-4722	210	46	(	(	PUNCT
ejpam-4722	210	47	ω1	ω1	PROPN
ejpam-4722	210	48	)	)	PUNCT
ejpam-4722	210	49	−mowv	−mowv	NOUN
ejpam-4722	210	50	(	(	PUNCT
ejpam-4722	210	51	ω2	ω2	ADJ
ejpam-4722	210	52	)	)	PUNCT
ejpam-4722	210	53	<	<	X
ejpam-4722	210	54	0	0	NUM
ejpam-4722	210	55	,	,	PUNCT
ejpam-4722	210	56	which	which	PRON
ejpam-4722	210	57	shows	show	VERB
ejpam-4722	210	58	the	the	DET
ejpam-4722	210	59	maximum	maximum	ADJ
ejpam-4722	210	60	weighted	weight	VERB
ejpam-4722	210	61	vertex	vertex	PROPN
ejpam-4722	210	62	mostar	mostar	PROPN
ejpam-4722	210	63	index	index	PROPN
ejpam-4722	210	64	.	.	PUNCT
ejpam-4722	211	1	f.	f.	PROPN
ejpam-4722	211	2	asmat	asmat	PROPN
ejpam-4722	211	3	et	et	PROPN
ejpam-4722	211	4	al	al	PROPN
ejpam-4722	211	5	.	.	PUNCT
ejpam-4722	211	6	/	/	SYM
ejpam-4722	211	7	eur	eur	PROPN
ejpam-4722	211	8	.	.	PUNCT
ejpam-4722	212	1	j.	j.	PROPN
ejpam-4722	212	2	pure	pure	PROPN
ejpam-4722	212	3	appl	appl	PROPN
ejpam-4722	212	4	.	.	PROPN
ejpam-4722	212	5	math	math	PROPN
ejpam-4722	212	6	,	,	PUNCT
ejpam-4722	212	7	16	16	NUM
ejpam-4722	212	8	(	(	PUNCT
ejpam-4722	212	9	3	3	NUM
ejpam-4722	212	10	)	)	PUNCT
ejpam-4722	212	11	(	(	PUNCT
ejpam-4722	212	12	2023	2023	NUM
ejpam-4722	212	13	)	)	PUNCT
ejpam-4722	212	14	,	,	PUNCT
ejpam-4722	212	15	1794	1794	NUM
ejpam-4722	212	16	-	-	SYM
ejpam-4722	212	17	1808	1808	NUM
ejpam-4722	212	18	1802	1802	NUM
ejpam-4722	212	19	lemma	lemma	PROPN
ejpam-4722	212	20	4	4	X
ejpam-4722	212	21	.	.	PUNCT
ejpam-4722	212	22	consider	consider	VERB
ejpam-4722	212	23	ω	ω	NUM
ejpam-4722	212	24	be	be	AUX
ejpam-4722	212	25	the	the	DET
ejpam-4722	212	26	graph	graph	NOUN
ejpam-4722	212	27	with	with	ADP
ejpam-4722	212	28	even	even	ADV
ejpam-4722	212	29	diameter	diameter	NOUN
ejpam-4722	212	30	and	and	CCONJ
ejpam-4722	212	31	t	t	PROPN
ejpam-4722	212	32	be	be	AUX
ejpam-4722	212	33	subgraph	subgraph	NOUN
ejpam-4722	212	34	of	of	ADP
ejpam-4722	212	35	ω	ω	PROPN
ejpam-4722	212	36	,	,	PUNCT
ejpam-4722	212	37	which	which	PRON
ejpam-4722	212	38	is	be	AUX
ejpam-4722	212	39	presented	present	VERB
ejpam-4722	212	40	by	by	ADP
ejpam-4722	212	41	ω1	ω1	PROPN
ejpam-4722	212	42	.	.	PROPN
ejpam-4722	213	1	to	to	PART
ejpam-4722	213	2	construct	construct	VERB
ejpam-4722	213	3	ω2	ω2	ADV
ejpam-4722	213	4	from	from	ADP
ejpam-4722	213	5	ω1	ω1	PROPN
ejpam-4722	213	6	,	,	PUNCT
ejpam-4722	213	7	remove	remove	VERB
ejpam-4722	213	8	all	all	PRON
ejpam-4722	213	9	n	n	PRON
ejpam-4722	214	1	−	−	NOUN
ejpam-4722	215	1	d	d	SYM
ejpam-4722	215	2	−	−	PROPN
ejpam-4722	215	3	1	1	NUM
ejpam-4722	215	4	pendent	pendent	NOUN
ejpam-4722	215	5	vertices	vertex	NOUN
ejpam-4722	215	6	and	and	CCONJ
ejpam-4722	215	7	identifying	identify	VERB
ejpam-4722	215	8	at	at	ADP
ejpam-4722	215	9	central	central	ADJ
ejpam-4722	215	10	vertex	vertex	NOUN
ejpam-4722	215	11	of	of	ADP
ejpam-4722	215	12	t	t	PROPN
ejpam-4722	215	13	.	.	PUNCT
ejpam-4722	216	1	then	then	ADV
ejpam-4722	216	2	mowv	mowv	NOUN
ejpam-4722	216	3	(	(	PUNCT
ejpam-4722	216	4	ω1	ω1	PROPN
ejpam-4722	216	5	)	)	PUNCT
ejpam-4722	216	6	<	<	X
ejpam-4722	216	7	mowv	mowv	NOUN
ejpam-4722	216	8	(	(	PUNCT
ejpam-4722	216	9	ω2	ω2	ADJ
ejpam-4722	216	10	)	)	PUNCT
ejpam-4722	216	11	.	.	PUNCT
ejpam-4722	217	1	proof	proof	NOUN
ejpam-4722	217	2	.	.	PUNCT
ejpam-4722	218	1	by	by	ADP
ejpam-4722	218	2	use	use	NOUN
ejpam-4722	218	3	of	of	ADP
ejpam-4722	218	4	corollary	corollary	ADJ
ejpam-4722	218	5	2	2	NUM
ejpam-4722	218	6	,	,	PUNCT
ejpam-4722	218	7	we	we	PRON
ejpam-4722	218	8	can	can	AUX
ejpam-4722	218	9	easily	easily	ADV
ejpam-4722	218	10	extend	extend	VERB
ejpam-4722	218	11	the	the	DET
ejpam-4722	218	12	graph	graph	NOUN
ejpam-4722	218	13	up	up	ADP
ejpam-4722	218	14	-	-	PUNCT
ejpam-4722	218	15	to	to	PART
ejpam-4722	218	16	n−	n−	NOUN
ejpam-4722	218	17	d−	d−	PROPN
ejpam-4722	218	18	1	1	NUM
ejpam-4722	218	19	pendent	pendent	NOUN
ejpam-4722	218	20	vertices	vertex	NOUN
ejpam-4722	218	21	linked	link	VERB
ejpam-4722	218	22	with	with	ADP
ejpam-4722	218	23	cut	cut	ADJ
ejpam-4722	218	24	edge	edge	NOUN
ejpam-4722	218	25	and	and	CCONJ
ejpam-4722	218	26	proof	proof	NOUN
ejpam-4722	218	27	is	be	AUX
ejpam-4722	218	28	obvious	obvious	ADJ
ejpam-4722	218	29	.	.	PUNCT
ejpam-4722	219	1	next	next	ADV
ejpam-4722	219	2	,	,	PUNCT
ejpam-4722	219	3	we	we	PRON
ejpam-4722	219	4	turn	turn	VERB
ejpam-4722	219	5	to	to	ADP
ejpam-4722	219	6	the	the	DET
ejpam-4722	219	7	proof	proof	NOUN
ejpam-4722	219	8	of	of	ADP
ejpam-4722	219	9	theorem	theorem	ADJ
ejpam-4722	219	10	3	3	NUM
ejpam-4722	219	11	.	.	PUNCT
ejpam-4722	219	12	proof	proof	NOUN
ejpam-4722	219	13	.	.	PUNCT
ejpam-4722	220	1	assume	assume	VERB
ejpam-4722	220	2	ω	ω	NUM
ejpam-4722	220	3	∈	∈	PROPN
ejpam-4722	220	4	t	t	PROPN
ejpam-4722	220	5	(	(	PUNCT
ejpam-4722	220	6	n	n	X
ejpam-4722	220	7	,	,	PUNCT
ejpam-4722	220	8	d	d	X
ejpam-4722	220	9	)	)	PUNCT
ejpam-4722	220	10	be	be	AUX
ejpam-4722	220	11	a	a	DET
ejpam-4722	220	12	graph	graph	NOUN
ejpam-4722	220	13	with	with	ADP
ejpam-4722	220	14	d	d	PROPN
ejpam-4722	220	15	≥	≥	NUM
ejpam-4722	220	16	1	1	NUM
ejpam-4722	220	17	and	and	CCONJ
ejpam-4722	220	18	n	n	PRON
ejpam-4722	220	19	≥	≥	NOUN
ejpam-4722	220	20	2	2	NUM
ejpam-4722	220	21	.	.	PUNCT
ejpam-4722	221	1	if	if	SCONJ
ejpam-4722	221	2	t	t	PROPN
ejpam-4722	221	3	(	(	PUNCT
ejpam-4722	221	4	n	n	CCONJ
ejpam-4722	221	5	,	,	PUNCT
ejpam-4722	221	6	d	d	NOUN
ejpam-4722	221	7	)	)	PUNCT
ejpam-4722	221	8	≇	≇	PROPN
ejpam-4722	221	9	ω	ω	PROPN
ejpam-4722	221	10	and	and	CCONJ
ejpam-4722	221	11	ω	ω	PROPN
ejpam-4722	221	12	has	have	AUX
ejpam-4722	221	13	cut	cut	VERB
ejpam-4722	221	14	edge	edge	NOUN
ejpam-4722	221	15	then	then	ADV
ejpam-4722	221	16	repeatedly	repeatedly	ADV
ejpam-4722	221	17	by	by	ADP
ejpam-4722	221	18	using	use	VERB
ejpam-4722	221	19	lemma	lemma	PROPN
ejpam-4722	221	20	2	2	NUM
ejpam-4722	221	21	,	,	PUNCT
ejpam-4722	221	22	we	we	PRON
ejpam-4722	221	23	acquire	acquire	VERB
ejpam-4722	221	24	sequence	sequence	NOUN
ejpam-4722	221	25	of	of	ADP
ejpam-4722	221	26	new	new	ADJ
ejpam-4722	221	27	tree	tree	NOUN
ejpam-4722	221	28	graphs	graph	NOUN
ejpam-4722	221	29	ω1,ω2,ω3	ω1,ω2,ω3	ADJ
ejpam-4722	221	30	,	,	PUNCT
ejpam-4722	221	31	...	...	PUNCT
ejpam-4722	221	32	,	,	PUNCT
ejpam-4722	221	33	ωα	ωα	X
ejpam-4722	221	34	,	,	PUNCT
ejpam-4722	221	35	where	where	SCONJ
ejpam-4722	221	36	ωα	ωα	PART
ejpam-4722	221	37	be	be	AUX
ejpam-4722	221	38	a	a	DET
ejpam-4722	221	39	tree	tree	NOUN
ejpam-4722	221	40	graph	graph	NOUN
ejpam-4722	221	41	without	without	ADP
ejpam-4722	221	42	edge	edge	NOUN
ejpam-4722	221	43	with	with	ADP
ejpam-4722	221	44	largest	large	ADJ
ejpam-4722	221	45	degree	degree	NOUN
ejpam-4722	221	46	sequence	sequence	NOUN
ejpam-4722	221	47	such	such	ADJ
ejpam-4722	221	48	that	that	DET
ejpam-4722	221	49	mowv	mowv	NOUN
ejpam-4722	221	50	(	(	PUNCT
ejpam-4722	221	51	ω1	ω1	PROPN
ejpam-4722	221	52	)	)	PUNCT
ejpam-4722	221	53	<	<	X
ejpam-4722	221	54	mowv	mowv	NOUN
ejpam-4722	221	55	(	(	PUNCT
ejpam-4722	221	56	ω2	ω2	ADJ
ejpam-4722	221	57	)	)	PUNCT
ejpam-4722	221	58	<	<	X
ejpam-4722	221	59	mowv	mowv	NOUN
ejpam-4722	221	60	(	(	PUNCT
ejpam-4722	221	61	ω3	ω3	PROPN
ejpam-4722	221	62	)	)	PUNCT
ejpam-4722	221	63	<	<	X
ejpam-4722	221	64	...	...	PUNCT
ejpam-4722	222	1	<	<	X
ejpam-4722	222	2	mowv	mowv	NOUN
ejpam-4722	222	3	(	(	PUNCT
ejpam-4722	222	4	ωα	ωα	NOUN
ejpam-4722	222	5	)	)	PUNCT
ejpam-4722	222	6	.	.	PUNCT
ejpam-4722	223	1	now	now	ADV
ejpam-4722	223	2	,	,	PUNCT
ejpam-4722	223	3	if	if	SCONJ
ejpam-4722	223	4	mowv	mowv	NOUN
ejpam-4722	223	5	(	(	PUNCT
ejpam-4722	223	6	ωα	ωα	NOUN
ejpam-4722	223	7	)	)	PUNCT
ejpam-4722	223	8	≇	≇	PROPN
ejpam-4722	223	9	t	t	PROPN
ejpam-4722	223	10	(	(	PUNCT
ejpam-4722	223	11	n̂	n̂	ADV
ejpam-4722	223	12	,	,	PUNCT
ejpam-4722	223	13	d	d	NOUN
ejpam-4722	223	14	)	)	PUNCT
ejpam-4722	223	15	and	and	CCONJ
ejpam-4722	223	16	mowv	mowv	NOUN
ejpam-4722	223	17	(	(	PUNCT
ejpam-4722	223	18	ωα	ωα	X
ejpam-4722	223	19	)	)	PUNCT
ejpam-4722	223	20	has	have	VERB
ejpam-4722	223	21	subgraph	subgraph	NOUN
ejpam-4722	223	22	with	with	ADP
ejpam-4722	223	23	n	n	CCONJ
ejpam-4722	223	24	−	−	PROPN
ejpam-4722	224	1	d	d	NOUN
ejpam-4722	224	2	−	−	PROPN
ejpam-4722	224	3	1	1	NUM
ejpam-4722	224	4	,	,	PUNCT
ejpam-4722	224	5	pendent	pendent	NOUN
ejpam-4722	224	6	vertices	vertex	NOUN
ejpam-4722	224	7	with	with	ADP
ejpam-4722	224	8	even	even	ADV
ejpam-4722	224	9	diameter	diameter	NOUN
ejpam-4722	224	10	then	then	ADV
ejpam-4722	224	11	repeatedly	repeatedly	ADV
ejpam-4722	224	12	using	use	VERB
ejpam-4722	224	13	lemma	lemma	PROPN
ejpam-4722	224	14	3	3	NUM
ejpam-4722	224	15	,	,	PUNCT
ejpam-4722	224	16	we	we	PRON
ejpam-4722	224	17	can	can	AUX
ejpam-4722	224	18	acquire	acquire	VERB
ejpam-4722	224	19	sequence	sequence	NOUN
ejpam-4722	224	20	of	of	ADP
ejpam-4722	224	21	tree	tree	NOUN
ejpam-4722	224	22	graph	graph	NOUN
ejpam-4722	224	23	such	such	ADJ
ejpam-4722	224	24	that	that	DET
ejpam-4722	224	25	ωα1	ωα1	NOUN
ejpam-4722	224	26	,	,	PUNCT
ejpam-4722	224	27	ωα2	ωα2	NOUN
ejpam-4722	224	28	,	,	PUNCT
ejpam-4722	224	29	ωα3	ωα3	PROPN
ejpam-4722	224	30	,	,	PUNCT
ejpam-4722	224	31	..	..	PUNCT
ejpam-4722	224	32	,	,	PUNCT
ejpam-4722	224	33	ωαβ	ωαβ	VERB
ejpam-4722	224	34	,	,	PUNCT
ejpam-4722	224	35	satisfying	satisfy	VERB
ejpam-4722	224	36	mowv	mowv	NOUN
ejpam-4722	224	37	(	(	PUNCT
ejpam-4722	224	38	ωα1	ωα1	ADV
ejpam-4722	224	39	)	)	PUNCT
ejpam-4722	224	40	<	<	X
ejpam-4722	224	41	mowv	mowv	NOUN
ejpam-4722	224	42	(	(	PUNCT
ejpam-4722	224	43	ωα2	ωα2	NOUN
ejpam-4722	224	44	)	)	PUNCT
ejpam-4722	224	45	<	<	X
ejpam-4722	225	1	mowv	mowv	NOUN
ejpam-4722	225	2	(	(	PUNCT
ejpam-4722	225	3	ωα3	ωα3	PROPN
ejpam-4722	225	4	)	)	PUNCT
ejpam-4722	225	5	<	<	X
ejpam-4722	225	6	...	...	PUNCT
ejpam-4722	226	1	<	<	X
ejpam-4722	226	2	mowv	mowv	NOUN
ejpam-4722	226	3	(	(	PUNCT
ejpam-4722	226	4	ωαβ	ωαβ	NOUN
ejpam-4722	226	5	)	)	PUNCT
ejpam-4722	226	6	,	,	PUNCT
ejpam-4722	226	7	where	where	SCONJ
ejpam-4722	226	8	ωαβ	ωαβ	VERB
ejpam-4722	226	9	be	be	AUX
ejpam-4722	226	10	a	a	DET
ejpam-4722	226	11	tree	tree	NOUN
ejpam-4722	226	12	graph	graph	NOUN
ejpam-4722	226	13	such	such	ADJ
ejpam-4722	226	14	that	that	DET
ejpam-4722	226	15	degree	degree	NOUN
ejpam-4722	226	16	of	of	ADP
ejpam-4722	226	17	central	central	ADJ
ejpam-4722	226	18	vertex	vertex	NOUN
ejpam-4722	226	19	with	with	ADP
ejpam-4722	226	20	even	even	ADV
ejpam-4722	226	21	diameter	diameter	NOUN
ejpam-4722	226	22	greater	great	ADJ
ejpam-4722	226	23	than	than	ADP
ejpam-4722	226	24	3	3	NUM
ejpam-4722	226	25	.	.	PUNCT
ejpam-4722	226	26	if	if	SCONJ
ejpam-4722	226	27	ωαβ	ωαβ	VERB
ejpam-4722	226	28	≇	≇	PROPN
ejpam-4722	226	29	t	t	PROPN
ejpam-4722	226	30	(	(	PUNCT
ejpam-4722	226	31	n̂	n̂	ADV
ejpam-4722	226	32	,	,	PUNCT
ejpam-4722	226	33	d	d	NOUN
ejpam-4722	226	34	)	)	PUNCT
ejpam-4722	226	35	,	,	PUNCT
ejpam-4722	226	36	then	then	ADV
ejpam-4722	226	37	repeatedly	repeatedly	ADV
ejpam-4722	226	38	using	use	VERB
ejpam-4722	226	39	lemma	lemma	PROPN
ejpam-4722	226	40	4	4	NUM
ejpam-4722	226	41	,	,	PUNCT
ejpam-4722	226	42	and	and	CCONJ
ejpam-4722	226	43	corollary	corollary	ADJ
ejpam-4722	226	44	2	2	NUM
ejpam-4722	226	45	,	,	PUNCT
ejpam-4722	226	46	we	we	PRON
ejpam-4722	226	47	have	have	VERB
ejpam-4722	226	48	ωαβ1	ωαβ1	NOUN
ejpam-4722	226	49	,	,	PUNCT
ejpam-4722	226	50	ωαβ2	ωαβ2	PROPN
ejpam-4722	226	51	,	,	PUNCT
ejpam-4722	226	52	ωαβ3	ωαβ3	PROPN
ejpam-4722	226	53	,	,	PUNCT
ejpam-4722	226	54	...	...	PUNCT
ejpam-4722	226	55	,	,	PUNCT
ejpam-4722	226	56	ωαβγ	ωαβγ	NOUN
ejpam-4722	226	57	,	,	PUNCT
ejpam-4722	226	58	satisfyingmowv	satisfyingmowv	PROPN
ejpam-4722	226	59	(	(	PUNCT
ejpam-4722	226	60	ωαβ1	ωαβ1	PROPN
ejpam-4722	226	61	)	)	PUNCT
ejpam-4722	226	62	<	<	X
ejpam-4722	226	63	mowv	mowv	NOUN
ejpam-4722	226	64	(	(	PUNCT
ejpam-4722	226	65	ωαβ2	ωαβ2	PROPN
ejpam-4722	226	66	)	)	PUNCT
ejpam-4722	226	67	<	<	X
ejpam-4722	227	1	mowv	mowv	NOUN
ejpam-4722	227	2	(	(	PUNCT
ejpam-4722	227	3	ωαβ3	ωαβ3	ADJ
ejpam-4722	227	4	)	)	PUNCT
ejpam-4722	227	5	<	<	X
ejpam-4722	227	6	...	...	PUNCT
ejpam-4722	228	1	<	<	X
ejpam-4722	228	2	mowv	mowv	NOUN
ejpam-4722	228	3	(	(	PUNCT
ejpam-4722	228	4	ωαβγ	ωαβγ	NOUN
ejpam-4722	228	5	)	)	PUNCT
ejpam-4722	228	6	,	,	PUNCT
ejpam-4722	228	7	wheremowv	wheremowv	NOUN
ejpam-4722	228	8	(	(	PUNCT
ejpam-4722	228	9	ωαβγ	ωαβγ	NOUN
ejpam-4722	228	10	)	)	PUNCT
ejpam-4722	228	11	∼=	∼=	PROPN
ejpam-4722	228	12	t	t	NOUN
ejpam-4722	228	13	(	(	PUNCT
ejpam-4722	228	14	n̂	n̂	ADV
ejpam-4722	228	15	,	,	PUNCT
ejpam-4722	228	16	d	d	NOUN
ejpam-4722	228	17	)	)	PUNCT
ejpam-4722	228	18	.	.	PUNCT
ejpam-4722	229	1	this	this	PRON
ejpam-4722	229	2	completes	complete	VERB
ejpam-4722	229	3	the	the	DET
ejpam-4722	229	4	proof	proof	NOUN
ejpam-4722	229	5	.	.	PUNCT
ejpam-4722	230	1	transformation	transformation	NOUN
ejpam-4722	230	2	1	1	NUM
ejpam-4722	230	3	.	.	PUNCT
ejpam-4722	230	4	suppose	suppose	VERB
ejpam-4722	230	5	that	that	SCONJ
ejpam-4722	230	6	k1	k1	PROPN
ejpam-4722	230	7	and	and	CCONJ
ejpam-4722	230	8	k2	k2	PROPN
ejpam-4722	230	9	are	be	AUX
ejpam-4722	230	10	two	two	NUM
ejpam-4722	230	11	graphs	graph	NOUN
ejpam-4722	230	12	with	with	ADP
ejpam-4722	230	13	hl	hl	NOUN
ejpam-4722	230	14	∈	∈	PROPN
ejpam-4722	230	15	vω(kl	vω(kl	PROPN
ejpam-4722	230	16	)	)	PUNCT
ejpam-4722	230	17	for	for	ADP
ejpam-4722	230	18	l	l	NOUN
ejpam-4722	230	19	=	=	PUNCT
ejpam-4722	230	20	{	{	PUNCT
ejpam-4722	230	21	1	1	NUM
ejpam-4722	230	22	,	,	PUNCT
ejpam-4722	230	23	2	2	NUM
ejpam-4722	230	24	}	}	PUNCT
ejpam-4722	230	25	.	.	PUNCT
ejpam-4722	231	1	suppose	suppose	VERB
ejpam-4722	231	2	that	that	SCONJ
ejpam-4722	231	3	pn	pn	PROPN
ejpam-4722	231	4	,	,	PUNCT
ejpam-4722	231	5	tn	tn	PROPN
ejpam-4722	231	6	,	,	PUNCT
ejpam-4722	231	7	sn	sn	PROPN
ejpam-4722	231	8	are	be	AUX
ejpam-4722	231	9	path	path	NOUN
ejpam-4722	231	10	,	,	PUNCT
ejpam-4722	231	11	tree	tree	NOUN
ejpam-4722	231	12	and	and	CCONJ
ejpam-4722	231	13	star	star	NOUN
ejpam-4722	231	14	of	of	ADP
ejpam-4722	231	15	the	the	DET
ejpam-4722	231	16	same	same	ADJ
ejpam-4722	231	17	order	order	NOUN
ejpam-4722	231	18	n	n	PRON
ejpam-4722	231	19	such	such	ADJ
ejpam-4722	231	20	that	that	DET
ejpam-4722	231	21	tn	tn	PROPN
ejpam-4722	231	22	≇	≇	PROPN
ejpam-4722	231	23	pn	pn	PROPN
ejpam-4722	231	24	and	and	CCONJ
ejpam-4722	231	25	tn	tn	PROPN
ejpam-4722	231	26	≇	≇	PROPN
ejpam-4722	231	27	sn	sn	PROPN
ejpam-4722	231	28	.	.	PUNCT
ejpam-4722	232	1	let	let	VERB
ejpam-4722	232	2	ω	ω	NUM
ejpam-4722	232	3	be	be	AUX
ejpam-4722	232	4	a	a	DET
ejpam-4722	232	5	generated	generate	VERB
ejpam-4722	232	6	graph	graph	NOUN
ejpam-4722	232	7	by	by	ADP
ejpam-4722	232	8	associating	associate	VERB
ejpam-4722	232	9	the	the	DET
ejpam-4722	232	10	node	node	ADJ
ejpam-4722	232	11	h1	h1	NOUN
ejpam-4722	232	12	with	with	ADP
ejpam-4722	232	13	one	one	NUM
ejpam-4722	232	14	end	end	NOUN
ejpam-4722	232	15	of	of	ADP
ejpam-4722	232	16	pn	pn	PROPN
ejpam-4722	232	17	and	and	CCONJ
ejpam-4722	232	18	associating	associate	VERB
ejpam-4722	232	19	the	the	DET
ejpam-4722	232	20	node	node	ADJ
ejpam-4722	232	21	h2	h2	NOUN
ejpam-4722	232	22	with	with	ADP
ejpam-4722	232	23	the	the	DET
ejpam-4722	232	24	other	other	ADJ
ejpam-4722	232	25	end	end	NOUN
ejpam-4722	232	26	of	of	ADP
ejpam-4722	232	27	pn	pn	PROPN
ejpam-4722	232	28	.	.	PROPN
ejpam-4722	232	29	next	next	ADV
ejpam-4722	232	30	,	,	PUNCT
ejpam-4722	232	31	let	let	VERB
ejpam-4722	232	32	ω	ω	NUM
ejpam-4722	232	33	′	′	NUM
ejpam-4722	232	34	be	be	AUX
ejpam-4722	232	35	a	a	DET
ejpam-4722	232	36	transformed	transform	VERB
ejpam-4722	232	37	graph	graph	NOUN
ejpam-4722	232	38	by	by	ADP
ejpam-4722	232	39	associating	associate	VERB
ejpam-4722	232	40	the	the	DET
ejpam-4722	232	41	vertex	vertex	NOUN
ejpam-4722	232	42	h1	h1	NOUN
ejpam-4722	232	43	and	and	CCONJ
ejpam-4722	232	44	h2	h2	PROPN
ejpam-4722	232	45	as	as	ADP
ejpam-4722	232	46	a	a	DET
ejpam-4722	232	47	new	new	ADJ
ejpam-4722	232	48	vertex	vertex	NOUN
ejpam-4722	232	49	h	h	NOUN
ejpam-4722	232	50	,	,	PUNCT
ejpam-4722	232	51	and	and	CCONJ
ejpam-4722	232	52	then	then	ADV
ejpam-4722	232	53	fix	fix	VERB
ejpam-4722	232	54	the	the	DET
ejpam-4722	232	55	vertex	vertex	NOUN
ejpam-4722	232	56	h	h	NOUN
ejpam-4722	232	57	with	with	ADP
ejpam-4722	232	58	the	the	DET
ejpam-4722	232	59	center	center	NOUN
ejpam-4722	232	60	of	of	ADP
ejpam-4722	232	61	sn	sn	PROPN
ejpam-4722	232	62	.	.	PUNCT
ejpam-4722	233	1	lemma	lemma	PROPN
ejpam-4722	233	2	5	5	NUM
ejpam-4722	233	3	.	.	PUNCT
ejpam-4722	234	1	we	we	PRON
ejpam-4722	234	2	say	say	VERB
ejpam-4722	234	3	that	that	SCONJ
ejpam-4722	234	4	ω	ω	PROPN
ejpam-4722	234	5	and	and	CCONJ
ejpam-4722	234	6	ω	ω	NUM
ejpam-4722	234	7	′	′	NOUN
ejpam-4722	234	8	are	be	AUX
ejpam-4722	234	9	graphs.then	graphs.then	PROPN
ejpam-4722	234	10	mowe	mowe	VERB
ejpam-4722	234	11	(	(	PUNCT
ejpam-4722	234	12	ω	ω	NOUN
ejpam-4722	234	13	)	)	PUNCT
ejpam-4722	234	14	<	<	X
ejpam-4722	234	15	mowe	mowe	NOUN
ejpam-4722	234	16	(	(	PUNCT
ejpam-4722	234	17	ω	ω	NOUN
ejpam-4722	234	18	′	′	NUM
ejpam-4722	234	19	)	)	PUNCT
ejpam-4722	234	20	.	.	PUNCT
ejpam-4722	235	1	proof	proof	NOUN
ejpam-4722	235	2	.	.	PUNCT
ejpam-4722	236	1	since	since	SCONJ
ejpam-4722	236	2	tn	tn	PROPN
ejpam-4722	236	3	≇	≇	PROPN
ejpam-4722	236	4	pn	pn	PROPN
ejpam-4722	236	5	and	and	CCONJ
ejpam-4722	236	6	tn	tn	PROPN
ejpam-4722	236	7	≇	≇	PROPN
ejpam-4722	236	8	sn	sn	PROPN
ejpam-4722	236	9	,	,	PUNCT
ejpam-4722	236	10	n	n	PRON
ejpam-4722	236	11	≥	≥	NOUN
ejpam-4722	236	12	4	4	NUM
ejpam-4722	236	13	for	for	ADP
ejpam-4722	236	14	any	any	DET
ejpam-4722	236	15	edge	edge	NOUN
ejpam-4722	236	16	e	e	NOUN
ejpam-4722	236	17	=	=	PUNCT
ejpam-4722	236	18	gh1	gh1	PROPN
ejpam-4722	236	19	∈	∈	PROPN
ejpam-4722	236	20	e(k1	e(k1	PRON
ejpam-4722	236	21	)	)	PUNCT
ejpam-4722	236	22	,	,	PUNCT
ejpam-4722	236	23	mg(e|ω	mg(e|ω	NOUN
ejpam-4722	236	24	)	)	PUNCT
ejpam-4722	236	25	−	−	PROPN
ejpam-4722	236	26	mh1(e|ω	mh1(e|ω	PROPN
ejpam-4722	236	27	)	)	PUNCT
ejpam-4722	236	28	=	=	PRON
ejpam-4722	236	29	mg(e|ω	mg(e|ω	PROPN
ejpam-4722	236	30	′	′	NUM
ejpam-4722	236	31	)	)	PUNCT
ejpam-4722	237	1	−	−	PROPN
ejpam-4722	237	2	mh1(e|ω	mh1(e|ω	PROPN
ejpam-4722	237	3	′	′	NUM
ejpam-4722	237	4	)	)	PUNCT
ejpam-4722	237	5	and	and	CCONJ
ejpam-4722	237	6	dω(g	dω(g	NOUN
ejpam-4722	237	7	)	)	PUNCT
ejpam-4722	237	8	+	+	CCONJ
ejpam-4722	237	9	dω(h1	dω(h1	NOUN
ejpam-4722	237	10	)	)	PUNCT
ejpam-4722	237	11	≤	≤	NUM
ejpam-4722	237	12	dω′	dω′	X
ejpam-4722	237	13	(	(	PUNCT
ejpam-4722	237	14	g	g	NOUN
ejpam-4722	237	15	)	)	PUNCT
ejpam-4722	238	1	+	+	CCONJ
ejpam-4722	238	2	dω′	dω′	X
ejpam-4722	238	3	(	(	PUNCT
ejpam-4722	238	4	h1	h1	PROPN
ejpam-4722	238	5	)	)	PUNCT
ejpam-4722	238	6	.	.	PUNCT
ejpam-4722	239	1	therefore,∑	therefore,∑	X
ejpam-4722	239	2	e	e	NOUN
ejpam-4722	239	3	=	=	NOUN
ejpam-4722	239	4	gh1∈e(k1	gh1∈e(k1	NOUN
ejpam-4722	239	5	)	)	PUNCT
ejpam-4722	239	6	dω(g	dω(g	NOUN
ejpam-4722	239	7	)	)	PUNCT
ejpam-4722	240	1	+	+	CCONJ
ejpam-4722	241	1	dω(h1)|mg(e|ω)−mh1(e|ω)|	dω(h1)|mg(e|ω)−mh1(e|ω)|	PROPN
ejpam-4722	241	2	,	,	PUNCT
ejpam-4722	241	3	<	<	X
ejpam-4722	241	4	∑	∑	PUNCT
ejpam-4722	241	5	e	e	NOUN
ejpam-4722	241	6	=	=	NOUN
ejpam-4722	241	7	gh1∈e(k1	gh1∈e(k1	NOUN
ejpam-4722	241	8	)	)	PUNCT
ejpam-4722	241	9	dω′	dω′	X
ejpam-4722	241	10	(	(	PUNCT
ejpam-4722	241	11	g	g	NOUN
ejpam-4722	241	12	)	)	PUNCT
ejpam-4722	242	1	+	+	CCONJ
ejpam-4722	242	2	dω′	dω′	X
ejpam-4722	242	3	(	(	PUNCT
ejpam-4722	242	4	h1)|mg(e|ω	h1)|mg(e|ω	NOUN
ejpam-4722	242	5	′	′	NOUN
ejpam-4722	242	6	)	)	PUNCT
ejpam-4722	242	7	−mh1(e|ω	−mh1(e|ω	NOUN
ejpam-4722	242	8	′	′	NUM
ejpam-4722	242	9	)	)	PUNCT
ejpam-4722	243	1	|	|	ADV
ejpam-4722	243	2	,	,	PUNCT
ejpam-4722	243	3	similarly	similarly	ADV
ejpam-4722	243	4	,	,	PUNCT
ejpam-4722	243	5	for	for	ADP
ejpam-4722	243	6	any	any	DET
ejpam-4722	243	7	edge	edge	NOUN
ejpam-4722	243	8	e	e	NOUN
ejpam-4722	243	9	=	=	SYM
ejpam-4722	243	10	g	g	PROPN
ejpam-4722	243	11	′	′	NUM
ejpam-4722	243	12	h2	h2	PROPN
ejpam-4722	243	13	∈	∈	PROPN
ejpam-4722	243	14	e(k1	e(k1	PRON
ejpam-4722	243	15	)	)	PUNCT
ejpam-4722	243	16	,	,	PUNCT
ejpam-4722	243	17	mg′	mg′	X
ejpam-4722	243	18	(	(	PUNCT
ejpam-4722	243	19	e|ω)−mh2(e|ω	e|ω)−mh2(e|ω	ADJ
ejpam-4722	243	20	)	)	PUNCT
ejpam-4722	243	21	=	=	SYM
ejpam-4722	243	22	mg′	mg′	X
ejpam-4722	243	23	(	(	PUNCT
ejpam-4722	243	24	e|ω	e|ω	NOUN
ejpam-4722	243	25	′	′	NUM
ejpam-4722	243	26	)	)	PUNCT
ejpam-4722	243	27	−mh2(e|ω	−mh2(e|ω	NOUN
ejpam-4722	243	28	′	′	NUM
ejpam-4722	243	29	)	)	PUNCT
ejpam-4722	244	1	and	and	CCONJ
ejpam-4722	244	2	dω(g	dω(g	NOUN
ejpam-4722	244	3	′	′	NUM
ejpam-4722	244	4	)	)	PUNCT
ejpam-4722	245	1	+	+	CCONJ
ejpam-4722	245	2	dω(h2	dω(h2	NOUN
ejpam-4722	245	3	)	)	PUNCT
ejpam-4722	245	4	≤	≤	NOUN
ejpam-4722	245	5	dω′	dω′	X
ejpam-4722	245	6	(	(	PUNCT
ejpam-4722	245	7	g	g	NOUN
ejpam-4722	245	8	′	′	NUM
ejpam-4722	245	9	)	)	PUNCT
ejpam-4722	246	1	+	+	CCONJ
ejpam-4722	246	2	dω′	dω′	X
ejpam-4722	246	3	(	(	PUNCT
ejpam-4722	246	4	h2	h2	NOUN
ejpam-4722	246	5	)	)	PUNCT
ejpam-4722	246	6	.	.	PUNCT
ejpam-4722	247	1	therefore,∑	therefore,∑	X
ejpam-4722	247	2	e	e	NOUN
ejpam-4722	247	3	=	=	NOUN
ejpam-4722	247	4	g′h2∈e(k1	g′h2∈e(k1	NUM
ejpam-4722	247	5	)	)	PUNCT
ejpam-4722	247	6	dω(g	dω(g	NOUN
ejpam-4722	247	7	′	′	NUM
ejpam-4722	247	8	)	)	PUNCT
ejpam-4722	248	1	+	+	CCONJ
ejpam-4722	248	2	deω(h2)|mg′	deω(h2)|mg′	PROPN
ejpam-4722	248	3	(	(	PUNCT
ejpam-4722	248	4	e|ω)−mh2(e|ω)|	e|ω)−mh2(e|ω)|	PROPN
ejpam-4722	248	5	,	,	PUNCT
ejpam-4722	248	6	f.	f.	PROPN
ejpam-4722	248	7	asmat	asmat	PROPN
ejpam-4722	248	8	et	et	PROPN
ejpam-4722	248	9	al	al	PROPN
ejpam-4722	248	10	.	.	PUNCT
ejpam-4722	248	11	/	/	SYM
ejpam-4722	248	12	eur	eur	PROPN
ejpam-4722	248	13	.	.	PUNCT
ejpam-4722	249	1	j.	j.	PROPN
ejpam-4722	249	2	pure	pure	PROPN
ejpam-4722	249	3	appl	appl	PROPN
ejpam-4722	249	4	.	.	PROPN
ejpam-4722	249	5	math	math	PROPN
ejpam-4722	249	6	,	,	PUNCT
ejpam-4722	249	7	16	16	NUM
ejpam-4722	249	8	(	(	PUNCT
ejpam-4722	249	9	3	3	NUM
ejpam-4722	249	10	)	)	PUNCT
ejpam-4722	249	11	(	(	PUNCT
ejpam-4722	249	12	2023	2023	NUM
ejpam-4722	249	13	)	)	PUNCT
ejpam-4722	249	14	,	,	PUNCT
ejpam-4722	249	15	1794	1794	NUM
ejpam-4722	249	16	-	-	SYM
ejpam-4722	249	17	1808	1808	NUM
ejpam-4722	249	18	1803	1803	NUM
ejpam-4722	249	19	<	<	X
ejpam-4722	249	20	∑	∑	PUNCT
ejpam-4722	249	21	e	e	X
ejpam-4722	249	22	=	=	NOUN
ejpam-4722	249	23	g′h2∈e(k1	g′h2∈e(k1	NOUN
ejpam-4722	249	24	)	)	PUNCT
ejpam-4722	249	25	dω′	dω′	X
ejpam-4722	249	26	(	(	PUNCT
ejpam-4722	249	27	g	g	NOUN
ejpam-4722	249	28	′	′	NUM
ejpam-4722	249	29	)	)	PUNCT
ejpam-4722	250	1	+	+	CCONJ
ejpam-4722	250	2	dω′	dω′	X
ejpam-4722	250	3	(	(	PUNCT
ejpam-4722	250	4	h2)|mg′	h2)|mg′	NOUN
ejpam-4722	250	5	(	(	PUNCT
ejpam-4722	250	6	e|ω	e|ω	NOUN
ejpam-4722	250	7	′	′	X
ejpam-4722	250	8	)	)	PUNCT
ejpam-4722	250	9	−mh2(e|ω	−mh2(e|ω	NOUN
ejpam-4722	250	10	′	′	NUM
ejpam-4722	250	11	)	)	PUNCT
ejpam-4722	251	1	|	|	ADV
ejpam-4722	251	2	,	,	PUNCT
ejpam-4722	251	3	for	for	ADP
ejpam-4722	251	4	any	any	DET
ejpam-4722	251	5	edge	edge	NOUN
ejpam-4722	251	6	e	e	NOUN
ejpam-4722	251	7	=	=	SYM
ejpam-4722	251	8	hk	hk	PROPN
ejpam-4722	251	9	∈	∈	PROPN
ejpam-4722	251	10	e(pn	e(pn	NUM
ejpam-4722	251	11	)	)	PUNCT
ejpam-4722	251	12	,	,	PUNCT
ejpam-4722	251	13	mh(e|ω	mh(e|ω	NOUN
ejpam-4722	251	14	)	)	PUNCT
ejpam-4722	251	15	−	−	ADP
ejpam-4722	251	16	mk(e|ω	mk(e|ω	NUM
ejpam-4722	251	17	)	)	PUNCT
ejpam-4722	251	18	=	=	SYM
ejpam-4722	251	19	|ω|	|ω|	PROPN
ejpam-4722	251	20	.	.	PROPN
ejpam-4722	251	21	similarly	similarly	ADV
ejpam-4722	251	22	,	,	PUNCT
ejpam-4722	251	23	e	e	PROPN
ejpam-4722	251	24	=	=	SYM
ejpam-4722	251	25	hk	hk	PROPN
ejpam-4722	251	26	∈	∈	PROPN
ejpam-4722	251	27	e(sn	e(sn	PROPN
ejpam-4722	251	28	)	)	PUNCT
ejpam-4722	251	29	,	,	PUNCT
ejpam-4722	251	30	mh(e|ω	mh(e|ω	ADV
ejpam-4722	251	31	′	′	NUM
ejpam-4722	251	32	)	)	PUNCT
ejpam-4722	252	1	−mk(e|ω	−mk(e|ω	PROPN
ejpam-4722	252	2	′	′	NUM
ejpam-4722	252	3	)	)	PUNCT
ejpam-4722	253	1	=	=	PUNCT
ejpam-4722	253	2	|ω′	|ω′	ADJ
ejpam-4722	253	3	|	|	ADV
ejpam-4722	253	4	.	.	PUNCT
ejpam-4722	254	1	therefore,∑	therefore,∑	X
ejpam-4722	254	2	e	e	X
ejpam-4722	254	3	=	=	PROPN
ejpam-4722	254	4	hk∈e(pn	hk∈e(pn	PROPN
ejpam-4722	254	5	)	)	PUNCT
ejpam-4722	254	6	dω(h	dω(h	PROPN
ejpam-4722	254	7	)	)	PUNCT
ejpam-4722	255	1	+	+	CCONJ
ejpam-4722	255	2	dω(k)|mh(e|ω)−mk(e|ω)|	dω(k)|mh(e|ω)−mk(e|ω)|	PROPN
ejpam-4722	255	3	,	,	PUNCT
ejpam-4722	255	4	<	<	X
ejpam-4722	255	5	∑	∑	PUNCT
ejpam-4722	255	6	e	e	X
ejpam-4722	255	7	=	=	ADJ
ejpam-4722	255	8	hk∈e(sn	hk∈e(sn	ADJ
ejpam-4722	255	9	)	)	PUNCT
ejpam-4722	255	10	dω′	dω′	PROPN
ejpam-4722	255	11	(	(	PUNCT
ejpam-4722	255	12	h	h	NOUN
ejpam-4722	255	13	)	)	PUNCT
ejpam-4722	256	1	+	+	CCONJ
ejpam-4722	256	2	dω′	dω′	X
ejpam-4722	256	3	(	(	PUNCT
ejpam-4722	256	4	k)|mh(e|ω	k)|mh(e|ω	NOUN
ejpam-4722	256	5	′	′	NUM
ejpam-4722	256	6	)	)	PUNCT
ejpam-4722	257	1	−mk(e|ω	−mk(e|ω	PROPN
ejpam-4722	257	2	′	′	NUM
ejpam-4722	257	3	)	)	PUNCT
ejpam-4722	258	1	|	|	ADV
ejpam-4722	258	2	,	,	PUNCT
ejpam-4722	258	3	which	which	PRON
ejpam-4722	258	4	is	be	AUX
ejpam-4722	258	5	obvious	obvious	ADJ
ejpam-4722	258	6	to	to	PART
ejpam-4722	258	7	show	show	VERB
ejpam-4722	258	8	that	that	SCONJ
ejpam-4722	258	9	mowe	mowe	NOUN
ejpam-4722	258	10	(	(	PUNCT
ejpam-4722	258	11	ω	ω	NOUN
ejpam-4722	258	12	)	)	PUNCT
ejpam-4722	258	13	<	<	X
ejpam-4722	258	14	mowe	mowe	NOUN
ejpam-4722	258	15	(	(	PUNCT
ejpam-4722	258	16	ω	ω	PROPN
ejpam-4722	258	17	′	′	NUM
ejpam-4722	258	18	)	)	PUNCT
ejpam-4722	259	1	<	<	X
ejpam-4722	259	2	0	0	X
ejpam-4722	259	3	.	.	PUNCT
ejpam-4722	260	1	the	the	DET
ejpam-4722	260	2	proof	proof	NOUN
ejpam-4722	260	3	is	be	AUX
ejpam-4722	260	4	complete	complete	ADJ
ejpam-4722	260	5	.	.	PUNCT
ejpam-4722	261	1	transformation	transformation	NOUN
ejpam-4722	261	2	2	2	X
ejpam-4722	261	3	.	.	PUNCT
ejpam-4722	262	1	let	let	VERB
ejpam-4722	262	2	k	k	PRON
ejpam-4722	262	3	be	be	AUX
ejpam-4722	262	4	a	a	DET
ejpam-4722	262	5	graph	graph	NOUN
ejpam-4722	262	6	with	with	ADP
ejpam-4722	262	7	u	u	NOUN
ejpam-4722	262	8	′	′	NOUN
ejpam-4722	262	9	∈	∈	PROPN
ejpam-4722	262	10	v	v	NOUN
ejpam-4722	262	11	(	(	PUNCT
ejpam-4722	262	12	k	k	NOUN
ejpam-4722	262	13	)	)	PUNCT
ejpam-4722	262	14	,	,	PUNCT
ejpam-4722	262	15	and	and	CCONJ
ejpam-4722	262	16	cp	cp	INTJ
ejpam-4722	262	17	be	be	AUX
ejpam-4722	262	18	a	a	DET
ejpam-4722	262	19	cycle	cycle	NOUN
ejpam-4722	262	20	of	of	ADP
ejpam-4722	262	21	order	order	NOUN
ejpam-4722	263	1	p.	p.	NOUN
ejpam-4722	263	2	the	the	DET
ejpam-4722	263	3	graph	graph	NOUN
ejpam-4722	263	4	k(u	k(u	PROPN
ejpam-4722	263	5	′	′	NUM
ejpam-4722	263	6	)	)	PUNCT
ejpam-4722	264	1	cp	cp	PROPN
ejpam-4722	264	2	is	be	AUX
ejpam-4722	264	3	constructed	construct	VERB
ejpam-4722	264	4	by	by	ADP
ejpam-4722	264	5	associating	associate	VERB
ejpam-4722	264	6	the	the	DET
ejpam-4722	264	7	vertex	vertex	NOUN
ejpam-4722	264	8	u	u	NOUN
ejpam-4722	264	9	′	′	NOUN
ejpam-4722	264	10	with	with	ADP
ejpam-4722	264	11	a	a	DET
ejpam-4722	264	12	vertex	vertex	NOUN
ejpam-4722	264	13	of	of	ADP
ejpam-4722	264	14	cp	cp	PROPN
ejpam-4722	264	15	.	.	PUNCT
ejpam-4722	265	1	let	let	VERB
ejpam-4722	265	2	ω	ω	NUM
ejpam-4722	265	3	be	be	AUX
ejpam-4722	265	4	a	a	DET
ejpam-4722	265	5	graph	graph	NOUN
ejpam-4722	265	6	generated	generate	VERB
ejpam-4722	265	7	from	from	ADP
ejpam-4722	265	8	k(u	k(u	PROPN
ejpam-4722	265	9	′	′	NUM
ejpam-4722	265	10	)	)	PUNCT
ejpam-4722	266	1	cp	cp	INTJ
ejpam-4722	266	2	by	by	ADP
ejpam-4722	266	3	connecting	connect	VERB
ejpam-4722	266	4	pendent	pendent	ADJ
ejpam-4722	266	5	edges	edge	NOUN
ejpam-4722	266	6	to	to	ADP
ejpam-4722	266	7	the	the	DET
ejpam-4722	266	8	vertices	vertex	NOUN
ejpam-4722	266	9	of	of	ADP
ejpam-4722	266	10	cp	cp	NUM
ejpam-4722	266	11	other	other	ADJ
ejpam-4722	266	12	than	than	ADP
ejpam-4722	266	13	u	u	NOUN
ejpam-4722	266	14	′	′	NOUN
ejpam-4722	266	15	.	.	PUNCT
ejpam-4722	267	1	next	next	ADV
ejpam-4722	267	2	,	,	PUNCT
ejpam-4722	267	3	let	let	VERB
ejpam-4722	267	4	ω	ω	NUM
ejpam-4722	267	5	′	′	NUM
ejpam-4722	267	6	be	be	AUX
ejpam-4722	267	7	a	a	DET
ejpam-4722	267	8	generated	generate	VERB
ejpam-4722	267	9	graph	graph	NOUN
ejpam-4722	267	10	from	from	ADP
ejpam-4722	267	11	ω	ω	NUM
ejpam-4722	267	12	by	by	ADP
ejpam-4722	267	13	moving	move	VERB
ejpam-4722	267	14	all	all	DET
ejpam-4722	267	15	pendent	pendent	ADJ
ejpam-4722	267	16	edges	edge	NOUN
ejpam-4722	267	17	,	,	PUNCT
ejpam-4722	267	18	which	which	PRON
ejpam-4722	267	19	are	be	AUX
ejpam-4722	267	20	attached	attach	VERB
ejpam-4722	267	21	at	at	ADP
ejpam-4722	267	22	vertices	vertex	NOUN
ejpam-4722	267	23	of	of	ADP
ejpam-4722	267	24	cp	cp	NUM
ejpam-4722	267	25	other	other	ADJ
ejpam-4722	267	26	than	than	ADP
ejpam-4722	267	27	u	u	NOUN
ejpam-4722	267	28	′	′	NOUN
ejpam-4722	267	29	,	,	PUNCT
ejpam-4722	267	30	on	on	ADP
ejpam-4722	267	31	u	u	NOUN
ejpam-4722	267	32	′	′	NOUN
ejpam-4722	267	33	.	.	PUNCT
ejpam-4722	268	1	given	give	VERB
ejpam-4722	268	2	that	that	PRON
ejpam-4722	268	3	,	,	PUNCT
ejpam-4722	268	4	|ω|	|ω|	PROPN
ejpam-4722	268	5	=	=	SYM
ejpam-4722	268	6	|ω′	|ω′	PROPN
ejpam-4722	268	7	|	|	ADV
ejpam-4722	268	8	.	.	PUNCT
ejpam-4722	269	1	lemma	lemma	PROPN
ejpam-4722	269	2	6	6	NUM
ejpam-4722	269	3	.	.	PUNCT
ejpam-4722	269	4	suppose	suppose	VERB
ejpam-4722	269	5	that	that	SCONJ
ejpam-4722	269	6	two	two	NUM
ejpam-4722	269	7	graphs	graph	NOUN
ejpam-4722	269	8	denoted	denote	VERB
ejpam-4722	269	9	by	by	ADP
ejpam-4722	269	10	ω	ω	PROPN
ejpam-4722	269	11	and	and	CCONJ
ejpam-4722	269	12	ω	ω	NUM
ejpam-4722	269	13	′	′	NUM
ejpam-4722	269	14	.	.	PUNCT
ejpam-4722	270	1	then	then	ADV
ejpam-4722	270	2	mowe	mowe	VERB
ejpam-4722	270	3	(	(	PUNCT
ejpam-4722	270	4	ω	ω	NOUN
ejpam-4722	270	5	)	)	PUNCT
ejpam-4722	270	6	<	<	X
ejpam-4722	270	7	mowe	mowe	NOUN
ejpam-4722	270	8	(	(	PUNCT
ejpam-4722	270	9	ω	ω	NOUN
ejpam-4722	270	10	′	′	NUM
ejpam-4722	270	11	)	)	PUNCT
ejpam-4722	270	12	.	.	PUNCT
ejpam-4722	271	1	proof	proof	NOUN
ejpam-4722	271	2	.	.	PUNCT
ejpam-4722	272	1	suppose	suppose	VERB
ejpam-4722	272	2	|ω|	|ω|	NOUN
ejpam-4722	272	3	=	=	SYM
ejpam-4722	272	4	|ω′	|ω′	PROPN
ejpam-4722	272	5	|	|	ADV
ejpam-4722	272	6	=	=	PUNCT
ejpam-4722	272	7	n.	n.	NOUN
ejpam-4722	272	8	in	in	ADP
ejpam-4722	272	9	ω	ω	PROPN
ejpam-4722	272	10	and	and	CCONJ
ejpam-4722	272	11	ω	ω	NUM
ejpam-4722	272	12	′	′	NUM
ejpam-4722	272	13	,	,	PUNCT
ejpam-4722	272	14	suppose	suppose	VERB
ejpam-4722	272	15	the	the	DET
ejpam-4722	272	16	vertices	vertex	NOUN
ejpam-4722	272	17	of	of	ADP
ejpam-4722	272	18	cp	cp	NUM
ejpam-4722	272	19	are	be	AUX
ejpam-4722	272	20	u	u	NOUN
ejpam-4722	272	21	′	′	ADJ
ejpam-4722	272	22	o(u	o(u	ADJ
ejpam-4722	272	23	′	′	NOUN
ejpam-4722	272	24	)	)	PUNCT
ejpam-4722	272	25	u	u	NOUN
ejpam-4722	272	26	′	′	NUM
ejpam-4722	272	27	1u	1u	NUM
ejpam-4722	272	28	′	′	NUM
ejpam-4722	272	29	2	2	NUM
ejpam-4722	272	30	,	,	PUNCT
ejpam-4722	272	31	..	..	PUNCT
ejpam-4722	272	32	,	,	PUNCT
ejpam-4722	272	33	u	u	NOUN
ejpam-4722	272	34	′	′	NOUN
ejpam-4722	272	35	p−1	p−1	NOUN
ejpam-4722	272	36	subsequently	subsequently	ADV
ejpam-4722	272	37	.	.	PUNCT
ejpam-4722	273	1	in	in	ADP
ejpam-4722	273	2	ω	ω	PROPN
ejpam-4722	273	3	,	,	PUNCT
ejpam-4722	273	4	suppose	suppose	VERB
ejpam-4722	273	5	that	that	SCONJ
ejpam-4722	273	6	yj	yj	PROPN
ejpam-4722	273	7	pendant	pendant	PROPN
ejpam-4722	273	8	edges	edge	NOUN
ejpam-4722	273	9	rooted	root	VERB
ejpam-4722	273	10	on	on	ADP
ejpam-4722	273	11	u	u	PROPN
ejpam-4722	273	12	′	′	PROPN
ejpam-4722	273	13	j	j	NOUN
ejpam-4722	273	14	for	for	ADP
ejpam-4722	273	15	1	1	NUM
ejpam-4722	273	16	≤	≤	NUM
ejpam-4722	273	17	j	j	PROPN
ejpam-4722	273	18	≤	≤	PROPN
ejpam-4722	273	19	p−	p−	NOUN
ejpam-4722	273	20	1	1	NUM
ejpam-4722	273	21	and	and	CCONJ
ejpam-4722	273	22	p−1∑	p−1∑	PROPN
ejpam-4722	274	1	j=1	j=1	PROPN
ejpam-4722	274	2	yj	yj	PROPN
ejpam-4722	274	3	=	=	PROPN
ejpam-4722	274	4	y.	y.	PROPN
ejpam-4722	274	5	since	since	ADV
ejpam-4722	274	6	,	,	PUNCT
ejpam-4722	274	7	dω(u	dω(u	X
ejpam-4722	274	8	′	′	NUM
ejpam-4722	274	9	)	)	PUNCT
ejpam-4722	275	1	=	=	NOUN
ejpam-4722	275	2	dω(u	dω(u	NOUN
ejpam-4722	275	3	′	′	NUM
ejpam-4722	275	4	)	)	PUNCT
ejpam-4722	276	1	−	−	PROPN
ejpam-4722	276	2	y.	y.	NOUN
ejpam-4722	276	3	for	for	ADP
ejpam-4722	276	4	any	any	DET
ejpam-4722	276	5	edge	edge	NOUN
ejpam-4722	276	6	e	e	NOUN
ejpam-4722	276	7	=	=	SYM
ejpam-4722	276	8	wu	wu	PROPN
ejpam-4722	276	9	′	′	NUM
ejpam-4722	276	10	∈	∈	PROPN
ejpam-4722	276	11	e(k	e(k	NOUN
ejpam-4722	276	12	)	)	PUNCT
ejpam-4722	276	13	,	,	PUNCT
ejpam-4722	276	14	dω(w	dω(w	NUM
ejpam-4722	276	15	)	)	PUNCT
ejpam-4722	276	16	+	+	CCONJ
ejpam-4722	276	17	dω(u	dω(u	NOUN
ejpam-4722	276	18	′	′	NUM
ejpam-4722	276	19	)	)	PUNCT
ejpam-4722	276	20	<	<	X
ejpam-4722	276	21	dω′	dω′	X
ejpam-4722	276	22	(	(	PUNCT
ejpam-4722	276	23	w	w	NOUN
ejpam-4722	276	24	)	)	PUNCT
ejpam-4722	276	25	+	+	CCONJ
ejpam-4722	276	26	dω′	dω′	X
ejpam-4722	276	27	(	(	PUNCT
ejpam-4722	276	28	u	u	NOUN
ejpam-4722	276	29	′	′	NUM
ejpam-4722	276	30	)	)	PUNCT
ejpam-4722	276	31	,	,	PUNCT
ejpam-4722	276	32	and	and	CCONJ
ejpam-4722	276	33	nw(e|ω)−	nw(e|ω)−	NOUN
ejpam-4722	276	34	nu′	nu′	X
ejpam-4722	276	35	(	(	PUNCT
ejpam-4722	276	36	e|ω	e|ω	NOUN
ejpam-4722	276	37	)	)	PUNCT
ejpam-4722	276	38	=	=	SYM
ejpam-4722	276	39	nw(e|ω	nw(e|ω	ADV
ejpam-4722	276	40	′	′	NUM
ejpam-4722	276	41	)	)	PUNCT
ejpam-4722	276	42	−	−	NOUN
ejpam-4722	276	43	nu′	nu′	ADV
ejpam-4722	276	44	(	(	PUNCT
ejpam-4722	276	45	e|ω′	e|ω′	PROPN
ejpam-4722	276	46	)	)	PUNCT
ejpam-4722	276	47	.	.	PUNCT
ejpam-4722	277	1	therefore	therefore	ADV
ejpam-4722	277	2	,	,	PUNCT
ejpam-4722	277	3	=	=	SYM
ejpam-4722	277	4	∑	∑	ADV
ejpam-4722	277	5	wu′∈e(k	wu′∈e(k	NOUN
ejpam-4722	277	6	)	)	PUNCT
ejpam-4722	277	7	(	(	PUNCT
ejpam-4722	277	8	dω(w	dω(w	NUM
ejpam-4722	277	9	)	)	PUNCT
ejpam-4722	277	10	+	+	CCONJ
ejpam-4722	277	11	dω(u	dω(u	NOUN
ejpam-4722	277	12	′	′	NUM
ejpam-4722	277	13	)	)	PUNCT
ejpam-4722	277	14	)	)	PUNCT
ejpam-4722	278	1	|nw(e|ω)−	|nw(e|ω)−	ADV
ejpam-4722	278	2	nu′	nu′	X
ejpam-4722	278	3	(	(	PUNCT
ejpam-4722	278	4	e|ω)|	e|ω)|	PROPN
ejpam-4722	278	5	,	,	PUNCT
ejpam-4722	278	6	−	−	NOUN
ejpam-4722	278	7	∑	∑	ADV
ejpam-4722	278	8	wu′∈e(k	wu′∈e(k	PROPN
ejpam-4722	278	9	)	)	PUNCT
ejpam-4722	278	10	dω′	dω′	X
ejpam-4722	278	11	(	(	PUNCT
ejpam-4722	278	12	w	w	NOUN
ejpam-4722	278	13	)	)	PUNCT
ejpam-4722	278	14	+	+	CCONJ
ejpam-4722	278	15	deω′	deω′	NUM
ejpam-4722	278	16	(	(	PUNCT
ejpam-4722	278	17	u	u	NOUN
ejpam-4722	278	18	′	′	NUM
ejpam-4722	278	19	)	)	PUNCT
ejpam-4722	278	20	nw(e|ω	nw(e|ω	PUNCT
ejpam-4722	278	21	′	′	NUM
ejpam-4722	278	22	)	)	PUNCT
ejpam-4722	278	23	−	−	NOUN
ejpam-4722	279	1	nu′	nu′	ADV
ejpam-4722	279	2	(	(	PUNCT
ejpam-4722	279	3	e|ω′	e|ω′	PROPN
ejpam-4722	279	4	)	)	PUNCT
ejpam-4722	279	5	,	,	PUNCT
ejpam-4722	279	6	<	<	X
ejpam-4722	279	7	0	0	PUNCT
ejpam-4722	279	8	in	in	ADP
ejpam-4722	279	9	ω	ω	PROPN
ejpam-4722	279	10	,	,	PUNCT
ejpam-4722	279	11	for	for	ADP
ejpam-4722	279	12	pendant	pendant	ADJ
ejpam-4722	279	13	edge	edge	NOUN
ejpam-4722	279	14	,	,	PUNCT
ejpam-4722	280	1	e	e	X
ejpam-4722	280	2	=	=	SYM
ejpam-4722	280	3	uju	uju	PROPN
ejpam-4722	280	4	′	′	PROPN
ejpam-4722	280	5	j	j	PROPN
ejpam-4722	280	6	rooted	root	VERB
ejpam-4722	280	7	on	on	ADP
ejpam-4722	280	8	u	u	PROPN
ejpam-4722	280	9	′	′	NUM
ejpam-4722	280	10	j	j	PROPN
ejpam-4722	280	11	(	(	PUNCT
ejpam-4722	280	12	1	1	NUM
ejpam-4722	280	13	≤	≤	NUM
ejpam-4722	280	14	j	j	PROPN
ejpam-4722	280	15	≤	≤	PROPN
ejpam-4722	281	1	p	p	PRON
ejpam-4722	281	2	−	−	PROPN
ejpam-4722	281	3	1	1	NUM
ejpam-4722	281	4	)	)	PUNCT
ejpam-4722	281	5	,	,	PUNCT
ejpam-4722	281	6	dω(uj	dω(uj	PROPN
ejpam-4722	281	7	)	)	PUNCT
ejpam-4722	282	1	+	+	CCONJ
ejpam-4722	282	2	dω(u	dω(u	NUM
ejpam-4722	282	3	′	′	NUM
ejpam-4722	282	4	j	j	NOUN
ejpam-4722	282	5	)	)	PUNCT
ejpam-4722	282	6	=	=	SYM
ejpam-4722	282	7	yj	yj	PROPN
ejpam-4722	282	8	+	+	ADJ
ejpam-4722	282	9	2	2	NUM
ejpam-4722	282	10	+	+	SYM
ejpam-4722	282	11	1	1	NUM
ejpam-4722	282	12	=	=	SYM
ejpam-4722	282	13	yj	yj	PROPN
ejpam-4722	282	14	+	+	NUM
ejpam-4722	282	15	3	3	NUM
ejpam-4722	282	16	and	and	CCONJ
ejpam-4722	282	17	nuj	nuj	NOUN
ejpam-4722	282	18	(	(	PUNCT
ejpam-4722	282	19	e|ω)−	e|ω)−	PROPN
ejpam-4722	282	20	n	n	CCONJ
ejpam-4722	282	21	u	u	NOUN
ejpam-4722	282	22	′	′	NUM
ejpam-4722	282	23	j	j	PROPN
ejpam-4722	282	24	(	(	PUNCT
ejpam-4722	282	25	e|ω	e|ω	NOUN
ejpam-4722	282	26	)	)	PUNCT
ejpam-4722	283	1	=	=	PUNCT
ejpam-4722	284	1	n−	n−	NOUN
ejpam-4722	284	2	d.	d.	NOUN
ejpam-4722	284	3	p−1∑	p−1∑	PROPN
ejpam-4722	284	4	j−1	j−1	PROPN
ejpam-4722	284	5	∑	∑	PROPN
ejpam-4722	284	6	uju	uju	PROPN
ejpam-4722	284	7	′	′	PROPN
ejpam-4722	284	8	j∈e(ω	j∈e(ω	PROPN
ejpam-4722	284	9	)	)	PUNCT
ejpam-4722	285	1	dω(uj	dω(uj	PROPN
ejpam-4722	285	2	)	)	PUNCT
ejpam-4722	286	1	+	+	CCONJ
ejpam-4722	286	2	dω(u	dω(u	NOUN
ejpam-4722	286	3	′	′	NUM
ejpam-4722	286	4	j)|nuj	j)|nuj	PROPN
ejpam-4722	286	5	(	(	PUNCT
ejpam-4722	286	6	e|ω)−	e|ω)−	PROPN
ejpam-4722	286	7	n	n	CCONJ
ejpam-4722	286	8	u	u	NOUN
ejpam-4722	287	1	′	′	NUM
ejpam-4722	287	2	j	j	PROPN
ejpam-4722	287	3	(	(	PUNCT
ejpam-4722	287	4	e|ω)|	e|ω)|	PROPN
ejpam-4722	287	5	=	=	PUNCT
ejpam-4722	287	6	(	(	PUNCT
ejpam-4722	287	7	n−	n−	NOUN
ejpam-4722	287	8	d	d	NOUN
ejpam-4722	287	9	)	)	PUNCT
ejpam-4722	288	1	p=1∑	p=1∑	NOUN
ejpam-4722	288	2	j=1	j=1	NOUN
ejpam-4722	288	3	yj(yj	yj(yj	PROPN
ejpam-4722	288	4	+	+	CCONJ
ejpam-4722	288	5	3	3	X
ejpam-4722	288	6	)	)	PUNCT
ejpam-4722	289	1	,	,	PUNCT
ejpam-4722	289	2	f.	f.	PROPN
ejpam-4722	289	3	asmat	asmat	PROPN
ejpam-4722	289	4	et	et	PROPN
ejpam-4722	289	5	al	al	PROPN
ejpam-4722	289	6	.	.	PUNCT
ejpam-4722	289	7	/	/	SYM
ejpam-4722	289	8	eur	eur	PROPN
ejpam-4722	289	9	.	.	PUNCT
ejpam-4722	290	1	j.	j.	PROPN
ejpam-4722	290	2	pure	pure	PROPN
ejpam-4722	290	3	appl	appl	PROPN
ejpam-4722	290	4	.	.	PROPN
ejpam-4722	290	5	math	math	PROPN
ejpam-4722	290	6	,	,	PUNCT
ejpam-4722	290	7	16	16	NUM
ejpam-4722	290	8	(	(	PUNCT
ejpam-4722	290	9	3	3	NUM
ejpam-4722	290	10	)	)	PUNCT
ejpam-4722	290	11	(	(	PUNCT
ejpam-4722	290	12	2023	2023	NUM
ejpam-4722	290	13	)	)	PUNCT
ejpam-4722	290	14	,	,	PUNCT
ejpam-4722	290	15	1794	1794	NUM
ejpam-4722	290	16	-	-	SYM
ejpam-4722	290	17	1808	1808	NUM
ejpam-4722	290	18	1804	1804	NUM
ejpam-4722	290	19	in	in	ADP
ejpam-4722	290	20	ω	ω	NUM
ejpam-4722	290	21	′	′	NUM
ejpam-4722	290	22	,	,	PUNCT
ejpam-4722	290	23	for	for	ADP
ejpam-4722	290	24	pendant	pendant	ADJ
ejpam-4722	290	25	edge	edge	NOUN
ejpam-4722	290	26	e	e	NOUN
ejpam-4722	290	27	=	=	SYM
ejpam-4722	290	28	uu	uu	ADJ
ejpam-4722	290	29	′	′	NOUN
ejpam-4722	290	30	rooted	root	VERB
ejpam-4722	290	31	on	on	ADP
ejpam-4722	290	32	u	u	NOUN
ejpam-4722	290	33	′	′	NOUN
ejpam-4722	290	34	which	which	PRON
ejpam-4722	290	35	is	be	AUX
ejpam-4722	290	36	not	not	PART
ejpam-4722	290	37	in	in	ADP
ejpam-4722	290	38	e(k	e(k	NOUN
ejpam-4722	290	39	)	)	PUNCT
ejpam-4722	290	40	and	and	CCONJ
ejpam-4722	290	41	dω′	dω′	PROPN
ejpam-4722	290	42	(	(	PUNCT
ejpam-4722	290	43	u	u	NOUN
ejpam-4722	290	44	)	)	PUNCT
ejpam-4722	290	45	=	=	SYM
ejpam-4722	290	46	1	1	NUM
ejpam-4722	290	47	,	,	PUNCT
ejpam-4722	290	48	dω′	dω′	X
ejpam-4722	290	49	(	(	PUNCT
ejpam-4722	290	50	u	u	NOUN
ejpam-4722	290	51	)	)	PUNCT
ejpam-4722	291	1	+	+	CCONJ
ejpam-4722	291	2	dω′	dω′	X
ejpam-4722	291	3	(	(	PUNCT
ejpam-4722	291	4	u	u	NOUN
ejpam-4722	291	5	′	′	NOUN
ejpam-4722	291	6	)	)	PUNCT
ejpam-4722	292	1	=	=	PUNCT
ejpam-4722	292	2	dω(u	dω(u	NOUN
ejpam-4722	292	3	′	′	NUM
ejpam-4722	292	4	)	)	PUNCT
ejpam-4722	293	1	+	+	CCONJ
ejpam-4722	293	2	y	y	PROPN
ejpam-4722	293	3	+	+	CCONJ
ejpam-4722	293	4	1	1	NUM
ejpam-4722	293	5	and	and	CCONJ
ejpam-4722	293	6	nu(e|ω	nu(e|ω	NUM
ejpam-4722	293	7	′	′	NUM
ejpam-4722	293	8	)	)	PUNCT
ejpam-4722	294	1	−	−	NOUN
ejpam-4722	294	2	nu′	nu′	ADV
ejpam-4722	295	1	(	(	PUNCT
ejpam-4722	295	2	e|ω′	e|ω′	PROPN
ejpam-4722	295	3	)	)	PUNCT
ejpam-4722	295	4	=	=	PUNCT
ejpam-4722	296	1	n−	n−	NOUN
ejpam-4722	296	2	d.∑	d.∑	ADV
ejpam-4722	296	3	uu′∈e(ω′	uu′∈e(ω′	PROPN
ejpam-4722	296	4	)	)	PUNCT
ejpam-4722	296	5	dω′	dω′	PROPN
ejpam-4722	296	6	(	(	PUNCT
ejpam-4722	296	7	u	u	NOUN
ejpam-4722	296	8	)	)	PUNCT
ejpam-4722	296	9	+	+	CCONJ
ejpam-4722	296	10	dω′	dω′	X
ejpam-4722	296	11	(	(	PUNCT
ejpam-4722	296	12	u	u	NOUN
ejpam-4722	296	13	′	′	NOUN
ejpam-4722	296	14	)	)	PUNCT
ejpam-4722	296	15	|nu(e|ω	|nu(e|ω	ADJ
ejpam-4722	296	16	′	′	NOUN
ejpam-4722	296	17	)	)	PUNCT
ejpam-4722	296	18	−	−	NOUN
ejpam-4722	296	19	nu′	nu′	ADV
ejpam-4722	296	20	(	(	PUNCT
ejpam-4722	296	21	e|ω′	e|ω′	PROPN
ejpam-4722	296	22	)	)	PUNCT
ejpam-4722	296	23	|	|	ADV
ejpam-4722	297	1	=	=	SYM
ejpam-4722	297	2	y(n−	y(n−	PROPN
ejpam-4722	297	3	d)(dω	d)(dω	VERB
ejpam-4722	297	4	+	+	CCONJ
ejpam-4722	297	5	y	y	PROPN
ejpam-4722	297	6	+	+	PROPN
ejpam-4722	297	7	1	1	NUM
ejpam-4722	297	8	)	)	PUNCT
ejpam-4722	297	9	,	,	PUNCT
ejpam-4722	297	10	there	there	PRON
ejpam-4722	297	11	is	be	VERB
ejpam-4722	297	12	two	two	NUM
ejpam-4722	297	13	possibilities	possibility	NOUN
ejpam-4722	297	14	,	,	PUNCT
ejpam-4722	297	15	either	either	CCONJ
ejpam-4722	297	16	p	p	PRON
ejpam-4722	297	17	is	be	AUX
ejpam-4722	297	18	even	even	ADV
ejpam-4722	297	19	or	or	CCONJ
ejpam-4722	297	20	p	p	NOUN
ejpam-4722	297	21	is	be	AUX
ejpam-4722	297	22	odd	odd	ADJ
ejpam-4722	297	23	.	.	PUNCT
ejpam-4722	298	1	first	first	ADV
ejpam-4722	298	2	we	we	PRON
ejpam-4722	298	3	suppose	suppose	VERB
ejpam-4722	298	4	p	p	NOUN
ejpam-4722	298	5	is	be	AUX
ejpam-4722	298	6	even	even	ADV
ejpam-4722	298	7	.	.	PUNCT
ejpam-4722	299	1	for	for	SCONJ
ejpam-4722	299	2	any	any	DET
ejpam-4722	299	3	edge	edge	NOUN
ejpam-4722	299	4	e	e	NOUN
ejpam-4722	299	5	=	=	SYM
ejpam-4722	299	6	u	u	SYM
ejpam-4722	299	7	′	′	NOUN
ejpam-4722	299	8	ju	ju	NOUN
ejpam-4722	299	9	′	′	NOUN
ejpam-4722	299	10	j+1	j+1	X
ejpam-4722	299	11	(	(	PUNCT
ejpam-4722	299	12	0	0	NUM
ejpam-4722	299	13	≤	≤	NUM
ejpam-4722	299	14	j	j	PROPN
ejpam-4722	299	15	≤	≤	PROPN
ejpam-4722	300	1	p	p	DET
ejpam-4722	300	2	−	−	PROPN
ejpam-4722	300	3	1	1	NUM
ejpam-4722	300	4	)	)	PUNCT
ejpam-4722	300	5	of	of	ADP
ejpam-4722	300	6	cp	cp	PROPN
ejpam-4722	300	7	in	in	ADP
ejpam-4722	300	8	ω	ω	PROPN
ejpam-4722	300	9	,	,	PUNCT
ejpam-4722	300	10	dω(u	dω(u	PUNCT
ejpam-4722	300	11	′	′	NUM
ejpam-4722	300	12	j	j	NOUN
ejpam-4722	300	13	)	)	PUNCT
ejpam-4722	301	1	+	+	CCONJ
ejpam-4722	301	2	dω(u	dω(u	NOUN
ejpam-4722	302	1	′	′	ADP
ejpam-4722	302	2	j+1	j+1	NUM
ejpam-4722	302	3	)	)	PUNCT
ejpam-4722	302	4	=	=	SYM
ejpam-4722	303	1	yj	yj	NOUN
ejpam-4722	303	2	+	+	NOUN
ejpam-4722	303	3	yj+1	yj+1	NUM
ejpam-4722	304	1	+	+	NUM
ejpam-4722	304	2	4	4	NUM
ejpam-4722	304	3	when	when	SCONJ
ejpam-4722	304	4	1	1	NUM
ejpam-4722	304	5	≤	≤	NUM
ejpam-4722	304	6	j	j	PROPN
ejpam-4722	304	7	≤	≤	PROPN
ejpam-4722	304	8	p−	p−	NOUN
ejpam-4722	304	9	2	2	NUM
ejpam-4722	304	10	,	,	PUNCT
ejpam-4722	304	11	dω(u	dω(u	X
ejpam-4722	304	12	′	′	NOUN
ejpam-4722	304	13	0	0	NUM
ejpam-4722	304	14	)	)	PUNCT
ejpam-4722	305	1	+	+	CCONJ
ejpam-4722	305	2	dω(u	dω(u	X
ejpam-4722	305	3	′	′	NUM
ejpam-4722	305	4	1	1	NUM
ejpam-4722	305	5	)	)	PUNCT
ejpam-4722	305	6	=	=	NOUN
ejpam-4722	305	7	dω(u	dω(u	NOUN
ejpam-4722	305	8	′	′	NUM
ejpam-4722	305	9	)	)	PUNCT
ejpam-4722	306	1	+	+	CCONJ
ejpam-4722	306	2	y1	y1	NOUN
ejpam-4722	306	3	+	+	NOUN
ejpam-4722	306	4	2	2	NUM
ejpam-4722	306	5	when	when	SCONJ
ejpam-4722	306	6	j	j	PROPN
ejpam-4722	306	7	=	=	SYM
ejpam-4722	306	8	0	0	PROPN
ejpam-4722	306	9	,	,	PUNCT
ejpam-4722	306	10	dω(u	dω(u	PUNCT
ejpam-4722	306	11	′	′	NUM
ejpam-4722	306	12	p−1	p−1	PROPN
ejpam-4722	306	13	)	)	PUNCT
ejpam-4722	307	1	+	+	CCONJ
ejpam-4722	307	2	dω(u	dω(u	PUNCT
ejpam-4722	307	3	′	′	NUM
ejpam-4722	307	4	0	0	NUM
ejpam-4722	307	5	)	)	PUNCT
ejpam-4722	307	6	=	=	NOUN
ejpam-4722	307	7	dω(u	dω(u	NOUN
ejpam-4722	307	8	′	′	NUM
ejpam-4722	307	9	)	)	PUNCT
ejpam-4722	308	1	+	+	CCONJ
ejpam-4722	309	1	yp−1	yp−1	ADJ
ejpam-4722	309	2	+	+	CCONJ
ejpam-4722	309	3	2	2	NUM
ejpam-4722	309	4	when	when	SCONJ
ejpam-4722	309	5	j	j	PROPN
ejpam-4722	309	6	=	=	NOUN
ejpam-4722	309	7	p−	p−	ADP
ejpam-4722	309	8	1	1	NUM
ejpam-4722	309	9	.	.	PUNCT
ejpam-4722	310	1	since	since	SCONJ
ejpam-4722	310	2	p	p	NOUN
ejpam-4722	310	3	is	be	AUX
ejpam-4722	310	4	even	even	ADV
ejpam-4722	310	5	n	n	PRON
ejpam-4722	310	6	u	u	NOUN
ejpam-4722	310	7	′	′	NUM
ejpam-4722	310	8	j	j	PROPN
ejpam-4722	310	9	(	(	PUNCT
ejpam-4722	310	10	e|ω)−	e|ω)−	PROPN
ejpam-4722	310	11	n	n	CCONJ
ejpam-4722	310	12	u	u	NOUN
ejpam-4722	310	13	′	′	NOUN
ejpam-4722	310	14	j+1	j+1	ADV
ejpam-4722	310	15	(	(	PUNCT
ejpam-4722	310	16	e|ω	e|ω	NOUN
ejpam-4722	310	17	)	)	PUNCT
ejpam-4722	311	1	=	=	SYM
ejpam-4722	311	2	n−	n−	NOUN
ejpam-4722	311	3	d.	d.	NOUN
ejpam-4722	311	4	=	=	PROPN
ejpam-4722	311	5	p−1∑	p−1∑	PROPN
ejpam-4722	311	6	j=0	j=0	PROPN
ejpam-4722	311	7	dω(u	dω(u	PUNCT
ejpam-4722	311	8	′	′	NUM
ejpam-4722	311	9	j	j	NOUN
ejpam-4722	311	10	)	)	PUNCT
ejpam-4722	312	1	+	+	CCONJ
ejpam-4722	312	2	dω(u	dω(u	NUM
ejpam-4722	312	3	′	′	NUM
ejpam-4722	312	4	j+1)|nu	j+1)|nu	X
ejpam-4722	313	1	′	′	NUM
ejpam-4722	313	2	j	j	PROPN
ejpam-4722	313	3	(	(	PUNCT
ejpam-4722	313	4	e|ω)−	e|ω)−	PROPN
ejpam-4722	313	5	n	n	CCONJ
ejpam-4722	313	6	u	u	NOUN
ejpam-4722	313	7	′	′	NOUN
ejpam-4722	313	8	j+1	j+1	X
ejpam-4722	313	9	(	(	PUNCT
ejpam-4722	313	10	e|ω)|	e|ω)|	PROPN
ejpam-4722	313	11	,	,	PUNCT
ejpam-4722	313	12	=	=	SYM
ejpam-4722	313	13	2(n−	2(n−	NUM
ejpam-4722	313	14	d)(dω(u	d)(dω(u	NOUN
ejpam-4722	313	15	′	′	NUM
ejpam-4722	313	16	)	)	PUNCT
ejpam-4722	314	1	+	+	CCONJ
ejpam-4722	314	2	y	y	PROPN
ejpam-4722	314	3	+	+	CCONJ
ejpam-4722	314	4	2(p−	2(p−	NUM
ejpam-4722	314	5	1	1	NUM
ejpam-4722	314	6	)	)	PUNCT
ejpam-4722	314	7	)	)	PUNCT
ejpam-4722	314	8	,	,	PUNCT
ejpam-4722	314	9	similarly	similarly	ADV
ejpam-4722	314	10	in	in	ADP
ejpam-4722	314	11	ω	ω	NUM
ejpam-4722	314	12	′	′	NUM
ejpam-4722	314	13	,	,	PUNCT
ejpam-4722	314	14	after	after	ADP
ejpam-4722	314	15	simplification	simplification	NOUN
ejpam-4722	314	16	we	we	PRON
ejpam-4722	314	17	have	have	VERB
ejpam-4722	314	18	,	,	PUNCT
ejpam-4722	314	19	=	=	SYM
ejpam-4722	314	20	p−1∑	p−1∑	X
ejpam-4722	314	21	j=0	j=0	PROPN
ejpam-4722	314	22	dω′	dω′	PROPN
ejpam-4722	314	23	(	(	PUNCT
ejpam-4722	314	24	u	u	NOUN
ejpam-4722	314	25	′	′	PROPN
ejpam-4722	314	26	j	j	NOUN
ejpam-4722	314	27	)	)	PUNCT
ejpam-4722	315	1	+	+	CCONJ
ejpam-4722	315	2	dω′	dω′	X
ejpam-4722	315	3	(	(	PUNCT
ejpam-4722	315	4	u	u	NOUN
ejpam-4722	315	5	′	′	NOUN
ejpam-4722	315	6	j+1)|nu	j+1)|nu	X
ejpam-4722	316	1	′	′	NUM
ejpam-4722	316	2	j	j	NOUN
ejpam-4722	316	3	(	(	PUNCT
ejpam-4722	316	4	e|ω′	e|ω′	PROPN
ejpam-4722	316	5	)	)	PUNCT
ejpam-4722	316	6	−	−	PROPN
ejpam-4722	316	7	n	n	CCONJ
ejpam-4722	316	8	u	u	NOUN
ejpam-4722	316	9	′	′	NOUN
ejpam-4722	316	10	j+1	j+1	PROPN
ejpam-4722	316	11	(	(	PUNCT
ejpam-4722	316	12	e|ω′	e|ω′	PROPN
ejpam-4722	316	13	)	)	PUNCT
ejpam-4722	316	14	|	|	ADV
ejpam-4722	316	15	,	,	PUNCT
ejpam-4722	316	16	=	=	PROPN
ejpam-4722	316	17	2(n−	2(n−	NUM
ejpam-4722	316	18	d)(dω′	d)(dω′	PROPN
ejpam-4722	316	19	(	(	PUNCT
ejpam-4722	316	20	u	u	NOUN
ejpam-4722	316	21	′	′	NOUN
ejpam-4722	316	22	)	)	PUNCT
ejpam-4722	317	1	+	+	CCONJ
ejpam-4722	318	1	2(p−	2(p−	NUM
ejpam-4722	318	2	1	1	NUM
ejpam-4722	318	3	)	)	PUNCT
ejpam-4722	318	4	)	)	PUNCT
ejpam-4722	319	1	=	=	PUNCT
ejpam-4722	320	1	2(n−	2(n−	NUM
ejpam-4722	320	2	d)(dω′	d)(dω′	PROPN
ejpam-4722	320	3	(	(	PUNCT
ejpam-4722	320	4	u	u	NOUN
ejpam-4722	320	5	′	′	NOUN
ejpam-4722	320	6	)	)	PUNCT
ejpam-4722	321	1	+	+	CCONJ
ejpam-4722	321	2	y	y	PROPN
ejpam-4722	321	3	+	+	CCONJ
ejpam-4722	321	4	2(p−	2(p−	NUM
ejpam-4722	321	5	1	1	NUM
ejpam-4722	321	6	)	)	PUNCT
ejpam-4722	321	7	)	)	PUNCT
ejpam-4722	321	8	,	,	PUNCT
ejpam-4722	321	9	by	by	ADP
ejpam-4722	321	10	using	use	VERB
ejpam-4722	321	11	the	the	DET
ejpam-4722	321	12	above	above	ADJ
ejpam-4722	321	13	calculations	calculation	NOUN
ejpam-4722	321	14	,	,	PUNCT
ejpam-4722	321	15	we	we	PRON
ejpam-4722	321	16	have	have	VERB
ejpam-4722	321	17	straightforward	straightforward	ADJ
ejpam-4722	321	18	result	result	NOUN
ejpam-4722	321	19	mowe	mowe	NOUN
ejpam-4722	321	20	(	(	PUNCT
ejpam-4722	321	21	ω)−mowe	ω)−mowe	NOUN
ejpam-4722	321	22	(	(	PUNCT
ejpam-4722	321	23	ω	ω	NOUN
ejpam-4722	321	24	′	′	NUM
ejpam-4722	321	25	)	)	PUNCT
ejpam-4722	322	1	=	=	PUNCT
ejpam-4722	322	2	p−1∑	p−1∑	NOUN
ejpam-4722	322	3	j=0	j=0	VERB
ejpam-4722	322	4	dω(u	dω(u	PUNCT
ejpam-4722	322	5	′	′	NUM
ejpam-4722	322	6	j	j	NOUN
ejpam-4722	322	7	)	)	PUNCT
ejpam-4722	323	1	+	+	CCONJ
ejpam-4722	323	2	dω(u	dω(u	NUM
ejpam-4722	323	3	′	′	NUM
ejpam-4722	323	4	j+1)|nu	j+1)|nu	X
ejpam-4722	324	1	′	′	NUM
ejpam-4722	324	2	j	j	PROPN
ejpam-4722	324	3	(	(	PUNCT
ejpam-4722	324	4	e|ω)−	e|ω)−	PROPN
ejpam-4722	324	5	n	n	CCONJ
ejpam-4722	324	6	u	u	NOUN
ejpam-4722	324	7	′	′	NOUN
ejpam-4722	324	8	j+1	j+1	X
ejpam-4722	324	9	(	(	PUNCT
ejpam-4722	324	10	e|ω)|	e|ω)|	PROPN
ejpam-4722	324	11	,	,	PUNCT
ejpam-4722	324	12	−	−	PROPN
ejpam-4722	324	13	p−1∑	p−1∑	PROPN
ejpam-4722	324	14	j=0	j=0	PROPN
ejpam-4722	324	15	dω′	dω′	PROPN
ejpam-4722	324	16	(	(	PUNCT
ejpam-4722	324	17	u	u	NOUN
ejpam-4722	324	18	′	′	PROPN
ejpam-4722	324	19	j	j	NOUN
ejpam-4722	324	20	)	)	PUNCT
ejpam-4722	325	1	+	+	CCONJ
ejpam-4722	325	2	dω′	dω′	X
ejpam-4722	325	3	(	(	PUNCT
ejpam-4722	325	4	u	u	NOUN
ejpam-4722	325	5	′	′	NOUN
ejpam-4722	325	6	j+1)|nu	j+1)|nu	X
ejpam-4722	326	1	′	′	NUM
ejpam-4722	326	2	j	j	NOUN
ejpam-4722	326	3	(	(	PUNCT
ejpam-4722	326	4	e|ω′	e|ω′	PROPN
ejpam-4722	326	5	)	)	PUNCT
ejpam-4722	326	6	−	−	PROPN
ejpam-4722	326	7	n	n	CCONJ
ejpam-4722	326	8	u	u	NOUN
ejpam-4722	326	9	′	′	NOUN
ejpam-4722	326	10	j+1	j+1	PROPN
ejpam-4722	326	11	(	(	PUNCT
ejpam-4722	326	12	e|ω′	e|ω′	PROPN
ejpam-4722	326	13	)	)	PUNCT
ejpam-4722	326	14	|	|	ADV
ejpam-4722	326	15	,	,	PUNCT
ejpam-4722	326	16	<	<	X
ejpam-4722	326	17	0	0	NUM
ejpam-4722	326	18	,	,	PUNCT
ejpam-4722	326	19	the	the	DET
ejpam-4722	326	20	result	result	NOUN
ejpam-4722	326	21	mowe	mowe	NOUN
ejpam-4722	326	22	(	(	PUNCT
ejpam-4722	326	23	ω	ω	NOUN
ejpam-4722	326	24	)	)	PUNCT
ejpam-4722	326	25	<	<	X
ejpam-4722	326	26	mowe	mowe	NOUN
ejpam-4722	326	27	(	(	PUNCT
ejpam-4722	326	28	ω	ω	NOUN
ejpam-4722	326	29	′	′	NUM
ejpam-4722	326	30	)	)	PUNCT
ejpam-4722	326	31	is	be	AUX
ejpam-4722	326	32	obvious	obvious	ADJ
ejpam-4722	326	33	similar	similar	ADJ
ejpam-4722	326	34	for	for	ADP
ejpam-4722	326	35	p	p	PROPN
ejpam-4722	326	36	is	be	AUX
ejpam-4722	326	37	odd	odd	ADJ
ejpam-4722	326	38	.	.	PUNCT
ejpam-4722	327	1	the	the	DET
ejpam-4722	327	2	proof	proof	NOUN
ejpam-4722	327	3	is	be	AUX
ejpam-4722	327	4	complete	complete	ADJ
ejpam-4722	327	5	.	.	PUNCT
ejpam-4722	328	1	transformation	transformation	NOUN
ejpam-4722	328	2	3	3	X
ejpam-4722	328	3	.	.	PUNCT
ejpam-4722	329	1	let	let	VERB
ejpam-4722	329	2	k	k	PRON
ejpam-4722	329	3	be	be	AUX
ejpam-4722	329	4	a	a	DET
ejpam-4722	329	5	graph	graph	NOUN
ejpam-4722	329	6	with	with	ADP
ejpam-4722	329	7	u	u	PROPN
ejpam-4722	329	8	∈	∈	PROPN
ejpam-4722	329	9	v	v	ADP
ejpam-4722	329	10	(	(	PUNCT
ejpam-4722	329	11	k	k	NOUN
ejpam-4722	329	12	)	)	PUNCT
ejpam-4722	329	13	such	such	ADJ
ejpam-4722	329	14	that	that	PRON
ejpam-4722	329	15	dk(u	dk(u	NUM
ejpam-4722	329	16	)	)	PUNCT
ejpam-4722	329	17	≥	≥	NOUN
ejpam-4722	329	18	2	2	NUM
ejpam-4722	329	19	,	,	PUNCT
ejpam-4722	329	20	and	and	CCONJ
ejpam-4722	329	21	cp	cp	INTJ
ejpam-4722	329	22	be	be	AUX
ejpam-4722	329	23	a	a	DET
ejpam-4722	329	24	cycle	cycle	NOUN
ejpam-4722	329	25	of	of	ADP
ejpam-4722	329	26	order	order	NOUN
ejpam-4722	329	27	p	p	NOUN
ejpam-4722	329	28	such	such	ADJ
ejpam-4722	329	29	that	that	SCONJ
ejpam-4722	329	30	p	p	NOUN
ejpam-4722	329	31	≥	≥	NUM
ejpam-4722	329	32	4	4	NUM
ejpam-4722	329	33	.	.	PUNCT
ejpam-4722	330	1	let	let	VERB
ejpam-4722	330	2	ω	ω	NUM
ejpam-4722	330	3	be	be	AUX
ejpam-4722	330	4	a	a	DET
ejpam-4722	330	5	generated	generate	VERB
ejpam-4722	330	6	graph	graph	NOUN
ejpam-4722	330	7	from	from	ADP
ejpam-4722	330	8	k(u)cp	k(u)cp	NOUN
ejpam-4722	330	9	by	by	ADP
ejpam-4722	330	10	combining	combine	VERB
ejpam-4722	330	11	a	a	DET
ejpam-4722	330	12	vertices	vertex	NOUN
ejpam-4722	330	13	of	of	ADP
ejpam-4722	330	14	cp	cp	NUM
ejpam-4722	330	15	with	with	ADP
ejpam-4722	330	16	u.	u.	PROPN
ejpam-4722	330	17	next	next	ADV
ejpam-4722	330	18	,	,	PUNCT
ejpam-4722	330	19	let	let	VERB
ejpam-4722	330	20	ω	ω	NUM
ejpam-4722	330	21	′	′	NUM
ejpam-4722	330	22	be	be	AUX
ejpam-4722	330	23	the	the	DET
ejpam-4722	330	24	graph	graph	NOUN
ejpam-4722	330	25	obtained	obtain	VERB
ejpam-4722	330	26	from	from	ADP
ejpam-4722	330	27	ω	ω	NUM
ejpam-4722	330	28	by	by	ADP
ejpam-4722	330	29	exchanging	exchange	VERB
ejpam-4722	330	30	cp	cp	PROPN
ejpam-4722	330	31	for	for	ADP
ejpam-4722	330	32	c3	c3	PROPN
ejpam-4722	330	33	and	and	CCONJ
ejpam-4722	330	34	p−	p−	NOUN
ejpam-4722	330	35	3	3	NUM
ejpam-4722	330	36	pendent	pendent	NOUN
ejpam-4722	330	37	edges	edge	NOUN
ejpam-4722	330	38	.	.	PUNCT
ejpam-4722	331	1	note	note	VERB
ejpam-4722	331	2	that	that	SCONJ
ejpam-4722	331	3	,	,	PUNCT
ejpam-4722	331	4	|ω|	|ω|	ADP
ejpam-4722	331	5	=	=	SYM
ejpam-4722	331	6	|ω′	|ω′	PROPN
ejpam-4722	331	7	|	|	ADV
ejpam-4722	331	8	.	.	PUNCT
ejpam-4722	332	1	lemma	lemma	PROPN
ejpam-4722	332	2	7	7	X
ejpam-4722	332	3	.	.	PUNCT
ejpam-4722	333	1	let	let	VERB
ejpam-4722	333	2	ω	ω	NOUN
ejpam-4722	333	3	and	and	CCONJ
ejpam-4722	333	4	ω	ω	NUM
ejpam-4722	333	5	′	′	NUM
ejpam-4722	333	6	be	be	VERB
ejpam-4722	333	7	two	two	NUM
ejpam-4722	333	8	connected	connected	ADJ
ejpam-4722	333	9	graphs	graph	NOUN
ejpam-4722	333	10	explained	explain	VERB
ejpam-4722	333	11	in	in	ADP
ejpam-4722	333	12	transformation	transformation	NOUN
ejpam-4722	333	13	3	3	NUM
ejpam-4722	333	14	.	.	PUNCT
ejpam-4722	334	1	then	then	ADV
ejpam-4722	334	2	mowe	mowe	VERB
ejpam-4722	334	3	(	(	PUNCT
ejpam-4722	334	4	ω	ω	NOUN
ejpam-4722	334	5	)	)	PUNCT
ejpam-4722	334	6	<	<	X
ejpam-4722	334	7	mowe	mowe	NOUN
ejpam-4722	334	8	(	(	PUNCT
ejpam-4722	334	9	ω	ω	NOUN
ejpam-4722	334	10	′	′	NUM
ejpam-4722	334	11	)	)	PUNCT
ejpam-4722	334	12	.	.	PUNCT
ejpam-4722	335	1	f.	f.	PROPN
ejpam-4722	335	2	asmat	asmat	PROPN
ejpam-4722	335	3	et	et	PROPN
ejpam-4722	335	4	al	al	PROPN
ejpam-4722	335	5	.	.	PUNCT
ejpam-4722	335	6	/	/	SYM
ejpam-4722	335	7	eur	eur	PROPN
ejpam-4722	335	8	.	.	PUNCT
ejpam-4722	336	1	j.	j.	PROPN
ejpam-4722	336	2	pure	pure	PROPN
ejpam-4722	336	3	appl	appl	PROPN
ejpam-4722	336	4	.	.	PROPN
ejpam-4722	336	5	math	math	PROPN
ejpam-4722	336	6	,	,	PUNCT
ejpam-4722	336	7	16	16	NUM
ejpam-4722	336	8	(	(	PUNCT
ejpam-4722	336	9	3	3	NUM
ejpam-4722	336	10	)	)	PUNCT
ejpam-4722	336	11	(	(	PUNCT
ejpam-4722	336	12	2023	2023	NUM
ejpam-4722	336	13	)	)	PUNCT
ejpam-4722	336	14	,	,	PUNCT
ejpam-4722	336	15	1794	1794	NUM
ejpam-4722	336	16	-	-	SYM
ejpam-4722	336	17	1808	1808	NUM
ejpam-4722	336	18	1805	1805	NUM
ejpam-4722	336	19	proof	proof	NOUN
ejpam-4722	336	20	.	.	PUNCT
ejpam-4722	336	21	suppose	suppose	VERB
ejpam-4722	336	22	|ω|	|ω|	NOUN
ejpam-4722	336	23	=	=	SYM
ejpam-4722	336	24	|ω′	|ω′	PROPN
ejpam-4722	336	25	|	|	ADV
ejpam-4722	336	26	=	=	SYM
ejpam-4722	336	27	n	n	NOUN
ejpam-4722	336	28	without	without	ADP
ejpam-4722	336	29	loss	loss	NOUN
ejpam-4722	336	30	of	of	ADP
ejpam-4722	336	31	generality	generality	NOUN
ejpam-4722	336	32	.	.	PUNCT
ejpam-4722	337	1	note	note	VERB
ejpam-4722	337	2	that	that	SCONJ
ejpam-4722	337	3	dω(u	dω(u	PUNCT
ejpam-4722	337	4	)	)	PUNCT
ejpam-4722	337	5	=	=	PUNCT
ejpam-4722	337	6	dω′	dω′	X
ejpam-4722	337	7	(	(	PUNCT
ejpam-4722	337	8	u)−	u)−	PROPN
ejpam-4722	337	9	(	(	PUNCT
ejpam-4722	337	10	p−	p−	NOUN
ejpam-4722	337	11	3	3	NUM
ejpam-4722	337	12	)	)	PUNCT
ejpam-4722	337	13	.	.	PUNCT
ejpam-4722	338	1	for	for	ADP
ejpam-4722	338	2	any	any	DET
ejpam-4722	338	3	edge	edge	NOUN
ejpam-4722	338	4	e	e	NOUN
ejpam-4722	338	5	=	=	SYM
ejpam-4722	338	6	uu	uu	INTJ
ejpam-4722	338	7	′	′	NUM
ejpam-4722	338	8	∈	∈	PROPN
ejpam-4722	338	9	e(k	e(k	NOUN
ejpam-4722	338	10	)	)	PUNCT
ejpam-4722	338	11	,	,	PUNCT
ejpam-4722	338	12	dω(u	dω(u	PUNCT
ejpam-4722	338	13	)	)	PUNCT
ejpam-4722	338	14	+	+	CCONJ
ejpam-4722	338	15	dω(u	dω(u	NOUN
ejpam-4722	338	16	′	′	NUM
ejpam-4722	338	17	)	)	PUNCT
ejpam-4722	338	18	<	<	X
ejpam-4722	338	19	dω′	dω′	X
ejpam-4722	338	20	(	(	PUNCT
ejpam-4722	338	21	u	u	NOUN
ejpam-4722	338	22	)	)	PUNCT
ejpam-4722	338	23	+	+	CCONJ
ejpam-4722	338	24	dω′	dω′	X
ejpam-4722	338	25	(	(	PUNCT
ejpam-4722	338	26	u	u	NOUN
ejpam-4722	338	27	′	′	NUM
ejpam-4722	338	28	)	)	PUNCT
ejpam-4722	338	29	,	,	PUNCT
ejpam-4722	338	30	and	and	CCONJ
ejpam-4722	338	31	mu(e|ω)−	mu(e|ω)−	NOUN
ejpam-4722	338	32	mu′	mu′	NOUN
ejpam-4722	338	33	(	(	PUNCT
ejpam-4722	338	34	e|ω	e|ω	ADV
ejpam-4722	338	35	)	)	PUNCT
ejpam-4722	338	36	=	=	PUNCT
ejpam-4722	338	37	mu(e|ω	mu(e|ω	NUM
ejpam-4722	338	38	′	′	NUM
ejpam-4722	338	39	)	)	PUNCT
ejpam-4722	338	40	−mu′	−mu′	PROPN
ejpam-4722	338	41	(	(	PUNCT
ejpam-4722	338	42	e|ω′	e|ω′	PROPN
ejpam-4722	338	43	)	)	PUNCT
ejpam-4722	338	44	.	.	PUNCT
ejpam-4722	339	1	therefore	therefore	ADV
ejpam-4722	339	2	,	,	PUNCT
ejpam-4722	339	3	=	=	PUNCT
ejpam-4722	339	4	∑	∑	PUNCT
ejpam-4722	339	5	e	e	NOUN
ejpam-4722	339	6	=	=	NOUN
ejpam-4722	339	7	uu′∈e(k	uu′∈e(k	ADV
ejpam-4722	339	8	)	)	PUNCT
ejpam-4722	339	9	dω(u	dω(u	PUNCT
ejpam-4722	339	10	)	)	PUNCT
ejpam-4722	340	1	+	+	CCONJ
ejpam-4722	340	2	dω(u	dω(u	NUM
ejpam-4722	340	3	′	′	NUM
ejpam-4722	340	4	)	)	PUNCT
ejpam-4722	340	5	|mu(e|ω)−mu′	|mu(e|ω)−mu′	PROPN
ejpam-4722	340	6	(	(	PUNCT
ejpam-4722	340	7	e|ω)|	e|ω)|	PROPN
ejpam-4722	340	8	,	,	PUNCT
ejpam-4722	340	9	−	−	X
ejpam-4722	340	10	∑	∑	PUNCT
ejpam-4722	340	11	e	e	NOUN
ejpam-4722	340	12	=	=	NOUN
ejpam-4722	340	13	uu′∈e(k	uu′∈e(k	ADV
ejpam-4722	340	14	)	)	PUNCT
ejpam-4722	340	15	dω′	dω′	X
ejpam-4722	340	16	(	(	PUNCT
ejpam-4722	340	17	u	u	NOUN
ejpam-4722	340	18	)	)	PUNCT
ejpam-4722	341	1	+	+	CCONJ
ejpam-4722	341	2	dω′	dω′	X
ejpam-4722	341	3	(	(	PUNCT
ejpam-4722	341	4	u	u	NOUN
ejpam-4722	341	5	′	′	NOUN
ejpam-4722	341	6	)	)	PUNCT
ejpam-4722	341	7	|mu(e|ω	|mu(e|ω	NOUN
ejpam-4722	341	8	′	′	NOUN
ejpam-4722	341	9	)	)	PUNCT
ejpam-4722	341	10	−mu′	−mu′	PROPN
ejpam-4722	341	11	(	(	PUNCT
ejpam-4722	341	12	e|ω′	e|ω′	PROPN
ejpam-4722	341	13	)	)	PUNCT
ejpam-4722	341	14	|	|	ADV
ejpam-4722	341	15	,	,	PUNCT
ejpam-4722	341	16	<	<	X
ejpam-4722	341	17	0	0	PUNCT
ejpam-4722	341	18	when	when	SCONJ
ejpam-4722	341	19	p	p	NOUN
ejpam-4722	341	20	is	be	AUX
ejpam-4722	341	21	odd	odd	ADJ
ejpam-4722	341	22	,	,	PUNCT
ejpam-4722	341	23	for	for	ADP
ejpam-4722	341	24	the	the	DET
ejpam-4722	341	25	edges	edge	NOUN
ejpam-4722	341	26	in	in	ADP
ejpam-4722	341	27	cp	cp	NUM
ejpam-4722	341	28	of	of	ADP
ejpam-4722	341	29	ω	ω	PROPN
ejpam-4722	341	30	=	=	PROPN
ejpam-4722	341	31	p−1∑	p−1∑	PROPN
ejpam-4722	341	32	j=0	j=0	PROPN
ejpam-4722	341	33	dω(uj	dω(uj	PROPN
ejpam-4722	341	34	)	)	PUNCT
ejpam-4722	342	1	+	+	CCONJ
ejpam-4722	342	2	dω(uj+1)|muj	dω(uj+1)|muj	ADJ
ejpam-4722	342	3	(	(	PUNCT
ejpam-4722	342	4	e|ω)−muj+1(e|ω	e|ω)−muj+1(e|ω	ADJ
ejpam-4722	342	5	)	)	PUNCT
ejpam-4722	342	6	,	,	PUNCT
ejpam-4722	342	7	=	=	PUNCT
ejpam-4722	342	8	4(p−	4(p−	NUM
ejpam-4722	342	9	1	1	NUM
ejpam-4722	342	10	)	)	PUNCT
ejpam-4722	342	11	+	+	CCONJ
ejpam-4722	342	12	(	(	PUNCT
ejpam-4722	342	13	n−	n−	NOUN
ejpam-4722	342	14	1)[2(dω(u	1)[2(dω(u	ADJ
ejpam-4722	342	15	)	)	PUNCT
ejpam-4722	342	16	+	+	CCONJ
ejpam-4722	342	17	2	2	X
ejpam-4722	342	18	)	)	PUNCT
ejpam-4722	342	19	+	+	CCONJ
ejpam-4722	342	20	4(p−	4(p−	NUM
ejpam-4722	342	21	3	3	NUM
ejpam-4722	342	22	)	)	PUNCT
ejpam-4722	342	23	]	]	PUNCT
ejpam-4722	342	24	,	,	PUNCT
ejpam-4722	342	25	when	when	SCONJ
ejpam-4722	342	26	p	p	NOUN
ejpam-4722	342	27	is	be	AUX
ejpam-4722	342	28	even	even	ADV
ejpam-4722	342	29	,	,	PUNCT
ejpam-4722	342	30	for	for	ADP
ejpam-4722	342	31	the	the	DET
ejpam-4722	342	32	edges	edge	NOUN
ejpam-4722	342	33	in	in	ADP
ejpam-4722	342	34	cp	cp	NUM
ejpam-4722	342	35	of	of	ADP
ejpam-4722	342	36	ω	ω	PROPN
ejpam-4722	342	37	=	=	PROPN
ejpam-4722	342	38	p−1∑	p−1∑	PROPN
ejpam-4722	342	39	j=0	j=0	PROPN
ejpam-4722	342	40	dω(uj	dω(uj	PROPN
ejpam-4722	342	41	)	)	PUNCT
ejpam-4722	343	1	+	+	CCONJ
ejpam-4722	343	2	dω(uj+1)|muj	dω(uj+1)|muj	ADJ
ejpam-4722	343	3	(	(	PUNCT
ejpam-4722	343	4	e|ω)−muj+1(e|ω)|	e|ω)−muj+1(e|ω)|	NUM
ejpam-4722	343	5	,	,	PUNCT
ejpam-4722	343	6	=	=	SYM
ejpam-4722	343	7	n[2(dω(u	n[2(dω(u	NUM
ejpam-4722	343	8	)	)	PUNCT
ejpam-4722	343	9	+	+	CCONJ
ejpam-4722	343	10	2	2	X
ejpam-4722	343	11	)	)	PUNCT
ejpam-4722	343	12	+	+	CCONJ
ejpam-4722	343	13	4(p−	4(p−	NUM
ejpam-4722	343	14	2	2	NUM
ejpam-4722	343	15	)	)	PUNCT
ejpam-4722	343	16	]	]	PUNCT
ejpam-4722	343	17	,	,	PUNCT
ejpam-4722	343	18	for	for	ADP
ejpam-4722	343	19	any	any	DET
ejpam-4722	343	20	pendant	pendant	ADJ
ejpam-4722	343	21	edge	edge	NOUN
ejpam-4722	343	22	uu	uu	X
ejpam-4722	343	23	′	′	NUM
ejpam-4722	343	24	rooted	root	VERB
ejpam-4722	343	25	on	on	ADP
ejpam-4722	343	26	u	u	PROPN
ejpam-4722	343	27	in	in	ADP
ejpam-4722	343	28	ω	ω	NUM
ejpam-4722	343	29	′	′	NUM
ejpam-4722	343	30	,	,	PUNCT
ejpam-4722	343	31	dω′	dω′	X
ejpam-4722	343	32	(	(	PUNCT
ejpam-4722	343	33	u	u	NOUN
ejpam-4722	343	34	)	)	PUNCT
ejpam-4722	344	1	+	+	CCONJ
ejpam-4722	344	2	dω′	dω′	X
ejpam-4722	344	3	(	(	PUNCT
ejpam-4722	344	4	u	u	NOUN
ejpam-4722	344	5	′	′	NOUN
ejpam-4722	344	6	)	)	PUNCT
ejpam-4722	345	1	=	=	PUNCT
ejpam-4722	345	2	dω′	dω′	X
ejpam-4722	345	3	(	(	PUNCT
ejpam-4722	345	4	u	u	NOUN
ejpam-4722	345	5	)	)	PUNCT
ejpam-4722	345	6	+	+	CCONJ
ejpam-4722	346	1	p	p	PRON
ejpam-4722	346	2	−	−	PROPN
ejpam-4722	346	3	2	2	NUM
ejpam-4722	346	4	,	,	PUNCT
ejpam-4722	346	5	and	and	CCONJ
ejpam-4722	346	6	mu(e|ω	mu(e|ω	NUM
ejpam-4722	346	7	′	′	NUM
ejpam-4722	346	8	)	)	PUNCT
ejpam-4722	346	9	−mu′	−mu′	PROPN
ejpam-4722	346	10	(	(	PUNCT
ejpam-4722	346	11	e|ω′	e|ω′	PROPN
ejpam-4722	346	12	)	)	PUNCT
ejpam-4722	346	13	=	=	PUNCT
ejpam-4722	346	14	n−	n−	NOUN
ejpam-4722	346	15	d	d	NOUN
ejpam-4722	346	16	and	and	CCONJ
ejpam-4722	346	17	dω′	dω′	X
ejpam-4722	346	18	=	=	SYM
ejpam-4722	347	1	1	1	X
ejpam-4722	347	2	.	.	PUNCT
ejpam-4722	347	3	therefore	therefore	ADV
ejpam-4722	347	4	,	,	PUNCT
ejpam-4722	347	5	=	=	PUNCT
ejpam-4722	347	6	∑	∑	PUNCT
ejpam-4722	347	7	e	e	X
ejpam-4722	347	8	=	=	ADJ
ejpam-4722	347	9	uu′∈e(ω′	uu′∈e(ω′	ADJ
ejpam-4722	347	10	)	)	PUNCT
ejpam-4722	347	11	\e(k	\e(k	NOUN
ejpam-4722	347	12	)	)	PUNCT
ejpam-4722	347	13	dω′	dω′	X
ejpam-4722	347	14	(	(	PUNCT
ejpam-4722	347	15	u	u	NOUN
ejpam-4722	347	16	)	)	PUNCT
ejpam-4722	347	17	+	+	CCONJ
ejpam-4722	347	18	dω′	dω′	X
ejpam-4722	347	19	(	(	PUNCT
ejpam-4722	347	20	u	u	NOUN
ejpam-4722	347	21	′	′	NOUN
ejpam-4722	347	22	)	)	PUNCT
ejpam-4722	347	23	|nu(e|ω	|nu(e|ω	ADJ
ejpam-4722	347	24	′	′	NOUN
ejpam-4722	347	25	)	)	PUNCT
ejpam-4722	347	26	−	−	NOUN
ejpam-4722	348	1	nu′	nu′	ADV
ejpam-4722	348	2	(	(	PUNCT
ejpam-4722	348	3	e|ω′	e|ω′	PROPN
ejpam-4722	348	4	)	)	PUNCT
ejpam-4722	348	5	|	|	ADV
ejpam-4722	348	6	,	,	PUNCT
ejpam-4722	348	7	=	=	PRON
ejpam-4722	348	8	(	(	PUNCT
ejpam-4722	348	9	p−	p−	NOUN
ejpam-4722	348	10	3)n[(dω(u	3)n[(dω(u	NOUN
ejpam-4722	348	11	)	)	PUNCT
ejpam-4722	348	12	)	)	PUNCT
ejpam-4722	349	1	+	+	CCONJ
ejpam-4722	349	2	(	(	PUNCT
ejpam-4722	349	3	p−	p−	NOUN
ejpam-4722	349	4	2	2	NUM
ejpam-4722	349	5	)	)	PUNCT
ejpam-4722	349	6	]	]	PUNCT
ejpam-4722	349	7	,	,	PUNCT
ejpam-4722	349	8	for	for	ADP
ejpam-4722	349	9	the	the	DET
ejpam-4722	349	10	edges	edge	NOUN
ejpam-4722	349	11	in	in	ADP
ejpam-4722	349	12	c3	c3	PROPN
ejpam-4722	349	13	of	of	ADP
ejpam-4722	349	14	ω	ω	PROPN
ejpam-4722	349	15	′	′	NUM
ejpam-4722	349	16	=	=	PUNCT
ejpam-4722	349	17	2∑	2∑	NUM
ejpam-4722	349	18	j=0	j=0	X
ejpam-4722	349	19	dω′	dω′	X
ejpam-4722	349	20	(	(	PUNCT
ejpam-4722	349	21	uj	uj	PROPN
ejpam-4722	349	22	)	)	PUNCT
ejpam-4722	349	23	+	+	CCONJ
ejpam-4722	349	24	deω′	deω′	NUM
ejpam-4722	349	25	(	(	PUNCT
ejpam-4722	349	26	uj+1)|muj	uj+1)|muj	PROPN
ejpam-4722	349	27	(	(	PUNCT
ejpam-4722	349	28	e|ω	e|ω	ADV
ejpam-4722	349	29	′	′	NUM
ejpam-4722	349	30	)	)	PUNCT
ejpam-4722	349	31	−muj+1(e|ω	−muj+1(e|ω	ADJ
ejpam-4722	349	32	′	′	NOUN
ejpam-4722	349	33	)	)	PUNCT
ejpam-4722	350	1	|	|	ADV
ejpam-4722	350	2	,	,	PUNCT
ejpam-4722	350	3	=	=	NOUN
ejpam-4722	350	4	8	8	NUM
ejpam-4722	351	1	+	+	CCONJ
ejpam-4722	351	2	[	[	X
ejpam-4722	351	3	2(dω′	2(dω′	NUM
ejpam-4722	351	4	(	(	PUNCT
ejpam-4722	351	5	u	u	NOUN
ejpam-4722	351	6	)	)	PUNCT
ejpam-4722	352	1	+	+	CCONJ
ejpam-4722	352	2	2)(n−	2)(n−	NUM
ejpam-4722	352	3	1	1	NUM
ejpam-4722	352	4	)	)	PUNCT
ejpam-4722	352	5	]	]	PUNCT
ejpam-4722	352	6	,	,	PUNCT
ejpam-4722	352	7	=	=	SYM
ejpam-4722	352	8	8	8	NUM
ejpam-4722	352	9	+	+	NUM
ejpam-4722	352	10	2(dω′	2(dω′	NUM
ejpam-4722	352	11	(	(	PUNCT
ejpam-4722	352	12	u	u	NOUN
ejpam-4722	352	13	)	)	PUNCT
ejpam-4722	352	14	+	+	CCONJ
ejpam-4722	352	15	p−	p−	NOUN
ejpam-4722	352	16	1)(n−	1)(n−	NUM
ejpam-4722	352	17	1	1	NUM
ejpam-4722	352	18	)	)	PUNCT
ejpam-4722	352	19	,	,	PUNCT
ejpam-4722	352	20	by	by	ADP
ejpam-4722	352	21	using	use	VERB
ejpam-4722	352	22	the	the	DET
ejpam-4722	352	23	above	above	ADJ
ejpam-4722	352	24	calculations	calculation	NOUN
ejpam-4722	352	25	,	,	PUNCT
ejpam-4722	352	26	we	we	PRON
ejpam-4722	352	27	have	have	VERB
ejpam-4722	352	28	straightforward	straightforward	ADJ
ejpam-4722	352	29	result	result	NOUN
ejpam-4722	352	30	mowe	mowe	NOUN
ejpam-4722	352	31	(	(	PUNCT
ejpam-4722	352	32	ω)−mowe	ω)−mowe	NOUN
ejpam-4722	352	33	(	(	PUNCT
ejpam-4722	352	34	ω	ω	NOUN
ejpam-4722	352	35	′	′	NUM
ejpam-4722	352	36	)	)	PUNCT
ejpam-4722	352	37	<	<	X
ejpam-4722	352	38	0	0	NUM
ejpam-4722	352	39	,	,	PUNCT
ejpam-4722	352	40	which	which	PRON
ejpam-4722	352	41	completes	complete	VERB
ejpam-4722	352	42	proof	proof	NOUN
ejpam-4722	352	43	.	.	PUNCT
ejpam-4722	353	1	references	reference	NOUN
ejpam-4722	353	2	1806	1806	NUM
ejpam-4722	353	3	transformation	transformation	NOUN
ejpam-4722	353	4	4	4	NUM
ejpam-4722	353	5	.	.	PUNCT
ejpam-4722	353	6	assume	assume	VERB
ejpam-4722	353	7	that	that	SCONJ
ejpam-4722	353	8	k	k	PROPN
ejpam-4722	353	9	is	be	AUX
ejpam-4722	353	10	a	a	DET
ejpam-4722	353	11	graph	graph	NOUN
ejpam-4722	353	12	and	and	CCONJ
ejpam-4722	353	13	cp	cp	INTJ
ejpam-4722	353	14	is	be	AUX
ejpam-4722	353	15	a	a	DET
ejpam-4722	353	16	cycle	cycle	NOUN
ejpam-4722	353	17	of	of	ADP
ejpam-4722	353	18	order	order	NOUN
ejpam-4722	354	1	p.	p.	NOUN
ejpam-4722	354	2	the	the	DET
ejpam-4722	354	3	graph	graph	NOUN
ejpam-4722	354	4	formed	form	VERB
ejpam-4722	354	5	by	by	ADP
ejpam-4722	354	6	associating	associate	VERB
ejpam-4722	354	7	the	the	DET
ejpam-4722	354	8	vertex	vertex	NOUN
ejpam-4722	354	9	u	u	NOUN
ejpam-4722	354	10	with	with	ADP
ejpam-4722	354	11	a	a	DET
ejpam-4722	354	12	vertex	vertex	NOUN
ejpam-4722	354	13	of	of	ADP
ejpam-4722	354	14	cp	cp	PROPN
ejpam-4722	354	15	is	be	AUX
ejpam-4722	354	16	denoted	denote	VERB
ejpam-4722	354	17	by	by	ADP
ejpam-4722	354	18	k(u)cp	k(u)cp	PROPN
ejpam-4722	354	19	.	.	PUNCT
ejpam-4722	355	1	let	let	VERB
ejpam-4722	355	2	ω	ω	NUM
ejpam-4722	355	3	be	be	AUX
ejpam-4722	355	4	the	the	DET
ejpam-4722	355	5	graph	graph	NOUN
ejpam-4722	355	6	formed	form	VERB
ejpam-4722	355	7	from	from	ADP
ejpam-4722	355	8	k(u)cp	k(u)cp	NOUN
ejpam-4722	355	9	by	by	ADP
ejpam-4722	355	10	attaching	attach	VERB
ejpam-4722	355	11	some	some	DET
ejpam-4722	355	12	triangles	triangle	NOUN
ejpam-4722	355	13	and	and	CCONJ
ejpam-4722	355	14	(	(	PUNCT
ejpam-4722	355	15	or	or	CCONJ
ejpam-4722	355	16	)	)	PUNCT
ejpam-4722	355	17	some	some	DET
ejpam-4722	355	18	pendent	pendent	NOUN
ejpam-4722	355	19	edges	edge	NOUN
ejpam-4722	355	20	to	to	ADP
ejpam-4722	355	21	the	the	DET
ejpam-4722	355	22	vertices	vertex	NOUN
ejpam-4722	355	23	of	of	ADP
ejpam-4722	355	24	cp	cp	NUM
ejpam-4722	355	25	except	except	SCONJ
ejpam-4722	355	26	u.	u.	PROPN
ejpam-4722	355	27	now	now	ADV
ejpam-4722	355	28	,	,	PUNCT
ejpam-4722	355	29	let	let	VERB
ejpam-4722	355	30	ω	ω	NUM
ejpam-4722	355	31	′	′	NUM
ejpam-4722	355	32	be	be	AUX
ejpam-4722	355	33	the	the	DET
ejpam-4722	355	34	graph	graph	NOUN
ejpam-4722	355	35	formed	form	VERB
ejpam-4722	355	36	from	from	ADP
ejpam-4722	355	37	ω	ω	NUM
ejpam-4722	355	38	by	by	ADP
ejpam-4722	355	39	shifting	shift	VERB
ejpam-4722	355	40	all	all	DET
ejpam-4722	355	41	triangles	triangle	NOUN
ejpam-4722	355	42	and	and	CCONJ
ejpam-4722	355	43	pendent	pendent	NOUN
ejpam-4722	355	44	edges	edge	NOUN
ejpam-4722	355	45	rooted	root	VERB
ejpam-4722	355	46	on	on	ADP
ejpam-4722	355	47	vertices	vertex	NOUN
ejpam-4722	355	48	of	of	ADP
ejpam-4722	355	49	cp	cp	NUM
ejpam-4722	355	50	except	except	SCONJ
ejpam-4722	355	51	for	for	SCONJ
ejpam-4722	355	52	u	u	PROPN
ejpam-4722	355	53	to	to	PART
ejpam-4722	355	54	u.	u.	AUX
ejpam-4722	355	55	given	give	VERB
ejpam-4722	355	56	that	that	SCONJ
ejpam-4722	355	57	|ω|	|ω|	PROPN
ejpam-4722	355	58	=	=	SYM
ejpam-4722	355	59	|ω′	|ω′	PROPN
ejpam-4722	355	60	|	|	ADV
ejpam-4722	355	61	.	.	PUNCT
ejpam-4722	356	1	lemma	lemma	PROPN
ejpam-4722	356	2	8	8	NUM
ejpam-4722	356	3	.	.	PUNCT
ejpam-4722	356	4	suppose	suppose	VERB
ejpam-4722	356	5	that	that	SCONJ
ejpam-4722	356	6	ω	ω	PROPN
ejpam-4722	356	7	and	and	CCONJ
ejpam-4722	356	8	ω	ω	NUM
ejpam-4722	356	9	′	′	NOUN
ejpam-4722	356	10	are	be	AUX
ejpam-4722	356	11	two	two	NUM
ejpam-4722	356	12	graphs	graph	NOUN
ejpam-4722	356	13	.	.	PUNCT
ejpam-4722	357	1	then	then	ADV
ejpam-4722	357	2	mowe	mowe	VERB
ejpam-4722	357	3	(	(	PUNCT
ejpam-4722	357	4	ω	ω	NOUN
ejpam-4722	357	5	)	)	PUNCT
ejpam-4722	357	6	<	<	X
ejpam-4722	357	7	mowe	mowe	NOUN
ejpam-4722	357	8	(	(	PUNCT
ejpam-4722	357	9	ω	ω	NOUN
ejpam-4722	357	10	′	′	NUM
ejpam-4722	357	11	)	)	PUNCT
ejpam-4722	357	12	.	.	PUNCT
ejpam-4722	358	1	we	we	PRON
ejpam-4722	358	2	leave	leave	VERB
ejpam-4722	358	3	to	to	ADP
ejpam-4722	358	4	the	the	DET
ejpam-4722	358	5	reader	reader	NOUN
ejpam-4722	358	6	the	the	DET
ejpam-4722	358	7	proof	proof	NOUN
ejpam-4722	358	8	of	of	ADP
ejpam-4722	358	9	lemma	lemma	PROPN
ejpam-4722	358	10	8	8	NUM
ejpam-4722	358	11	,	,	PUNCT
ejpam-4722	358	12	since	since	SCONJ
ejpam-4722	358	13	it	it	PRON
ejpam-4722	358	14	is	be	AUX
ejpam-4722	358	15	similar	similar	ADJ
ejpam-4722	358	16	to	to	ADP
ejpam-4722	358	17	the	the	DET
ejpam-4722	358	18	proof	proof	NOUN
ejpam-4722	358	19	of	of	ADP
ejpam-4722	358	20	lemma	lemma	PROPN
ejpam-4722	358	21	6	6	NUM
ejpam-4722	358	22	.	.	PUNCT
ejpam-4722	358	23	transformation	transformation	NOUN
ejpam-4722	358	24	5	5	NUM
ejpam-4722	358	25	.	.	PUNCT
ejpam-4722	359	1	let	let	VERB
ejpam-4722	359	2	ck	ck	PRON
ejpam-4722	359	3	be	be	AUX
ejpam-4722	359	4	a	a	DET
ejpam-4722	359	5	cycle	cycle	NOUN
ejpam-4722	359	6	with	with	ADP
ejpam-4722	359	7	r	r	NOUN
ejpam-4722	359	8	≥	≥	NUM
ejpam-4722	359	9	4	4	NUM
ejpam-4722	359	10	and	and	CCONJ
ejpam-4722	359	11	u	u	NOUN
ejpam-4722	359	12	′	′	NOUN
ejpam-4722	359	13	,	,	PUNCT
ejpam-4722	359	14	u	u	NOUN
ejpam-4722	359	15	′	′	NOUN
ejpam-4722	359	16	1	1	NUM
ejpam-4722	359	17	,	,	PUNCT
ejpam-4722	359	18	...	...	PUNCT
ejpam-4722	359	19	,	,	PUNCT
ejpam-4722	359	20	u	u	NOUN
ejpam-4722	359	21	′	′	NOUN
ejpam-4722	359	22	k−1	k−1	PROPN
ejpam-4722	359	23	are	be	AUX
ejpam-4722	359	24	the	the	DET
ejpam-4722	359	25	vertices	vertex	NOUN
ejpam-4722	359	26	of	of	ADP
ejpam-4722	359	27	ck	ck	NOUN
ejpam-4722	359	28	subsequently	subsequently	ADV
ejpam-4722	359	29	.	.	PUNCT
ejpam-4722	360	1	let	let	VERB
ejpam-4722	360	2	ko	ko	PROPN
ejpam-4722	360	3	be	be	AUX
ejpam-4722	360	4	a	a	DET
ejpam-4722	360	5	cactus	cactus	NOUN
ejpam-4722	360	6	graph	graph	NOUN
ejpam-4722	360	7	such	such	ADJ
ejpam-4722	360	8	that	that	SCONJ
ejpam-4722	360	9	d(ko	d(ko	PROPN
ejpam-4722	360	10	)	)	PUNCT
ejpam-4722	360	11	≥	≥	NOUN
ejpam-4722	360	12	2	2	NUM
ejpam-4722	360	13	and	and	CCONJ
ejpam-4722	360	14	all	all	DET
ejpam-4722	360	15	cycles	cycle	NOUN
ejpam-4722	360	16	in	in	ADP
ejpam-4722	360	17	ko	ko	PROPN
ejpam-4722	360	18	are	be	AUX
ejpam-4722	360	19	triangles	triangle	NOUN
ejpam-4722	360	20	.	.	PUNCT
ejpam-4722	361	1	suppose	suppose	VERB
ejpam-4722	361	2	w	w	X
ejpam-4722	361	3	,	,	PUNCT
ejpam-4722	361	4	x	x	PRON
ejpam-4722	361	5	are	be	AUX
ejpam-4722	361	6	two	two	NUM
ejpam-4722	361	7	vertices	vertex	NOUN
ejpam-4722	361	8	of	of	ADP
ejpam-4722	361	9	v	v	NOUN
ejpam-4722	361	10	(	(	PUNCT
ejpam-4722	361	11	ko	ko	PROPN
ejpam-4722	361	12	)	)	PUNCT
ejpam-4722	361	13	such	such	ADJ
ejpam-4722	361	14	that	that	PRON
ejpam-4722	361	15	w	w	NOUN
ejpam-4722	361	16	,	,	PUNCT
ejpam-4722	361	17	x	x	PRON
ejpam-4722	361	18	are	be	AUX
ejpam-4722	361	19	in	in	ADP
ejpam-4722	361	20	some	some	DET
ejpam-4722	361	21	triangles	triangle	NOUN
ejpam-4722	361	22	of	of	ADP
ejpam-4722	361	23	ko	ko	PROPN
ejpam-4722	361	24	and	and	CCONJ
ejpam-4722	361	25	d(ko)(w	d(ko)(w	PROPN
ejpam-4722	361	26	)	)	PUNCT
ejpam-4722	361	27	=	=	SYM
ejpam-4722	361	28	d(ko)(x	d(ko)(x	NOUN
ejpam-4722	361	29	)	)	PUNCT
ejpam-4722	361	30	=	=	SYM
ejpam-4722	362	1	2	2	X
ejpam-4722	362	2	.	.	PUNCT
ejpam-4722	362	3	let	let	VERB
ejpam-4722	362	4	ω	ω	NUM
ejpam-4722	362	5	be	be	AUX
ejpam-4722	362	6	the	the	DET
ejpam-4722	362	7	resulting	result	VERB
ejpam-4722	362	8	graph	graph	NOUN
ejpam-4722	362	9	by	by	ADP
ejpam-4722	362	10	associating	associate	VERB
ejpam-4722	362	11	u	u	PRON
ejpam-4722	362	12	′	′	NOUN
ejpam-4722	362	13	and	and	CCONJ
ejpam-4722	362	14	x	x	X
ejpam-4722	362	15	via	via	ADP
ejpam-4722	362	16	a	a	DET
ejpam-4722	362	17	path	path	NOUN
ejpam-4722	362	18	(	(	PUNCT
ejpam-4722	362	19	the	the	DET
ejpam-4722	362	20	length	length	NOUN
ejpam-4722	362	21	of	of	ADP
ejpam-4722	362	22	the	the	DET
ejpam-4722	362	23	path	path	NOUN
ejpam-4722	362	24	≥	≥	NOUN
ejpam-4722	362	25	0	0	NUM
ejpam-4722	362	26	)	)	PUNCT
ejpam-4722	362	27	,	,	PUNCT
ejpam-4722	362	28	and	and	CCONJ
ejpam-4722	362	29	fix	fix	VERB
ejpam-4722	362	30	u	u	NOUN
ejpam-4722	362	31	′	′	NUM
ejpam-4722	362	32	j	j	NOUN
ejpam-4722	363	1	where	where	SCONJ
ejpam-4722	363	2	i	i	PRON
ejpam-4722	363	3	̸=	̸=	PROPN
ejpam-4722	363	4	0	0	NUM
ejpam-4722	363	5	with	with	ADP
ejpam-4722	363	6	one	one	NUM
ejpam-4722	363	7	vertex	vertex	NOUN
ejpam-4722	363	8	of	of	ADP
ejpam-4722	363	9	a	a	DET
ejpam-4722	363	10	graph	graph	NOUN
ejpam-4722	363	11	k.	k.	PROPN
ejpam-4722	363	12	next	next	ADV
ejpam-4722	363	13	,	,	PUNCT
ejpam-4722	363	14	let	let	VERB
ejpam-4722	363	15	ω	ω	NUM
ejpam-4722	363	16	′	′	NUM
ejpam-4722	363	17	be	be	AUX
ejpam-4722	363	18	a	a	DET
ejpam-4722	363	19	generated	generate	VERB
ejpam-4722	363	20	graph	graph	NOUN
ejpam-4722	363	21	from	from	ADP
ejpam-4722	363	22	ω	ω	NUM
ejpam-4722	363	23	by	by	ADP
ejpam-4722	363	24	exclude	exclude	NOUN
ejpam-4722	363	25	the	the	DET
ejpam-4722	363	26	edge	edge	NOUN
ejpam-4722	363	27	u	u	NOUN
ejpam-4722	363	28	′	′	NUM
ejpam-4722	363	29	jy	jy	PROPN
ejpam-4722	363	30	for	for	ADP
ejpam-4722	363	31	any	any	DET
ejpam-4722	363	32	y	y	PROPN
ejpam-4722	363	33	∈	∈	PROPN
ejpam-4722	363	34	vk	vk	NOUN
ejpam-4722	363	35	and	and	CCONJ
ejpam-4722	363	36	addition	addition	NOUN
ejpam-4722	363	37	of	of	ADP
ejpam-4722	363	38	edge	edge	NOUN
ejpam-4722	363	39	wy	wy	PROPN
ejpam-4722	363	40	.	.	PUNCT
ejpam-4722	364	1	lemma	lemma	PROPN
ejpam-4722	364	2	9	9	NUM
ejpam-4722	364	3	.	.	PUNCT
ejpam-4722	364	4	suppose	suppose	VERB
ejpam-4722	364	5	ω	ω	PROPN
ejpam-4722	364	6	and	and	CCONJ
ejpam-4722	364	7	ω	ω	NUM
ejpam-4722	364	8	′	′	NOUN
ejpam-4722	364	9	are	be	AUX
ejpam-4722	364	10	two	two	NUM
ejpam-4722	364	11	graphs	graph	NOUN
ejpam-4722	364	12	.	.	PUNCT
ejpam-4722	365	1	then	then	ADV
ejpam-4722	365	2	mowe	mowe	VERB
ejpam-4722	365	3	(	(	PUNCT
ejpam-4722	365	4	ω	ω	NOUN
ejpam-4722	365	5	)	)	PUNCT
ejpam-4722	365	6	>	>	X
ejpam-4722	366	1	mowe	mowe	NOUN
ejpam-4722	366	2	(	(	PUNCT
ejpam-4722	366	3	ω	ω	NOUN
ejpam-4722	366	4	′	′	NUM
ejpam-4722	366	5	)	)	PUNCT
ejpam-4722	366	6	.	.	PUNCT
ejpam-4722	367	1	the	the	DET
ejpam-4722	367	2	proof	proof	NOUN
ejpam-4722	367	3	of	of	ADP
ejpam-4722	367	4	lemma	lemma	PROPN
ejpam-4722	367	5	9	9	NUM
ejpam-4722	367	6	,	,	PUNCT
ejpam-4722	367	7	leave	leave	VERB
ejpam-4722	367	8	to	to	ADP
ejpam-4722	367	9	readers	reader	NOUN
ejpam-4722	367	10	,	,	PUNCT
ejpam-4722	367	11	since	since	SCONJ
ejpam-4722	367	12	it	it	PRON
ejpam-4722	367	13	is	be	AUX
ejpam-4722	367	14	evidently	evidently	ADV
ejpam-4722	367	15	analogous	analogous	ADJ
ejpam-4722	367	16	to	to	ADP
ejpam-4722	367	17	the	the	DET
ejpam-4722	367	18	proof	proof	NOUN
ejpam-4722	367	19	of	of	ADP
ejpam-4722	367	20	lemma	lemma	PROPN
ejpam-4722	367	21	7	7	NUM
ejpam-4722	367	22	.	.	PUNCT
ejpam-4722	368	1	next	next	ADV
ejpam-4722	368	2	,	,	PUNCT
ejpam-4722	368	3	we	we	PRON
ejpam-4722	368	4	turn	turn	VERB
ejpam-4722	368	5	to	to	ADP
ejpam-4722	368	6	the	the	DET
ejpam-4722	368	7	proof	proof	NOUN
ejpam-4722	368	8	of	of	ADP
ejpam-4722	368	9	theorem	theorem	ADJ
ejpam-4722	368	10	4	4	NUM
ejpam-4722	368	11	.	.	PUNCT
ejpam-4722	369	1	proof	proof	NOUN
ejpam-4722	369	2	.	.	PUNCT
ejpam-4722	370	1	by	by	ADP
ejpam-4722	370	2	using	use	VERB
ejpam-4722	370	3	lemmas	lemmas	PROPN
ejpam-4722	370	4	1	1	NUM
ejpam-4722	370	5	,	,	PUNCT
ejpam-4722	370	6	5	5	NUM
ejpam-4722	370	7	,	,	PUNCT
ejpam-4722	370	8	6	6	NUM
ejpam-4722	370	9	,	,	PUNCT
ejpam-4722	370	10	7	7	NUM
ejpam-4722	370	11	,	,	PUNCT
ejpam-4722	370	12	8	8	NUM
ejpam-4722	370	13	,	,	PUNCT
ejpam-4722	370	14	and	and	CCONJ
ejpam-4722	370	15	9	9	NUM
ejpam-4722	370	16	for	for	ADP
ejpam-4722	370	17	any	any	DET
ejpam-4722	370	18	graph	graph	NOUN
ejpam-4722	370	19	ω	ω	NUM
ejpam-4722	370	20	∈	∈	PROPN
ejpam-4722	370	21	c(n	c(n	PROPN
ejpam-4722	370	22	,	,	PUNCT
ejpam-4722	370	23	k	k	NOUN
ejpam-4722	370	24	)	)	PUNCT
ejpam-4722	370	25	,	,	PUNCT
ejpam-4722	370	26	mowe	mowe	NOUN
ejpam-4722	370	27	(	(	PUNCT
ejpam-4722	370	28	ω	ω	NOUN
ejpam-4722	370	29	)	)	PUNCT
ejpam-4722	370	30	<	<	X
ejpam-4722	370	31	mowe	mowe	NOUN
ejpam-4722	370	32	(	(	PUNCT
ejpam-4722	370	33	s	s	VERB
ejpam-4722	370	34	∗,k	∗,k	NOUN
ejpam-4722	370	35	n	n	NOUN
ejpam-4722	370	36	)	)	PUNCT
ejpam-4722	370	37	and	and	CCONJ
ejpam-4722	370	38	the	the	DET
ejpam-4722	370	39	equality	equality	NOUN
ejpam-4722	370	40	holds	hold	VERB
ejpam-4722	370	41	if	if	SCONJ
ejpam-4722	370	42	and	and	CCONJ
ejpam-4722	370	43	only	only	ADV
ejpam-4722	370	44	if	if	SCONJ
ejpam-4722	370	45	ω	ω	PRON
ejpam-4722	370	46	∼=	∼=	PROPN
ejpam-4722	370	47	s∗,kn	s∗,kn	NOUN
ejpam-4722	370	48	.	.	PUNCT
ejpam-4722	371	1	it	it	PRON
ejpam-4722	371	2	is	be	AUX
ejpam-4722	371	3	easy	easy	ADJ
ejpam-4722	371	4	to	to	PART
ejpam-4722	371	5	compute	compute	VERB
ejpam-4722	371	6	that	that	DET
ejpam-4722	371	7	mowe	mowe	NOUN
ejpam-4722	371	8	(	(	PUNCT
ejpam-4722	371	9	ω	ω	NOUN
ejpam-4722	371	10	)	)	PUNCT
ejpam-4722	371	11	=	=	SYM
ejpam-4722	371	12	n3	n3	NOUN
ejpam-4722	371	13	+	+	CCONJ
ejpam-4722	372	1	(	(	PUNCT
ejpam-4722	372	2	k	k	PROPN
ejpam-4722	372	3	−	−	PROPN
ejpam-4722	372	4	4)n2	4)n2	NUM
ejpam-4722	372	5	+	+	CCONJ
ejpam-4722	372	6	(	(	PUNCT
ejpam-4722	372	7	−3k	−3k	PROPN
ejpam-4722	372	8	+	+	NUM
ejpam-4722	372	9	5)n−	5)n−	PROPN
ejpam-4722	372	10	(	(	PUNCT
ejpam-4722	372	11	2n+	2n+	NUM
ejpam-4722	372	12	4	4	NUM
ejpam-4722	372	13	)	)	PUNCT
ejpam-4722	372	14	.	.	PUNCT
ejpam-4722	373	1	the	the	DET
ejpam-4722	373	2	proof	proof	NOUN
ejpam-4722	373	3	completes	complete	VERB
ejpam-4722	373	4	.	.	PUNCT
ejpam-4722	374	1	acknowledgements	acknowledgement	NOUN
ejpam-4722	374	2	the	the	DET
ejpam-4722	374	3	authors	author	NOUN
ejpam-4722	374	4	are	be	AUX
ejpam-4722	374	5	grateful	grateful	ADJ
ejpam-4722	374	6	to	to	ADP
ejpam-4722	374	7	two	two	NUM
ejpam-4722	374	8	anonymous	anonymous	ADJ
ejpam-4722	374	9	referees	referee	NOUN
ejpam-4722	374	10	for	for	ADP
ejpam-4722	374	11	their	their	PRON
ejpam-4722	374	12	valuable	valuable	ADJ
ejpam-4722	374	13	comments	comment	NOUN
ejpam-4722	374	14	and	and	CCONJ
ejpam-4722	374	15	corrections	correction	NOUN
ejpam-4722	374	16	,	,	PUNCT
ejpam-4722	374	17	which	which	PRON
ejpam-4722	374	18	have	have	AUX
ejpam-4722	374	19	led	lead	VERB
ejpam-4722	374	20	to	to	ADP
ejpam-4722	374	21	considerable	considerable	ADJ
ejpam-4722	374	22	improvement	improvement	NOUN
ejpam-4722	374	23	of	of	ADP
ejpam-4722	374	24	the	the	DET
ejpam-4722	374	25	presentation	presentation	NOUN
ejpam-4722	374	26	of	of	ADP
ejpam-4722	374	27	this	this	DET
ejpam-4722	374	28	work	work	NOUN
ejpam-4722	374	29	.	.	PUNCT
ejpam-4722	375	1	this	this	DET
ejpam-4722	375	2	project	project	NOUN
ejpam-4722	375	3	is	be	AUX
ejpam-4722	375	4	funded	fund	VERB
ejpam-4722	375	5	by	by	ADP
ejpam-4722	375	6	king	king	PROPN
ejpam-4722	375	7	saud	saud	PROPN
ejpam-4722	375	8	university	university	PROPN
ejpam-4722	375	9	,	,	PUNCT
ejpam-4722	375	10	riyadh	riyadh	PROPN
ejpam-4722	375	11	,	,	PUNCT
ejpam-4722	375	12	saudi	saudi	PROPN
ejpam-4722	375	13	arabia	arabia	PROPN
ejpam-4722	375	14	.	.	PUNCT
ejpam-4722	376	1	research	research	NOUN
ejpam-4722	376	2	supporting	support	VERB
ejpam-4722	376	3	project	project	NOUN
ejpam-4722	376	4	number	number	NOUN
ejpam-4722	376	5	(	(	PUNCT
ejpam-4722	376	6	rsp2023r167	rsp2023r167	ADJ
ejpam-4722	376	7	)	)	PUNCT
ejpam-4722	376	8	,	,	PUNCT
ejpam-4722	376	9	king	king	PROPN
ejpam-4722	376	10	saud	saud	PROPN
ejpam-4722	376	11	university	university	PROPN
ejpam-4722	376	12	,	,	PUNCT
ejpam-4722	376	13	riyadh	riyadh	PROPN
ejpam-4722	376	14	,	,	PUNCT
ejpam-4722	376	15	saudi	saudi	PROPN
ejpam-4722	376	16	arabia	arabia	PROPN
ejpam-4722	376	17	.	.	PUNCT
ejpam-4722	377	1	references	reference	NOUN
ejpam-4722	377	2	[	[	X
ejpam-4722	377	3	1	1	NUM
ejpam-4722	377	4	]	]	X
ejpam-4722	377	5	lowell	lowell	PROPN
ejpam-4722	377	6	abrams	abrams	PROPN
ejpam-4722	377	7	and	and	CCONJ
ejpam-4722	377	8	l	l	PROPN
ejpam-4722	377	9	-	-	PROPN
ejpam-4722	377	10	k	k	PROPN
ejpam-4722	377	11	lauderdale	lauderdale	PROPN
ejpam-4722	377	12	.	.	PUNCT
ejpam-4722	378	1	on	on	ADP
ejpam-4722	378	2	a	a	DET
ejpam-4722	378	3	ratio	ratio	NOUN
ejpam-4722	378	4	of	of	ADP
ejpam-4722	378	5	wiener	wiener	NOUN
ejpam-4722	378	6	indices	index	NOUN
ejpam-4722	378	7	for	for	ADP
ejpam-4722	378	8	embedded	embed	VERB
ejpam-4722	378	9	graphs	graph	NOUN
ejpam-4722	378	10	.	.	PUNCT
ejpam-4722	379	1	discrete	discrete	ADJ
ejpam-4722	379	2	mathematics	mathematic	NOUN
ejpam-4722	379	3	,	,	PUNCT
ejpam-4722	379	4	346(5):113320	346(5):113320	PROPN
ejpam-4722	379	5	,	,	PUNCT
ejpam-4722	379	6	2023	2023	NUM
ejpam-4722	379	7	.	.	PUNCT
ejpam-4722	380	1	[	[	X
ejpam-4722	380	2	2	2	X
ejpam-4722	380	3	]	]	X
ejpam-4722	380	4	akbar	akbar	X
ejpam-4722	380	5	ali	ali	PROPN
ejpam-4722	380	6	and	and	CCONJ
ejpam-4722	380	7	tomislav	tomislav	PROPN
ejpam-4722	380	8	došlić.	došlić.	PROPN
ejpam-4722	380	9	mostar	mostar	PROPN
ejpam-4722	380	10	index	index	PROPN
ejpam-4722	380	11	:	:	PUNCT
ejpam-4722	380	12	results	result	NOUN
ejpam-4722	380	13	and	and	CCONJ
ejpam-4722	380	14	perspectives	perspective	NOUN
ejpam-4722	380	15	.	.	PUNCT
ejpam-4722	381	1	applied	apply	VERB
ejpam-4722	381	2	mathematics	mathematic	NOUN
ejpam-4722	381	3	and	and	CCONJ
ejpam-4722	381	4	computation	computation	NOUN
ejpam-4722	381	5	,	,	PUNCT
ejpam-4722	381	6	404:126245	404:126245	NUM
ejpam-4722	381	7	,	,	PUNCT
ejpam-4722	381	8	2021	2021	NUM
ejpam-4722	381	9	.	.	PUNCT
ejpam-4722	382	1	[	[	X
ejpam-4722	382	2	3	3	NUM
ejpam-4722	382	3	]	]	X
ejpam-4722	382	4	micheal	micheal	NOUN
ejpam-4722	382	5	arockiaraj	arockiaraj	PROPN
ejpam-4722	382	6	,	,	PUNCT
ejpam-4722	382	7	joseph	joseph	PROPN
ejpam-4722	382	8	clement	clement	PROPN
ejpam-4722	382	9	,	,	PUNCT
ejpam-4722	382	10	and	and	CCONJ
ejpam-4722	382	11	niko	niko	PROPN
ejpam-4722	382	12	tratnik	tratnik	PROPN
ejpam-4722	382	13	.	.	PUNCT
ejpam-4722	383	1	mostar	mostar	PROPN
ejpam-4722	383	2	indices	index	NOUN
ejpam-4722	383	3	of	of	ADP
ejpam-4722	383	4	carbon	carbon	NOUN
ejpam-4722	383	5	nanostructures	nanostructure	NOUN
ejpam-4722	383	6	and	and	CCONJ
ejpam-4722	383	7	circumscribed	circumscribed	ADJ
ejpam-4722	383	8	donut	donut	NOUN
ejpam-4722	383	9	benzenoid	benzenoid	NOUN
ejpam-4722	383	10	systems	system	NOUN
ejpam-4722	383	11	.	.	PUNCT
ejpam-4722	384	1	international	international	ADJ
ejpam-4722	384	2	journal	journal	NOUN
ejpam-4722	384	3	of	of	ADP
ejpam-4722	384	4	quantum	quantum	ADJ
ejpam-4722	384	5	chemistry	chemistry	NOUN
ejpam-4722	384	6	,	,	PUNCT
ejpam-4722	384	7	119(24):e26043	119(24):e26043	NUM
ejpam-4722	384	8	,	,	PUNCT
ejpam-4722	384	9	2019	2019	NUM
ejpam-4722	384	10	.	.	PUNCT
ejpam-4722	385	1	references	reference	NOUN
ejpam-4722	385	2	1807	1807	NUM
ejpam-4722	385	3	[	[	X
ejpam-4722	385	4	4	4	NUM
ejpam-4722	385	5	]	]	X
ejpam-4722	385	6	micheal	micheal	NOUN
ejpam-4722	385	7	arockiaraj	arockiaraj	VERB
ejpam-4722	385	8	,	,	PUNCT
ejpam-4722	385	9	a	a	DET
ejpam-4722	385	10	berin	berin	NOUN
ejpam-4722	385	11	greeni	greeni	NOUN
ejpam-4722	385	12	,	,	PUNCT
ejpam-4722	385	13	and	and	CCONJ
ejpam-4722	385	14	ar	ar	PROPN
ejpam-4722	385	15	abul	abul	PROPN
ejpam-4722	385	16	kalaam	kalaam	PROPN
ejpam-4722	385	17	.	.	PUNCT
ejpam-4722	386	1	linear	linear	PROPN
ejpam-4722	386	2	versus	versus	ADP
ejpam-4722	386	3	cubic	cubic	ADJ
ejpam-4722	386	4	regression	regression	NOUN
ejpam-4722	386	5	models	model	NOUN
ejpam-4722	386	6	for	for	ADP
ejpam-4722	386	7	analyzing	analyze	VERB
ejpam-4722	386	8	generalized	generalize	VERB
ejpam-4722	386	9	reverse	reverse	NOUN
ejpam-4722	386	10	degree	degree	NOUN
ejpam-4722	386	11	based	base	VERB
ejpam-4722	386	12	topological	topological	ADJ
ejpam-4722	386	13	indices	index	NOUN
ejpam-4722	386	14	of	of	ADP
ejpam-4722	386	15	certain	certain	ADJ
ejpam-4722	386	16	latest	late	ADJ
ejpam-4722	386	17	corona	corona	NOUN
ejpam-4722	386	18	treatment	treatment	NOUN
ejpam-4722	386	19	drug	drug	NOUN
ejpam-4722	386	20	molecules	molecule	NOUN
ejpam-4722	386	21	.	.	PUNCT
ejpam-4722	387	1	international	international	ADJ
ejpam-4722	387	2	journal	journal	NOUN
ejpam-4722	387	3	of	of	ADP
ejpam-4722	387	4	quantum	quantum	ADJ
ejpam-4722	387	5	chemistry	chemistry	NOUN
ejpam-4722	387	6	,	,	PUNCT
ejpam-4722	387	7	page	page	NOUN
ejpam-4722	387	8	e27136	e27136	PROPN
ejpam-4722	387	9	,	,	PUNCT
ejpam-4722	387	10	2023	2023	NUM
ejpam-4722	387	11	.	.	PUNCT
ejpam-4722	388	1	[	[	X
ejpam-4722	388	2	5	5	NUM
ejpam-4722	388	3	]	]	PUNCT
ejpam-4722	388	4	t	t	PROPN
ejpam-4722	388	5	asir	asir	PROPN
ejpam-4722	388	6	and	and	CCONJ
ejpam-4722	388	7	v	v	NUM
ejpam-4722	388	8	rabikka	rabikka	NOUN
ejpam-4722	388	9	.	.	PUNCT
ejpam-4722	389	1	the	the	DET
ejpam-4722	389	2	wiener	wiener	NOUN
ejpam-4722	389	3	index	index	NOUN
ejpam-4722	389	4	of	of	ADP
ejpam-4722	389	5	the	the	DET
ejpam-4722	389	6	zero	zero	NUM
ejpam-4722	389	7	-	-	PUNCT
ejpam-4722	389	8	divisor	divisor	NOUN
ejpam-4722	389	9	graph	graph	NOUN
ejpam-4722	389	10	of	of	ADP
ejpam-4722	389	11	zn	zn	PROPN
ejpam-4722	389	12	.	.	PUNCT
ejpam-4722	389	13	discrete	discrete	ADJ
ejpam-4722	389	14	applied	apply	VERB
ejpam-4722	389	15	mathematics	mathematic	NOUN
ejpam-4722	389	16	,	,	PUNCT
ejpam-4722	389	17	319:461–471	319:461–471	NUM
ejpam-4722	389	18	,	,	PUNCT
ejpam-4722	389	19	2022	2022	NUM
ejpam-4722	389	20	.	.	PUNCT
ejpam-4722	390	1	[	[	X
ejpam-4722	390	2	6	6	NUM
ejpam-4722	390	3	]	]	PUNCT
ejpam-4722	390	4	bojana	bojana	PROPN
ejpam-4722	390	5	borovićanin	borovićanin	PROPN
ejpam-4722	390	6	,	,	PUNCT
ejpam-4722	390	7	boris	boris	PROPN
ejpam-4722	390	8	furtula	furtula	PROPN
ejpam-4722	390	9	,	,	PUNCT
ejpam-4722	390	10	and	and	CCONJ
ejpam-4722	390	11	marija	marija	VERB
ejpam-4722	390	12	jerotijević.	jerotijević.	PROPN
ejpam-4722	390	13	on	on	ADP
ejpam-4722	390	14	the	the	DET
ejpam-4722	390	15	minimum	minimum	ADJ
ejpam-4722	390	16	harary	harary	NOUN
ejpam-4722	390	17	index	index	NOUN
ejpam-4722	390	18	of	of	ADP
ejpam-4722	390	19	graphs	graph	NOUN
ejpam-4722	390	20	with	with	ADP
ejpam-4722	390	21	a	a	DET
ejpam-4722	390	22	given	give	VERB
ejpam-4722	390	23	diameter	diameter	NOUN
ejpam-4722	390	24	or	or	CCONJ
ejpam-4722	390	25	independence	independence	NOUN
ejpam-4722	390	26	number	number	NOUN
ejpam-4722	390	27	.	.	PUNCT
ejpam-4722	391	1	discrete	discrete	ADJ
ejpam-4722	391	2	applied	apply	VERB
ejpam-4722	391	3	mathematics	mathematic	NOUN
ejpam-4722	391	4	,	,	PUNCT
ejpam-4722	391	5	320:331–345	320:331–345	NUM
ejpam-4722	391	6	,	,	PUNCT
ejpam-4722	391	7	2022	2022	NUM
ejpam-4722	391	8	.	.	PUNCT
ejpam-4722	392	1	[	[	X
ejpam-4722	392	2	7	7	X
ejpam-4722	392	3	]	]	X
ejpam-4722	392	4	simon	simon	PROPN
ejpam-4722	392	5	brezovnik	brezovnik	PROPN
ejpam-4722	392	6	,	,	PUNCT
ejpam-4722	392	7	matthias	matthias	PROPN
ejpam-4722	392	8	dehmer	dehmer	NOUN
ejpam-4722	392	9	,	,	PUNCT
ejpam-4722	392	10	niko	niko	PROPN
ejpam-4722	392	11	tratnik	tratnik	PROPN
ejpam-4722	392	12	,	,	PUNCT
ejpam-4722	392	13	and	and	CCONJ
ejpam-4722	392	14	petra	petra	PROPN
ejpam-4722	392	15	žigert	žigert	PROPN
ejpam-4722	392	16	pleteršek	pleteršek	PROPN
ejpam-4722	392	17	.	.	PUNCT
ejpam-4722	393	1	szeged	szeged	PROPN
ejpam-4722	393	2	and	and	CCONJ
ejpam-4722	393	3	mostar	mostar	PROPN
ejpam-4722	393	4	root	root	PROPN
ejpam-4722	393	5	-	-	PUNCT
ejpam-4722	393	6	indices	index	NOUN
ejpam-4722	393	7	of	of	ADP
ejpam-4722	393	8	graphs	graph	NOUN
ejpam-4722	393	9	.	.	PUNCT
ejpam-4722	394	1	applied	apply	VERB
ejpam-4722	394	2	mathematics	mathematic	NOUN
ejpam-4722	394	3	and	and	CCONJ
ejpam-4722	394	4	computation	computation	NOUN
ejpam-4722	394	5	,	,	PUNCT
ejpam-4722	394	6	442:127736	442:127736	PROPN
ejpam-4722	394	7	,	,	PUNCT
ejpam-4722	394	8	2023	2023	NUM
ejpam-4722	394	9	.	.	PUNCT
ejpam-4722	395	1	[	[	X
ejpam-4722	395	2	8	8	NUM
ejpam-4722	395	3	]	]	X
ejpam-4722	395	4	matteo	matteo	PROPN
ejpam-4722	395	5	cavaleri	cavaleri	PROPN
ejpam-4722	395	6	,	,	PUNCT
ejpam-4722	395	7	daniele	daniele	PROPN
ejpam-4722	395	8	dangeli	dangeli	PROPN
ejpam-4722	395	9	,	,	PUNCT
ejpam-4722	395	10	alfredo	alfredo	NOUN
ejpam-4722	395	11	donno	donno	VERB
ejpam-4722	395	12	,	,	PUNCT
ejpam-4722	395	13	and	and	CCONJ
ejpam-4722	395	14	stefan	stefan	PROPN
ejpam-4722	395	15	hammer	hammer	PROPN
ejpam-4722	395	16	.	.	PUNCT
ejpam-4722	396	1	wiener	wiener	NOUN
ejpam-4722	396	2	,	,	PUNCT
ejpam-4722	396	3	edge	edge	NOUN
ejpam-4722	396	4	-	-	PUNCT
ejpam-4722	396	5	wiener	wiener	NOUN
ejpam-4722	396	6	,	,	PUNCT
ejpam-4722	396	7	and	and	CCONJ
ejpam-4722	396	8	vertex	vertex	NOUN
ejpam-4722	396	9	-	-	PUNCT
ejpam-4722	396	10	edge	edge	NOUN
ejpam-4722	396	11	-	-	PUNCT
ejpam-4722	396	12	wiener	wiener	NOUN
ejpam-4722	396	13	index	index	NOUN
ejpam-4722	396	14	of	of	ADP
ejpam-4722	396	15	basilica	basilica	NOUN
ejpam-4722	396	16	graphs	graph	NOUN
ejpam-4722	396	17	.	.	PUNCT
ejpam-4722	397	1	discrete	discrete	ADJ
ejpam-4722	397	2	applied	apply	VERB
ejpam-4722	397	3	mathematics	mathematic	NOUN
ejpam-4722	397	4	,	,	PUNCT
ejpam-4722	397	5	307:32–49	307:32–49	NUM
ejpam-4722	397	6	,	,	PUNCT
ejpam-4722	397	7	2022	2022	NUM
ejpam-4722	397	8	.	.	PUNCT
ejpam-4722	398	1	[	[	X
ejpam-4722	398	2	9	9	NUM
ejpam-4722	398	3	]	]	SYM
ejpam-4722	398	4	shubo	shubo	X
ejpam-4722	398	5	chen	chen	PROPN
ejpam-4722	398	6	.	.	PUNCT
ejpam-4722	399	1	cacti	cacti	VERB
ejpam-4722	399	2	with	with	ADP
ejpam-4722	399	3	the	the	DET
ejpam-4722	399	4	smallest	small	ADJ
ejpam-4722	399	5	,	,	PUNCT
ejpam-4722	399	6	second	second	ADV
ejpam-4722	399	7	smallest	small	ADJ
ejpam-4722	399	8	,	,	PUNCT
ejpam-4722	399	9	and	and	CCONJ
ejpam-4722	399	10	third	third	ADJ
ejpam-4722	399	11	smallest	small	ADJ
ejpam-4722	399	12	gutman	gutman	NOUN
ejpam-4722	399	13	index	index	PROPN
ejpam-4722	399	14	.	.	PUNCT
ejpam-4722	400	1	journal	journal	PROPN
ejpam-4722	400	2	of	of	ADP
ejpam-4722	400	3	combinatorial	combinatorial	ADJ
ejpam-4722	400	4	optimization	optimization	NOUN
ejpam-4722	400	5	,	,	PUNCT
ejpam-4722	400	6	31(1):327–332	31(1):327–332	PROPN
ejpam-4722	400	7	,	,	PUNCT
ejpam-4722	400	8	2016	2016	NUM
ejpam-4722	400	9	.	.	PUNCT
ejpam-4722	401	1	[	[	X
ejpam-4722	401	2	10	10	NUM
ejpam-4722	401	3	]	]	X
ejpam-4722	401	4	kinkar	kinkar	PROPN
ejpam-4722	401	5	ch	ch	PROPN
ejpam-4722	401	6	das	das	PROPN
ejpam-4722	401	7	and	and	CCONJ
ejpam-4722	401	8	mohammad	mohammad	PROPN
ejpam-4722	401	9	j	j	PROPN
ejpam-4722	401	10	nadjafi	nadjafi	PROPN
ejpam-4722	401	11	-	-	PUNCT
ejpam-4722	401	12	arani	arani	NOUN
ejpam-4722	401	13	.	.	PUNCT
ejpam-4722	402	1	on	on	ADP
ejpam-4722	402	2	maximum	maximum	PROPN
ejpam-4722	402	3	wiener	wiener	NOUN
ejpam-4722	402	4	index	index	NOUN
ejpam-4722	402	5	of	of	ADP
ejpam-4722	402	6	trees	tree	NOUN
ejpam-4722	402	7	and	and	CCONJ
ejpam-4722	402	8	graphs	graph	NOUN
ejpam-4722	402	9	with	with	ADP
ejpam-4722	402	10	given	give	VERB
ejpam-4722	402	11	radius	radius	NOUN
ejpam-4722	402	12	.	.	PUNCT
ejpam-4722	402	13	journal	journal	PROPN
ejpam-4722	402	14	of	of	ADP
ejpam-4722	402	15	combinatorial	combinatorial	ADJ
ejpam-4722	402	16	optimization	optimization	NOUN
ejpam-4722	402	17	,	,	PUNCT
ejpam-4722	402	18	34(2):574–587	34(2):574–587	PROPN
ejpam-4722	402	19	,	,	PUNCT
ejpam-4722	402	20	2017	2017	NUM
ejpam-4722	402	21	.	.	PUNCT
ejpam-4722	403	1	[	[	X
ejpam-4722	403	2	11	11	NUM
ejpam-4722	403	3	]	]	X
ejpam-4722	403	4	kinkar	kinkar	PROPN
ejpam-4722	403	5	chandra	chandra	PROPN
ejpam-4722	403	6	das	das	PROPN
ejpam-4722	403	7	,	,	PUNCT
ejpam-4722	403	8	suresh	suresh	PROPN
ejpam-4722	403	9	elumalai	elumalai	PROPN
ejpam-4722	403	10	,	,	PUNCT
ejpam-4722	403	11	surojit	surojit	PROPN
ejpam-4722	403	12	ghosh	ghosh	PROPN
ejpam-4722	403	13	,	,	PUNCT
ejpam-4722	403	14	and	and	CCONJ
ejpam-4722	403	15	toufik	toufik	PROPN
ejpam-4722	403	16	mansour	mansour	PROPN
ejpam-4722	403	17	.	.	PROPN
ejpam-4722	404	1	on	on	ADP
ejpam-4722	404	2	the	the	DET
ejpam-4722	404	3	merrifield	merrifield	PROPN
ejpam-4722	404	4	–	–	PUNCT
ejpam-4722	404	5	simmons	simmon	NOUN
ejpam-4722	404	6	index	index	NOUN
ejpam-4722	404	7	of	of	ADP
ejpam-4722	404	8	tricyclic	tricyclic	ADJ
ejpam-4722	404	9	graphs	graph	NOUN
ejpam-4722	404	10	.	.	PUNCT
ejpam-4722	405	1	discrete	discrete	ADJ
ejpam-4722	405	2	applied	applied	ADJ
ejpam-4722	405	3	mathematics	mathematic	NOUN
ejpam-4722	405	4	,	,	PUNCT
ejpam-4722	405	5	322:342–354	322:342–354	NUM
ejpam-4722	405	6	,	,	PUNCT
ejpam-4722	405	7	2022	2022	NUM
ejpam-4722	405	8	.	.	PUNCT
ejpam-4722	406	1	[	[	X
ejpam-4722	406	2	12	12	NUM
ejpam-4722	406	3	]	]	X
ejpam-4722	406	4	kecai	kecai	PROPN
ejpam-4722	406	5	deng	deng	PROPN
ejpam-4722	406	6	and	and	CCONJ
ejpam-4722	406	7	shuchao	shuchao	PROPN
ejpam-4722	406	8	li	li	PROPN
ejpam-4722	406	9	.	.	PROPN
ejpam-4722	406	10	extremal	extremal	PROPN
ejpam-4722	406	11	catacondensed	catacondense	VERB
ejpam-4722	406	12	benzenoids	benzenoid	NOUN
ejpam-4722	406	13	with	with	ADP
ejpam-4722	406	14	respect	respect	NOUN
ejpam-4722	406	15	to	to	ADP
ejpam-4722	406	16	the	the	DET
ejpam-4722	406	17	mostar	mostar	PROPN
ejpam-4722	406	18	index	index	PROPN
ejpam-4722	406	19	.	.	PUNCT
ejpam-4722	407	1	journal	journal	PROPN
ejpam-4722	407	2	of	of	ADP
ejpam-4722	407	3	mathematical	mathematical	ADJ
ejpam-4722	407	4	chemistry	chemistry	NOUN
ejpam-4722	407	5	,	,	PUNCT
ejpam-4722	407	6	58(7):1437–1465	58(7):1437–1465	NUM
ejpam-4722	407	7	,	,	PUNCT
ejpam-4722	407	8	2020	2020	NUM
ejpam-4722	407	9	.	.	PUNCT
ejpam-4722	408	1	[	[	X
ejpam-4722	408	2	13	13	NUM
ejpam-4722	408	3	]	]	X
ejpam-4722	408	4	kecai	kecai	PROPN
ejpam-4722	408	5	deng	deng	PROPN
ejpam-4722	408	6	and	and	CCONJ
ejpam-4722	408	7	shuchao	shuchao	ADJ
ejpam-4722	408	8	li	li	PROPN
ejpam-4722	408	9	.	.	PROPN
ejpam-4722	409	1	on	on	ADP
ejpam-4722	409	2	the	the	DET
ejpam-4722	409	3	extremal	extremal	ADJ
ejpam-4722	409	4	mostar	mostar	PROPN
ejpam-4722	409	5	indices	index	NOUN
ejpam-4722	409	6	of	of	ADP
ejpam-4722	409	7	trees	tree	NOUN
ejpam-4722	409	8	with	with	ADP
ejpam-4722	409	9	a	a	DET
ejpam-4722	409	10	given	give	VERB
ejpam-4722	409	11	segment	segment	NOUN
ejpam-4722	409	12	sequence	sequence	NOUN
ejpam-4722	409	13	.	.	PUNCT
ejpam-4722	410	1	bulletin	bulletin	NOUN
ejpam-4722	410	2	of	of	ADP
ejpam-4722	410	3	the	the	DET
ejpam-4722	410	4	malaysian	malaysian	PROPN
ejpam-4722	410	5	mathematical	mathematical	PROPN
ejpam-4722	410	6	sciences	sciences	PROPN
ejpam-4722	410	7	society	society	NOUN
ejpam-4722	410	8	,	,	PUNCT
ejpam-4722	410	9	pages	page	NOUN
ejpam-4722	410	10	1–20	1–20	PROPN
ejpam-4722	410	11	,	,	PUNCT
ejpam-4722	410	12	2022	2022	NUM
ejpam-4722	410	13	.	.	PUNCT
ejpam-4722	411	1	[	[	X
ejpam-4722	411	2	14	14	NUM
ejpam-4722	411	3	]	]	X
ejpam-4722	411	4	kecai	kecai	PROPN
ejpam-4722	411	5	deng	deng	PROPN
ejpam-4722	411	6	and	and	CCONJ
ejpam-4722	411	7	shuchao	shuchao	ADJ
ejpam-4722	411	8	li	li	PROPN
ejpam-4722	411	9	.	.	PROPN
ejpam-4722	412	1	on	on	ADP
ejpam-4722	412	2	the	the	DET
ejpam-4722	412	3	extremal	extremal	ADJ
ejpam-4722	412	4	mostar	mostar	PROPN
ejpam-4722	412	5	indices	index	NOUN
ejpam-4722	412	6	of	of	ADP
ejpam-4722	412	7	trees	tree	NOUN
ejpam-4722	412	8	with	with	ADP
ejpam-4722	412	9	a	a	DET
ejpam-4722	412	10	given	give	VERB
ejpam-4722	412	11	segment	segment	NOUN
ejpam-4722	412	12	sequence	sequence	NOUN
ejpam-4722	412	13	.	.	PUNCT
ejpam-4722	413	1	bulletin	bulletin	NOUN
ejpam-4722	413	2	of	of	ADP
ejpam-4722	413	3	the	the	DET
ejpam-4722	413	4	malaysian	malaysian	PROPN
ejpam-4722	413	5	mathematical	mathematical	PROPN
ejpam-4722	413	6	sciences	sciences	PROPN
ejpam-4722	413	7	society	society	NOUN
ejpam-4722	413	8	,	,	PUNCT
ejpam-4722	413	9	pages	page	NOUN
ejpam-4722	413	10	1–20	1–20	PROPN
ejpam-4722	413	11	,	,	PUNCT
ejpam-4722	413	12	2022	2022	NUM
ejpam-4722	413	13	.	.	PUNCT
ejpam-4722	414	1	[	[	X
ejpam-4722	414	2	15	15	NUM
ejpam-4722	414	3	]	]	X
ejpam-4722	414	4	tomislav	tomislav	PROPN
ejpam-4722	414	5	došlić	došlić	PROPN
ejpam-4722	414	6	,	,	PUNCT
ejpam-4722	414	7	ivica	ivica	PROPN
ejpam-4722	414	8	martinjak	martinjak	PROPN
ejpam-4722	414	9	,	,	PUNCT
ejpam-4722	414	10	riste	riste	NOUN
ejpam-4722	414	11	škrekovski	škrekovski	PROPN
ejpam-4722	414	12	,	,	PUNCT
ejpam-4722	414	13	sanja	sanja	X
ejpam-4722	414	14	tipurić	tipurić	PROPN
ejpam-4722	414	15	spužević	spužević	PROPN
ejpam-4722	414	16	,	,	PUNCT
ejpam-4722	414	17	and	and	CCONJ
ejpam-4722	414	18	ivana	ivana	PROPN
ejpam-4722	414	19	zubac	zubac	PROPN
ejpam-4722	414	20	.	.	PUNCT
ejpam-4722	415	1	mostar	mostar	PROPN
ejpam-4722	415	2	index	index	PROPN
ejpam-4722	415	3	.	.	PUNCT
ejpam-4722	416	1	journal	journal	PROPN
ejpam-4722	416	2	of	of	ADP
ejpam-4722	416	3	mathematical	mathematical	ADJ
ejpam-4722	416	4	chemistry	chemistry	NOUN
ejpam-4722	416	5	,	,	PUNCT
ejpam-4722	416	6	56(10):2995–3013	56(10):2995–3013	NUM
ejpam-4722	416	7	,	,	PUNCT
ejpam-4722	416	8	2018	2018	NUM
ejpam-4722	416	9	.	.	PUNCT
ejpam-4722	417	1	[	[	X
ejpam-4722	417	2	16	16	NUM
ejpam-4722	417	3	]	]	X
ejpam-4722	417	4	ma	ma	PROPN
ejpam-4722	417	5	christine	christine	PROPN
ejpam-4722	417	6	g	g	PROPN
ejpam-4722	417	7	egan	egan	PROPN
ejpam-4722	417	8	,	,	PUNCT
ejpam-4722	417	9	john	john	PROPN
ejpam-4722	417	10	rafael	rafael	PROPN
ejpam-4722	417	11	m	m	PROPN
ejpam-4722	417	12	antalan	antalan	PROPN
ejpam-4722	417	13	,	,	PUNCT
ejpam-4722	417	14	et	et	PROPN
ejpam-4722	417	15	al	al	PROPN
ejpam-4722	417	16	.	.	PROPN
ejpam-4722	418	1	on	on	ADP
ejpam-4722	418	2	the	the	DET
ejpam-4722	418	3	wiener	wiener	NOUN
ejpam-4722	418	4	and	and	CCONJ
ejpam-4722	418	5	harary	harary	ADJ
ejpam-4722	418	6	index	index	NOUN
ejpam-4722	418	7	of	of	ADP
ejpam-4722	418	8	splitting	splitting	NOUN
ejpam-4722	418	9	graphs	graph	NOUN
ejpam-4722	418	10	.	.	PUNCT
ejpam-4722	419	1	european	european	ADJ
ejpam-4722	419	2	journal	journal	PROPN
ejpam-4722	419	3	of	of	ADP
ejpam-4722	419	4	pure	pure	ADJ
ejpam-4722	419	5	and	and	CCONJ
ejpam-4722	419	6	applied	applied	ADJ
ejpam-4722	419	7	mathematics	mathematic	NOUN
ejpam-4722	419	8	,	,	PUNCT
ejpam-4722	419	9	15(2):602–619	15(2):602–619	NUM
ejpam-4722	419	10	,	,	PUNCT
ejpam-4722	419	11	2022	2022	NUM
ejpam-4722	419	12	.	.	PUNCT
ejpam-4722	420	1	[	[	X
ejpam-4722	420	2	17	17	NUM
ejpam-4722	420	3	]	]	X
ejpam-4722	420	4	hongbo	hongbo	PROPN
ejpam-4722	420	5	hua	hua	PROPN
ejpam-4722	420	6	.	.	PROPN
ejpam-4722	421	1	on	on	ADP
ejpam-4722	421	2	the	the	DET
ejpam-4722	421	3	quotients	quotient	NOUN
ejpam-4722	421	4	between	between	ADP
ejpam-4722	421	5	the	the	DET
ejpam-4722	421	6	eccentric	eccentric	ADJ
ejpam-4722	421	7	connectivity	connectivity	NOUN
ejpam-4722	421	8	index	index	NOUN
ejpam-4722	421	9	and	and	CCONJ
ejpam-4722	421	10	the	the	DET
ejpam-4722	421	11	eccentric	eccentric	ADJ
ejpam-4722	421	12	distance	distance	NOUN
ejpam-4722	421	13	sum	sum	NOUN
ejpam-4722	421	14	of	of	ADP
ejpam-4722	421	15	graphs	graph	NOUN
ejpam-4722	421	16	with	with	ADP
ejpam-4722	421	17	diameter	diameter	NOUN
ejpam-4722	421	18	2	2	NUM
ejpam-4722	421	19	.	.	NOUN
ejpam-4722	421	20	discrete	discrete	ADJ
ejpam-4722	421	21	applied	apply	VERB
ejpam-4722	421	22	mathematics	mathematic	NOUN
ejpam-4722	421	23	,	,	PUNCT
ejpam-4722	421	24	285:297–300	285:297–300	NUM
ejpam-4722	421	25	,	,	PUNCT
ejpam-4722	421	26	2020	2020	NUM
ejpam-4722	421	27	.	.	PUNCT
ejpam-4722	422	1	[	[	X
ejpam-4722	422	2	18	18	NUM
ejpam-4722	422	3	]	]	X
ejpam-4722	422	4	hongbo	hongbo	PROPN
ejpam-4722	422	5	hua	hua	PROPN
ejpam-4722	422	6	and	and	CCONJ
ejpam-4722	422	7	kinkar	kinkar	PROPN
ejpam-4722	422	8	ch	ch	PROPN
ejpam-4722	422	9	das	das	PROPN
ejpam-4722	422	10	.	.	PUNCT
ejpam-4722	423	1	on	on	ADP
ejpam-4722	423	2	the	the	DET
ejpam-4722	423	3	wiener	wiener	NOUN
ejpam-4722	423	4	polarity	polarity	NOUN
ejpam-4722	423	5	index	index	NOUN
ejpam-4722	423	6	of	of	ADP
ejpam-4722	423	7	graphs	graph	NOUN
ejpam-4722	423	8	.	.	PUNCT
ejpam-4722	424	1	applied	apply	VERB
ejpam-4722	424	2	mathematics	mathematic	NOUN
ejpam-4722	424	3	and	and	CCONJ
ejpam-4722	424	4	computation	computation	NOUN
ejpam-4722	424	5	,	,	PUNCT
ejpam-4722	424	6	280:162–167	280:162–167	NUM
ejpam-4722	424	7	,	,	PUNCT
ejpam-4722	424	8	2016	2016	NUM
ejpam-4722	424	9	.	.	PUNCT
ejpam-4722	425	1	[	[	X
ejpam-4722	425	2	19	19	NUM
ejpam-4722	425	3	]	]	X
ejpam-4722	425	4	muhammad	muhammad	PROPN
ejpam-4722	425	5	imran	imran	PROPN
ejpam-4722	425	6	,	,	PUNCT
ejpam-4722	425	7	shehnaz	shehnaz	PROPN
ejpam-4722	425	8	akhter	akhter	PROPN
ejpam-4722	425	9	,	,	PUNCT
ejpam-4722	425	10	farhana	farhana	PROPN
ejpam-4722	425	11	yasmeen	yasmeen	PROPN
ejpam-4722	425	12	,	,	PUNCT
ejpam-4722	425	13	and	and	CCONJ
ejpam-4722	425	14	kashif	kashif	PROPN
ejpam-4722	425	15	ali	ali	PROPN
ejpam-4722	425	16	.	.	PUNCT
ejpam-4722	426	1	the	the	DET
ejpam-4722	426	2	weighted	weight	VERB
ejpam-4722	426	3	mostar	mostar	PROPN
ejpam-4722	426	4	invariants	invariant	NOUN
ejpam-4722	426	5	of	of	ADP
ejpam-4722	426	6	phthalocyanines	phthalocyanine	NOUN
ejpam-4722	426	7	,	,	PUNCT
ejpam-4722	426	8	triazine	triazine	NOUN
ejpam-4722	426	9	-	-	PUNCT
ejpam-4722	426	10	based	base	VERB
ejpam-4722	426	11	and	and	CCONJ
ejpam-4722	426	12	nanostar	nanostar	ADJ
ejpam-4722	426	13	dendrimers	dendrimer	NOUN
ejpam-4722	426	14	.	.	PUNCT
ejpam-4722	427	1	polycyclic	polycyclic	ADJ
ejpam-4722	427	2	aromatic	aromatic	ADJ
ejpam-4722	427	3	compounds	compound	NOUN
ejpam-4722	427	4	,	,	PUNCT
ejpam-4722	427	5	43(1):772–789	43(1):772–789	PROPN
ejpam-4722	427	6	,	,	PUNCT
ejpam-4722	427	7	2023	2023	NUM
ejpam-4722	427	8	.	.	PUNCT
ejpam-4722	428	1	references	reference	NOUN
ejpam-4722	428	2	1808	1808	NUM
ejpam-4722	429	1	[	[	X
ejpam-4722	429	2	20	20	NUM
ejpam-4722	429	3	]	]	X
ejpam-4722	429	4	p	p	X
ejpam-4722	429	5	kandan	kandan	PROPN
ejpam-4722	429	6	,	,	PUNCT
ejpam-4722	429	7	s	s	VERB
ejpam-4722	429	8	subramanian	subramanian	ADJ
ejpam-4722	429	9	,	,	PUNCT
ejpam-4722	429	10	and	and	CCONJ
ejpam-4722	429	11	p	p	PROPN
ejpam-4722	429	12	rajesh	rajesh	PROPN
ejpam-4722	429	13	.	.	PUNCT
ejpam-4722	430	1	weighted	weight	VERB
ejpam-4722	430	2	mostar	mostar	PROPN
ejpam-4722	430	3	indices	index	NOUN
ejpam-4722	430	4	of	of	ADP
ejpam-4722	430	5	certain	certain	ADJ
ejpam-4722	430	6	graphs	graph	NOUN
ejpam-4722	430	7	.	.	PUNCT
ejpam-4722	431	1	adv	adv	PROPN
ejpam-4722	431	2	.	.	PUNCT
ejpam-4722	431	3	math	math	PROPN
ejpam-4722	431	4	.	.	PUNCT
ejpam-4722	432	1	sci	sci	PROPN
ejpam-4722	432	2	.	.	PUNCT
ejpam-4722	433	1	j	j	PROPN
ejpam-4722	433	2	,	,	PUNCT
ejpam-4722	433	3	10:3093–3111	10:3093–3111	NUM
ejpam-4722	433	4	,	,	PUNCT
ejpam-4722	433	5	2021	2021	NUM
ejpam-4722	433	6	.	.	PUNCT
ejpam-4722	434	1	[	[	X
ejpam-4722	434	2	21	21	NUM
ejpam-4722	434	3	]	]	X
ejpam-4722	434	4	sandi	sandi	PROPN
ejpam-4722	434	5	klavžar	klavžar	PROPN
ejpam-4722	434	6	,	,	PUNCT
ejpam-4722	434	7	shuchao	shuchao	ADJ
ejpam-4722	434	8	li	li	PROPN
ejpam-4722	434	9	,	,	PUNCT
ejpam-4722	434	10	and	and	CCONJ
ejpam-4722	434	11	huihui	huihui	PROPN
ejpam-4722	434	12	zhang	zhang	PROPN
ejpam-4722	434	13	.	.	PUNCT
ejpam-4722	435	1	on	on	ADP
ejpam-4722	435	2	the	the	DET
ejpam-4722	435	3	difference	difference	NOUN
ejpam-4722	435	4	between	between	ADP
ejpam-4722	435	5	the	the	DET
ejpam-4722	435	6	(	(	PUNCT
ejpam-4722	435	7	revised	revised	ADJ
ejpam-4722	435	8	)	)	PUNCT
ejpam-4722	435	9	szeged	szeged	PROPN
ejpam-4722	435	10	index	index	NOUN
ejpam-4722	435	11	and	and	CCONJ
ejpam-4722	435	12	the	the	DET
ejpam-4722	435	13	wiener	wiener	NOUN
ejpam-4722	435	14	index	index	NOUN
ejpam-4722	435	15	of	of	ADP
ejpam-4722	435	16	cacti	cacti	PROPN
ejpam-4722	435	17	.	.	PUNCT
ejpam-4722	436	1	discrete	discrete	ADJ
ejpam-4722	436	2	applied	apply	VERB
ejpam-4722	436	3	mathematics	mathematic	NOUN
ejpam-4722	436	4	,	,	PUNCT
ejpam-4722	436	5	247:77–89	247:77–89	NUM
ejpam-4722	436	6	,	,	PUNCT
ejpam-4722	436	7	2018	2018	NUM
ejpam-4722	436	8	.	.	PUNCT
ejpam-4722	437	1	[	[	X
ejpam-4722	437	2	22	22	NUM
ejpam-4722	437	3	]	]	X
ejpam-4722	437	4	hui	hui	PROPN
ejpam-4722	437	5	lei	lei	PROPN
ejpam-4722	437	6	,	,	PUNCT
ejpam-4722	437	7	tao	tao	PROPN
ejpam-4722	437	8	li	li	PROPN
ejpam-4722	437	9	,	,	PUNCT
ejpam-4722	437	10	yongtang	yongtang	PROPN
ejpam-4722	437	11	shi	shi	PROPN
ejpam-4722	437	12	,	,	PUNCT
ejpam-4722	437	13	and	and	CCONJ
ejpam-4722	437	14	hua	hua	PROPN
ejpam-4722	437	15	wang	wang	PROPN
ejpam-4722	437	16	.	.	PUNCT
ejpam-4722	438	1	wiener	wiener	NOUN
ejpam-4722	438	2	polarity	polarity	NOUN
ejpam-4722	438	3	index	index	NOUN
ejpam-4722	438	4	and	and	CCONJ
ejpam-4722	438	5	its	its	PRON
ejpam-4722	438	6	generalization	generalization	NOUN
ejpam-4722	438	7	in	in	ADP
ejpam-4722	438	8	trees	tree	NOUN
ejpam-4722	438	9	.	.	PUNCT
ejpam-4722	439	1	match	match	PROPN
ejpam-4722	439	2	commun	commun	PROPN
ejpam-4722	439	3	.	.	PUNCT
ejpam-4722	440	1	math	math	PROPN
ejpam-4722	440	2	.	.	PUNCT
ejpam-4722	441	1	comput	comput	NOUN
ejpam-4722	441	2	.	.	PUNCT
ejpam-4722	442	1	chem	chem	NOUN
ejpam-4722	442	2	,	,	PUNCT
ejpam-4722	442	3	78(1):199–212	78(1):199–212	NOUN
ejpam-4722	442	4	,	,	PUNCT
ejpam-4722	442	5	2017	2017	NUM
ejpam-4722	442	6	.	.	PUNCT
ejpam-4722	443	1	[	[	X
ejpam-4722	443	2	23	23	NUM
ejpam-4722	443	3	]	]	X
ejpam-4722	443	4	guorong	guorong	PROPN
ejpam-4722	443	5	liu	liu	PROPN
ejpam-4722	443	6	and	and	CCONJ
ejpam-4722	443	7	kecai	kecai	PROPN
ejpam-4722	443	8	deng	deng	PROPN
ejpam-4722	443	9	.	.	PUNCT
ejpam-4722	444	1	the	the	DET
ejpam-4722	444	2	maximum	maximum	PROPN
ejpam-4722	444	3	mostar	mostar	PROPN
ejpam-4722	444	4	indices	index	NOUN
ejpam-4722	444	5	of	of	ADP
ejpam-4722	444	6	unicyclic	unicyclic	ADJ
ejpam-4722	444	7	graphs	graph	NOUN
ejpam-4722	444	8	with	with	ADP
ejpam-4722	444	9	given	give	VERB
ejpam-4722	444	10	diameter	diameter	NOUN
ejpam-4722	444	11	.	.	PUNCT
ejpam-4722	445	1	applied	apply	VERB
ejpam-4722	445	2	mathematics	mathematic	NOUN
ejpam-4722	445	3	and	and	CCONJ
ejpam-4722	445	4	computation	computation	NOUN
ejpam-4722	445	5	,	,	PUNCT
ejpam-4722	445	6	439:127636	439:127636	NOUN
ejpam-4722	445	7	,	,	PUNCT
ejpam-4722	445	8	2023	2023	NUM
ejpam-4722	445	9	.	.	PUNCT
ejpam-4722	446	1	[	[	X
ejpam-4722	446	2	24	24	NUM
ejpam-4722	446	3	]	]	X
ejpam-4722	446	4	hechao	hechao	PROPN
ejpam-4722	446	5	liu	liu	PROPN
ejpam-4722	446	6	,	,	PUNCT
ejpam-4722	446	7	ling	ling	PROPN
ejpam-4722	446	8	song	song	NOUN
ejpam-4722	446	9	,	,	PUNCT
ejpam-4722	446	10	qiqi	qiqi	PROPN
ejpam-4722	446	11	xiao	xiao	PROPN
ejpam-4722	446	12	,	,	PUNCT
ejpam-4722	446	13	and	and	CCONJ
ejpam-4722	446	14	zikai	zikai	PROPN
ejpam-4722	446	15	tang	tang	PROPN
ejpam-4722	446	16	.	.	PUNCT
ejpam-4722	447	1	on	on	ADP
ejpam-4722	447	2	edge	edge	PROPN
ejpam-4722	447	3	mostar	mostar	PROPN
ejpam-4722	447	4	index	index	NOUN
ejpam-4722	447	5	of	of	ADP
ejpam-4722	447	6	graphs	graph	NOUN
ejpam-4722	447	7	.	.	PUNCT
ejpam-4722	448	1	iranian	iranian	ADJ
ejpam-4722	448	2	journal	journal	PROPN
ejpam-4722	448	3	of	of	ADP
ejpam-4722	448	4	mathematical	mathematical	ADJ
ejpam-4722	448	5	chemistry	chemistry	NOUN
ejpam-4722	448	6	,	,	PUNCT
ejpam-4722	448	7	11(2):95–106	11(2):95–106	NUM
ejpam-4722	448	8	,	,	PUNCT
ejpam-4722	448	9	2020	2020	NUM
ejpam-4722	448	10	.	.	PUNCT
ejpam-4722	449	1	[	[	X
ejpam-4722	449	2	25	25	NUM
ejpam-4722	449	3	]	]	X
ejpam-4722	449	4	štefko	štefko	PROPN
ejpam-4722	449	5	miklavič	miklavič	NOUN
ejpam-4722	449	6	,	,	PUNCT
ejpam-4722	449	7	johannes	johannes	PROPN
ejpam-4722	449	8	pardey	pardey	NOUN
ejpam-4722	449	9	,	,	PUNCT
ejpam-4722	449	10	dieter	dieter	VERB
ejpam-4722	449	11	rautenbach	rautenbach	NOUN
ejpam-4722	449	12	,	,	PUNCT
ejpam-4722	449	13	and	and	CCONJ
ejpam-4722	449	14	florian	florian	PROPN
ejpam-4722	449	15	werner	werner	PROPN
ejpam-4722	449	16	.	.	PUNCT
ejpam-4722	450	1	maximizing	maximize	VERB
ejpam-4722	450	2	the	the	DET
ejpam-4722	450	3	mostar	mostar	PROPN
ejpam-4722	450	4	index	index	NOUN
ejpam-4722	450	5	for	for	ADP
ejpam-4722	450	6	bipartite	bipartite	NOUN
ejpam-4722	450	7	graphs	graph	NOUN
ejpam-4722	450	8	and	and	CCONJ
ejpam-4722	450	9	split	split	ADJ
ejpam-4722	450	10	graphs	graph	NOUN
ejpam-4722	450	11	.	.	PUNCT
ejpam-4722	451	1	discrete	discrete	ADJ
ejpam-4722	451	2	optimization	optimization	NOUN
ejpam-4722	451	3	,	,	PUNCT
ejpam-4722	451	4	48:100768	48:100768	NUM
ejpam-4722	451	5	,	,	PUNCT
ejpam-4722	451	6	2023	2023	NUM
ejpam-4722	451	7	.	.	PUNCT
ejpam-4722	452	1	[	[	X
ejpam-4722	452	2	26	26	NUM
ejpam-4722	452	3	]	]	PUNCT
ejpam-4722	452	4	aleksandra	aleksandra	PROPN
ejpam-4722	452	5	tepeh	tepeh	PROPN
ejpam-4722	452	6	.	.	PUNCT
ejpam-4722	453	1	extremal	extremal	ADJ
ejpam-4722	453	2	bicyclic	bicyclic	NOUN
ejpam-4722	453	3	graphs	graph	NOUN
ejpam-4722	453	4	with	with	ADP
ejpam-4722	453	5	respect	respect	NOUN
ejpam-4722	453	6	to	to	ADP
ejpam-4722	453	7	mostar	mostar	PROPN
ejpam-4722	453	8	index	index	PROPN
ejpam-4722	453	9	.	.	PUNCT
ejpam-4722	454	1	applied	apply	VERB
ejpam-4722	454	2	mathematics	mathematic	NOUN
ejpam-4722	454	3	and	and	CCONJ
ejpam-4722	454	4	computation	computation	NOUN
ejpam-4722	454	5	,	,	PUNCT
ejpam-4722	454	6	355:319–324	355:319–324	NUM
ejpam-4722	454	7	,	,	PUNCT
ejpam-4722	454	8	2019	2019	NUM
ejpam-4722	454	9	.	.	PUNCT
ejpam-4722	455	1	[	[	X
ejpam-4722	455	2	27	27	NUM
ejpam-4722	455	3	]	]	X
ejpam-4722	455	4	asad	asad	PROPN
ejpam-4722	455	5	ullah	ullah	PROPN
ejpam-4722	455	6	,	,	PUNCT
ejpam-4722	455	7	muhammad	muhammad	PROPN
ejpam-4722	455	8	qasim	qasim	PROPN
ejpam-4722	455	9	,	,	PUNCT
ejpam-4722	455	10	shahid	shahid	PROPN
ejpam-4722	455	11	zaman	zaman	PROPN
ejpam-4722	455	12	,	,	PUNCT
ejpam-4722	455	13	and	and	CCONJ
ejpam-4722	455	14	asad	asad	PROPN
ejpam-4722	455	15	khan	khan	PROPN
ejpam-4722	455	16	.	.	PUNCT
ejpam-4722	456	1	computational	computational	ADJ
ejpam-4722	456	2	and	and	CCONJ
ejpam-4722	456	3	comparative	comparative	ADJ
ejpam-4722	456	4	aspects	aspect	NOUN
ejpam-4722	456	5	of	of	ADP
ejpam-4722	456	6	two	two	NUM
ejpam-4722	456	7	carbon	carbon	NOUN
ejpam-4722	456	8	nanosheets	nanosheet	NOUN
ejpam-4722	456	9	with	with	ADP
ejpam-4722	456	10	respect	respect	NOUN
ejpam-4722	456	11	to	to	ADP
ejpam-4722	456	12	some	some	DET
ejpam-4722	456	13	novel	novel	ADJ
ejpam-4722	456	14	topological	topological	ADJ
ejpam-4722	456	15	indices	index	NOUN
ejpam-4722	456	16	.	.	PUNCT
ejpam-4722	457	1	ain	ain	PROPN
ejpam-4722	457	2	shams	sham	VERB
ejpam-4722	457	3	engineering	engineering	NOUN
ejpam-4722	457	4	journal	journal	NOUN
ejpam-4722	457	5	,	,	PUNCT
ejpam-4722	457	6	13(4):101672	13(4):101672	NUM
ejpam-4722	457	7	,	,	PUNCT
ejpam-4722	457	8	2022	2022	NUM
ejpam-4722	457	9	.	.	PUNCT
ejpam-4722	458	1	[	[	X
ejpam-4722	458	2	28	28	NUM
ejpam-4722	458	3	]	]	SYM
ejpam-4722	458	4	min	min	PROPN
ejpam-4722	458	5	wang	wang	PROPN
ejpam-4722	458	6	and	and	CCONJ
ejpam-4722	458	7	mengmeng	mengmeng	PROPN
ejpam-4722	458	8	liu	liu	PROPN
ejpam-4722	458	9	.	.	PUNCT
ejpam-4722	459	1	on	on	ADP
ejpam-4722	459	2	the	the	DET
ejpam-4722	459	3	difference	difference	NOUN
ejpam-4722	459	4	between	between	ADP
ejpam-4722	459	5	the	the	DET
ejpam-4722	459	6	szeged	szeged	PROPN
ejpam-4722	459	7	index	index	NOUN
ejpam-4722	459	8	and	and	CCONJ
ejpam-4722	459	9	the	the	DET
ejpam-4722	459	10	wiener	wiener	NOUN
ejpam-4722	459	11	index	index	NOUN
ejpam-4722	459	12	of	of	ADP
ejpam-4722	459	13	cacti	cacti	PROPN
ejpam-4722	459	14	.	.	PUNCT
ejpam-4722	460	1	discrete	discrete	ADJ
ejpam-4722	460	2	applied	apply	VERB
ejpam-4722	460	3	mathematics	mathematic	NOUN
ejpam-4722	460	4	,	,	PUNCT
ejpam-4722	460	5	311:35–37	311:35–37	PROPN
ejpam-4722	460	6	,	,	PUNCT
ejpam-4722	460	7	2022	2022	NUM
ejpam-4722	460	8	.	.	PUNCT
ejpam-4722	461	1	[	[	X
ejpam-4722	461	2	29	29	NUM
ejpam-4722	461	3	]	]	X
ejpam-4722	461	4	shujing	shuje	VERB
ejpam-4722	461	5	wang	wang	PROPN
ejpam-4722	461	6	.	.	PUNCT
ejpam-4722	462	1	on	on	ADP
ejpam-4722	462	2	extremal	extremal	ADJ
ejpam-4722	462	3	cacti	cacti	NOUN
ejpam-4722	462	4	with	with	ADP
ejpam-4722	462	5	respect	respect	NOUN
ejpam-4722	462	6	to	to	ADP
ejpam-4722	462	7	the	the	DET
ejpam-4722	462	8	revised	revise	VERB
ejpam-4722	462	9	szeged	szeged	PROPN
ejpam-4722	462	10	index	index	PROPN
ejpam-4722	462	11	.	.	PUNCT
ejpam-4722	463	1	discrete	discrete	VERB
ejpam-4722	463	2	applied	applied	ADJ
ejpam-4722	463	3	mathematics	mathematic	NOUN
ejpam-4722	463	4	,	,	PUNCT
ejpam-4722	463	5	233:231–239	233:231–239	NUM
ejpam-4722	463	6	,	,	PUNCT
ejpam-4722	463	7	2017	2017	NUM
ejpam-4722	463	8	.	.	PUNCT
ejpam-4722	464	1	[	[	X
ejpam-4722	464	2	30	30	NUM
ejpam-4722	464	3	]	]	X
ejpam-4722	464	4	shujing	shuje	VERB
ejpam-4722	464	5	wang	wang	PROPN
ejpam-4722	464	6	.	.	PUNCT
ejpam-4722	465	1	on	on	ADP
ejpam-4722	465	2	extremal	extremal	ADJ
ejpam-4722	465	3	cacti	cacti	NOUN
ejpam-4722	465	4	with	with	ADP
ejpam-4722	465	5	respect	respect	NOUN
ejpam-4722	465	6	to	to	ADP
ejpam-4722	465	7	the	the	DET
ejpam-4722	465	8	szeged	szeged	PROPN
ejpam-4722	465	9	index	index	PROPN
ejpam-4722	465	10	.	.	PUNCT
ejpam-4722	466	1	applied	apply	VERB
ejpam-4722	466	2	mathematics	mathematic	NOUN
ejpam-4722	466	3	and	and	CCONJ
ejpam-4722	466	4	computation	computation	NOUN
ejpam-4722	466	5	,	,	PUNCT
ejpam-4722	466	6	309:85–92	309:85–92	NUM
ejpam-4722	466	7	,	,	PUNCT
ejpam-4722	466	8	2017	2017	NUM
ejpam-4722	466	9	.	.	PUNCT
ejpam-4722	467	1	[	[	X
ejpam-4722	467	2	31	31	NUM
ejpam-4722	467	3	]	]	X
ejpam-4722	467	4	harry	harry	PROPN
ejpam-4722	467	5	wiener	wiener	PROPN
ejpam-4722	467	6	.	.	PUNCT
ejpam-4722	468	1	structural	structural	ADJ
ejpam-4722	468	2	determination	determination	NOUN
ejpam-4722	468	3	of	of	ADP
ejpam-4722	468	4	paraffin	paraffin	NOUN
ejpam-4722	468	5	boiling	boiling	NOUN
ejpam-4722	468	6	points	point	NOUN
ejpam-4722	468	7	.	.	PUNCT
ejpam-4722	469	1	journal	journal	NOUN
ejpam-4722	469	2	of	of	ADP
ejpam-4722	469	3	the	the	DET
ejpam-4722	469	4	american	american	PROPN
ejpam-4722	469	5	chemical	chemical	PROPN
ejpam-4722	469	6	society	society	PROPN
ejpam-4722	469	7	,	,	PUNCT
ejpam-4722	469	8	69(1):17–20	69(1):17–20	NUM
ejpam-4722	469	9	,	,	PUNCT
ejpam-4722	469	10	1947	1947	NUM
ejpam-4722	469	11	.	.	PUNCT
ejpam-4722	470	1	[	[	X
ejpam-4722	470	2	32	32	NUM
ejpam-4722	470	3	]	]	PUNCT
ejpam-4722	470	4	harry	harry	PROPN
ejpam-4722	470	5	wiener	wiener	PROPN
ejpam-4722	470	6	.	.	PUNCT
ejpam-4722	471	1	structural	structural	ADJ
ejpam-4722	471	2	determination	determination	NOUN
ejpam-4722	471	3	of	of	ADP
ejpam-4722	471	4	paraffin	paraffin	NOUN
ejpam-4722	471	5	boiling	boiling	NOUN
ejpam-4722	471	6	points	point	NOUN
ejpam-4722	471	7	.	.	PUNCT
ejpam-4722	472	1	journal	journal	NOUN
ejpam-4722	472	2	of	of	ADP
ejpam-4722	472	3	the	the	DET
ejpam-4722	472	4	american	american	PROPN
ejpam-4722	472	5	chemical	chemical	PROPN
ejpam-4722	472	6	society	society	PROPN
ejpam-4722	472	7	,	,	PUNCT
ejpam-4722	472	8	69(1):17–20	69(1):17–20	NUM
ejpam-4722	472	9	,	,	PUNCT
ejpam-4722	472	10	1947	1947	NUM
ejpam-4722	472	11	.	.	PUNCT
ejpam-4722	473	1	[	[	X
ejpam-4722	473	2	33	33	NUM
ejpam-4722	473	3	]	]	X
ejpam-4722	473	4	ke	ke	PROPN
ejpam-4722	473	5	xiang	xiang	PROPN
ejpam-4722	473	6	xu	xu	PROPN
ejpam-4722	473	7	,	,	PUNCT
ejpam-4722	473	8	kinkar	kinkar	PROPN
ejpam-4722	473	9	chandra	chandra	PROPN
ejpam-4722	473	10	das	das	PROPN
ejpam-4722	473	11	,	,	PUNCT
ejpam-4722	473	12	ivan	ivan	PROPN
ejpam-4722	473	13	gutman	gutman	PROPN
ejpam-4722	473	14	,	,	PUNCT
ejpam-4722	473	15	and	and	CCONJ
ejpam-4722	473	16	meng	meng	PROPN
ejpam-4722	473	17	lu	lu	PROPN
ejpam-4722	473	18	wang	wang	PROPN
ejpam-4722	473	19	.	.	PUNCT
ejpam-4722	474	1	comparison	comparison	NOUN
ejpam-4722	474	2	between	between	ADP
ejpam-4722	474	3	merrifield	merrifield	PROPN
ejpam-4722	474	4	-	-	PUNCT
ejpam-4722	474	5	simmons	simmon	NOUN
ejpam-4722	474	6	index	index	NOUN
ejpam-4722	474	7	and	and	CCONJ
ejpam-4722	474	8	wiener	wiener	NOUN
ejpam-4722	474	9	index	index	NOUN
ejpam-4722	474	10	of	of	ADP
ejpam-4722	474	11	graphs	graph	NOUN
ejpam-4722	474	12	.	.	PUNCT
ejpam-4722	475	1	acta	acta	PROPN
ejpam-4722	475	2	mathematica	mathematica	PROPN
ejpam-4722	475	3	sinica	sinica	PROPN
ejpam-4722	475	4	,	,	PUNCT
ejpam-4722	475	5	english	english	ADJ
ejpam-4722	475	6	series	series	NOUN
ejpam-4722	475	7	,	,	PUNCT
ejpam-4722	475	8	pages	page	NOUN
ejpam-4722	475	9	1–11	1–11	PROPN
ejpam-4722	475	10	,	,	PUNCT
ejpam-4722	475	11	2022	2022	NUM
ejpam-4722	475	12	.	.	PUNCT
ejpam-4722	476	1	[	[	X
ejpam-4722	476	2	34	34	NUM
ejpam-4722	476	3	]	]	X
ejpam-4722	476	4	farhana	farhana	PROPN
ejpam-4722	476	5	yasmeen	yasmeen	PROPN
ejpam-4722	476	6	,	,	PUNCT
ejpam-4722	476	7	shehnaz	shehnaz	PROPN
ejpam-4722	476	8	akhter	akhter	PROPN
ejpam-4722	476	9	,	,	PUNCT
ejpam-4722	476	10	kashif	kashif	PROPN
ejpam-4722	476	11	ali	ali	PROPN
ejpam-4722	476	12	,	,	PUNCT
ejpam-4722	476	13	and	and	CCONJ
ejpam-4722	476	14	syed	syed	ADJ
ejpam-4722	476	15	tahir	tahir	PROPN
ejpam-4722	476	16	raza	raza	PROPN
ejpam-4722	476	17	rizvi	rizvi	PROPN
ejpam-4722	476	18	.	.	PUNCT
ejpam-4722	477	1	edge	edge	PROPN
ejpam-4722	477	2	mostar	mostar	PROPN
ejpam-4722	477	3	indices	index	NOUN
ejpam-4722	477	4	of	of	ADP
ejpam-4722	477	5	cacti	cacti	ADJ
ejpam-4722	477	6	graph	graph	NOUN
ejpam-4722	477	7	with	with	ADP
ejpam-4722	477	8	fixed	fix	VERB
ejpam-4722	477	9	cycles	cycle	NOUN
ejpam-4722	477	10	.	.	PUNCT
ejpam-4722	478	1	frontiers	frontier	NOUN
ejpam-4722	478	2	in	in	ADP
ejpam-4722	478	3	chemistry	chemistry	NOUN
ejpam-4722	478	4	,	,	PUNCT
ejpam-4722	478	5	9:440	9:440	NUM
ejpam-4722	478	6	,	,	PUNCT
ejpam-4722	478	7	2021	2021	NUM
ejpam-4722	478	8	.	.	PUNCT
ejpam-4722	479	1	[	[	X
ejpam-4722	479	2	35	35	NUM
ejpam-4722	479	3	]	]	X
ejpam-4722	479	4	shahid	shahid	PROPN
ejpam-4722	479	5	zaman	zaman	PROPN
ejpam-4722	479	6	,	,	PUNCT
ejpam-4722	479	7	mehwish	mehwish	PROPN
ejpam-4722	479	8	jalani	jalani	PROPN
ejpam-4722	479	9	,	,	PUNCT
ejpam-4722	479	10	asad	asad	PROPN
ejpam-4722	479	11	ullah	ullah	PROPN
ejpam-4722	479	12	,	,	PUNCT
ejpam-4722	479	13	mubashir	mubashir	PROPN
ejpam-4722	479	14	ali	ali	PROPN
ejpam-4722	479	15	,	,	PUNCT
ejpam-4722	479	16	and	and	CCONJ
ejpam-4722	479	17	tayyba	tayyba	ADJ
ejpam-4722	479	18	shahzadi	shahzadi	PROPN
ejpam-4722	479	19	.	.	PUNCT
ejpam-4722	480	1	on	on	ADP
ejpam-4722	480	2	the	the	DET
ejpam-4722	480	3	topological	topological	ADJ
ejpam-4722	480	4	descriptors	descriptor	NOUN
ejpam-4722	480	5	and	and	CCONJ
ejpam-4722	480	6	structural	structural	ADJ
ejpam-4722	480	7	analysis	analysis	NOUN
ejpam-4722	480	8	of	of	ADP
ejpam-4722	480	9	cerium	cerium	ADJ
ejpam-4722	480	10	oxide	oxide	NOUN
ejpam-4722	480	11	nanostructures	nanostructure	NOUN
ejpam-4722	480	12	.	.	PUNCT
ejpam-4722	481	1	chemical	chemical	NOUN
ejpam-4722	481	2	papers	paper	NOUN
ejpam-4722	481	3	,	,	PUNCT
ejpam-4722	481	4	77(5):2917–2922	77(5):2917–2922	PROPN
ejpam-4722	481	5	,	,	PUNCT
ejpam-4722	481	6	2023	2023	NUM
ejpam-4722	481	7	.	.	PUNCT
ejpam-4722	482	1	[	[	X
ejpam-4722	482	2	36	36	NUM
ejpam-4722	482	3	]	]	X
ejpam-4722	482	4	wanping	wanping	PROPN
ejpam-4722	482	5	zhang	zhang	PROPN
ejpam-4722	482	6	,	,	PUNCT
ejpam-4722	482	7	jixiang	jixiang	PROPN
ejpam-4722	482	8	meng	meng	PROPN
ejpam-4722	482	9	,	,	PUNCT
ejpam-4722	482	10	and	and	CCONJ
ejpam-4722	482	11	baoyindureng	baoyindureng	PROPN
ejpam-4722	482	12	wu	wu	PROPN
ejpam-4722	482	13	.	.	PUNCT
ejpam-4722	483	1	extremal	extremal	ADJ
ejpam-4722	483	2	graphs	graph	NOUN
ejpam-4722	483	3	with	with	ADP
ejpam-4722	483	4	respect	respect	NOUN
ejpam-4722	483	5	to	to	ADP
ejpam-4722	483	6	two	two	NUM
ejpam-4722	483	7	distance	distance	NOUN
ejpam-4722	483	8	-	-	PUNCT
ejpam-4722	483	9	based	base	VERB
ejpam-4722	483	10	topological	topological	ADJ
ejpam-4722	483	11	indices	index	NOUN
ejpam-4722	483	12	.	.	PUNCT
ejpam-4722	484	1	discrete	discrete	ADJ
ejpam-4722	484	2	applied	apply	VERB
ejpam-4722	484	3	mathematics	mathematic	NOUN
ejpam-4722	484	4	,	,	PUNCT
ejpam-4722	484	5	317:63–74	317:63–74	PROPN
ejpam-4722	484	6	,	,	PUNCT
ejpam-4722	484	7	2022	2022	NUM
ejpam-4722	484	8	.	.	PUNCT