id	sid	tid	token	lemma	pos
ejpam-6540	1	1	european	european	PROPN
ejpam-6540	1	2	journal	journal	PROPN
ejpam-6540	1	3	of	of	ADP
ejpam-6540	1	4	pure	pure	ADJ
ejpam-6540	1	5	and	and	CCONJ
ejpam-6540	1	6	applied	applied	ADJ
ejpam-6540	1	7	mathematics	mathematic	NOUN
ejpam-6540	1	8	2025	2025	NUM
ejpam-6540	1	9	,	,	PUNCT
ejpam-6540	1	10	vol	vol	NOUN
ejpam-6540	1	11	.	.	PROPN
ejpam-6540	1	12	18	18	NUM
ejpam-6540	1	13	,	,	PUNCT
ejpam-6540	1	14	issue	issue	NOUN
ejpam-6540	1	15	3	3	NUM
ejpam-6540	1	16	,	,	PUNCT
ejpam-6540	1	17	article	article	NOUN
ejpam-6540	1	18	number	number	NOUN
ejpam-6540	1	19	6540	6540	NUM
ejpam-6540	1	20	issn	issn	PROPN
ejpam-6540	1	21	1307	1307	NUM
ejpam-6540	1	22	-	-	SYM
ejpam-6540	1	23	5543	5543	NUM
ejpam-6540	1	24	–	–	PUNCT
ejpam-6540	1	25	ejpam.com	ejpam.com	X
ejpam-6540	1	26	published	publish	VERB
ejpam-6540	1	27	by	by	ADP
ejpam-6540	1	28	new	new	PROPN
ejpam-6540	1	29	york	york	PROPN
ejpam-6540	1	30	business	business	PROPN
ejpam-6540	1	31	global	global	ADJ
ejpam-6540	1	32	resolving	resolve	VERB
ejpam-6540	1	33	parameters	parameter	NOUN
ejpam-6540	1	34	in	in	ADP
ejpam-6540	1	35	generalized	generalized	ADJ
ejpam-6540	1	36	sierpiński	sierpiński	ADJ
ejpam-6540	1	37	networks	network	NOUN
ejpam-6540	1	38	over	over	ADP
ejpam-6540	1	39	cycle	cycle	NOUN
ejpam-6540	1	40	of	of	ADP
ejpam-6540	1	41	length	length	NOUN
ejpam-6540	1	42	five	five	NUM
ejpam-6540	1	43	k.	k.	NOUN
ejpam-6540	1	44	bharani	bharani	PROPN
ejpam-6540	1	45	dharan1	dharan1	PROPN
ejpam-6540	1	46	,	,	PUNCT
ejpam-6540	1	47	s.	s.	PROPN
ejpam-6540	1	48	radha1,∗	radha1,∗	PROPN
ejpam-6540	1	49	1	1	NUM
ejpam-6540	1	50	department	department	NOUN
ejpam-6540	1	51	of	of	ADP
ejpam-6540	1	52	mathematics	mathematic	NOUN
ejpam-6540	1	53	,	,	PUNCT
ejpam-6540	1	54	school	school	NOUN
ejpam-6540	1	55	of	of	ADP
ejpam-6540	1	56	advanced	advanced	ADJ
ejpam-6540	1	57	sciences	science	NOUN
ejpam-6540	1	58	,	,	PUNCT
ejpam-6540	1	59	vellore	vellore	PROPN
ejpam-6540	1	60	institute	institute	PROPN
ejpam-6540	1	61	of	of	ADP
ejpam-6540	1	62	technology	technology	PROPN
ejpam-6540	1	63	,	,	PUNCT
ejpam-6540	1	64	chennai	chennai	PROPN
ejpam-6540	1	65	,	,	PUNCT
ejpam-6540	1	66	tamil	tamil	PROPN
ejpam-6540	1	67	nadu	nadu	PROPN
ejpam-6540	1	68	,	,	PUNCT
ejpam-6540	1	69	india	india	PROPN
ejpam-6540	1	70	600127	600127	NUM
ejpam-6540	1	71	abstract	abstract	NOUN
ejpam-6540	1	72	.	.	PUNCT
ejpam-6540	2	1	the	the	DET
ejpam-6540	2	2	fascinating	fascinating	ADJ
ejpam-6540	2	3	family	family	NOUN
ejpam-6540	2	4	of	of	ADP
ejpam-6540	2	5	fractal	fractal	NOUN
ejpam-6540	2	6	-	-	PUNCT
ejpam-6540	2	7	based	base	VERB
ejpam-6540	2	8	networks	network	NOUN
ejpam-6540	2	9	known	know	VERB
ejpam-6540	2	10	as	as	ADP
ejpam-6540	2	11	generalized	generalized	ADJ
ejpam-6540	2	12	sierpiński	sierpiński	ADJ
ejpam-6540	2	13	networks	network	NOUN
ejpam-6540	2	14	has	have	AUX
ejpam-6540	2	15	garnered	garner	VERB
ejpam-6540	2	16	significant	significant	ADJ
ejpam-6540	2	17	interest	interest	NOUN
ejpam-6540	2	18	across	across	ADP
ejpam-6540	2	19	various	various	ADJ
ejpam-6540	2	20	research	research	NOUN
ejpam-6540	2	21	domains	domain	NOUN
ejpam-6540	2	22	and	and	CCONJ
ejpam-6540	2	23	practical	practical	ADJ
ejpam-6540	2	24	applications	application	NOUN
ejpam-6540	2	25	.	.	PUNCT
ejpam-6540	3	1	these	these	DET
ejpam-6540	3	2	graphs	graph	NOUN
ejpam-6540	3	3	exhibit	exhibit	VERB
ejpam-6540	3	4	self	self	NOUN
ejpam-6540	3	5	-	-	PUNCT
ejpam-6540	3	6	similar	similar	ADJ
ejpam-6540	3	7	structures	structure	NOUN
ejpam-6540	3	8	,	,	PUNCT
ejpam-6540	3	9	making	make	VERB
ejpam-6540	3	10	them	they	PRON
ejpam-6540	3	11	particularly	particularly	ADV
ejpam-6540	3	12	valuable	valuable	ADJ
ejpam-6540	3	13	in	in	ADP
ejpam-6540	3	14	areas	area	NOUN
ejpam-6540	3	15	such	such	ADJ
ejpam-6540	3	16	as	as	ADP
ejpam-6540	3	17	antenna	antenna	NOUN
ejpam-6540	3	18	structures	structure	NOUN
ejpam-6540	3	19	,	,	PUNCT
ejpam-6540	3	20	interconnection	interconnection	NOUN
ejpam-6540	3	21	networks	network	NOUN
ejpam-6540	3	22	and	and	CCONJ
ejpam-6540	3	23	the	the	DET
ejpam-6540	3	24	porous	porous	ADJ
ejpam-6540	3	25	materials	material	NOUN
ejpam-6540	3	26	.	.	PUNCT
ejpam-6540	4	1	their	their	PRON
ejpam-6540	4	2	recursive	recursive	ADJ
ejpam-6540	4	3	nature	nature	NOUN
ejpam-6540	4	4	and	and	CCONJ
ejpam-6540	4	5	hierarchical	hierarchical	ADJ
ejpam-6540	4	6	organization	organization	NOUN
ejpam-6540	4	7	enhance	enhance	VERB
ejpam-6540	4	8	their	their	PRON
ejpam-6540	4	9	relevance	relevance	NOUN
ejpam-6540	4	10	in	in	ADP
ejpam-6540	4	11	modeling	model	VERB
ejpam-6540	4	12	complex	complex	ADJ
ejpam-6540	4	13	systems	system	NOUN
ejpam-6540	4	14	and	and	CCONJ
ejpam-6540	4	15	network	network	NOUN
ejpam-6540	4	16	structures	structure	NOUN
ejpam-6540	4	17	.	.	PUNCT
ejpam-6540	5	1	a	a	DET
ejpam-6540	5	2	key	key	ADJ
ejpam-6540	5	3	parameter	parameter	NOUN
ejpam-6540	5	4	for	for	ADP
ejpam-6540	5	5	analyzing	analyze	VERB
ejpam-6540	5	6	these	these	DET
ejpam-6540	5	7	graphs	graph	NOUN
ejpam-6540	5	8	is	be	AUX
ejpam-6540	5	9	the	the	DET
ejpam-6540	5	10	metric	metric	ADJ
ejpam-6540	5	11	dimension	dimension	NOUN
ejpam-6540	5	12	,	,	PUNCT
ejpam-6540	5	13	which	which	PRON
ejpam-6540	5	14	represents	represent	VERB
ejpam-6540	5	15	the	the	DET
ejpam-6540	5	16	smallest	small	ADJ
ejpam-6540	5	17	set	set	NOUN
ejpam-6540	5	18	of	of	ADP
ejpam-6540	5	19	reference	reference	NOUN
ejpam-6540	5	20	vertices	vertex	NOUN
ejpam-6540	5	21	(	(	PUNCT
ejpam-6540	5	22	or	or	CCONJ
ejpam-6540	5	23	landmarks	landmark	NOUN
ejpam-6540	5	24	)	)	PUNCT
ejpam-6540	5	25	needed	need	VERB
ejpam-6540	5	26	to	to	PART
ejpam-6540	5	27	uniquely	uniquely	ADV
ejpam-6540	5	28	identify	identify	VERB
ejpam-6540	5	29	the	the	DET
ejpam-6540	5	30	distances	distance	NOUN
ejpam-6540	5	31	between	between	ADP
ejpam-6540	5	32	all	all	DET
ejpam-6540	5	33	other	other	ADJ
ejpam-6540	5	34	vertices	vertex	NOUN
ejpam-6540	5	35	in	in	ADP
ejpam-6540	5	36	the	the	DET
ejpam-6540	5	37	graph	graph	NOUN
ejpam-6540	5	38	.	.	PUNCT
ejpam-6540	6	1	this	this	DET
ejpam-6540	6	2	parameter	parameter	NOUN
ejpam-6540	6	3	is	be	AUX
ejpam-6540	6	4	crucial	crucial	ADJ
ejpam-6540	6	5	for	for	ADP
ejpam-6540	6	6	network	network	NOUN
ejpam-6540	6	7	localization	localization	NOUN
ejpam-6540	6	8	,	,	PUNCT
ejpam-6540	6	9	efficient	efficient	ADJ
ejpam-6540	6	10	routing	routing	NOUN
ejpam-6540	6	11	,	,	PUNCT
ejpam-6540	6	12	and	and	CCONJ
ejpam-6540	6	13	information	information	NOUN
ejpam-6540	6	14	retrieval	retrieval	NOUN
ejpam-6540	6	15	.	.	PUNCT
ejpam-6540	7	1	beyond	beyond	ADP
ejpam-6540	7	2	the	the	DET
ejpam-6540	7	3	standard	standard	ADJ
ejpam-6540	7	4	metric	metric	ADJ
ejpam-6540	7	5	dimension	dimension	NOUN
ejpam-6540	7	6	,	,	PUNCT
ejpam-6540	7	7	other	other	ADJ
ejpam-6540	7	8	variations	variation	NOUN
ejpam-6540	7	9	play	play	VERB
ejpam-6540	7	10	important	important	ADJ
ejpam-6540	7	11	roles	role	NOUN
ejpam-6540	7	12	in	in	ADP
ejpam-6540	7	13	different	different	ADJ
ejpam-6540	7	14	applications	application	NOUN
ejpam-6540	7	15	.	.	PUNCT
ejpam-6540	8	1	the	the	DET
ejpam-6540	8	2	fault	fault	NOUN
ejpam-6540	8	3	-	-	PUNCT
ejpam-6540	8	4	tolerant	tolerant	ADJ
ejpam-6540	8	5	metric	metric	ADJ
ejpam-6540	8	6	dimension	dimension	NOUN
ejpam-6540	8	7	is	be	AUX
ejpam-6540	8	8	essential	essential	ADJ
ejpam-6540	8	9	in	in	ADP
ejpam-6540	8	10	robust	robust	ADJ
ejpam-6540	8	11	network	network	NOUN
ejpam-6540	8	12	design	design	NOUN
ejpam-6540	8	13	,	,	PUNCT
ejpam-6540	8	14	ensuring	ensure	VERB
ejpam-6540	8	15	that	that	SCONJ
ejpam-6540	8	16	localization	localization	NOUN
ejpam-6540	8	17	remains	remain	VERB
ejpam-6540	8	18	possible	possible	ADJ
ejpam-6540	8	19	even	even	ADV
ejpam-6540	8	20	if	if	SCONJ
ejpam-6540	8	21	certain	certain	ADJ
ejpam-6540	8	22	reference	reference	NOUN
ejpam-6540	8	23	points	point	VERB
ejpam-6540	8	24	fail	fail	VERB
ejpam-6540	8	25	.	.	PUNCT
ejpam-6540	9	1	the	the	DET
ejpam-6540	9	2	edge	edge	NOUN
ejpam-6540	9	3	metric	metric	ADJ
ejpam-6540	9	4	dimension	dimension	NOUN
ejpam-6540	9	5	is	be	AUX
ejpam-6540	9	6	widely	widely	ADV
ejpam-6540	9	7	used	use	VERB
ejpam-6540	9	8	in	in	ADP
ejpam-6540	9	9	network	network	NOUN
ejpam-6540	9	10	security	security	NOUN
ejpam-6540	9	11	and	and	CCONJ
ejpam-6540	9	12	surveillance	surveillance	NOUN
ejpam-6540	9	13	,	,	PUNCT
ejpam-6540	9	14	where	where	SCONJ
ejpam-6540	9	15	monitoring	monitor	VERB
ejpam-6540	9	16	specific	specific	ADJ
ejpam-6540	9	17	connections	connection	NOUN
ejpam-6540	9	18	is	be	AUX
ejpam-6540	9	19	more	more	ADV
ejpam-6540	9	20	relevant	relevant	ADJ
ejpam-6540	9	21	than	than	ADP
ejpam-6540	9	22	individual	individual	ADJ
ejpam-6540	9	23	nodes	node	NOUN
ejpam-6540	9	24	.	.	PUNCT
ejpam-6540	10	1	meanwhile	meanwhile	ADV
ejpam-6540	10	2	,	,	PUNCT
ejpam-6540	10	3	the	the	DET
ejpam-6540	10	4	fault	fault	NOUN
ejpam-6540	10	5	-	-	PUNCT
ejpam-6540	10	6	tolerant	tolerant	ADJ
ejpam-6540	10	7	edge	edge	NOUN
ejpam-6540	10	8	metric	metric	ADJ
ejpam-6540	10	9	dimension	dimension	NOUN
ejpam-6540	10	10	has	have	VERB
ejpam-6540	10	11	applications	application	NOUN
ejpam-6540	10	12	in	in	ADP
ejpam-6540	10	13	resilient	resilient	ADJ
ejpam-6540	10	14	communication	communication	NOUN
ejpam-6540	10	15	networks	network	NOUN
ejpam-6540	10	16	,	,	PUNCT
ejpam-6540	10	17	guaranteeing	guarantee	VERB
ejpam-6540	10	18	reliable	reliable	ADJ
ejpam-6540	10	19	identification	identification	NOUN
ejpam-6540	10	20	of	of	ADP
ejpam-6540	10	21	edges	edge	NOUN
ejpam-6540	10	22	even	even	ADV
ejpam-6540	10	23	under	under	ADP
ejpam-6540	10	24	failure	failure	NOUN
ejpam-6540	10	25	conditions	condition	NOUN
ejpam-6540	10	26	.	.	PUNCT
ejpam-6540	11	1	in	in	ADP
ejpam-6540	11	2	this	this	DET
ejpam-6540	11	3	study	study	NOUN
ejpam-6540	11	4	,	,	PUNCT
ejpam-6540	11	5	we	we	PRON
ejpam-6540	11	6	specifically	specifically	ADV
ejpam-6540	11	7	examine	examine	VERB
ejpam-6540	11	8	the	the	DET
ejpam-6540	11	9	metric	metric	ADJ
ejpam-6540	11	10	,	,	PUNCT
ejpam-6540	11	11	fault	fault	NOUN
ejpam-6540	11	12	-	-	PUNCT
ejpam-6540	11	13	tolerant	tolerant	ADJ
ejpam-6540	11	14	metric	metric	ADJ
ejpam-6540	11	15	,	,	PUNCT
ejpam-6540	11	16	edge	edge	NOUN
ejpam-6540	11	17	metric	metric	ADJ
ejpam-6540	11	18	,	,	PUNCT
ejpam-6540	11	19	and	and	CCONJ
ejpam-6540	11	20	fault	fault	NOUN
ejpam-6540	11	21	-	-	PUNCT
ejpam-6540	11	22	tolerant	tolerant	ADJ
ejpam-6540	11	23	edge	edge	NOUN
ejpam-6540	11	24	metric	metric	ADJ
ejpam-6540	11	25	dimensions	dimension	NOUN
ejpam-6540	11	26	of	of	ADP
ejpam-6540	11	27	generalized	generalized	ADJ
ejpam-6540	11	28	sierpiński	sierpiński	ADJ
ejpam-6540	11	29	networks	network	NOUN
ejpam-6540	11	30	over	over	ADP
ejpam-6540	11	31	c5	c5	PROPN
ejpam-6540	11	32	.	.	PUNCT
ejpam-6540	12	1	these	these	DET
ejpam-6540	12	2	findings	finding	NOUN
ejpam-6540	12	3	provide	provide	VERB
ejpam-6540	12	4	deeper	deep	ADJ
ejpam-6540	12	5	insights	insight	NOUN
ejpam-6540	12	6	into	into	ADP
ejpam-6540	12	7	their	their	PRON
ejpam-6540	12	8	structural	structural	ADJ
ejpam-6540	12	9	properties	property	NOUN
ejpam-6540	12	10	and	and	CCONJ
ejpam-6540	12	11	distinguish	distinguish	VERB
ejpam-6540	12	12	them	they	PRON
ejpam-6540	12	13	from	from	ADP
ejpam-6540	12	14	traditional	traditional	ADJ
ejpam-6540	12	15	cycle	cycle	NOUN
ejpam-6540	12	16	networks	network	NOUN
ejpam-6540	12	17	,	,	PUNCT
ejpam-6540	12	18	highlighting	highlight	VERB
ejpam-6540	12	19	their	their	PRON
ejpam-6540	12	20	potential	potential	NOUN
ejpam-6540	12	21	in	in	ADP
ejpam-6540	12	22	real	real	ADJ
ejpam-6540	12	23	-	-	PUNCT
ejpam-6540	12	24	world	world	NOUN
ejpam-6540	12	25	applications	application	NOUN
ejpam-6540	12	26	.	.	PUNCT
ejpam-6540	13	1	2020	2020	NUM
ejpam-6540	13	2	mathematics	mathematic	NOUN
ejpam-6540	13	3	subject	subject	NOUN
ejpam-6540	13	4	classifications	classification	NOUN
ejpam-6540	13	5	:	:	PUNCT
ejpam-6540	13	6	05c12	05c12	NUM
ejpam-6540	13	7	,	,	PUNCT
ejpam-6540	13	8	94c15	94c15	NUM
ejpam-6540	13	9	,	,	PUNCT
ejpam-6540	13	10	68m10	68m10	NUM
ejpam-6540	13	11	key	key	ADJ
ejpam-6540	13	12	words	word	NOUN
ejpam-6540	13	13	and	and	CCONJ
ejpam-6540	13	14	phrases	phrase	NOUN
ejpam-6540	13	15	:	:	PUNCT
ejpam-6540	13	16	generalized	generalized	ADJ
ejpam-6540	13	17	sierpiński	sierpiński	ADJ
ejpam-6540	13	18	network	network	NOUN
ejpam-6540	13	19	;	;	PUNCT
ejpam-6540	13	20	metric	metric	ADJ
ejpam-6540	13	21	dimension	dimension	NOUN
ejpam-6540	13	22	;	;	PUNCT
ejpam-6540	13	23	fault	fault	NOUN
ejpam-6540	13	24	-	-	PUNCT
ejpam-6540	13	25	tolerant	tolerant	ADJ
ejpam-6540	13	26	metric	metric	ADJ
ejpam-6540	13	27	dimension	dimension	NOUN
ejpam-6540	13	28	;	;	PUNCT
ejpam-6540	13	29	edge	edge	NOUN
ejpam-6540	13	30	metric	metric	ADJ
ejpam-6540	13	31	dimension	dimension	NOUN
ejpam-6540	13	32	;	;	PUNCT
ejpam-6540	13	33	fault	fault	NOUN
ejpam-6540	13	34	-	-	PUNCT
ejpam-6540	13	35	tolerant	tolerant	ADJ
ejpam-6540	13	36	edge	edge	NOUN
ejpam-6540	13	37	metric	metric	ADJ
ejpam-6540	13	38	dimension	dimension	NOUN
ejpam-6540	13	39	1	1	NUM
ejpam-6540	13	40	.	.	PUNCT
ejpam-6540	14	1	introduction	introduction	NOUN
ejpam-6540	14	2	graph	graph	NOUN
ejpam-6540	14	3	theory	theory	NOUN
ejpam-6540	14	4	plays	play	VERB
ejpam-6540	14	5	a	a	DET
ejpam-6540	14	6	crucial	crucial	ADJ
ejpam-6540	14	7	role	role	NOUN
ejpam-6540	14	8	in	in	ADP
ejpam-6540	14	9	distributed	distribute	VERB
ejpam-6540	14	10	parallel	parallel	ADJ
ejpam-6540	14	11	computing	computing	NOUN
ejpam-6540	14	12	by	by	ADP
ejpam-6540	14	13	providing	provide	VERB
ejpam-6540	14	14	a	a	DET
ejpam-6540	14	15	mathematical	mathematical	ADJ
ejpam-6540	14	16	framework	framework	NOUN
ejpam-6540	14	17	for	for	ADP
ejpam-6540	14	18	modeling	modeling	NOUN
ejpam-6540	14	19	,	,	PUNCT
ejpam-6540	14	20	analyzing	analyzing	NOUN
ejpam-6540	14	21	,	,	PUNCT
ejpam-6540	14	22	and	and	CCONJ
ejpam-6540	14	23	optimizing	optimize	VERB
ejpam-6540	14	24	system	system	NOUN
ejpam-6540	14	25	performance	performance	NOUN
ejpam-6540	14	26	[	[	X
ejpam-6540	14	27	1	1	NUM
ejpam-6540	14	28	]	]	PUNCT
ejpam-6540	14	29	.	.	PUNCT
ejpam-6540	15	1	in	in	ADP
ejpam-6540	15	2	∗corresponding	∗corresponde	VERB
ejpam-6540	15	3	author	author	NOUN
ejpam-6540	15	4	.	.	PUNCT
ejpam-6540	16	1	doi	doi	PROPN
ejpam-6540	16	2	:	:	PUNCT
ejpam-6540	16	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6540	https://doi.org/10.29020/nybg.ejpam.v18i3.6540	PROPN
ejpam-6540	16	4	email	email	NOUN
ejpam-6540	16	5	addresses	address	NOUN
ejpam-6540	16	6	:	:	PUNCT
ejpam-6540	16	7	bharanidharan.k2022@vitstudent.ac.in	bharanidharan.k2022@vitstudent.ac.in	PROPN
ejpam-6540	16	8	(	(	PUNCT
ejpam-6540	16	9	k.	k.	PROPN
ejpam-6540	16	10	bharani	bharani	PROPN
ejpam-6540	16	11	dharan	dharan	PROPN
ejpam-6540	16	12	)	)	PUNCT
ejpam-6540	16	13	,	,	PUNCT
ejpam-6540	16	14	radha.s@vit.ac.in	radha.s@vit.ac.in	PROPN
ejpam-6540	16	15	(	(	PUNCT
ejpam-6540	16	16	s.	s.	PROPN
ejpam-6540	16	17	radha	radha	PROPN
ejpam-6540	16	18	)	)	PUNCT
ejpam-6540	16	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6540	16	20	1	1	NUM
ejpam-6540	16	21	copyright	copyright	NOUN
ejpam-6540	16	22	:	:	PUNCT
ejpam-6540	17	1	©	©	PROPN
ejpam-6540	17	2	2025	2025	NUM
ejpam-6540	17	3	the	the	DET
ejpam-6540	17	4	author(s	author(s	NOUN
ejpam-6540	17	5	)	)	PUNCT
ejpam-6540	17	6	.	.	PUNCT
ejpam-6540	18	1	(	(	PUNCT
ejpam-6540	18	2	cc	cc	NOUN
ejpam-6540	18	3	by	by	ADP
ejpam-6540	18	4	-	-	PUNCT
ejpam-6540	18	5	nc	nc	PROPN
ejpam-6540	18	6	4.0	4.0	NUM
ejpam-6540	18	7	)	)	PUNCT
ejpam-6540	18	8	k.	k.	PROPN
ejpam-6540	18	9	b.	b.	PROPN
ejpam-6540	18	10	dharan	dharan	PROPN
ejpam-6540	18	11	,	,	PUNCT
ejpam-6540	18	12	s.	s.	PROPN
ejpam-6540	18	13	radha	radha	PROPN
ejpam-6540	18	14	/	/	PUNCT
ejpam-6540	18	15	eur	eur	PROPN
ejpam-6540	18	16	.	.	PUNCT
ejpam-6540	19	1	j.	j.	PROPN
ejpam-6540	19	2	pure	pure	PROPN
ejpam-6540	19	3	appl	appl	PROPN
ejpam-6540	19	4	.	.	PROPN
ejpam-6540	19	5	math	math	PROPN
ejpam-6540	19	6	,	,	PUNCT
ejpam-6540	19	7	18	18	NUM
ejpam-6540	19	8	(	(	PUNCT
ejpam-6540	19	9	3	3	NUM
ejpam-6540	19	10	)	)	PUNCT
ejpam-6540	19	11	(	(	PUNCT
ejpam-6540	19	12	2025	2025	NUM
ejpam-6540	19	13	)	)	PUNCT
ejpam-6540	19	14	,	,	PUNCT
ejpam-6540	19	15	6540	6540	NUM
ejpam-6540	19	16	2	2	NUM
ejpam-6540	19	17	of	of	ADP
ejpam-6540	19	18	17	17	NUM
ejpam-6540	19	19	such	such	ADJ
ejpam-6540	19	20	systems	system	NOUN
ejpam-6540	19	21	,	,	PUNCT
ejpam-6540	19	22	multiple	multiple	ADJ
ejpam-6540	19	23	processors	processor	NOUN
ejpam-6540	19	24	collaborate	collaborate	VERB
ejpam-6540	19	25	to	to	PART
ejpam-6540	19	26	execute	execute	VERB
ejpam-6540	19	27	tasks	task	NOUN
ejpam-6540	19	28	efficiently	efficiently	ADV
ejpam-6540	19	29	,	,	PUNCT
ejpam-6540	19	30	requiring	require	VERB
ejpam-6540	19	31	wellstructured	wellstructure	VERB
ejpam-6540	19	32	communication	communication	NOUN
ejpam-6540	19	33	and	and	CCONJ
ejpam-6540	19	34	coordination	coordination	NOUN
ejpam-6540	19	35	,	,	PUNCT
ejpam-6540	19	36	which	which	PRON
ejpam-6540	19	37	can	can	AUX
ejpam-6540	19	38	be	be	AUX
ejpam-6540	19	39	effectively	effectively	ADV
ejpam-6540	19	40	represented	represent	VERB
ejpam-6540	19	41	using	use	VERB
ejpam-6540	19	42	graphs	graph	NOUN
ejpam-6540	19	43	[	[	X
ejpam-6540	19	44	2	2	NUM
ejpam-6540	19	45	]	]	PUNCT
ejpam-6540	19	46	.	.	PUNCT
ejpam-6540	20	1	various	various	ADJ
ejpam-6540	20	2	graph	graph	NOUN
ejpam-6540	20	3	-	-	PUNCT
ejpam-6540	20	4	theoretic	theoretic	NOUN
ejpam-6540	20	5	techniques	technique	NOUN
ejpam-6540	20	6	enhance	enhance	VERB
ejpam-6540	20	7	different	different	ADJ
ejpam-6540	20	8	aspects	aspect	NOUN
ejpam-6540	20	9	of	of	ADP
ejpam-6540	20	10	parallel	parallel	ADJ
ejpam-6540	20	11	computing	computing	NOUN
ejpam-6540	20	12	,	,	PUNCT
ejpam-6540	20	13	such	such	ADJ
ejpam-6540	20	14	as	as	ADP
ejpam-6540	20	15	task	task	NOUN
ejpam-6540	20	16	scheduling	scheduling	NOUN
ejpam-6540	20	17	,	,	PUNCT
ejpam-6540	20	18	load	load	NOUN
ejpam-6540	20	19	balancing	balancing	NOUN
ejpam-6540	20	20	,	,	PUNCT
ejpam-6540	20	21	fault	fault	VERB
ejpam-6540	20	22	tolerance	tolerance	NOUN
ejpam-6540	20	23	,	,	PUNCT
ejpam-6540	20	24	and	and	CCONJ
ejpam-6540	20	25	network	network	NOUN
ejpam-6540	20	26	optimization	optimization	NOUN
ejpam-6540	20	27	[	[	X
ejpam-6540	20	28	3	3	NUM
ejpam-6540	20	29	]	]	PUNCT
ejpam-6540	20	30	.	.	PUNCT
ejpam-6540	21	1	graph	graph	NOUN
ejpam-6540	21	2	partitioning	partitioning	NOUN
ejpam-6540	21	3	helps	help	VERB
ejpam-6540	21	4	distribute	distribute	VERB
ejpam-6540	21	5	workloads	workload	NOUN
ejpam-6540	21	6	evenly	evenly	ADV
ejpam-6540	21	7	,	,	PUNCT
ejpam-6540	21	8	preventing	prevent	VERB
ejpam-6540	21	9	bottlenecks	bottleneck	NOUN
ejpam-6540	21	10	,	,	PUNCT
ejpam-6540	21	11	while	while	SCONJ
ejpam-6540	21	12	interconnection	interconnection	NOUN
ejpam-6540	21	13	network	network	NOUN
ejpam-6540	21	14	models	model	NOUN
ejpam-6540	21	15	,	,	PUNCT
ejpam-6540	21	16	including	include	VERB
ejpam-6540	21	17	hypercubes	hypercube	NOUN
ejpam-6540	21	18	,	,	PUNCT
ejpam-6540	21	19	meshes	mesh	NOUN
ejpam-6540	21	20	,	,	PUNCT
ejpam-6540	21	21	and	and	CCONJ
ejpam-6540	21	22	trees	tree	NOUN
ejpam-6540	21	23	,	,	PUNCT
ejpam-6540	21	24	assist	assist	VERB
ejpam-6540	21	25	in	in	ADP
ejpam-6540	21	26	minimizing	minimize	VERB
ejpam-6540	21	27	communication	communication	NOUN
ejpam-6540	21	28	latency	latency	NOUN
ejpam-6540	21	29	[	[	X
ejpam-6540	21	30	4	4	NUM
ejpam-6540	21	31	]	]	PUNCT
ejpam-6540	21	32	.	.	PUNCT
ejpam-6540	22	1	connectivity	connectivity	NOUN
ejpam-6540	22	2	and	and	CCONJ
ejpam-6540	22	3	domination	domination	NOUN
ejpam-6540	22	4	properties	property	NOUN
ejpam-6540	22	5	contribute	contribute	VERB
ejpam-6540	22	6	to	to	PART
ejpam-6540	22	7	fault	fault	VERB
ejpam-6540	22	8	tolerance	tolerance	NOUN
ejpam-6540	22	9	by	by	ADP
ejpam-6540	22	10	ensuring	ensure	VERB
ejpam-6540	22	11	alternative	alternative	ADJ
ejpam-6540	22	12	paths	path	NOUN
ejpam-6540	22	13	in	in	ADP
ejpam-6540	22	14	case	case	NOUN
ejpam-6540	22	15	of	of	ADP
ejpam-6540	22	16	node	node	NOUN
ejpam-6540	22	17	or	or	CCONJ
ejpam-6540	22	18	link	link	VERB
ejpam-6540	22	19	failures	failure	NOUN
ejpam-6540	22	20	[	[	X
ejpam-6540	22	21	5	5	NUM
ejpam-6540	22	22	]	]	PUNCT
ejpam-6540	22	23	.	.	PUNCT
ejpam-6540	23	1	graph	graph	NOUN
ejpam-6540	23	2	-	-	PUNCT
ejpam-6540	23	3	based	base	VERB
ejpam-6540	23	4	methods	method	NOUN
ejpam-6540	23	5	like	like	ADP
ejpam-6540	23	6	similarity	similarity	NOUN
ejpam-6540	23	7	and	and	CCONJ
ejpam-6540	23	8	clustering	clustering	NOUN
ejpam-6540	23	9	also	also	ADV
ejpam-6540	23	10	enhance	enhance	VERB
ejpam-6540	23	11	security	security	NOUN
ejpam-6540	23	12	through	through	ADP
ejpam-6540	23	13	anomaly	anomaly	NOUN
ejpam-6540	23	14	detection	detection	NOUN
ejpam-6540	23	15	in	in	ADP
ejpam-6540	23	16	network	network	NOUN
ejpam-6540	23	17	traffic	traffic	NOUN
ejpam-6540	23	18	,	,	PUNCT
ejpam-6540	23	19	helping	helping	AUX
ejpam-6540	23	20	mitigate	mitigate	VERB
ejpam-6540	23	21	unauthorized	unauthorized	ADJ
ejpam-6540	23	22	access	access	NOUN
ejpam-6540	23	23	and	and	CCONJ
ejpam-6540	23	24	cyber	cyber	NOUN
ejpam-6540	23	25	threats	threat	NOUN
ejpam-6540	23	26	[	[	X
ejpam-6540	23	27	6	6	NUM
ejpam-6540	23	28	]	]	PUNCT
ejpam-6540	23	29	.	.	PUNCT
ejpam-6540	24	1	additionally	additionally	ADV
ejpam-6540	24	2	,	,	PUNCT
ejpam-6540	24	3	shortest	short	ADJ
ejpam-6540	24	4	path	path	NOUN
ejpam-6540	24	5	algorithms	algorithm	NOUN
ejpam-6540	24	6	improve	improve	VERB
ejpam-6540	24	7	data	data	NOUN
ejpam-6540	24	8	transmission	transmission	NOUN
ejpam-6540	24	9	efficiency	efficiency	NOUN
ejpam-6540	24	10	,	,	PUNCT
ejpam-6540	24	11	reducing	reduce	VERB
ejpam-6540	24	12	congestion	congestion	NOUN
ejpam-6540	24	13	in	in	ADP
ejpam-6540	24	14	communication	communication	NOUN
ejpam-6540	24	15	networks	network	NOUN
ejpam-6540	24	16	[	[	X
ejpam-6540	24	17	7	7	NUM
ejpam-6540	24	18	]	]	PUNCT
ejpam-6540	24	19	.	.	PUNCT
ejpam-6540	25	1	an	an	DET
ejpam-6540	25	2	effective	effective	ADJ
ejpam-6540	25	3	approach	approach	NOUN
ejpam-6540	25	4	particularly	particularly	ADV
ejpam-6540	25	5	in	in	ADP
ejpam-6540	25	6	designing	design	VERB
ejpam-6540	25	7	scalable	scalable	ADJ
ejpam-6540	25	8	and	and	CCONJ
ejpam-6540	25	9	robust	robust	ADJ
ejpam-6540	25	10	parallel	parallel	ADJ
ejpam-6540	25	11	computing	computing	NOUN
ejpam-6540	25	12	networks	network	NOUN
ejpam-6540	25	13	involves	involve	VERB
ejpam-6540	25	14	fractal	fractal	ADJ
ejpam-6540	25	15	-	-	PUNCT
ejpam-6540	25	16	structured	structure	VERB
ejpam-6540	25	17	graphs	graph	NOUN
ejpam-6540	25	18	,	,	PUNCT
ejpam-6540	25	19	such	such	ADJ
ejpam-6540	25	20	as	as	ADP
ejpam-6540	25	21	generalized	generalized	ADJ
ejpam-6540	25	22	sierpiński	sierpiński	ADJ
ejpam-6540	25	23	networks	network	NOUN
ejpam-6540	25	24	and	and	CCONJ
ejpam-6540	25	25	fractal	fractal	ADJ
ejpam-6540	25	26	cubic	cubic	ADJ
ejpam-6540	25	27	networks	network	NOUN
ejpam-6540	25	28	which	which	PRON
ejpam-6540	25	29	exhibit	exhibit	VERB
ejpam-6540	25	30	self	self	NOUN
ejpam-6540	25	31	-	-	PUNCT
ejpam-6540	25	32	similarity	similarity	NOUN
ejpam-6540	25	33	and	and	CCONJ
ejpam-6540	25	34	hierarchical	hierarchical	ADJ
ejpam-6540	25	35	organization	organization	NOUN
ejpam-6540	25	36	[	[	X
ejpam-6540	25	37	8	8	NUM
ejpam-6540	25	38	,	,	PUNCT
ejpam-6540	25	39	9	9	NUM
ejpam-6540	25	40	]	]	PUNCT
ejpam-6540	25	41	.	.	PUNCT
ejpam-6540	26	1	these	these	DET
ejpam-6540	26	2	graphs	graph	NOUN
ejpam-6540	26	3	offer	offer	VERB
ejpam-6540	26	4	several	several	ADJ
ejpam-6540	26	5	advantages	advantage	NOUN
ejpam-6540	26	6	,	,	PUNCT
ejpam-6540	26	7	including	include	VERB
ejpam-6540	26	8	seamless	seamless	ADJ
ejpam-6540	26	9	scalability	scalability	NOUN
ejpam-6540	26	10	,	,	PUNCT
ejpam-6540	26	11	as	as	SCONJ
ejpam-6540	26	12	their	their	PRON
ejpam-6540	26	13	recursive	recursive	ADJ
ejpam-6540	26	14	nature	nature	NOUN
ejpam-6540	26	15	allows	allow	VERB
ejpam-6540	26	16	for	for	ADP
ejpam-6540	26	17	structured	structured	ADJ
ejpam-6540	26	18	expansion	expansion	NOUN
ejpam-6540	26	19	without	without	ADP
ejpam-6540	26	20	compromising	compromise	VERB
ejpam-6540	26	21	efficiency	efficiency	NOUN
ejpam-6540	26	22	[	[	X
ejpam-6540	26	23	10	10	NUM
ejpam-6540	26	24	]	]	PUNCT
ejpam-6540	26	25	.	.	PUNCT
ejpam-6540	27	1	their	their	PRON
ejpam-6540	27	2	hierarchical	hierarchical	ADJ
ejpam-6540	27	3	architecture	architecture	NOUN
ejpam-6540	27	4	enables	enable	VERB
ejpam-6540	27	5	optimized	optimize	VERB
ejpam-6540	27	6	routing	routing	NOUN
ejpam-6540	27	7	and	and	CCONJ
ejpam-6540	27	8	communication	communication	NOUN
ejpam-6540	27	9	,	,	PUNCT
ejpam-6540	27	10	reducing	reduce	VERB
ejpam-6540	27	11	congestion	congestion	NOUN
ejpam-6540	27	12	and	and	CCONJ
ejpam-6540	27	13	improving	improve	VERB
ejpam-6540	27	14	data	data	NOUN
ejpam-6540	27	15	flow	flow	NOUN
ejpam-6540	27	16	[	[	X
ejpam-6540	27	17	11	11	NUM
ejpam-6540	27	18	]	]	PUNCT
ejpam-6540	27	19	.	.	PUNCT
ejpam-6540	28	1	moreover	moreover	ADV
ejpam-6540	28	2	,	,	PUNCT
ejpam-6540	28	3	their	their	PRON
ejpam-6540	28	4	inherent	inherent	ADJ
ejpam-6540	28	5	redundancy	redundancy	NOUN
ejpam-6540	28	6	enhances	enhance	VERB
ejpam-6540	28	7	fault	fault	NOUN
ejpam-6540	28	8	tolerance	tolerance	NOUN
ejpam-6540	28	9	,	,	PUNCT
ejpam-6540	28	10	ensuring	ensure	VERB
ejpam-6540	28	11	system	system	NOUN
ejpam-6540	28	12	resilience	resilience	NOUN
ejpam-6540	28	13	even	even	ADV
ejpam-6540	28	14	in	in	ADP
ejpam-6540	28	15	the	the	DET
ejpam-6540	28	16	event	event	NOUN
ejpam-6540	28	17	of	of	ADP
ejpam-6540	28	18	node	node	NOUN
ejpam-6540	28	19	or	or	CCONJ
ejpam-6540	28	20	link	link	NOUN
ejpam-6540	28	21	failures	failure	NOUN
ejpam-6540	28	22	.	.	PUNCT
ejpam-6540	29	1	the	the	DET
ejpam-6540	29	2	structured	structured	ADJ
ejpam-6540	29	3	nature	nature	NOUN
ejpam-6540	29	4	of	of	ADP
ejpam-6540	29	5	fractal	fractal	ADJ
ejpam-6540	29	6	graphs	graph	NOUN
ejpam-6540	29	7	also	also	ADV
ejpam-6540	29	8	facilitates	facilitate	VERB
ejpam-6540	29	9	balanced	balanced	ADJ
ejpam-6540	29	10	workload	workload	NOUN
ejpam-6540	29	11	distribution	distribution	NOUN
ejpam-6540	29	12	,	,	PUNCT
ejpam-6540	29	13	improving	improve	VERB
ejpam-6540	29	14	computational	computational	ADJ
ejpam-6540	29	15	efficiency	efficiency	NOUN
ejpam-6540	29	16	while	while	SCONJ
ejpam-6540	29	17	simultaneously	simultaneously	ADV
ejpam-6540	29	18	reducing	reduce	VERB
ejpam-6540	29	19	energy	energy	NOUN
ejpam-6540	29	20	consumption	consumption	NOUN
ejpam-6540	29	21	in	in	ADP
ejpam-6540	29	22	communication	communication	NOUN
ejpam-6540	29	23	,	,	PUNCT
ejpam-6540	29	24	making	make	VERB
ejpam-6540	29	25	them	they	PRON
ejpam-6540	29	26	ideal	ideal	ADJ
ejpam-6540	29	27	for	for	ADP
ejpam-6540	29	28	energy	energy	NOUN
ejpam-6540	29	29	-	-	PUNCT
ejpam-6540	29	30	efficient	efficient	ADJ
ejpam-6540	29	31	parallel	parallel	ADJ
ejpam-6540	29	32	computing	computing	NOUN
ejpam-6540	29	33	architectures	architecture	NOUN
ejpam-6540	30	1	[	[	X
ejpam-6540	30	2	12	12	NUM
ejpam-6540	30	3	]	]	PUNCT
ejpam-6540	30	4	.	.	PUNCT
ejpam-6540	31	1	these	these	DET
ejpam-6540	31	2	networks	network	NOUN
ejpam-6540	31	3	have	have	VERB
ejpam-6540	31	4	applications	application	NOUN
ejpam-6540	31	5	in	in	ADP
ejpam-6540	31	6	various	various	ADJ
ejpam-6540	31	7	artificial	artificial	ADJ
ejpam-6540	31	8	and	and	CCONJ
ejpam-6540	31	9	natural	natural	ADJ
ejpam-6540	31	10	systems	system	NOUN
ejpam-6540	31	11	,	,	PUNCT
ejpam-6540	31	12	including	include	VERB
ejpam-6540	31	13	neuroscience	neuroscience	NOUN
ejpam-6540	31	14	[	[	X
ejpam-6540	31	15	13	13	NUM
ejpam-6540	31	16	]	]	PUNCT
ejpam-6540	31	17	,	,	PUNCT
ejpam-6540	31	18	computer	computer	NOUN
ejpam-6540	31	19	networks	network	NOUN
ejpam-6540	31	20	and	and	CCONJ
ejpam-6540	31	21	musics	music	NOUN
ejpam-6540	31	22	[	[	X
ejpam-6540	31	23	14	14	NUM
ejpam-6540	31	24	]	]	PUNCT
ejpam-6540	31	25	.	.	PUNCT
ejpam-6540	32	1	they	they	PRON
ejpam-6540	32	2	also	also	ADV
ejpam-6540	32	3	assist	assist	VERB
ejpam-6540	32	4	in	in	ADP
ejpam-6540	32	5	analyzing	analyze	VERB
ejpam-6540	32	6	complex	complex	ADJ
ejpam-6540	32	7	biological	biological	ADJ
ejpam-6540	32	8	structures	structure	NOUN
ejpam-6540	32	9	like	like	ADP
ejpam-6540	32	10	bacterial	bacterial	ADJ
ejpam-6540	32	11	growth	growth	NOUN
ejpam-6540	32	12	patterns	pattern	NOUN
ejpam-6540	32	13	[	[	X
ejpam-6540	32	14	15	15	NUM
ejpam-6540	32	15	]	]	PUNCT
ejpam-6540	32	16	.	.	PUNCT
ejpam-6540	33	1	among	among	ADP
ejpam-6540	33	2	these	these	DET
ejpam-6540	33	3	structures	structure	NOUN
ejpam-6540	33	4	,	,	PUNCT
ejpam-6540	33	5	sierpiński	sierpiński	ADJ
ejpam-6540	33	6	networks	network	NOUN
ejpam-6540	33	7	are	be	AUX
ejpam-6540	33	8	particularly	particularly	ADV
ejpam-6540	33	9	relevant	relevant	ADJ
ejpam-6540	33	10	to	to	ADP
ejpam-6540	33	11	parallel	parallel	ADJ
ejpam-6540	33	12	computing	computing	NOUN
ejpam-6540	33	13	,	,	PUNCT
ejpam-6540	33	14	especially	especially	ADV
ejpam-6540	33	15	in	in	ADP
ejpam-6540	33	16	designing	design	VERB
ejpam-6540	33	17	high	high	ADJ
ejpam-6540	33	18	-	-	PUNCT
ejpam-6540	33	19	performance	performance	NOUN
ejpam-6540	33	20	computing	compute	VERB
ejpam-6540	33	21	clusters	cluster	NOUN
ejpam-6540	33	22	and	and	CCONJ
ejpam-6540	33	23	supercomputers	supercomputer	NOUN
ejpam-6540	33	24	.	.	PUNCT
ejpam-6540	34	1	overall	overall	ADV
ejpam-6540	34	2	,	,	PUNCT
ejpam-6540	34	3	graph	graph	NOUN
ejpam-6540	34	4	theory	theory	NOUN
ejpam-6540	34	5	,	,	PUNCT
ejpam-6540	34	6	particularly	particularly	ADV
ejpam-6540	34	7	through	through	ADP
ejpam-6540	34	8	fractal	fractal	ADV
ejpam-6540	34	9	-	-	PUNCT
ejpam-6540	34	10	based	base	VERB
ejpam-6540	34	11	structures	structure	NOUN
ejpam-6540	34	12	,	,	PUNCT
ejpam-6540	34	13	significantly	significantly	ADV
ejpam-6540	34	14	contributes	contribute	VERB
ejpam-6540	34	15	to	to	ADP
ejpam-6540	34	16	optimizing	optimize	VERB
ejpam-6540	34	17	distributed	distribute	VERB
ejpam-6540	34	18	parallel	parallel	ADJ
ejpam-6540	34	19	computing	computing	NOUN
ejpam-6540	34	20	by	by	ADP
ejpam-6540	34	21	enhancing	enhance	VERB
ejpam-6540	34	22	performance	performance	NOUN
ejpam-6540	34	23	,	,	PUNCT
ejpam-6540	34	24	scalability	scalability	NOUN
ejpam-6540	34	25	,	,	PUNCT
ejpam-6540	34	26	security	security	NOUN
ejpam-6540	34	27	,	,	PUNCT
ejpam-6540	34	28	and	and	CCONJ
ejpam-6540	34	29	reliability	reliability	NOUN
ejpam-6540	34	30	,	,	PUNCT
ejpam-6540	34	31	making	make	VERB
ejpam-6540	34	32	it	it	PRON
ejpam-6540	34	33	a	a	DET
ejpam-6540	34	34	key	key	ADJ
ejpam-6540	34	35	tool	tool	NOUN
ejpam-6540	34	36	in	in	ADP
ejpam-6540	34	37	high	high	ADJ
ejpam-6540	34	38	-	-	PUNCT
ejpam-6540	34	39	performance	performance	NOUN
ejpam-6540	34	40	computing	computing	NOUN
ejpam-6540	34	41	system	system	NOUN
ejpam-6540	34	42	design	design	NOUN
ejpam-6540	34	43	[	[	X
ejpam-6540	34	44	16	16	NUM
ejpam-6540	34	45	]	]	PUNCT
ejpam-6540	34	46	.	.	PUNCT
ejpam-6540	35	1	the	the	DET
ejpam-6540	35	2	sierpiński	sierpiński	ADJ
ejpam-6540	35	3	network	network	NOUN
ejpam-6540	35	4	is	be	AUX
ejpam-6540	35	5	distinguished	distinguish	VERB
ejpam-6540	35	6	by	by	ADP
ejpam-6540	35	7	its	its	PRON
ejpam-6540	35	8	recursive	recursive	ADJ
ejpam-6540	35	9	hierarchical	hierarchical	ADJ
ejpam-6540	35	10	arrangement	arrangement	NOUN
ejpam-6540	35	11	,	,	PUNCT
ejpam-6540	35	12	where	where	SCONJ
ejpam-6540	35	13	each	each	DET
ejpam-6540	35	14	level	level	NOUN
ejpam-6540	35	15	represents	represent	VERB
ejpam-6540	35	16	a	a	DET
ejpam-6540	35	17	smaller	small	ADJ
ejpam-6540	35	18	version	version	NOUN
ejpam-6540	35	19	of	of	ADP
ejpam-6540	35	20	the	the	DET
ejpam-6540	35	21	overall	overall	ADJ
ejpam-6540	35	22	structure	structure	NOUN
ejpam-6540	35	23	.	.	PUNCT
ejpam-6540	36	1	because	because	SCONJ
ejpam-6540	36	2	of	of	ADP
ejpam-6540	36	3	these	these	DET
ejpam-6540	36	4	characteristics	characteristic	NOUN
ejpam-6540	36	5	,	,	PUNCT
ejpam-6540	36	6	they	they	PRON
ejpam-6540	36	7	are	be	AUX
ejpam-6540	36	8	seen	see	VERB
ejpam-6540	36	9	to	to	PART
ejpam-6540	36	10	be	be	AUX
ejpam-6540	36	11	a	a	DET
ejpam-6540	36	12	viable	viable	ADJ
ejpam-6540	36	13	topology	topology	NOUN
ejpam-6540	36	14	for	for	ADP
ejpam-6540	36	15	systems	system	NOUN
ejpam-6540	36	16	that	that	PRON
ejpam-6540	36	17	use	use	VERB
ejpam-6540	36	18	parallel	parallel	ADJ
ejpam-6540	36	19	computing	computing	NOUN
ejpam-6540	36	20	,	,	PUNCT
ejpam-6540	36	21	especially	especially	ADV
ejpam-6540	36	22	in	in	ADP
ejpam-6540	36	23	fields	field	NOUN
ejpam-6540	36	24	of	of	ADP
ejpam-6540	36	25	study	study	NOUN
ejpam-6540	36	26	that	that	PRON
ejpam-6540	36	27	are	be	AUX
ejpam-6540	36	28	looking	look	VERB
ejpam-6540	36	29	into	into	ADP
ejpam-6540	36	30	new	new	ADJ
ejpam-6540	36	31	network	network	NOUN
ejpam-6540	36	32	architectures	architecture	NOUN
ejpam-6540	36	33	to	to	PART
ejpam-6540	36	34	improve	improve	VERB
ejpam-6540	36	35	fault	fault	NOUN
ejpam-6540	36	36	tolerance	tolerance	NOUN
ejpam-6540	36	37	,	,	PUNCT
ejpam-6540	36	38	scalability	scalability	NOUN
ejpam-6540	36	39	,	,	PUNCT
ejpam-6540	36	40	and	and	CCONJ
ejpam-6540	36	41	efficiency	efficiency	NOUN
ejpam-6540	36	42	[	[	X
ejpam-6540	36	43	8	8	NUM
ejpam-6540	36	44	]	]	PUNCT
ejpam-6540	36	45	.	.	PUNCT
ejpam-6540	37	1	tower	tower	NOUN
ejpam-6540	37	2	of	of	ADP
ejpam-6540	37	3	hanoi	hanoi	PROPN
ejpam-6540	37	4	graphs	graph	NOUN
ejpam-6540	37	5	with	with	ADP
ejpam-6540	37	6	three	three	NUM
ejpam-6540	37	7	pegs	peg	NOUN
ejpam-6540	37	8	are	be	AUX
ejpam-6540	37	9	a	a	DET
ejpam-6540	37	10	particular	particular	ADJ
ejpam-6540	37	11	type	type	NOUN
ejpam-6540	37	12	of	of	ADP
ejpam-6540	37	13	sierpiński	sierpiński	ADJ
ejpam-6540	37	14	networks	network	NOUN
ejpam-6540	37	15	that	that	PRON
ejpam-6540	37	16	occur	occur	VERB
ejpam-6540	37	17	when	when	SCONJ
ejpam-6540	37	18	the	the	DET
ejpam-6540	37	19	base	base	NOUN
ejpam-6540	37	20	graph	graph	NOUN
ejpam-6540	37	21	is	be	AUX
ejpam-6540	37	22	a	a	DET
ejpam-6540	37	23	complete	complete	ADJ
ejpam-6540	37	24	graph	graph	NOUN
ejpam-6540	37	25	k3	k3	VERB
ejpam-6540	37	26	.	.	PUNCT
ejpam-6540	38	1	recursive	recursive	ADJ
ejpam-6540	38	2	networks	network	NOUN
ejpam-6540	38	3	are	be	AUX
ejpam-6540	38	4	created	create	VERB
ejpam-6540	38	5	by	by	ADP
ejpam-6540	38	6	extending	extend	VERB
ejpam-6540	38	7	sierpiński	sierpiński	ADJ
ejpam-6540	38	8	graphs	graph	NOUN
ejpam-6540	38	9	by	by	ADP
ejpam-6540	38	10	appending	append	VERB
ejpam-6540	38	11	an	an	DET
ejpam-6540	38	12	open	open	ADJ
ejpam-6540	38	13	connection	connection	NOUN
ejpam-6540	38	14	to	to	ADP
ejpam-6540	38	15	their	their	PRON
ejpam-6540	38	16	extreme	extreme	ADJ
ejpam-6540	38	17	vertices	vertex	NOUN
ejpam-6540	38	18	.	.	PUNCT
ejpam-6540	39	1	these	these	DET
ejpam-6540	39	2	networks	network	NOUN
ejpam-6540	39	3	have	have	AUX
ejpam-6540	39	4	been	be	AUX
ejpam-6540	39	5	used	use	VERB
ejpam-6540	39	6	in	in	ADP
ejpam-6540	39	7	very	very	ADV
ejpam-6540	39	8	large	large	ADJ
ejpam-6540	39	9	scale	scale	NOUN
ejpam-6540	39	10	integration	integration	NOUN
ejpam-6540	39	11	(	(	PUNCT
ejpam-6540	39	12	vlsi	vlsi	NOUN
ejpam-6540	39	13	)	)	PUNCT
ejpam-6540	39	14	designs	design	NOUN
ejpam-6540	39	15	since	since	SCONJ
ejpam-6540	39	16	their	their	PRON
ejpam-6540	39	17	initial	initial	ADJ
ejpam-6540	39	18	introduction	introduction	NOUN
ejpam-6540	39	19	in	in	ADP
ejpam-6540	39	20	1988	1988	NUM
ejpam-6540	39	21	as	as	ADP
ejpam-6540	39	22	a	a	DET
ejpam-6540	39	23	foundation	foundation	NOUN
ejpam-6540	39	24	for	for	ADP
ejpam-6540	39	25	message	message	NOUN
ejpam-6540	39	26	-	-	PUNCT
ejpam-6540	39	27	passing	pass	VERB
ejpam-6540	39	28	architectures	architecture	NOUN
ejpam-6540	39	29	[	[	X
ejpam-6540	39	30	17	17	NUM
ejpam-6540	39	31	]	]	PUNCT
ejpam-6540	39	32	.	.	PUNCT
ejpam-6540	40	1	sierpiński	sierpiński	ADJ
ejpam-6540	40	2	graphs	graph	NOUN
ejpam-6540	40	3	were	be	AUX
ejpam-6540	40	4	created	create	VERB
ejpam-6540	40	5	in	in	ADP
ejpam-6540	40	6	the	the	DET
ejpam-6540	40	7	late	late	ADJ
ejpam-6540	40	8	1990s	1990	NOUN
ejpam-6540	40	9	when	when	SCONJ
ejpam-6540	40	10	sierpiński	sierpiński	ADJ
ejpam-6540	40	11	labelings	labeling	NOUN
ejpam-6540	40	12	were	be	AUX
ejpam-6540	40	13	applied	apply	VERB
ejpam-6540	40	14	to	to	ADP
ejpam-6540	40	15	wk	wk	NOUN
ejpam-6540	40	16	-	-	PUNCT
ejpam-6540	40	17	recursive	recursive	ADJ
ejpam-6540	40	18	networks	network	NOUN
ejpam-6540	40	19	[	[	X
ejpam-6540	40	20	18	18	NUM
ejpam-6540	40	21	]	]	PUNCT
ejpam-6540	40	22	.	.	PUNCT
ejpam-6540	41	1	deeper	deep	ADJ
ejpam-6540	41	2	investigation	investigation	NOUN
ejpam-6540	41	3	of	of	ADP
ejpam-6540	41	4	their	their	PRON
ejpam-6540	41	5	characteristics	characteristic	NOUN
ejpam-6540	41	6	has	have	AUX
ejpam-6540	41	7	been	be	AUX
ejpam-6540	41	8	made	make	VERB
ejpam-6540	41	9	k.	k.	PROPN
ejpam-6540	41	10	b.	b.	PROPN
ejpam-6540	41	11	dharan	dharan	PROPN
ejpam-6540	41	12	,	,	PUNCT
ejpam-6540	41	13	s.	s.	PROPN
ejpam-6540	41	14	radha	radha	PROPN
ejpam-6540	41	15	/	/	PUNCT
ejpam-6540	41	16	eur	eur	PROPN
ejpam-6540	41	17	.	.	PUNCT
ejpam-6540	42	1	j.	j.	PROPN
ejpam-6540	42	2	pure	pure	PROPN
ejpam-6540	42	3	appl	appl	PROPN
ejpam-6540	42	4	.	.	PROPN
ejpam-6540	42	5	math	math	PROPN
ejpam-6540	42	6	,	,	PUNCT
ejpam-6540	42	7	18	18	NUM
ejpam-6540	42	8	(	(	PUNCT
ejpam-6540	42	9	3	3	NUM
ejpam-6540	42	10	)	)	PUNCT
ejpam-6540	42	11	(	(	PUNCT
ejpam-6540	42	12	2025	2025	NUM
ejpam-6540	42	13	)	)	PUNCT
ejpam-6540	42	14	,	,	PUNCT
ejpam-6540	42	15	6540	6540	NUM
ejpam-6540	42	16	3	3	NUM
ejpam-6540	42	17	of	of	ADP
ejpam-6540	42	18	17	17	NUM
ejpam-6540	42	19	possible	possible	ADJ
ejpam-6540	42	20	by	by	ADP
ejpam-6540	42	21	this	this	DET
ejpam-6540	42	22	labelling	labelling	NOUN
ejpam-6540	42	23	strategy	strategy	NOUN
ejpam-6540	42	24	.	.	PUNCT
ejpam-6540	43	1	in	in	ADP
ejpam-6540	43	2	[	[	X
ejpam-6540	43	3	19	19	NUM
ejpam-6540	43	4	]	]	PUNCT
ejpam-6540	43	5	,	,	PUNCT
ejpam-6540	43	6	a	a	DET
ejpam-6540	43	7	number	number	NOUN
ejpam-6540	43	8	of	of	ADP
ejpam-6540	43	9	significant	significant	ADJ
ejpam-6540	43	10	features	feature	NOUN
ejpam-6540	43	11	of	of	ADP
ejpam-6540	43	12	sierpiński	sierpiński	ADJ
ejpam-6540	43	13	graphs	graph	NOUN
ejpam-6540	43	14	have	have	AUX
ejpam-6540	43	15	been	be	AUX
ejpam-6540	43	16	discussed	discuss	VERB
ejpam-6540	43	17	.	.	PUNCT
ejpam-6540	44	1	these	these	DET
ejpam-6540	44	2	networks	network	NOUN
ejpam-6540	44	3	have	have	AUX
ejpam-6540	44	4	been	be	AUX
ejpam-6540	44	5	shown	show	VERB
ejpam-6540	44	6	to	to	PART
ejpam-6540	44	7	have	have	VERB
ejpam-6540	44	8	hamiltonian	hamiltonian	ADJ
ejpam-6540	44	9	characteristics	characteristic	NOUN
ejpam-6540	44	10	and	and	CCONJ
ejpam-6540	44	11	their	their	PRON
ejpam-6540	44	12	geodesic	geodesic	ADJ
ejpam-6540	44	13	distances	distance	NOUN
ejpam-6540	44	14	between	between	ADP
ejpam-6540	44	15	vertices	vertex	NOUN
ejpam-6540	44	16	have	have	AUX
ejpam-6540	44	17	been	be	AUX
ejpam-6540	44	18	calculated	calculate	VERB
ejpam-6540	44	19	[	[	X
ejpam-6540	44	20	20	20	NUM
ejpam-6540	44	21	]	]	PUNCT
ejpam-6540	44	22	.	.	PUNCT
ejpam-6540	45	1	additional	additional	ADJ
ejpam-6540	45	2	metrics	metric	NOUN
ejpam-6540	45	3	have	have	AUX
ejpam-6540	45	4	been	be	AUX
ejpam-6540	45	5	examined	examine	VERB
ejpam-6540	45	6	,	,	PUNCT
ejpam-6540	45	7	such	such	ADJ
ejpam-6540	45	8	as	as	ADP
ejpam-6540	45	9	median	median	ADJ
ejpam-6540	45	10	values	value	NOUN
ejpam-6540	45	11	,	,	PUNCT
ejpam-6540	45	12	average	average	ADJ
ejpam-6540	45	13	eccentricity	eccentricity	NOUN
ejpam-6540	45	14	,	,	PUNCT
ejpam-6540	45	15	and	and	CCONJ
ejpam-6540	45	16	connectedness	connectedness	NOUN
ejpam-6540	45	17	[	[	X
ejpam-6540	45	18	21–23	21–23	X
ejpam-6540	45	19	]	]	X
ejpam-6540	45	20	.	.	PUNCT
ejpam-6540	46	1	furthermore	furthermore	ADV
ejpam-6540	46	2	,	,	PUNCT
ejpam-6540	46	3	several	several	ADJ
ejpam-6540	46	4	sierpiński	sierpiński	ADJ
ejpam-6540	46	5	graph	graph	NOUN
ejpam-6540	46	6	topological	topological	ADJ
ejpam-6540	46	7	descriptors	descriptor	NOUN
ejpam-6540	46	8	have	have	AUX
ejpam-6540	46	9	been	be	AUX
ejpam-6540	46	10	studied	study	VERB
ejpam-6540	46	11	[	[	PUNCT
ejpam-6540	46	12	24	24	NUM
ejpam-6540	46	13	]	]	PUNCT
ejpam-6540	46	14	,	,	PUNCT
ejpam-6540	46	15	which	which	PRON
ejpam-6540	46	16	has	have	AUX
ejpam-6540	46	17	shed	shed	VERB
ejpam-6540	46	18	light	light	NOUN
ejpam-6540	46	19	on	on	ADP
ejpam-6540	46	20	the	the	DET
ejpam-6540	46	21	shortest	short	ADJ
ejpam-6540	46	22	path	path	NOUN
ejpam-6540	46	23	structures	structure	NOUN
ejpam-6540	46	24	in	in	ADP
ejpam-6540	46	25	these	these	DET
ejpam-6540	46	26	networks	network	NOUN
ejpam-6540	46	27	[	[	X
ejpam-6540	46	28	25	25	NUM
ejpam-6540	46	29	]	]	PUNCT
ejpam-6540	46	30	.	.	PUNCT
ejpam-6540	47	1	complete	complete	ADJ
ejpam-6540	47	2	graphs	graph	NOUN
ejpam-6540	47	3	serve	serve	VERB
ejpam-6540	47	4	as	as	ADP
ejpam-6540	47	5	the	the	DET
ejpam-6540	47	6	basic	basic	ADJ
ejpam-6540	47	7	building	building	NOUN
ejpam-6540	47	8	blocks	block	NOUN
ejpam-6540	47	9	for	for	ADP
ejpam-6540	47	10	the	the	DET
ejpam-6540	47	11	construction	construction	NOUN
ejpam-6540	47	12	of	of	ADP
ejpam-6540	47	13	classical	classical	ADJ
ejpam-6540	47	14	sierpiński	sierpiński	ADJ
ejpam-6540	47	15	networks	network	NOUN
ejpam-6540	47	16	,	,	PUNCT
ejpam-6540	47	17	as	as	SCONJ
ejpam-6540	47	18	described	describe	VERB
ejpam-6540	47	19	in	in	ADP
ejpam-6540	47	20	[	[	X
ejpam-6540	47	21	18	18	NUM
ejpam-6540	47	22	]	]	PUNCT
ejpam-6540	47	23	.	.	PUNCT
ejpam-6540	48	1	in	in	ADP
ejpam-6540	48	2	[	[	X
ejpam-6540	48	3	19	19	NUM
ejpam-6540	48	4	]	]	PUNCT
ejpam-6540	48	5	,	,	PUNCT
ejpam-6540	48	6	a	a	DET
ejpam-6540	48	7	more	more	ADV
ejpam-6540	48	8	expansive	expansive	ADJ
ejpam-6540	48	9	category	category	NOUN
ejpam-6540	48	10	called	call	VERB
ejpam-6540	48	11	as	as	SCONJ
ejpam-6540	48	12	generalised	generalise	VERB
ejpam-6540	48	13	sierpiński	sierpiński	PROPN
ejpam-6540	48	14	networks	network	NOUN
ejpam-6540	48	15	was	be	AUX
ejpam-6540	48	16	established	establish	VERB
ejpam-6540	48	17	and	and	CCONJ
ejpam-6540	48	18	given	give	VERB
ejpam-6540	48	19	the	the	DET
ejpam-6540	48	20	survey	survey	NOUN
ejpam-6540	48	21	about	about	ADP
ejpam-6540	48	22	their	their	PRON
ejpam-6540	48	23	various	various	ADJ
ejpam-6540	48	24	graph	graph	NOUN
ejpam-6540	48	25	theoretical	theoretical	ADJ
ejpam-6540	48	26	properties	property	NOUN
ejpam-6540	48	27	.	.	PUNCT
ejpam-6540	49	1	the	the	DET
ejpam-6540	49	2	concept	concept	NOUN
ejpam-6540	49	3	of	of	ADP
ejpam-6540	49	4	the	the	DET
ejpam-6540	49	5	sierpiński	sierpiński	ADJ
ejpam-6540	49	6	product	product	NOUN
ejpam-6540	49	7	g⊗fh	g⊗fh	NOUN
ejpam-6540	49	8	,	,	PUNCT
ejpam-6540	49	9	where	where	SCONJ
ejpam-6540	49	10	f	f	X
ejpam-6540	49	11	:	:	PUNCT
ejpam-6540	49	12	v	v	X
ejpam-6540	49	13	(	(	PUNCT
ejpam-6540	49	14	g	g	NOUN
ejpam-6540	49	15	)	)	PUNCT
ejpam-6540	49	16	→	→	SYM
ejpam-6540	49	17	v	v	X
ejpam-6540	49	18	(	(	PUNCT
ejpam-6540	49	19	h	h	NOUN
ejpam-6540	49	20	)	)	PUNCT
ejpam-6540	49	21	,	,	PUNCT
ejpam-6540	49	22	generalizes	generalize	VERB
ejpam-6540	49	23	the	the	DET
ejpam-6540	49	24	construction	construction	NOUN
ejpam-6540	49	25	of	of	ADP
ejpam-6540	49	26	sierpiński	sierpiński	ADJ
ejpam-6540	49	27	-	-	PUNCT
ejpam-6540	49	28	type	type	NOUN
ejpam-6540	49	29	graphs	graph	NOUN
ejpam-6540	49	30	by	by	ADP
ejpam-6540	49	31	embedding	embed	VERB
ejpam-6540	49	32	copies	copy	NOUN
ejpam-6540	49	33	of	of	ADP
ejpam-6540	49	34	h	h	NOUN
ejpam-6540	49	35	based	base	VERB
ejpam-6540	49	36	on	on	ADP
ejpam-6540	49	37	the	the	DET
ejpam-6540	49	38	structure	structure	NOUN
ejpam-6540	49	39	of	of	ADP
ejpam-6540	49	40	g.	g.	PROPN
ejpam-6540	49	41	this	this	DET
ejpam-6540	49	42	construction	construction	NOUN
ejpam-6540	49	43	and	and	CCONJ
ejpam-6540	49	44	related	relate	VERB
ejpam-6540	49	45	metric	metric	ADJ
ejpam-6540	49	46	properties	property	NOUN
ejpam-6540	49	47	have	have	AUX
ejpam-6540	49	48	been	be	AUX
ejpam-6540	49	49	rigorously	rigorously	ADV
ejpam-6540	49	50	studied	study	VERB
ejpam-6540	49	51	in	in	ADP
ejpam-6540	49	52	[	[	X
ejpam-6540	49	53	26	26	NUM
ejpam-6540	49	54	]	]	PUNCT
ejpam-6540	49	55	.	.	PUNCT
ejpam-6540	50	1	the	the	DET
ejpam-6540	50	2	study	study	NOUN
ejpam-6540	50	3	of	of	ADP
ejpam-6540	50	4	metric	metric	ADJ
ejpam-6540	50	5	dimension	dimension	NOUN
ejpam-6540	50	6	in	in	ADP
ejpam-6540	50	7	recursive	recursive	ADJ
ejpam-6540	50	8	and	and	CCONJ
ejpam-6540	50	9	fractal	fractal	ADV
ejpam-6540	50	10	-	-	PUNCT
ejpam-6540	50	11	based	base	VERB
ejpam-6540	50	12	networks	network	NOUN
ejpam-6540	50	13	has	have	AUX
ejpam-6540	50	14	drawn	draw	VERB
ejpam-6540	50	15	increasing	increase	VERB
ejpam-6540	50	16	attention	attention	NOUN
ejpam-6540	50	17	due	due	ADP
ejpam-6540	50	18	to	to	ADP
ejpam-6540	50	19	its	its	PRON
ejpam-6540	50	20	implications	implication	NOUN
ejpam-6540	50	21	in	in	ADP
ejpam-6540	50	22	network	network	NOUN
ejpam-6540	50	23	navigation	navigation	NOUN
ejpam-6540	50	24	and	and	CCONJ
ejpam-6540	50	25	information	information	NOUN
ejpam-6540	50	26	retrieval	retrieval	NOUN
ejpam-6540	50	27	[	[	X
ejpam-6540	50	28	27–32	27–32	NUM
ejpam-6540	50	29	]	]	PUNCT
ejpam-6540	50	30	.	.	PUNCT
ejpam-6540	51	1	in	in	ADP
ejpam-6540	51	2	particular	particular	ADJ
ejpam-6540	51	3	,	,	PUNCT
ejpam-6540	51	4	the	the	DET
ejpam-6540	51	5	work	work	NOUN
ejpam-6540	51	6	presented	present	VERB
ejpam-6540	51	7	in	in	ADP
ejpam-6540	51	8	[	[	X
ejpam-6540	51	9	33	33	NUM
ejpam-6540	51	10	]	]	PUNCT
ejpam-6540	51	11	investigates	investigate	VERB
ejpam-6540	51	12	the	the	DET
ejpam-6540	51	13	metric	metric	ADJ
ejpam-6540	51	14	dimension	dimension	NOUN
ejpam-6540	51	15	and	and	CCONJ
ejpam-6540	51	16	its	its	PRON
ejpam-6540	51	17	variants	variant	NOUN
ejpam-6540	51	18	for	for	ADP
ejpam-6540	51	19	generalized	generalized	ADJ
ejpam-6540	51	20	sierpiński	sierpiński	ADJ
ejpam-6540	51	21	networks	network	NOUN
ejpam-6540	51	22	constructed	construct	VERB
ejpam-6540	51	23	over	over	ADP
ejpam-6540	51	24	c4	c4	NOUN
ejpam-6540	51	25	,	,	PUNCT
ejpam-6540	51	26	which	which	PRON
ejpam-6540	51	27	are	be	AUX
ejpam-6540	51	28	known	know	VERB
ejpam-6540	51	29	to	to	PART
ejpam-6540	51	30	be	be	AUX
ejpam-6540	51	31	spanning	span	VERB
ejpam-6540	51	32	subgraphs	subgraph	NOUN
ejpam-6540	51	33	of	of	ADP
ejpam-6540	51	34	hypercubes	hypercube	NOUN
ejpam-6540	51	35	.	.	PUNCT
ejpam-6540	52	1	their	their	PRON
ejpam-6540	52	2	analysis	analysis	NOUN
ejpam-6540	52	3	showcases	showcase	VERB
ejpam-6540	52	4	the	the	DET
ejpam-6540	52	5	interplay	interplay	NOUN
ejpam-6540	52	6	between	between	ADP
ejpam-6540	52	7	structural	structural	ADJ
ejpam-6540	52	8	properties	property	NOUN
ejpam-6540	52	9	,	,	PUNCT
ejpam-6540	52	10	such	such	ADJ
ejpam-6540	52	11	as	as	ADP
ejpam-6540	52	12	vertex	vertex	NOUN
ejpam-6540	52	13	twins	twin	NOUN
ejpam-6540	52	14	,	,	PUNCT
ejpam-6540	52	15	and	and	CCONJ
ejpam-6540	52	16	the	the	DET
ejpam-6540	52	17	complexity	complexity	NOUN
ejpam-6540	52	18	of	of	ADP
ejpam-6540	52	19	resolving	resolve	VERB
ejpam-6540	52	20	sets	set	NOUN
ejpam-6540	52	21	.	.	PUNCT
ejpam-6540	53	1	motivated	motivate	VERB
ejpam-6540	53	2	by	by	ADP
ejpam-6540	53	3	these	these	DET
ejpam-6540	53	4	findings	finding	NOUN
ejpam-6540	53	5	,	,	PUNCT
ejpam-6540	53	6	we	we	PRON
ejpam-6540	53	7	extend	extend	VERB
ejpam-6540	53	8	the	the	DET
ejpam-6540	53	9	investigation	investigation	NOUN
ejpam-6540	53	10	to	to	ADP
ejpam-6540	53	11	the	the	DET
ejpam-6540	53	12	class	class	NOUN
ejpam-6540	53	13	of	of	ADP
ejpam-6540	53	14	generalized	generalized	ADJ
ejpam-6540	53	15	sierpiński	sierpiński	ADJ
ejpam-6540	53	16	networks	network	NOUN
ejpam-6540	53	17	over	over	ADP
ejpam-6540	53	18	c5	c5	PROPN
ejpam-6540	53	19	,	,	PUNCT
ejpam-6540	53	20	exploring	explore	VERB
ejpam-6540	53	21	how	how	SCONJ
ejpam-6540	53	22	the	the	DET
ejpam-6540	53	23	odd	odd	ADJ
ejpam-6540	53	24	cycle	cycle	NOUN
ejpam-6540	53	25	structure	structure	NOUN
ejpam-6540	53	26	influences	influence	VERB
ejpam-6540	53	27	the	the	DET
ejpam-6540	53	28	metric	metric	ADJ
ejpam-6540	53	29	dimension	dimension	NOUN
ejpam-6540	53	30	and	and	CCONJ
ejpam-6540	53	31	its	its	PRON
ejpam-6540	53	32	fault	fault	NOUN
ejpam-6540	53	33	-	-	PUNCT
ejpam-6540	53	34	tolerant	tolerant	ADJ
ejpam-6540	53	35	variants	variant	NOUN
ejpam-6540	53	36	.	.	PUNCT
ejpam-6540	54	1	2	2	X
ejpam-6540	54	2	.	.	X
ejpam-6540	54	3	preliminaries	preliminary	NOUN
ejpam-6540	54	4	let	let	VERB
ejpam-6540	54	5	γ	γ	X
ejpam-6540	54	6	=	=	SYM
ejpam-6540	54	7	(	(	PUNCT
ejpam-6540	54	8	v(γ),e(γ	v(γ),e(γ	NUM
ejpam-6540	54	9	)	)	PUNCT
ejpam-6540	54	10	)	)	PUNCT
ejpam-6540	54	11	be	be	AUX
ejpam-6540	54	12	a	a	DET
ejpam-6540	54	13	graph	graph	NOUN
ejpam-6540	54	14	of	of	ADP
ejpam-6540	54	15	order	order	NOUN
ejpam-6540	54	16	n.	n.	NOUN
ejpam-6540	54	17	for	for	ADP
ejpam-6540	54	18	h	h	PROPN
ejpam-6540	54	19	∈	∈	PROPN
ejpam-6540	54	20	n	n	CCONJ
ejpam-6540	54	21	,	,	PUNCT
ejpam-6540	54	22	the	the	DET
ejpam-6540	54	23	generalized	generalized	ADJ
ejpam-6540	54	24	sierpiński	sierpiński	ADJ
ejpam-6540	54	25	graph	graph	NOUN
ejpam-6540	54	26	[	[	X
ejpam-6540	54	27	19	19	NUM
ejpam-6540	54	28	]	]	PUNCT
ejpam-6540	54	29	,	,	PUNCT
ejpam-6540	54	30	denoted	denote	VERB
ejpam-6540	54	31	as	as	ADP
ejpam-6540	54	32	sh	sh	PROPN
ejpam-6540	54	33	γ	γ	PROPN
ejpam-6540	54	34	,	,	PUNCT
ejpam-6540	54	35	has	have	VERB
ejpam-6540	54	36	the	the	DET
ejpam-6540	54	37	vertex	vertex	NOUN
ejpam-6540	54	38	set	set	VERB
ejpam-6540	54	39	v(sh	v(sh	PROPN
ejpam-6540	54	40	γ	γ	NOUN
ejpam-6540	54	41	)	)	PUNCT
ejpam-6540	55	1	=	=	PUNCT
ejpam-6540	55	2	v(γ)h	v(γ)h	PROPN
ejpam-6540	55	3	.	.	PUNCT
ejpam-6540	56	1	the	the	DET
ejpam-6540	56	2	notation	notation	NOUN
ejpam-6540	56	3	for	for	ADP
ejpam-6540	56	4	a	a	DET
ejpam-6540	56	5	vertex	vertex	NOUN
ejpam-6540	56	6	g	g	NOUN
ejpam-6540	56	7	=	=	SYM
ejpam-6540	56	8	(	(	PUNCT
ejpam-6540	56	9	g1	g1	PROPN
ejpam-6540	56	10	,	,	PUNCT
ejpam-6540	56	11	g2	g2	PROPN
ejpam-6540	56	12	,	,	PUNCT
ejpam-6540	56	13	.	.	PUNCT
ejpam-6540	56	14	.	.	PUNCT
ejpam-6540	56	15	.	.	PUNCT
ejpam-6540	57	1	,	,	PUNCT
ejpam-6540	57	2	gh	gh	PROPN
ejpam-6540	57	3	)	)	PUNCT
ejpam-6540	57	4	in	in	ADP
ejpam-6540	57	5	v(sh	v(sh	PROPN
ejpam-6540	57	6	γ	γ	X
ejpam-6540	57	7	)	)	PUNCT
ejpam-6540	57	8	is	be	AUX
ejpam-6540	57	9	abbreviated	abbreviate	VERB
ejpam-6540	57	10	as	as	ADP
ejpam-6540	57	11	g	g	PROPN
ejpam-6540	57	12	=	=	SYM
ejpam-6540	57	13	g1g2	g1g2	PROPN
ejpam-6540	57	14	.	.	PUNCT
ejpam-6540	57	15	.	.	PUNCT
ejpam-6540	57	16	.	.	PUNCT
ejpam-6540	58	1	gh	gh	PROPN
ejpam-6540	58	2	.	.	PUNCT
ejpam-6540	59	1	two	two	NUM
ejpam-6540	59	2	vertices	vertex	NOUN
ejpam-6540	59	3	,	,	PUNCT
ejpam-6540	59	4	f	f	PROPN
ejpam-6540	59	5	=	=	SYM
ejpam-6540	59	6	f1f2	f1f2	X
ejpam-6540	59	7	.	.	PUNCT
ejpam-6540	59	8	.	.	PUNCT
ejpam-6540	59	9	.	.	PUNCT
ejpam-6540	60	1	fh	fh	PROPN
ejpam-6540	60	2	and	and	CCONJ
ejpam-6540	60	3	g	g	PROPN
ejpam-6540	60	4	=	=	SYM
ejpam-6540	60	5	g1g2	g1g2	PROPN
ejpam-6540	60	6	.	.	PUNCT
ejpam-6540	60	7	.	.	PUNCT
ejpam-6540	60	8	.	.	PUNCT
ejpam-6540	61	1	gh	gh	PROPN
ejpam-6540	61	2	,	,	PUNCT
ejpam-6540	61	3	are	be	AUX
ejpam-6540	61	4	adjacent	adjacent	ADJ
ejpam-6540	61	5	if	if	SCONJ
ejpam-6540	61	6	there	there	PRON
ejpam-6540	61	7	exists	exist	VERB
ejpam-6540	61	8	an	an	DET
ejpam-6540	61	9	index	index	NOUN
ejpam-6540	61	10	x	x	SYM
ejpam-6540	61	11	∈	∈	PROPN
ejpam-6540	61	12	zh+1	zh+1	X
ejpam-6540	61	13	\	\	X
ejpam-6540	61	14	{	{	PUNCT
ejpam-6540	61	15	0	0	NUM
ejpam-6540	61	16	}	}	PUNCT
ejpam-6540	61	17	such	such	ADJ
ejpam-6540	61	18	that	that	SCONJ
ejpam-6540	61	19	for	for	ADP
ejpam-6540	61	20	all	all	DET
ejpam-6540	61	21	y	y	PROPN
ejpam-6540	61	22	∈	∈	PROPN
ejpam-6540	61	23	zh+1	zh+1	X
ejpam-6540	61	24	\	\	X
ejpam-6540	61	25	{	{	PUNCT
ejpam-6540	61	26	0	0	NUM
ejpam-6540	61	27	}	}	PUNCT
ejpam-6540	61	28	,	,	PUNCT
ejpam-6540	61	29	the	the	DET
ejpam-6540	61	30	following	follow	VERB
ejpam-6540	61	31	properties	property	NOUN
ejpam-6540	61	32	hold	hold	VERB
ejpam-6540	61	33	:	:	PUNCT
ejpam-6540	61	34	i	i	PRON
ejpam-6540	61	35	)	)	PUNCT
ejpam-6540	62	1	if	if	SCONJ
ejpam-6540	62	2	y	y	PROPN
ejpam-6540	62	3	<	<	X
ejpam-6540	62	4	x	x	X
ejpam-6540	62	5	,	,	PUNCT
ejpam-6540	62	6	then	then	ADV
ejpam-6540	62	7	fy	fy	PROPN
ejpam-6540	62	8	=	=	PUNCT
ejpam-6540	62	9	gy	gy	PROPN
ejpam-6540	62	10	;	;	PUNCT
ejpam-6540	62	11	ii	ii	NOUN
ejpam-6540	62	12	)	)	PUNCT
ejpam-6540	62	13	if	if	SCONJ
ejpam-6540	62	14	y	y	PROPN
ejpam-6540	62	15	=	=	SYM
ejpam-6540	62	16	x	x	NOUN
ejpam-6540	62	17	,	,	PUNCT
ejpam-6540	62	18	then	then	ADV
ejpam-6540	62	19	fx	fx	ADP
ejpam-6540	62	20	̸=	̸=	PROPN
ejpam-6540	62	21	gx	gx	PROPN
ejpam-6540	62	22	and	and	CCONJ
ejpam-6540	62	23	fxgx	fxgx	VERB
ejpam-6540	62	24	∈	∈	PROPN
ejpam-6540	62	25	e(g	e(g	PROPN
ejpam-6540	62	26	)	)	PUNCT
ejpam-6540	62	27	;	;	PUNCT
ejpam-6540	62	28	iii	iii	X
ejpam-6540	62	29	)	)	PUNCT
ejpam-6540	62	30	if	if	SCONJ
ejpam-6540	62	31	y	y	PROPN
ejpam-6540	62	32	>	>	X
ejpam-6540	62	33	x	x	PROPN
ejpam-6540	62	34	,	,	PUNCT
ejpam-6540	62	35	then	then	ADV
ejpam-6540	62	36	fy	fy	PROPN
ejpam-6540	62	37	=	=	PROPN
ejpam-6540	62	38	gx	gx	PROPN
ejpam-6540	62	39	and	and	CCONJ
ejpam-6540	62	40	fy	fy	PROPN
ejpam-6540	62	41	=	=	PROPN
ejpam-6540	62	42	gx	gx	PROPN
ejpam-6540	62	43	.	.	PROPN
ejpam-6540	63	1	for	for	ADP
ejpam-6540	63	2	example	example	NOUN
ejpam-6540	63	3	,	,	PUNCT
ejpam-6540	63	4	the	the	DET
ejpam-6540	63	5	graphs	graph	NOUN
ejpam-6540	63	6	s1	s1	NOUN
ejpam-6540	63	7	k4	k4	NOUN
ejpam-6540	63	8	and	and	CCONJ
ejpam-6540	63	9	s2	s2	NOUN
ejpam-6540	63	10	k4	k4	NOUN
ejpam-6540	63	11	are	be	AUX
ejpam-6540	63	12	depicted	depict	VERB
ejpam-6540	63	13	in	in	ADP
ejpam-6540	63	14	figure	figure	NOUN
ejpam-6540	63	15	1	1	NUM
ejpam-6540	63	16	.	.	PUNCT
ejpam-6540	64	1	the	the	DET
ejpam-6540	64	2	graph	graph	NOUN
ejpam-6540	64	3	sh	sh	PROPN
ejpam-6540	64	4	γ	γ	NOUN
ejpam-6540	64	5	can	can	AUX
ejpam-6540	64	6	be	be	AUX
ejpam-6540	64	7	constructed	construct	VERB
ejpam-6540	64	8	recursively	recursively	ADV
ejpam-6540	64	9	from	from	ADP
ejpam-6540	64	10	a	a	DET
ejpam-6540	64	11	base	base	NOUN
ejpam-6540	64	12	graph	graph	NOUN
ejpam-6540	64	13	γ	γ	PROPN
ejpam-6540	64	14	as	as	SCONJ
ejpam-6540	64	15	follows	follow	VERB
ejpam-6540	64	16	.	.	PUNCT
ejpam-6540	65	1	let	let	VERB
ejpam-6540	65	2	s1	s1	PROPN
ejpam-6540	65	3	γ	γ	X
ejpam-6540	65	4	=	=	SYM
ejpam-6540	65	5	γ	γ	PROPN
ejpam-6540	65	6	.	.	PROPN
ejpam-6540	65	7	for	for	ADP
ejpam-6540	65	8	each	each	DET
ejpam-6540	65	9	h	h	NOUN
ejpam-6540	65	10	≥	≥	NOUN
ejpam-6540	65	11	2	2	NUM
ejpam-6540	65	12	,	,	PUNCT
ejpam-6540	65	13	consider	consider	VERB
ejpam-6540	65	14	n	n	PRON
ejpam-6540	65	15	disjoint	disjoint	NOUN
ejpam-6540	65	16	copies	copy	NOUN
ejpam-6540	65	17	of	of	ADP
ejpam-6540	65	18	the	the	DET
ejpam-6540	65	19	graph	graph	NOUN
ejpam-6540	65	20	sh−1	sh−1	NOUN
ejpam-6540	65	21	γ	γ	NOUN
ejpam-6540	65	22	.	.	PUNCT
ejpam-6540	66	1	in	in	ADP
ejpam-6540	66	2	the	the	DET
ejpam-6540	66	3	xth	xth	PROPN
ejpam-6540	66	4	copy	copy	NOUN
ejpam-6540	66	5	,	,	PUNCT
ejpam-6540	66	6	where	where	SCONJ
ejpam-6540	66	7	x	x	PUNCT
ejpam-6540	66	8	∈	∈	PROPN
ejpam-6540	66	9	zn	zn	PROPN
ejpam-6540	66	10	,	,	PUNCT
ejpam-6540	66	11	prefix	prefix	VERB
ejpam-6540	66	12	each	each	DET
ejpam-6540	66	13	vertex	vertex	NOUN
ejpam-6540	66	14	label	label	NOUN
ejpam-6540	66	15	with	with	ADP
ejpam-6540	66	16	the	the	DET
ejpam-6540	66	17	index	index	NOUN
ejpam-6540	66	18	x.	x.	NOUN
ejpam-6540	66	19	these	these	DET
ejpam-6540	66	20	subgraphs	subgraph	NOUN
ejpam-6540	66	21	are	be	AUX
ejpam-6540	66	22	denoted	denote	VERB
ejpam-6540	66	23	by	by	ADP
ejpam-6540	66	24	xsh−1	xsh−1	NOUN
ejpam-6540	66	25	γ	γ	PROPN
ejpam-6540	66	26	,	,	PUNCT
ejpam-6540	66	27	for	for	ADP
ejpam-6540	66	28	all	all	DET
ejpam-6540	66	29	x	x	SYM
ejpam-6540	66	30	∈	∈	PROPN
ejpam-6540	66	31	zn	zn	X
ejpam-6540	66	32	.	.	PUNCT
ejpam-6540	67	1	furthermore	furthermore	ADV
ejpam-6540	67	2	,	,	PUNCT
ejpam-6540	67	3	if	if	SCONJ
ejpam-6540	67	4	two	two	NUM
ejpam-6540	67	5	vertices	vertex	NOUN
ejpam-6540	67	6	f	f	PROPN
ejpam-6540	67	7	and	and	CCONJ
ejpam-6540	67	8	g	g	PROPN
ejpam-6540	67	9	are	be	AUX
ejpam-6540	67	10	adjacent	adjacent	ADJ
ejpam-6540	67	11	in	in	ADP
ejpam-6540	67	12	γ	γ	PROPN
ejpam-6540	67	13	,	,	PUNCT
ejpam-6540	67	14	then	then	ADV
ejpam-6540	67	15	in	in	ADP
ejpam-6540	67	16	sh	sh	PROPN
ejpam-6540	67	17	γ	γ	X
ejpam-6540	67	18	,	,	PUNCT
ejpam-6540	67	19	the	the	DET
ejpam-6540	67	20	vertex	vertex	NOUN
ejpam-6540	67	21	labeled	label	VERB
ejpam-6540	67	22	fgh−1	fgh−1	PROPN
ejpam-6540	67	23	is	be	AUX
ejpam-6540	67	24	adjacent	adjacent	ADJ
ejpam-6540	67	25	to	to	ADP
ejpam-6540	67	26	the	the	DET
ejpam-6540	67	27	vertex	vertex	NOUN
ejpam-6540	67	28	labeled	label	VERB
ejpam-6540	68	1	gfh−1	gfh−1	PROPN
ejpam-6540	68	2	.	.	PROPN
ejpam-6540	68	3	generalized	generalize	VERB
ejpam-6540	68	4	sierpiński	sierpiński	PROPN
ejpam-6540	68	5	networks	network	NOUN
ejpam-6540	68	6	have	have	AUX
ejpam-6540	68	7	been	be	AUX
ejpam-6540	68	8	used	use	VERB
ejpam-6540	68	9	to	to	PART
ejpam-6540	68	10	represent	represent	VERB
ejpam-6540	68	11	polymer	polymer	NOUN
ejpam-6540	68	12	networks	network	NOUN
ejpam-6540	68	13	[	[	X
ejpam-6540	68	14	34	34	NUM
ejpam-6540	68	15	]	]	PUNCT
ejpam-6540	68	16	.	.	PUNCT
ejpam-6540	69	1	roman	roman	ADJ
ejpam-6540	69	2	domination	domination	NOUN
ejpam-6540	70	1	[	[	X
ejpam-6540	70	2	35	35	NUM
ejpam-6540	70	3	]	]	X
ejpam-6540	70	4	,	,	PUNCT
ejpam-6540	70	5	strong	strong	ADJ
ejpam-6540	70	6	metric	metric	ADJ
ejpam-6540	70	7	dimension	dimension	NOUN
ejpam-6540	71	1	[	[	X
ejpam-6540	71	2	36	36	NUM
ejpam-6540	71	3	]	]	PUNCT
ejpam-6540	71	4	,	,	PUNCT
ejpam-6540	71	5	and	and	CCONJ
ejpam-6540	71	6	other	other	ADJ
ejpam-6540	71	7	graph	graph	NOUN
ejpam-6540	71	8	-	-	PUNCT
ejpam-6540	71	9	theoretic	theoretic	NOUN
ejpam-6540	71	10	features	feature	NOUN
ejpam-6540	71	11	k.	k.	PROPN
ejpam-6540	71	12	b.	b.	PROPN
ejpam-6540	71	13	dharan	dharan	PROPN
ejpam-6540	71	14	,	,	PUNCT
ejpam-6540	71	15	s.	s.	PROPN
ejpam-6540	71	16	radha	radha	PROPN
ejpam-6540	71	17	/	/	PUNCT
ejpam-6540	71	18	eur	eur	PROPN
ejpam-6540	71	19	.	.	PUNCT
ejpam-6540	72	1	j.	j.	PROPN
ejpam-6540	72	2	pure	pure	PROPN
ejpam-6540	72	3	appl	appl	PROPN
ejpam-6540	72	4	.	.	PROPN
ejpam-6540	72	5	math	math	PROPN
ejpam-6540	72	6	,	,	PUNCT
ejpam-6540	72	7	18	18	NUM
ejpam-6540	72	8	(	(	PUNCT
ejpam-6540	72	9	3	3	NUM
ejpam-6540	72	10	)	)	PUNCT
ejpam-6540	72	11	(	(	PUNCT
ejpam-6540	72	12	2025	2025	NUM
ejpam-6540	72	13	)	)	PUNCT
ejpam-6540	72	14	,	,	PUNCT
ejpam-6540	72	15	6540	6540	NUM
ejpam-6540	72	16	4	4	NUM
ejpam-6540	72	17	of	of	ADP
ejpam-6540	72	18	17	17	NUM
ejpam-6540	72	19	(	(	PUNCT
ejpam-6540	72	20	a	a	NOUN
ejpam-6540	72	21	)	)	PUNCT
ejpam-6540	72	22	(	(	PUNCT
ejpam-6540	72	23	b	b	X
ejpam-6540	72	24	)	)	PUNCT
ejpam-6540	72	25	figure	figure	NOUN
ejpam-6540	72	26	1	1	NUM
ejpam-6540	72	27	:	:	PUNCT
ejpam-6540	72	28	(	(	PUNCT
ejpam-6540	72	29	a)s1	a)s1	PROPN
ejpam-6540	72	30	k4	k4	NOUN
ejpam-6540	72	31	∼=	∼=	PROPN
ejpam-6540	72	32	k4	k4	NOUN
ejpam-6540	72	33	(	(	PUNCT
ejpam-6540	72	34	b)s2	b)s2	NOUN
ejpam-6540	72	35	k4	k4	NOUN
ejpam-6540	72	36	such	such	ADJ
ejpam-6540	72	37	as	as	ADP
ejpam-6540	72	38	chromatic	chromatic	ADJ
ejpam-6540	72	39	number	number	NOUN
ejpam-6540	72	40	,	,	PUNCT
ejpam-6540	72	41	vertex	vertex	NOUN
ejpam-6540	72	42	cover	cover	NOUN
ejpam-6540	72	43	number	number	NOUN
ejpam-6540	72	44	and	and	CCONJ
ejpam-6540	72	45	clique	clique	ADJ
ejpam-6540	72	46	number	number	NOUN
ejpam-6540	72	47	for	for	ADP
ejpam-6540	72	48	sh	sh	PROPN
ejpam-6540	72	49	g	g	PROPN
ejpam-6540	72	50	are	be	AUX
ejpam-6540	72	51	already	already	ADV
ejpam-6540	72	52	determined	determine	VERB
ejpam-6540	72	53	.	.	PUNCT
ejpam-6540	73	1	the	the	DET
ejpam-6540	73	2	topological	topological	ADJ
ejpam-6540	73	3	indices	index	NOUN
ejpam-6540	73	4	of	of	ADP
ejpam-6540	73	5	generalized	generalized	ADJ
ejpam-6540	73	6	sierpiński	sierpiński	ADJ
ejpam-6540	73	7	networks	network	NOUN
ejpam-6540	73	8	are	be	AUX
ejpam-6540	73	9	examined	examine	VERB
ejpam-6540	73	10	in	in	ADP
ejpam-6540	73	11	[	[	X
ejpam-6540	73	12	34	34	NUM
ejpam-6540	73	13	]	]	PUNCT
ejpam-6540	73	14	.	.	PUNCT
ejpam-6540	74	1	in	in	ADP
ejpam-6540	74	2	this	this	DET
ejpam-6540	74	3	work	work	NOUN
ejpam-6540	74	4	,	,	PUNCT
ejpam-6540	74	5	we	we	PRON
ejpam-6540	74	6	particularly	particularly	ADV
ejpam-6540	74	7	analyze	analyze	VERB
ejpam-6540	74	8	the	the	DET
ejpam-6540	74	9	family	family	NOUN
ejpam-6540	74	10	of	of	ADP
ejpam-6540	74	11	sh	sh	PROPN
ejpam-6540	74	12	c5	c5	PROPN
ejpam-6540	74	13	and	and	CCONJ
ejpam-6540	74	14	calculate	calculate	VERB
ejpam-6540	74	15	its	its	PRON
ejpam-6540	74	16	metric	metric	ADJ
ejpam-6540	74	17	,	,	PUNCT
ejpam-6540	74	18	fault	fault	NOUN
ejpam-6540	74	19	-	-	PUNCT
ejpam-6540	74	20	tolerant	tolerant	ADJ
ejpam-6540	74	21	metric	metric	ADJ
ejpam-6540	74	22	,	,	PUNCT
ejpam-6540	74	23	edge	edge	NOUN
ejpam-6540	74	24	metric	metric	ADJ
ejpam-6540	74	25	and	and	CCONJ
ejpam-6540	74	26	fault	fault	NOUN
ejpam-6540	74	27	-	-	PUNCT
ejpam-6540	74	28	tolerant	tolerant	ADJ
ejpam-6540	74	29	edge	edge	NOUN
ejpam-6540	74	30	metric	metric	ADJ
ejpam-6540	74	31	dimensions	dimension	NOUN
ejpam-6540	74	32	.	.	PUNCT
ejpam-6540	75	1	the	the	DET
ejpam-6540	75	2	graphs	graph	NOUN
ejpam-6540	75	3	s1	s1	PROPN
ejpam-6540	75	4	c5	c5	PROPN
ejpam-6540	75	5	,	,	PUNCT
ejpam-6540	75	6	s2	s2	PROPN
ejpam-6540	75	7	c5	c5	PROPN
ejpam-6540	75	8	and	and	CCONJ
ejpam-6540	75	9	s3	s3	PROPN
ejpam-6540	75	10	c5	c5	PROPN
ejpam-6540	75	11	are	be	AUX
ejpam-6540	75	12	listed	list	VERB
ejpam-6540	75	13	in	in	ADP
ejpam-6540	75	14	the	the	DET
ejpam-6540	75	15	figure	figure	NOUN
ejpam-6540	75	16	2	2	NUM
ejpam-6540	75	17	.	.	NOUN
ejpam-6540	75	18	0	0	NUM
ejpam-6540	75	19	1	1	NUM
ejpam-6540	75	20	23	23	NUM
ejpam-6540	75	21	4	4	NUM
ejpam-6540	75	22	(	(	PUNCT
ejpam-6540	75	23	a	a	NOUN
ejpam-6540	75	24	)	)	PUNCT
ejpam-6540	75	25	00	00	NUM
ejpam-6540	75	26	01	01	NUM
ejpam-6540	75	27	0203	0203	NUM
ejpam-6540	75	28	04	04	NUM
ejpam-6540	75	29	10	10	NUM
ejpam-6540	75	30	11	11	NUM
ejpam-6540	75	31	12	12	NUM
ejpam-6540	75	32	13	13	NUM
ejpam-6540	75	33	14	14	NUM
ejpam-6540	75	34	20	20	NUM
ejpam-6540	75	35	2124	2124	NUM
ejpam-6540	75	36	22	22	NUM
ejpam-6540	75	37	23	23	NUM
ejpam-6540	75	38	30	30	NUM
ejpam-6540	75	39	31	31	NUM
ejpam-6540	75	40	32	32	NUM
ejpam-6540	75	41	33	33	NUM
ejpam-6540	75	42	34	34	NUM
ejpam-6540	75	43	40	40	NUM
ejpam-6540	75	44	41	41	NUM
ejpam-6540	75	45	42	42	NUM
ejpam-6540	75	46	43	43	NUM
ejpam-6540	75	47	44	44	NUM
ejpam-6540	75	48	(	(	PUNCT
ejpam-6540	75	49	b	b	NOUN
ejpam-6540	75	50	)	)	PUNCT
ejpam-6540	75	51	000	000	NUM
ejpam-6540	75	52	001	001	NUM
ejpam-6540	75	53	002003	002003	NUM
ejpam-6540	75	54	004	004	NUM
ejpam-6540	75	55	010	010	NUM
ejpam-6540	75	56	011	011	NUM
ejpam-6540	75	57	012013	012013	NUM
ejpam-6540	75	58	014	014	NUM
ejpam-6540	75	59	020	020	NUM
ejpam-6540	75	60	021	021	NUM
ejpam-6540	75	61	000	000	NUM
ejpam-6540	75	62	001	001	NUM
ejpam-6540	75	63	002003	002003	NUM
ejpam-6540	75	64	004	004	NUM
ejpam-6540	75	65	010	010	NUM
ejpam-6540	75	66	011	011	NUM
ejpam-6540	75	67	012013	012013	NUM
ejpam-6540	75	68	014	014	NUM
ejpam-6540	75	69	022	022	NUM
ejpam-6540	75	70	023	023	NUM
ejpam-6540	75	71	024	024	NUM
ejpam-6540	75	72	030	030	NUM
ejpam-6540	75	73	031	031	NUM
ejpam-6540	75	74	032	032	NUM
ejpam-6540	75	75	033	033	NUM
ejpam-6540	75	76	034	034	NUM
ejpam-6540	75	77	040	040	NUM
ejpam-6540	75	78	041	041	NUM
ejpam-6540	75	79	042	042	NUM
ejpam-6540	75	80	043	043	NUM
ejpam-6540	75	81	044	044	NUM
ejpam-6540	75	82	120	120	NUM
ejpam-6540	75	83	121	121	NUM
ejpam-6540	75	84	100	100	NUM
ejpam-6540	75	85	101	101	NUM
ejpam-6540	75	86	102103	102103	NUM
ejpam-6540	75	87	104	104	NUM
ejpam-6540	75	88	110	110	NUM
ejpam-6540	75	89	111	111	NUM
ejpam-6540	75	90	112113	112113	NUM
ejpam-6540	75	91	114	114	NUM
ejpam-6540	75	92	122	122	NUM
ejpam-6540	75	93	124	124	NUM
ejpam-6540	75	94	130	130	NUM
ejpam-6540	75	95	131	131	NUM
ejpam-6540	75	96	132	132	NUM
ejpam-6540	75	97	134	134	NUM
ejpam-6540	75	98	140	140	NUM
ejpam-6540	75	99	141	141	NUM
ejpam-6540	75	100	142143	142143	NUM
ejpam-6540	75	101	144	144	NUM
ejpam-6540	75	102	420	420	NUM
ejpam-6540	75	103	421	421	NUM
ejpam-6540	75	104	400	400	NUM
ejpam-6540	75	105	401	401	NUM
ejpam-6540	75	106	402403	402403	NUM
ejpam-6540	75	107	404	404	NUM
ejpam-6540	75	108	410	410	NUM
ejpam-6540	75	109	411	411	NUM
ejpam-6540	75	110	412	412	NUM
ejpam-6540	75	111	413	413	NUM
ejpam-6540	75	112	414	414	NUM
ejpam-6540	75	113	422	422	NUM
ejpam-6540	75	114	424	424	NUM
ejpam-6540	75	115	430	430	NUM
ejpam-6540	75	116	431	431	NUM
ejpam-6540	75	117	432	432	NUM
ejpam-6540	75	118	434	434	NUM
ejpam-6540	75	119	440	440	NUM
ejpam-6540	75	120	441	441	NUM
ejpam-6540	75	121	442	442	NUM
ejpam-6540	75	122	443	443	NUM
ejpam-6540	75	123	444	444	NUM
ejpam-6540	75	124	320	320	NUM
ejpam-6540	75	125	321	321	NUM
ejpam-6540	75	126	300	300	NUM
ejpam-6540	75	127	301	301	NUM
ejpam-6540	75	128	302	302	NUM
ejpam-6540	75	129	303	303	NUM
ejpam-6540	75	130	304	304	NUM
ejpam-6540	75	131	310	310	NUM
ejpam-6540	75	132	311	311	NUM
ejpam-6540	75	133	312313	312313	NUM
ejpam-6540	75	134	314	314	NUM
ejpam-6540	75	135	322	322	NUM
ejpam-6540	75	136	324	324	NUM
ejpam-6540	75	137	330	330	NUM
ejpam-6540	75	138	332	332	NUM
ejpam-6540	75	139	332	332	NUM
ejpam-6540	75	140	334	334	NUM
ejpam-6540	75	141	340	340	NUM
ejpam-6540	75	142	341	341	NUM
ejpam-6540	75	143	342	342	NUM
ejpam-6540	75	144	343	343	NUM
ejpam-6540	75	145	344	344	NUM
ejpam-6540	75	146	220	220	NUM
ejpam-6540	75	147	221	221	NUM
ejpam-6540	75	148	200	200	NUM
ejpam-6540	75	149	201	201	NUM
ejpam-6540	75	150	202203	202203	NUM
ejpam-6540	75	151	204	204	NUM
ejpam-6540	75	152	210	210	NUM
ejpam-6540	75	153	211	211	NUM
ejpam-6540	75	154	212	212	NUM
ejpam-6540	75	155	213	213	NUM
ejpam-6540	75	156	214	214	NUM
ejpam-6540	75	157	222	222	NUM
ejpam-6540	75	158	224	224	NUM
ejpam-6540	75	159	230	230	NUM
ejpam-6540	75	160	231	231	NUM
ejpam-6540	75	161	232	232	NUM
ejpam-6540	75	162	234	234	NUM
ejpam-6540	75	163	240	240	NUM
ejpam-6540	75	164	241	241	NUM
ejpam-6540	75	165	242	242	NUM
ejpam-6540	75	166	243	243	NUM
ejpam-6540	75	167	244	244	NUM
ejpam-6540	75	168	123	123	NUM
ejpam-6540	75	169	133	133	NUM
ejpam-6540	75	170	223233323333	223233323333	NUM
ejpam-6540	75	171	423	423	NUM
ejpam-6540	75	172	433	433	NUM
ejpam-6540	75	173	(	(	PUNCT
ejpam-6540	75	174	c	c	NOUN
ejpam-6540	75	175	)	)	PUNCT
ejpam-6540	75	176	figure	figure	NOUN
ejpam-6540	75	177	2	2	NUM
ejpam-6540	75	178	:	:	PUNCT
ejpam-6540	75	179	(	(	PUNCT
ejpam-6540	75	180	a)s1	a)s1	PROPN
ejpam-6540	75	181	c5	c5	PROPN
ejpam-6540	75	182	(	(	PUNCT
ejpam-6540	75	183	b)s2	b)s2	PROPN
ejpam-6540	75	184	c5	c5	PROPN
ejpam-6540	75	185	(	(	PUNCT
ejpam-6540	75	186	c)s3	c)s3	PROPN
ejpam-6540	75	187	c5	c5	PROPN
ejpam-6540	75	188	k.	k.	PROPN
ejpam-6540	75	189	b.	b.	PROPN
ejpam-6540	75	190	dharan	dharan	PROPN
ejpam-6540	75	191	,	,	PUNCT
ejpam-6540	75	192	s.	s.	PROPN
ejpam-6540	75	193	radha	radha	PROPN
ejpam-6540	75	194	/	/	PUNCT
ejpam-6540	75	195	eur	eur	PROPN
ejpam-6540	75	196	.	.	PUNCT
ejpam-6540	76	1	j.	j.	PROPN
ejpam-6540	76	2	pure	pure	PROPN
ejpam-6540	76	3	appl	appl	PROPN
ejpam-6540	76	4	.	.	PROPN
ejpam-6540	76	5	math	math	PROPN
ejpam-6540	76	6	,	,	PUNCT
ejpam-6540	76	7	18	18	NUM
ejpam-6540	76	8	(	(	PUNCT
ejpam-6540	76	9	3	3	NUM
ejpam-6540	76	10	)	)	PUNCT
ejpam-6540	76	11	(	(	PUNCT
ejpam-6540	76	12	2025	2025	NUM
ejpam-6540	76	13	)	)	PUNCT
ejpam-6540	76	14	,	,	PUNCT
ejpam-6540	76	15	6540	6540	NUM
ejpam-6540	76	16	5	5	NUM
ejpam-6540	76	17	of	of	ADP
ejpam-6540	76	18	17	17	NUM
ejpam-6540	76	19	2.1	2.1	NUM
ejpam-6540	76	20	.	.	PUNCT
ejpam-6540	77	1	metric	metric	ADJ
ejpam-6540	77	2	basis	basis	NOUN
ejpam-6540	77	3	and	and	CCONJ
ejpam-6540	77	4	fault	fault	NOUN
ejpam-6540	77	5	-	-	PUNCT
ejpam-6540	77	6	tolerant	tolerant	ADJ
ejpam-6540	77	7	basis	basis	NOUN
ejpam-6540	77	8	networks	network	NOUN
ejpam-6540	77	9	are	be	AUX
ejpam-6540	77	10	considered	consider	VERB
ejpam-6540	77	11	to	to	PART
ejpam-6540	77	12	be	be	AUX
ejpam-6540	77	13	graphs	graph	NOUN
ejpam-6540	77	14	with	with	ADP
ejpam-6540	77	15	intriguing	intriguing	ADJ
ejpam-6540	77	16	properties	property	NOUN
ejpam-6540	77	17	based	base	VERB
ejpam-6540	77	18	on	on	ADP
ejpam-6540	77	19	graph	graph	NOUN
ejpam-6540	77	20	theory	theory	NOUN
ejpam-6540	77	21	.	.	PUNCT
ejpam-6540	78	1	the	the	DET
ejpam-6540	78	2	effectiveness	effectiveness	NOUN
ejpam-6540	78	3	of	of	ADP
ejpam-6540	78	4	locating	locate	VERB
ejpam-6540	78	5	and	and	CCONJ
ejpam-6540	78	6	differentiating	differentiate	VERB
ejpam-6540	78	7	each	each	DET
ejpam-6540	78	8	vertex	vertex	NOUN
ejpam-6540	78	9	of	of	ADP
ejpam-6540	78	10	a	a	DET
ejpam-6540	78	11	graph	graph	NOUN
ejpam-6540	78	12	using	use	VERB
ejpam-6540	78	13	a	a	DET
ejpam-6540	78	14	small	small	ADJ
ejpam-6540	78	15	number	number	NOUN
ejpam-6540	78	16	of	of	ADP
ejpam-6540	78	17	landmarks	landmark	NOUN
ejpam-6540	78	18	is	be	AUX
ejpam-6540	78	19	measured	measure	VERB
ejpam-6540	78	20	by	by	ADP
ejpam-6540	78	21	its	its	PRON
ejpam-6540	78	22	metric	metric	ADJ
ejpam-6540	78	23	dimension	dimension	NOUN
ejpam-6540	78	24	[	[	X
ejpam-6540	78	25	37–39	37–39	NUM
ejpam-6540	78	26	]	]	PUNCT
ejpam-6540	78	27	.	.	PUNCT
ejpam-6540	79	1	location	location	NOUN
ejpam-6540	79	2	-	-	PUNCT
ejpam-6540	79	3	based	base	VERB
ejpam-6540	79	4	services	service	NOUN
ejpam-6540	79	5	,	,	PUNCT
ejpam-6540	79	6	robotics	robotic	NOUN
ejpam-6540	79	7	and	and	CCONJ
ejpam-6540	79	8	network	network	NOUN
ejpam-6540	79	9	design	design	NOUN
ejpam-6540	79	10	are	be	AUX
ejpam-6540	79	11	just	just	ADV
ejpam-6540	79	12	a	a	DET
ejpam-6540	79	13	few	few	ADJ
ejpam-6540	79	14	of	of	ADP
ejpam-6540	79	15	the	the	DET
ejpam-6540	79	16	domains	domain	NOUN
ejpam-6540	79	17	where	where	SCONJ
ejpam-6540	79	18	metric	metric	ADJ
ejpam-6540	79	19	dimension	dimension	NOUN
ejpam-6540	79	20	finds	find	VERB
ejpam-6540	79	21	use	use	NOUN
ejpam-6540	79	22	[	[	X
ejpam-6540	79	23	40	40	NUM
ejpam-6540	79	24	,	,	PUNCT
ejpam-6540	79	25	41	41	NUM
ejpam-6540	79	26	]	]	PUNCT
ejpam-6540	79	27	.	.	PUNCT
ejpam-6540	80	1	it	it	PRON
ejpam-6540	80	2	aids	aid	VERB
ejpam-6540	80	3	in	in	ADP
ejpam-6540	80	4	determining	determine	VERB
ejpam-6540	80	5	the	the	DET
ejpam-6540	80	6	best	good	ADJ
ejpam-6540	80	7	locations	location	NOUN
ejpam-6540	80	8	for	for	ADP
ejpam-6540	80	9	sensors	sensor	NOUN
ejpam-6540	80	10	inside	inside	ADP
ejpam-6540	80	11	a	a	DET
ejpam-6540	80	12	network	network	NOUN
ejpam-6540	80	13	to	to	PART
ejpam-6540	80	14	guarantee	guarantee	VERB
ejpam-6540	80	15	accurate	accurate	ADJ
ejpam-6540	80	16	location	location	NOUN
ejpam-6540	80	17	identification	identification	NOUN
ejpam-6540	80	18	[	[	X
ejpam-6540	80	19	42	42	NUM
ejpam-6540	80	20	]	]	PUNCT
ejpam-6540	80	21	.	.	PUNCT
ejpam-6540	81	1	determining	determine	VERB
ejpam-6540	81	2	an	an	DET
ejpam-6540	81	3	exact	exact	ADJ
ejpam-6540	81	4	value	value	NOUN
ejpam-6540	81	5	of	of	ADP
ejpam-6540	81	6	this	this	DET
ejpam-6540	81	7	parameter	parameter	NOUN
ejpam-6540	81	8	of	of	ADP
ejpam-6540	81	9	a	a	DET
ejpam-6540	81	10	graph	graph	NOUN
ejpam-6540	81	11	is	be	AUX
ejpam-6540	81	12	difficult	difficult	ADJ
ejpam-6540	81	13	task	task	NOUN
ejpam-6540	81	14	.	.	PUNCT
ejpam-6540	82	1	there	there	PRON
ejpam-6540	82	2	are	be	VERB
ejpam-6540	82	3	effective	effective	ADJ
ejpam-6540	82	4	methods	method	NOUN
ejpam-6540	82	5	for	for	ADP
ejpam-6540	82	6	calculating	calculate	VERB
ejpam-6540	82	7	this	this	DET
ejpam-6540	82	8	parameter	parameter	NOUN
ejpam-6540	82	9	for	for	ADP
ejpam-6540	82	10	some	some	DET
ejpam-6540	82	11	graph	graph	NOUN
ejpam-6540	82	12	types	type	NOUN
ejpam-6540	82	13	like	like	ADP
ejpam-6540	82	14	trees	tree	NOUN
ejpam-6540	82	15	.	.	PUNCT
ejpam-6540	83	1	the	the	DET
ejpam-6540	83	2	problem	problem	NOUN
ejpam-6540	83	3	of	of	ADP
ejpam-6540	83	4	determining	determine	VERB
ejpam-6540	83	5	this	this	DET
ejpam-6540	83	6	parameter	parameter	NOUN
ejpam-6540	83	7	for	for	ADP
ejpam-6540	83	8	directed	direct	VERB
ejpam-6540	83	9	graphs	graph	NOUN
ejpam-6540	83	10	is	be	AUX
ejpam-6540	83	11	np	np	INTJ
ejpam-6540	83	12	-	-	ADJ
ejpam-6540	83	13	hard	hard	ADJ
ejpam-6540	83	14	[	[	X
ejpam-6540	83	15	29	29	NUM
ejpam-6540	83	16	]	]	PUNCT
ejpam-6540	83	17	,	,	PUNCT
ejpam-6540	83	18	bipartite	bipartite	ADJ
ejpam-6540	83	19	graphs[43	graphs[43	PROPN
ejpam-6540	83	20	]	]	PUNCT
ejpam-6540	83	21	and	and	CCONJ
ejpam-6540	83	22	general	general	ADJ
ejpam-6540	83	23	graphs	graph	NOUN
ejpam-6540	83	24	[	[	X
ejpam-6540	83	25	37	37	NUM
ejpam-6540	83	26	]	]	PUNCT
ejpam-6540	83	27	.	.	PUNCT
ejpam-6540	84	1	despite	despite	SCONJ
ejpam-6540	84	2	the	the	DET
ejpam-6540	84	3	computational	computational	ADJ
ejpam-6540	84	4	difficulties	difficulty	NOUN
ejpam-6540	84	5	,	,	PUNCT
ejpam-6540	84	6	this	this	DET
ejpam-6540	84	7	parameter	parameter	NOUN
ejpam-6540	84	8	is	be	AUX
ejpam-6540	84	9	calculated	calculate	VERB
ejpam-6540	84	10	for	for	ADP
ejpam-6540	84	11	many	many	ADJ
ejpam-6540	84	12	graph	graph	NOUN
ejpam-6540	84	13	networks	network	NOUN
ejpam-6540	84	14	,	,	PUNCT
ejpam-6540	84	15	such	such	ADJ
ejpam-6540	84	16	as	as	ADP
ejpam-6540	84	17	honeycomb	honeycomb	NOUN
ejpam-6540	84	18	[	[	X
ejpam-6540	84	19	44	44	NUM
ejpam-6540	84	20	]	]	PUNCT
ejpam-6540	84	21	,	,	PUNCT
ejpam-6540	84	22	butterfly	butterfly	NOUN
ejpam-6540	84	23	[	[	X
ejpam-6540	84	24	43	43	NUM
ejpam-6540	84	25	]	]	PUNCT
ejpam-6540	84	26	,	,	PUNCT
ejpam-6540	84	27	beneš	beneš	X
ejpam-6540	85	1	[	[	X
ejpam-6540	85	2	43	43	NUM
ejpam-6540	85	3	]	]	PUNCT
ejpam-6540	85	4	,	,	PUNCT
ejpam-6540	85	5	circulant	circulant	ADJ
ejpam-6540	85	6	graphs	graph	NOUN
ejpam-6540	85	7	[	[	X
ejpam-6540	85	8	45	45	NUM
ejpam-6540	85	9	]	]	PUNCT
ejpam-6540	85	10	,	,	PUNCT
ejpam-6540	85	11	generalized	generalized	ADJ
ejpam-6540	85	12	subdivision	subdivision	NOUN
ejpam-6540	85	13	of	of	ADP
ejpam-6540	85	14	prism	prism	NOUN
ejpam-6540	85	15	[	[	X
ejpam-6540	85	16	46	46	NUM
ejpam-6540	85	17	]	]	PUNCT
ejpam-6540	85	18	,	,	PUNCT
ejpam-6540	85	19	chemical	chemical	NOUN
ejpam-6540	85	20	structures	structure	NOUN
ejpam-6540	85	21	[	[	X
ejpam-6540	85	22	47	47	NUM
ejpam-6540	85	23	]	]	PUNCT
ejpam-6540	85	24	,	,	PUNCT
ejpam-6540	85	25	convex	convex	VERB
ejpam-6540	85	26	triangular	triangular	NOUN
ejpam-6540	85	27	networks	network	NOUN
ejpam-6540	85	28	[	[	X
ejpam-6540	85	29	48	48	NUM
ejpam-6540	85	30	]	]	PUNCT
ejpam-6540	85	31	,	,	PUNCT
ejpam-6540	85	32	multistage	multistage	NOUN
ejpam-6540	85	33	interconnection	interconnection	NOUN
ejpam-6540	85	34	networks	network	NOUN
ejpam-6540	85	35	[	[	X
ejpam-6540	85	36	49	49	NUM
ejpam-6540	85	37	]	]	PUNCT
ejpam-6540	85	38	and	and	CCONJ
ejpam-6540	85	39	sierpiński	sierpiński	VERB
ejpam-6540	85	40	[	[	PUNCT
ejpam-6540	85	41	50	50	NUM
ejpam-6540	85	42	]	]	PUNCT
ejpam-6540	85	43	.	.	PUNCT
ejpam-6540	86	1	a	a	DET
ejpam-6540	86	2	current	current	ADJ
ejpam-6540	86	3	assessment	assessment	NOUN
ejpam-6540	86	4	of	of	ADP
ejpam-6540	86	5	the	the	DET
ejpam-6540	86	6	literature	literature	NOUN
ejpam-6540	86	7	on	on	ADP
ejpam-6540	86	8	metric	metric	ADJ
ejpam-6540	86	9	dimension	dimension	NOUN
ejpam-6540	86	10	could	could	AUX
ejpam-6540	86	11	be	be	AUX
ejpam-6540	86	12	found	find	VERB
ejpam-6540	86	13	in	in	ADP
ejpam-6540	86	14	[	[	X
ejpam-6540	86	15	51	51	NUM
ejpam-6540	86	16	]	]	PUNCT
ejpam-6540	86	17	.	.	PUNCT
ejpam-6540	87	1	the	the	DET
ejpam-6540	87	2	distance	distance	NOUN
ejpam-6540	87	3	dγ(f	dγ(f	PUNCT
ejpam-6540	87	4	,	,	PUNCT
ejpam-6540	87	5	g	g	NOUN
ejpam-6540	87	6	)	)	PUNCT
ejpam-6540	87	7	in	in	ADP
ejpam-6540	87	8	a	a	DET
ejpam-6540	87	9	connected	connected	ADJ
ejpam-6540	87	10	graph	graph	NOUN
ejpam-6540	87	11	γ	γ	X
ejpam-6540	87	12	is	be	AUX
ejpam-6540	87	13	defined	define	VERB
ejpam-6540	87	14	as	as	ADP
ejpam-6540	87	15	the	the	DET
ejpam-6540	87	16	smallest	small	ADJ
ejpam-6540	87	17	number	number	NOUN
ejpam-6540	87	18	of	of	ADP
ejpam-6540	87	19	edges	edge	NOUN
ejpam-6540	87	20	required	require	VERB
ejpam-6540	87	21	to	to	PART
ejpam-6540	87	22	travel	travel	VERB
ejpam-6540	87	23	from	from	ADP
ejpam-6540	87	24	a	a	DET
ejpam-6540	87	25	vertex	vertex	NOUN
ejpam-6540	87	26	f	f	NOUN
ejpam-6540	87	27	to	to	ADP
ejpam-6540	87	28	a	a	DET
ejpam-6540	87	29	vertex	vertex	NOUN
ejpam-6540	87	30	g.	g.	NOUN
ejpam-6540	87	31	for	for	ADP
ejpam-6540	87	32	a	a	DET
ejpam-6540	87	33	vertex	vertex	NOUN
ejpam-6540	87	34	u	u	NOUN
ejpam-6540	87	35	and	and	CCONJ
ejpam-6540	87	36	an	an	DET
ejpam-6540	87	37	edge	edge	NOUN
ejpam-6540	87	38	e	e	NOUN
ejpam-6540	87	39	=	=	SYM
ejpam-6540	87	40	fg	fg	PROPN
ejpam-6540	87	41	(	(	PUNCT
ejpam-6540	87	42	with	with	ADP
ejpam-6540	87	43	f	f	PROPN
ejpam-6540	87	44	,	,	PUNCT
ejpam-6540	87	45	g	g	PROPN
ejpam-6540	87	46	∈	∈	PROPN
ejpam-6540	87	47	v(γ	v(γ	NOUN
ejpam-6540	87	48	)	)	PUNCT
ejpam-6540	87	49	)	)	PUNCT
ejpam-6540	87	50	,	,	PUNCT
ejpam-6540	87	51	the	the	DET
ejpam-6540	87	52	distance	distance	NOUN
ejpam-6540	87	53	from	from	ADP
ejpam-6540	87	54	u	u	PRON
ejpam-6540	87	55	to	to	ADP
ejpam-6540	87	56	the	the	DET
ejpam-6540	87	57	edge	edge	NOUN
ejpam-6540	87	58	e	e	NOUN
ejpam-6540	87	59	is	be	AUX
ejpam-6540	87	60	defined	define	VERB
ejpam-6540	87	61	as	as	ADP
ejpam-6540	87	62	dγ(u	dγ(u	X
ejpam-6540	87	63	,	,	PUNCT
ejpam-6540	87	64	e	e	NOUN
ejpam-6540	87	65	)	)	PUNCT
ejpam-6540	87	66	=	=	SYM
ejpam-6540	87	67	min{dγ(u	min{dγ(u	PROPN
ejpam-6540	87	68	,	,	PUNCT
ejpam-6540	87	69	f	f	NOUN
ejpam-6540	87	70	)	)	PUNCT
ejpam-6540	87	71	,	,	PUNCT
ejpam-6540	87	72	dγ(u	dγ(u	PROPN
ejpam-6540	87	73	,	,	PUNCT
ejpam-6540	87	74	g	g	NOUN
ejpam-6540	87	75	)	)	PUNCT
ejpam-6540	87	76	}	}	PUNCT
ejpam-6540	87	77	.	.	PUNCT
ejpam-6540	88	1	given	give	VERB
ejpam-6540	88	2	an	an	DET
ejpam-6540	88	3	ordered	order	VERB
ejpam-6540	88	4	subset	subset	NOUN
ejpam-6540	88	5	y	y	PROPN
ejpam-6540	88	6	=	=	PUNCT
ejpam-6540	88	7	{	{	PUNCT
ejpam-6540	88	8	y1	y1	PROPN
ejpam-6540	88	9	,	,	PUNCT
ejpam-6540	88	10	y2	y2	PROPN
ejpam-6540	88	11	,	,	PUNCT
ejpam-6540	88	12	.	.	PUNCT
ejpam-6540	88	13	.	.	PUNCT
ejpam-6540	88	14	.	.	PUNCT
ejpam-6540	89	1	,	,	PUNCT
ejpam-6540	89	2	yℓ	yℓ	X
ejpam-6540	89	3	}	}	PUNCT
ejpam-6540	89	4	⊆	⊆	NUM
ejpam-6540	89	5	v(γ	v(γ	NOUN
ejpam-6540	89	6	)	)	PUNCT
ejpam-6540	89	7	,	,	PUNCT
ejpam-6540	89	8	the	the	DET
ejpam-6540	89	9	representation	representation	NOUN
ejpam-6540	89	10	of	of	ADP
ejpam-6540	89	11	a	a	DET
ejpam-6540	89	12	vertex	vertex	NOUN
ejpam-6540	89	13	v	v	ADP
ejpam-6540	89	14	∈	∈	PROPN
ejpam-6540	89	15	v(γ	v(γ	NOUN
ejpam-6540	89	16	)	)	PUNCT
ejpam-6540	89	17	with	with	ADP
ejpam-6540	89	18	respect	respect	NOUN
ejpam-6540	89	19	to	to	ADP
ejpam-6540	89	20	y	y	PROPN
ejpam-6540	89	21	is	be	AUX
ejpam-6540	89	22	the	the	DET
ejpam-6540	89	23	ℓ-tuple	ℓ-tuple	PROPN
ejpam-6540	89	24	r(v|y	r(v|y	NUM
ejpam-6540	89	25	)	)	PUNCT
ejpam-6540	90	1	=	=	PRON
ejpam-6540	90	2	(	(	PUNCT
ejpam-6540	90	3	dγ(v	dγ(v	NOUN
ejpam-6540	90	4	,	,	PUNCT
ejpam-6540	90	5	y1	y1	NOUN
ejpam-6540	90	6	)	)	PUNCT
ejpam-6540	90	7	,	,	PUNCT
ejpam-6540	90	8	dγ(v	dγ(v	NOUN
ejpam-6540	90	9	,	,	PUNCT
ejpam-6540	90	10	y2	y2	PROPN
ejpam-6540	90	11	)	)	PUNCT
ejpam-6540	90	12	,	,	PUNCT
ejpam-6540	90	13	.	.	PUNCT
ejpam-6540	90	14	.	.	PUNCT
ejpam-6540	91	1	.	.	PUNCT
ejpam-6540	92	1	,	,	PUNCT
ejpam-6540	92	2	dγ(v	dγ(v	NOUN
ejpam-6540	92	3	,	,	PUNCT
ejpam-6540	92	4	yℓ	yℓ	PROPN
ejpam-6540	92	5	)	)	PUNCT
ejpam-6540	92	6	)	)	PUNCT
ejpam-6540	92	7	.	.	PUNCT
ejpam-6540	93	1	a	a	DET
ejpam-6540	93	2	subset	subset	NOUN
ejpam-6540	93	3	y	y	NOUN
ejpam-6540	93	4	is	be	AUX
ejpam-6540	93	5	called	call	VERB
ejpam-6540	93	6	a	a	DET
ejpam-6540	93	7	resolving	resolving	NOUN
ejpam-6540	93	8	set	set	VERB
ejpam-6540	93	9	if	if	SCONJ
ejpam-6540	93	10	each	each	DET
ejpam-6540	93	11	vertex	vertex	NOUN
ejpam-6540	93	12	in	in	ADP
ejpam-6540	93	13	γ	γ	PROPN
ejpam-6540	93	14	has	have	VERB
ejpam-6540	93	15	a	a	DET
ejpam-6540	93	16	unique	unique	ADJ
ejpam-6540	93	17	representation	representation	NOUN
ejpam-6540	93	18	concerning	concern	VERB
ejpam-6540	93	19	y.	y.	NOUN
ejpam-6540	93	20	the	the	DET
ejpam-6540	93	21	metric	metric	ADJ
ejpam-6540	93	22	dimension	dimension	NOUN
ejpam-6540	93	23	of	of	ADP
ejpam-6540	93	24	γ	γ	PROPN
ejpam-6540	93	25	,	,	PUNCT
ejpam-6540	93	26	denoted	denote	VERB
ejpam-6540	93	27	by	by	ADP
ejpam-6540	93	28	dim(γ	dim(γ	NOUN
ejpam-6540	93	29	)	)	PUNCT
ejpam-6540	93	30	,	,	PUNCT
ejpam-6540	93	31	is	be	AUX
ejpam-6540	93	32	the	the	DET
ejpam-6540	93	33	minimum	minimum	ADJ
ejpam-6540	93	34	cardinality	cardinality	NOUN
ejpam-6540	93	35	among	among	ADP
ejpam-6540	93	36	all	all	DET
ejpam-6540	93	37	resolving	resolve	VERB
ejpam-6540	93	38	sets	set	NOUN
ejpam-6540	93	39	in	in	ADP
ejpam-6540	93	40	γ	γ	PROPN
ejpam-6540	93	41	.	.	PROPN
ejpam-6540	93	42	for	for	ADP
ejpam-6540	93	43	the	the	DET
ejpam-6540	93	44	sierpiński	sierpiński	ADJ
ejpam-6540	93	45	network	network	NOUN
ejpam-6540	93	46	s2	s2	PROPN
ejpam-6540	93	47	c5	c5	PROPN
ejpam-6540	93	48	,	,	PUNCT
ejpam-6540	93	49	the	the	DET
ejpam-6540	93	50	two	two	NUM
ejpam-6540	93	51	vertex	vertex	NOUN
ejpam-6540	93	52	subset	subset	NOUN
ejpam-6540	93	53	w	w	NOUN
ejpam-6540	93	54	=	=	PUNCT
ejpam-6540	93	55	{	{	PUNCT
ejpam-6540	93	56	00	00	NUM
ejpam-6540	93	57	,	,	PUNCT
ejpam-6540	93	58	20	20	NUM
ejpam-6540	93	59	}	}	PUNCT
ejpam-6540	93	60	is	be	AUX
ejpam-6540	93	61	enough	enough	ADJ
ejpam-6540	93	62	to	to	PART
ejpam-6540	93	63	make	make	VERB
ejpam-6540	93	64	other	other	ADJ
ejpam-6540	93	65	vertices	vertex	NOUN
ejpam-6540	93	66	to	to	PART
ejpam-6540	93	67	be	be	AUX
ejpam-6540	93	68	resolved	resolve	VERB
ejpam-6540	93	69	.	.	PUNCT
ejpam-6540	94	1	we	we	PRON
ejpam-6540	94	2	can	can	AUX
ejpam-6540	94	3	easily	easily	ADV
ejpam-6540	94	4	verify	verify	VERB
ejpam-6540	94	5	that	that	SCONJ
ejpam-6540	94	6	the	the	DET
ejpam-6540	94	7	representation	representation	NOUN
ejpam-6540	94	8	of	of	ADP
ejpam-6540	94	9	each	each	DET
ejpam-6540	94	10	vertex	vertex	NOUN
ejpam-6540	94	11	with	with	ADP
ejpam-6540	94	12	respect	respect	NOUN
ejpam-6540	94	13	to	to	ADP
ejpam-6540	94	14	the	the	DET
ejpam-6540	94	15	set	set	NOUN
ejpam-6540	94	16	{	{	PUNCT
ejpam-6540	94	17	00	00	NUM
ejpam-6540	94	18	,	,	PUNCT
ejpam-6540	94	19	20	20	NUM
ejpam-6540	94	20	}	}	PUNCT
ejpam-6540	94	21	are	be	AUX
ejpam-6540	94	22	distint	distint	ADJ
ejpam-6540	94	23	in	in	ADP
ejpam-6540	94	24	the	the	DET
ejpam-6540	94	25	figure	figure	NOUN
ejpam-6540	94	26	3	3	NUM
ejpam-6540	94	27	and	and	CCONJ
ejpam-6540	94	28	the	the	DET
ejpam-6540	94	29	cardinality	cardinality	NOUN
ejpam-6540	94	30	of	of	ADP
ejpam-6540	94	31	resolving	resolve	VERB
ejpam-6540	94	32	set	set	NOUN
ejpam-6540	94	33	can	can	AUX
ejpam-6540	94	34	not	not	PART
ejpam-6540	94	35	be	be	AUX
ejpam-6540	94	36	1	1	NUM
ejpam-6540	94	37	for	for	ADP
ejpam-6540	94	38	s2	s2	NOUN
ejpam-6540	94	39	c5	c5	PROPN
ejpam-6540	94	40	as	as	SCONJ
ejpam-6540	94	41	it	it	PRON
ejpam-6540	94	42	is	be	AUX
ejpam-6540	94	43	not	not	PART
ejpam-6540	94	44	isomorphic	isomorphic	ADJ
ejpam-6540	94	45	to	to	ADP
ejpam-6540	94	46	a	a	DET
ejpam-6540	94	47	path	path	NOUN
ejpam-6540	94	48	.	.	PUNCT
ejpam-6540	95	1	then	then	ADV
ejpam-6540	95	2	the	the	DET
ejpam-6540	95	3	set	set	NOUN
ejpam-6540	95	4	w	w	NOUN
ejpam-6540	95	5	is	be	AUX
ejpam-6540	95	6	a	a	DET
ejpam-6540	95	7	metric	metric	ADJ
ejpam-6540	95	8	basis	basis	NOUN
ejpam-6540	95	9	for	for	ADP
ejpam-6540	95	10	s2	s2	PROPN
ejpam-6540	95	11	c5	c5	PROPN
ejpam-6540	95	12	.	.	PUNCT
ejpam-6540	96	1	this	this	PRON
ejpam-6540	96	2	implies	imply	VERB
ejpam-6540	96	3	dim(s2	dim(s2	PROPN
ejpam-6540	96	4	c5	c5	PROPN
ejpam-6540	96	5	)	)	PUNCT
ejpam-6540	97	1	=	=	PUNCT
ejpam-6540	97	2	2	2	X
ejpam-6540	97	3	.	.	PUNCT
ejpam-6540	97	4	(	(	PUNCT
ejpam-6540	97	5	0,6	0,6	NUM
ejpam-6540	97	6	)	)	PUNCT
ejpam-6540	97	7	(	(	PUNCT
ejpam-6540	97	8	1,5	1,5	NUM
ejpam-6540	97	9	)	)	PUNCT
ejpam-6540	97	10	(	(	PUNCT
ejpam-6540	97	11	2,6	2,6	NUM
ejpam-6540	97	12	)	)	PUNCT
ejpam-6540	97	13	(	(	PUNCT
ejpam-6540	97	14	2,7	2,7	NUM
ejpam-6540	97	15	)	)	PUNCT
ejpam-6540	97	16	(	(	PUNCT
ejpam-6540	97	17	1,7	1,7	NUM
ejpam-6540	97	18	)	)	PUNCT
ejpam-6540	97	19	(	(	PUNCT
ejpam-6540	97	20	2,4	2,4	NUM
ejpam-6540	97	21	)	)	PUNCT
ejpam-6540	97	22	(	(	PUNCT
ejpam-6540	97	23	3,3	3,3	NUM
ejpam-6540	97	24	)	)	PUNCT
ejpam-6540	97	25	(	(	PUNCT
ejpam-6540	97	26	4,2	4,2	NUM
ejpam-6540	97	27	)	)	PUNCT
ejpam-6540	97	28	(	(	PUNCT
ejpam-6540	97	29	4,3	4,3	NUM
ejpam-6540	97	30	)	)	PUNCT
ejpam-6540	97	31	(	(	PUNCT
ejpam-6540	97	32	3,4	3,4	NUM
ejpam-6540	97	33	)	)	PUNCT
ejpam-6540	97	34	(	(	PUNCT
ejpam-6540	97	35	6,0	6,0	NUM
ejpam-6540	97	36	)	)	PUNCT
ejpam-6540	97	37	(	(	PUNCT
ejpam-6540	97	38	5,1)(7,1	5,1)(7,1	NUM
ejpam-6540	97	39	)	)	PUNCT
ejpam-6540	97	40	(	(	PUNCT
ejpam-6540	97	41	6,2	6,2	NUM
ejpam-6540	97	42	)	)	PUNCT
ejpam-6540	97	43	(	(	PUNCT
ejpam-6540	97	44	7,2	7,2	NUM
ejpam-6540	97	45	)	)	PUNCT
ejpam-6540	97	46	(	(	PUNCT
ejpam-6540	97	47	6,5	6,5	NUM
ejpam-6540	97	48	)	)	PUNCT
ejpam-6540	97	49	(	(	PUNCT
ejpam-6540	97	50	7,4	7,4	NUM
ejpam-6540	97	51	)	)	PUNCT
ejpam-6540	97	52	(	(	PUNCT
ejpam-6540	97	53	7,3	7,3	NUM
ejpam-6540	97	54	)	)	PUNCT
ejpam-6540	97	55	(	(	PUNCT
ejpam-6540	97	56	6,4	6,4	NUM
ejpam-6540	97	57	)	)	PUNCT
ejpam-6540	97	58	(	(	PUNCT
ejpam-6540	97	59	5,5	5,5	NUM
ejpam-6540	97	60	)	)	PUNCT
ejpam-6540	97	61	(	(	PUNCT
ejpam-6540	97	62	2,8	2,8	NUM
ejpam-6540	97	63	)	)	PUNCT
ejpam-6540	97	64	(	(	PUNCT
ejpam-6540	97	65	3,7	3,7	NUM
ejpam-6540	97	66	)	)	PUNCT
ejpam-6540	97	67	(	(	PUNCT
ejpam-6540	97	68	3,8	3,8	NUM
ejpam-6540	97	69	)	)	PUNCT
ejpam-6540	97	70	(	(	PUNCT
ejpam-6540	97	71	4,7	4,7	NUM
ejpam-6540	97	72	)	)	PUNCT
ejpam-6540	97	73	(	(	PUNCT
ejpam-6540	97	74	4,6	4,6	X
ejpam-6540	97	75	)	)	PUNCT
ejpam-6540	97	76	figure	figure	NOUN
ejpam-6540	97	77	3	3	NUM
ejpam-6540	97	78	:	:	PUNCT
ejpam-6540	97	79	metric	metric	ADJ
ejpam-6540	97	80	representation	representation	NOUN
ejpam-6540	97	81	of	of	ADP
ejpam-6540	97	82	each	each	DET
ejpam-6540	97	83	vertex	vertex	NOUN
ejpam-6540	97	84	with	with	ADP
ejpam-6540	97	85	respect	respect	NOUN
ejpam-6540	97	86	to	to	ADP
ejpam-6540	97	87	the	the	DET
ejpam-6540	97	88	set	set	NOUN
ejpam-6540	97	89	w	w	NOUN
ejpam-6540	97	90	=	=	PUNCT
ejpam-6540	97	91	{	{	PUNCT
ejpam-6540	97	92	00	00	NUM
ejpam-6540	97	93	,	,	PUNCT
ejpam-6540	97	94	20	20	NUM
ejpam-6540	97	95	}	}	PUNCT
ejpam-6540	97	96	in	in	ADP
ejpam-6540	97	97	s2	s2	PROPN
ejpam-6540	97	98	c5	c5	PROPN
ejpam-6540	97	99	many	many	ADJ
ejpam-6540	97	100	variations	variation	NOUN
ejpam-6540	97	101	have	have	AUX
ejpam-6540	97	102	been	be	AUX
ejpam-6540	97	103	developed	develop	VERB
ejpam-6540	97	104	from	from	ADP
ejpam-6540	97	105	this	this	DET
ejpam-6540	97	106	well	well	ADV
ejpam-6540	97	107	-	-	PUNCT
ejpam-6540	97	108	established	establish	VERB
ejpam-6540	97	109	concept	concept	NOUN
ejpam-6540	97	110	in	in	ADP
ejpam-6540	97	111	the	the	DET
ejpam-6540	97	112	literak	literak	NOUN
ejpam-6540	97	113	.	.	PUNCT
ejpam-6540	98	1	b.	b.	PROPN
ejpam-6540	98	2	dharan	dharan	PROPN
ejpam-6540	98	3	,	,	PUNCT
ejpam-6540	98	4	s.	s.	PROPN
ejpam-6540	98	5	radha	radha	PROPN
ejpam-6540	98	6	/	/	PUNCT
ejpam-6540	98	7	eur	eur	PROPN
ejpam-6540	98	8	.	.	PUNCT
ejpam-6540	99	1	j.	j.	PROPN
ejpam-6540	99	2	pure	pure	PROPN
ejpam-6540	99	3	appl	appl	PROPN
ejpam-6540	99	4	.	.	PROPN
ejpam-6540	99	5	math	math	PROPN
ejpam-6540	99	6	,	,	PUNCT
ejpam-6540	99	7	18	18	NUM
ejpam-6540	99	8	(	(	PUNCT
ejpam-6540	99	9	3	3	NUM
ejpam-6540	99	10	)	)	PUNCT
ejpam-6540	99	11	(	(	PUNCT
ejpam-6540	99	12	2025	2025	NUM
ejpam-6540	99	13	)	)	PUNCT
ejpam-6540	99	14	,	,	PUNCT
ejpam-6540	99	15	6540	6540	NUM
ejpam-6540	99	16	6	6	NUM
ejpam-6540	99	17	of	of	ADP
ejpam-6540	99	18	17	17	NUM
ejpam-6540	99	19	ture	ture	NOUN
ejpam-6540	99	20	[	[	X
ejpam-6540	99	21	18	18	NUM
ejpam-6540	99	22	,	,	PUNCT
ejpam-6540	99	23	52–56	52–56	NUM
ejpam-6540	99	24	]	]	PUNCT
ejpam-6540	99	25	.	.	PUNCT
ejpam-6540	100	1	fault	fault	NOUN
ejpam-6540	100	2	-	-	PUNCT
ejpam-6540	100	3	tolerant	tolerant	ADJ
ejpam-6540	100	4	metric	metric	ADJ
ejpam-6540	100	5	dimension	dimension	NOUN
ejpam-6540	100	6	is	be	AUX
ejpam-6540	100	7	one	one	NUM
ejpam-6540	100	8	of	of	ADP
ejpam-6540	100	9	these	these	DET
ejpam-6540	100	10	new	new	ADJ
ejpam-6540	100	11	and	and	CCONJ
ejpam-6540	100	12	highly	highly	ADV
ejpam-6540	100	13	motivated	motivated	ADJ
ejpam-6540	100	14	variants	variant	NOUN
ejpam-6540	100	15	.	.	PUNCT
ejpam-6540	101	1	the	the	DET
ejpam-6540	101	2	key	key	ADJ
ejpam-6540	101	3	idea	idea	NOUN
ejpam-6540	101	4	in	in	ADP
ejpam-6540	101	5	this	this	DET
ejpam-6540	101	6	version	version	NOUN
ejpam-6540	101	7	is	be	AUX
ejpam-6540	101	8	that	that	SCONJ
ejpam-6540	101	9	even	even	ADV
ejpam-6540	101	10	if	if	SCONJ
ejpam-6540	101	11	one	one	NUM
ejpam-6540	101	12	vertex	vertex	NOUN
ejpam-6540	101	13	in	in	ADP
ejpam-6540	101	14	the	the	DET
ejpam-6540	101	15	chosen	choose	VERB
ejpam-6540	101	16	set	set	NOUN
ejpam-6540	101	17	of	of	ADP
ejpam-6540	101	18	vertices	vertex	NOUN
ejpam-6540	101	19	becomes	become	VERB
ejpam-6540	101	20	flawed	flawed	ADJ
ejpam-6540	101	21	or	or	CCONJ
ejpam-6540	101	22	unusable	unusable	ADJ
ejpam-6540	101	23	,	,	PUNCT
ejpam-6540	101	24	the	the	DET
ejpam-6540	101	25	graph	graph	NOUN
ejpam-6540	101	26	must	must	AUX
ejpam-6540	101	27	still	still	ADV
ejpam-6540	101	28	be	be	AUX
ejpam-6540	101	29	resolved	resolve	VERB
ejpam-6540	101	30	using	use	VERB
ejpam-6540	101	31	that	that	DET
ejpam-6540	101	32	set	set	NOUN
ejpam-6540	101	33	.	.	PUNCT
ejpam-6540	102	1	let	let	VERB
ejpam-6540	102	2	f	f	PROPN
ejpam-6540	102	3	⊆	⊆	NUM
ejpam-6540	102	4	v(γ	v(γ	NOUN
ejpam-6540	102	5	)	)	PUNCT
ejpam-6540	102	6	is	be	AUX
ejpam-6540	102	7	called	call	VERB
ejpam-6540	102	8	a	a	DET
ejpam-6540	102	9	fault	fault	NOUN
ejpam-6540	102	10	-	-	PUNCT
ejpam-6540	102	11	tolerant	tolerant	ADJ
ejpam-6540	102	12	resolving	resolving	NOUN
ejpam-6540	102	13	set	set	NOUN
ejpam-6540	102	14	,	,	PUNCT
ejpam-6540	102	15	if	if	SCONJ
ejpam-6540	102	16	we	we	PRON
ejpam-6540	102	17	have	have	VERB
ejpam-6540	102	18	r(u|f	r(u|f	VERB
ejpam-6540	102	19	\	\	NOUN
ejpam-6540	102	20	{	{	PUNCT
ejpam-6540	102	21	x	x	NOUN
ejpam-6540	102	22	}	}	PUNCT
ejpam-6540	102	23	)	)	PUNCT
ejpam-6540	102	24	̸=	̸=	PROPN
ejpam-6540	102	25	r(v|f	r(v|f	NOUN
ejpam-6540	102	26	\	\	NOUN
ejpam-6540	102	27	{	{	PUNCT
ejpam-6540	102	28	x	x	NOUN
ejpam-6540	102	29	}	}	PUNCT
ejpam-6540	102	30	)	)	PUNCT
ejpam-6540	102	31	,	,	PUNCT
ejpam-6540	102	32	for	for	ADP
ejpam-6540	102	33	every	every	DET
ejpam-6540	102	34	x	x	SYM
ejpam-6540	102	35	∈	∈	PROPN
ejpam-6540	102	36	f	f	PROPN
ejpam-6540	102	37	and	and	CCONJ
ejpam-6540	102	38	u	u	PROPN
ejpam-6540	102	39	,	,	PUNCT
ejpam-6540	102	40	v	v	NOUN
ejpam-6540	102	41	∈	∈	NOUN
ejpam-6540	102	42	v(γ)(for	v(γ)(for	ADP
ejpam-6540	102	43	every	every	DET
ejpam-6540	102	44	pair	pair	NOUN
ejpam-6540	102	45	of	of	ADP
ejpam-6540	102	46	distinct	distinct	ADJ
ejpam-6540	102	47	vertices	vertex	NOUN
ejpam-6540	102	48	u	u	NOUN
ejpam-6540	102	49	,	,	PUNCT
ejpam-6540	102	50	v	v	NOUN
ejpam-6540	102	51	∈	∈	PROPN
ejpam-6540	102	52	v(γ	v(γ	NOUN
ejpam-6540	102	53	)	)	PUNCT
ejpam-6540	102	54	,	,	PUNCT
ejpam-6540	102	55	there	there	PRON
ejpam-6540	102	56	exist	exist	VERB
ejpam-6540	102	57	at	at	ADV
ejpam-6540	102	58	least	least	ADV
ejpam-6540	102	59	two	two	NUM
ejpam-6540	102	60	vertices	vertex	NOUN
ejpam-6540	102	61	x	x	X
ejpam-6540	102	62	,	,	PUNCT
ejpam-6540	102	63	y	y	PROPN
ejpam-6540	102	64	∈	∈	PROPN
ejpam-6540	102	65	f	f	PROPN
ejpam-6540	102	66	such	such	ADJ
ejpam-6540	102	67	that	that	DET
ejpam-6540	102	68	dγ(u	dγ(u	NOUN
ejpam-6540	102	69	,	,	PUNCT
ejpam-6540	102	70	x	x	X
ejpam-6540	102	71	)	)	PUNCT
ejpam-6540	102	72	̸=	̸=	PROPN
ejpam-6540	102	73	dγ(v	dγ(v	X
ejpam-6540	102	74	,	,	PUNCT
ejpam-6540	102	75	x	x	NOUN
ejpam-6540	102	76	)	)	PUNCT
ejpam-6540	102	77	and	and	CCONJ
ejpam-6540	102	78	dγ(u	dγ(u	PROPN
ejpam-6540	102	79	,	,	PUNCT
ejpam-6540	102	80	y	y	NOUN
ejpam-6540	102	81	)	)	PUNCT
ejpam-6540	102	82	̸=	̸=	PROPN
ejpam-6540	102	83	dγ(v	dγ(v	X
ejpam-6540	102	84	,	,	PUNCT
ejpam-6540	102	85	y	y	NOUN
ejpam-6540	102	86	)	)	PUNCT
ejpam-6540	102	87	)	)	PUNCT
ejpam-6540	102	88	.	.	PUNCT
ejpam-6540	103	1	among	among	ADP
ejpam-6540	103	2	all	all	DET
ejpam-6540	103	3	such	such	ADJ
ejpam-6540	103	4	sets	set	NOUN
ejpam-6540	103	5	,	,	PUNCT
ejpam-6540	103	6	one	one	NUM
ejpam-6540	103	7	with	with	ADP
ejpam-6540	103	8	the	the	DET
ejpam-6540	103	9	smallest	small	ADJ
ejpam-6540	103	10	possible	possible	ADJ
ejpam-6540	103	11	size	size	NOUN
ejpam-6540	103	12	is	be	AUX
ejpam-6540	103	13	called	call	VERB
ejpam-6540	103	14	a	a	DET
ejpam-6540	103	15	fault	fault	NOUN
ejpam-6540	103	16	-	-	PUNCT
ejpam-6540	103	17	tolerant	tolerant	ADJ
ejpam-6540	103	18	metric	metric	ADJ
ejpam-6540	103	19	basis	basis	NOUN
ejpam-6540	103	20	.	.	PUNCT
ejpam-6540	104	1	the	the	DET
ejpam-6540	104	2	number	number	NOUN
ejpam-6540	104	3	of	of	ADP
ejpam-6540	104	4	vertices	vertex	NOUN
ejpam-6540	104	5	in	in	ADP
ejpam-6540	104	6	a	a	DET
ejpam-6540	104	7	fault	fault	NOUN
ejpam-6540	104	8	-	-	PUNCT
ejpam-6540	104	9	tolerant	tolerant	ADJ
ejpam-6540	104	10	metric	metric	ADJ
ejpam-6540	104	11	basis	basis	NOUN
ejpam-6540	104	12	is	be	AUX
ejpam-6540	104	13	known	know	VERB
ejpam-6540	104	14	as	as	ADP
ejpam-6540	104	15	the	the	DET
ejpam-6540	104	16	fault	fault	NOUN
ejpam-6540	104	17	-	-	PUNCT
ejpam-6540	104	18	tolerant	tolerant	ADJ
ejpam-6540	104	19	metric	metric	ADJ
ejpam-6540	104	20	dimension	dimension	NOUN
ejpam-6540	104	21	of	of	ADP
ejpam-6540	104	22	γ	γ	PROPN
ejpam-6540	104	23	,	,	PUNCT
ejpam-6540	104	24	and	and	CCONJ
ejpam-6540	104	25	it	it	PRON
ejpam-6540	104	26	is	be	AUX
ejpam-6540	104	27	denoted	denote	VERB
ejpam-6540	104	28	by	by	ADP
ejpam-6540	104	29	dim′(γ	dim′(γ	NOUN
ejpam-6540	104	30	)	)	PUNCT
ejpam-6540	104	31	.	.	PUNCT
ejpam-6540	105	1	this	this	DET
ejpam-6540	105	2	idea	idea	NOUN
ejpam-6540	105	3	was	be	AUX
ejpam-6540	105	4	first	first	ADV
ejpam-6540	105	5	presented	present	VERB
ejpam-6540	105	6	in	in	ADP
ejpam-6540	105	7	[	[	X
ejpam-6540	105	8	57	57	NUM
ejpam-6540	105	9	]	]	PUNCT
ejpam-6540	105	10	,	,	PUNCT
ejpam-6540	105	11	and	and	CCONJ
ejpam-6540	105	12	was	be	AUX
ejpam-6540	105	13	further	far	ADV
ejpam-6540	105	14	discussed	discuss	VERB
ejpam-6540	105	15	in	in	ADP
ejpam-6540	105	16	[	[	X
ejpam-6540	105	17	5	5	NUM
ejpam-6540	105	18	,	,	PUNCT
ejpam-6540	105	19	45	45	NUM
ejpam-6540	105	20	,	,	PUNCT
ejpam-6540	105	21	58	58	NUM
ejpam-6540	105	22	]	]	PUNCT
ejpam-6540	105	23	.	.	PUNCT
ejpam-6540	106	1	2.2	2.2	NUM
ejpam-6540	106	2	.	.	PUNCT
ejpam-6540	106	3	edge	edge	NOUN
ejpam-6540	106	4	metric	metric	ADJ
ejpam-6540	106	5	and	and	CCONJ
ejpam-6540	106	6	fault	fault	NOUN
ejpam-6540	106	7	-	-	PUNCT
ejpam-6540	106	8	tolerant	tolerant	ADJ
ejpam-6540	106	9	edge	edge	NOUN
ejpam-6540	106	10	metric	metric	ADJ
ejpam-6540	106	11	basis	basis	NOUN
ejpam-6540	106	12	in	in	ADP
ejpam-6540	106	13	parallel	parallel	ADJ
ejpam-6540	106	14	computing	computing	NOUN
ejpam-6540	106	15	systems	system	NOUN
ejpam-6540	106	16	,	,	PUNCT
ejpam-6540	106	17	an	an	DET
ejpam-6540	106	18	interconnection	interconnection	NOUN
ejpam-6540	106	19	network	network	NOUN
ejpam-6540	106	20	comprising	comprise	VERB
ejpam-6540	106	21	a	a	DET
ejpam-6540	106	22	structured	structured	ADJ
ejpam-6540	106	23	configuration	configuration	NOUN
ejpam-6540	106	24	of	of	ADP
ejpam-6540	106	25	processors	processor	NOUN
ejpam-6540	106	26	and	and	CCONJ
ejpam-6540	106	27	communication	communication	NOUN
ejpam-6540	106	28	links	link	NOUN
ejpam-6540	106	29	,	,	PUNCT
ejpam-6540	106	30	plays	play	VERB
ejpam-6540	106	31	a	a	DET
ejpam-6540	106	32	vital	vital	ADJ
ejpam-6540	106	33	role	role	NOUN
ejpam-6540	106	34	in	in	ADP
ejpam-6540	106	35	facilitating	facilitate	VERB
ejpam-6540	106	36	data	datum	NOUN
ejpam-6540	106	37	exchange	exchange	NOUN
ejpam-6540	106	38	among	among	ADP
ejpam-6540	106	39	processors	processor	NOUN
ejpam-6540	106	40	.	.	PUNCT
ejpam-6540	107	1	efficient	efficient	ADJ
ejpam-6540	107	2	fault	fault	NOUN
ejpam-6540	107	3	detection	detection	NOUN
ejpam-6540	107	4	within	within	ADP
ejpam-6540	107	5	such	such	ADJ
ejpam-6540	107	6	networks	network	NOUN
ejpam-6540	107	7	requires	require	VERB
ejpam-6540	107	8	the	the	DET
ejpam-6540	107	9	ability	ability	NOUN
ejpam-6540	107	10	to	to	PART
ejpam-6540	107	11	distinguish	distinguish	VERB
ejpam-6540	107	12	between	between	ADP
ejpam-6540	107	13	communication	communication	NOUN
ejpam-6540	107	14	links	link	NOUN
ejpam-6540	107	15	.	.	PUNCT
ejpam-6540	108	1	this	this	PRON
ejpam-6540	108	2	can	can	AUX
ejpam-6540	108	3	be	be	AUX
ejpam-6540	108	4	accomplished	accomplish	VERB
ejpam-6540	108	5	by	by	ADP
ejpam-6540	108	6	identifying	identify	VERB
ejpam-6540	108	7	a	a	DET
ejpam-6540	108	8	minimal	minimal	ADJ
ejpam-6540	108	9	set	set	NOUN
ejpam-6540	108	10	of	of	ADP
ejpam-6540	108	11	vertices	vertex	NOUN
ejpam-6540	108	12	capable	capable	ADJ
ejpam-6540	108	13	of	of	ADP
ejpam-6540	108	14	uniquely	uniquely	ADV
ejpam-6540	108	15	determining	determine	VERB
ejpam-6540	108	16	every	every	DET
ejpam-6540	108	17	edge	edge	NOUN
ejpam-6540	108	18	in	in	ADP
ejpam-6540	108	19	the	the	DET
ejpam-6540	108	20	network	network	NOUN
ejpam-6540	108	21	graph	graph	NOUN
ejpam-6540	108	22	.	.	PUNCT
ejpam-6540	109	1	a	a	DET
ejpam-6540	109	2	subset	subset	NOUN
ejpam-6540	109	3	s	s	VERB
ejpam-6540	109	4	⊆	⊆	NUM
ejpam-6540	109	5	v(γ	v(γ	NOUN
ejpam-6540	109	6	)	)	PUNCT
ejpam-6540	109	7	is	be	AUX
ejpam-6540	109	8	called	call	VERB
ejpam-6540	109	9	an	an	DET
ejpam-6540	109	10	edge	edge	NOUN
ejpam-6540	109	11	resolving	resolve	VERB
ejpam-6540	109	12	set	set	VERB
ejpam-6540	109	13	if	if	SCONJ
ejpam-6540	109	14	,	,	PUNCT
ejpam-6540	109	15	for	for	ADP
ejpam-6540	109	16	every	every	DET
ejpam-6540	109	17	pair	pair	NOUN
ejpam-6540	109	18	of	of	ADP
ejpam-6540	109	19	distinct	distinct	ADJ
ejpam-6540	109	20	edges	edge	NOUN
ejpam-6540	109	21	e1	e1	NOUN
ejpam-6540	109	22	,	,	PUNCT
ejpam-6540	109	23	e2	e2	PROPN
ejpam-6540	109	24	∈	∈	PROPN
ejpam-6540	109	25	e(γ	e(γ	PROPN
ejpam-6540	109	26	)	)	PUNCT
ejpam-6540	109	27	,	,	PUNCT
ejpam-6540	109	28	there	there	PRON
ejpam-6540	109	29	exists	exist	VERB
ejpam-6540	109	30	a	a	DET
ejpam-6540	109	31	vertex	vertex	NOUN
ejpam-6540	109	32	w	w	ADP
ejpam-6540	109	33	∈	∈	NOUN
ejpam-6540	109	34	s	s	VERB
ejpam-6540	109	35	such	such	ADJ
ejpam-6540	109	36	that	that	PRON
ejpam-6540	109	37	dγ(w	dγ(w	NOUN
ejpam-6540	109	38	,	,	PUNCT
ejpam-6540	109	39	e1	e1	NOUN
ejpam-6540	109	40	)	)	PUNCT
ejpam-6540	109	41	̸=	̸=	PROPN
ejpam-6540	109	42	dγ(w	dγ(w	X
ejpam-6540	109	43	,	,	PUNCT
ejpam-6540	109	44	e2	e2	PROPN
ejpam-6540	109	45	)	)	PUNCT
ejpam-6540	109	46	.	.	PUNCT
ejpam-6540	110	1	the	the	DET
ejpam-6540	110	2	smallest	small	ADJ
ejpam-6540	110	3	possible	possible	ADJ
ejpam-6540	110	4	size	size	NOUN
ejpam-6540	110	5	of	of	ADP
ejpam-6540	110	6	such	such	DET
ejpam-6540	110	7	a	a	DET
ejpam-6540	110	8	set	set	NOUN
ejpam-6540	110	9	is	be	AUX
ejpam-6540	110	10	defined	define	VERB
ejpam-6540	110	11	as	as	ADP
ejpam-6540	110	12	the	the	DET
ejpam-6540	110	13	edge	edge	NOUN
ejpam-6540	110	14	metric	metric	ADJ
ejpam-6540	110	15	dimension	dimension	NOUN
ejpam-6540	110	16	of	of	ADP
ejpam-6540	110	17	γ	γ	PROPN
ejpam-6540	110	18	,	,	PUNCT
ejpam-6540	110	19	denoted	denote	VERB
ejpam-6540	110	20	by	by	ADP
ejpam-6540	110	21	dime(γ	dime(γ	PROPN
ejpam-6540	110	22	)	)	PUNCT
ejpam-6540	110	23	.	.	PUNCT
ejpam-6540	111	1	kelenc	kelenc	PROPN
ejpam-6540	111	2	et	et	PROPN
ejpam-6540	111	3	al	al	PROPN
ejpam-6540	111	4	.	.	PUNCT
ejpam-6540	112	1	[	[	X
ejpam-6540	112	2	52	52	NUM
ejpam-6540	112	3	]	]	PUNCT
ejpam-6540	112	4	were	be	AUX
ejpam-6540	112	5	the	the	DET
ejpam-6540	112	6	first	first	ADJ
ejpam-6540	112	7	to	to	PART
ejpam-6540	112	8	study	study	VERB
ejpam-6540	112	9	this	this	DET
ejpam-6540	112	10	metric	metric	ADJ
ejpam-6540	112	11	dimension	dimension	NOUN
ejpam-6540	112	12	variant	variant	NOUN
ejpam-6540	112	13	and	and	CCONJ
ejpam-6540	112	14	proved	prove	VERB
ejpam-6540	112	15	its	its	PRON
ejpam-6540	112	16	npcompleteness	npcompleteness	NOUN
ejpam-6540	112	17	.	.	PUNCT
ejpam-6540	113	1	since	since	SCONJ
ejpam-6540	113	2	then	then	ADV
ejpam-6540	113	3	,	,	PUNCT
ejpam-6540	113	4	numerous	numerous	ADJ
ejpam-6540	113	5	research	research	NOUN
ejpam-6540	113	6	articles	article	NOUN
ejpam-6540	113	7	have	have	AUX
ejpam-6540	113	8	explored	explore	VERB
ejpam-6540	113	9	this	this	DET
ejpam-6540	113	10	topic	topic	NOUN
ejpam-6540	113	11	,	,	PUNCT
ejpam-6540	113	12	including	include	VERB
ejpam-6540	113	13	studies	study	NOUN
ejpam-6540	113	14	on	on	ADP
ejpam-6540	113	15	the	the	DET
ejpam-6540	113	16	dimension	dimension	NOUN
ejpam-6540	113	17	of	of	ADP
ejpam-6540	113	18	convex	convex	ADJ
ejpam-6540	113	19	polytope	polytope	NOUN
ejpam-6540	113	20	graphs	graph	NOUN
ejpam-6540	113	21	[	[	X
ejpam-6540	113	22	59	59	NUM
ejpam-6540	113	23	]	]	PUNCT
ejpam-6540	113	24	,	,	PUNCT
ejpam-6540	113	25	web	web	NOUN
ejpam-6540	113	26	graphs	graph	NOUN
ejpam-6540	113	27	,	,	PUNCT
ejpam-6540	113	28	prism	prism	NOUN
ejpam-6540	113	29	-	-	PUNCT
ejpam-6540	113	30	related	relate	VERB
ejpam-6540	113	31	graphs	graph	NOUN
ejpam-6540	113	32	,	,	PUNCT
ejpam-6540	113	33	generalized	generalized	ADJ
ejpam-6540	113	34	petersen	petersen	NOUN
ejpam-6540	113	35	graphs	graph	NOUN
ejpam-6540	113	36	[	[	X
ejpam-6540	113	37	60	60	NUM
ejpam-6540	113	38	]	]	PUNCT
ejpam-6540	113	39	and	and	CCONJ
ejpam-6540	113	40	silicate	silicate	ADJ
ejpam-6540	113	41	networks	network	NOUN
ejpam-6540	113	42	[	[	X
ejpam-6540	113	43	61	61	NUM
ejpam-6540	113	44	]	]	PUNCT
ejpam-6540	113	45	.	.	PUNCT
ejpam-6540	114	1	other	other	ADJ
ejpam-6540	114	2	works	work	NOUN
ejpam-6540	114	3	have	have	AUX
ejpam-6540	114	4	examined	examine	VERB
ejpam-6540	114	5	this	this	DET
ejpam-6540	114	6	parameter	parameter	NOUN
ejpam-6540	114	7	for	for	ADP
ejpam-6540	114	8	erdős	erdős	ADJ
ejpam-6540	114	9	–	–	PUNCT
ejpam-6540	114	10	rényi	rényi	NOUN
ejpam-6540	114	11	random	random	ADJ
ejpam-6540	114	12	graphs	graph	NOUN
ejpam-6540	114	13	[	[	X
ejpam-6540	114	14	62	62	NUM
ejpam-6540	114	15	]	]	PUNCT
ejpam-6540	114	16	,	,	PUNCT
ejpam-6540	114	17	certain	certain	ADJ
ejpam-6540	114	18	classes	class	NOUN
ejpam-6540	114	19	of	of	ADP
ejpam-6540	114	20	planar	planar	ADJ
ejpam-6540	114	21	graphs	graph	NOUN
ejpam-6540	114	22	[	[	X
ejpam-6540	114	23	63	63	NUM
ejpam-6540	114	24	]	]	PUNCT
ejpam-6540	114	25	,	,	PUNCT
ejpam-6540	114	26	and	and	CCONJ
ejpam-6540	114	27	the	the	DET
ejpam-6540	114	28	identification	identification	NOUN
ejpam-6540	114	29	of	of	ADP
ejpam-6540	114	30	graph	graph	NOUN
ejpam-6540	114	31	network	network	NOUN
ejpam-6540	114	32	with	with	ADP
ejpam-6540	114	33	higher	high	ADJ
ejpam-6540	114	34	dimension	dimension	NOUN
ejpam-6540	114	35	[	[	X
ejpam-6540	114	36	64	64	NUM
ejpam-6540	114	37	,	,	PUNCT
ejpam-6540	114	38	65	65	NUM
ejpam-6540	114	39	]	]	PUNCT
ejpam-6540	114	40	.	.	PUNCT
ejpam-6540	115	1	in	in	ADP
ejpam-6540	115	2	[	[	X
ejpam-6540	115	3	66	66	NUM
ejpam-6540	115	4	]	]	PUNCT
ejpam-6540	115	5	,	,	PUNCT
ejpam-6540	115	6	the	the	DET
ejpam-6540	115	7	metric	metric	ADJ
ejpam-6540	115	8	and	and	CCONJ
ejpam-6540	115	9	edge	edge	VERB
ejpam-6540	115	10	metric	metric	ADJ
ejpam-6540	115	11	dimension	dimension	NOUN
ejpam-6540	115	12	of	of	ADP
ejpam-6540	115	13	hypercubes	hypercube	NOUN
ejpam-6540	115	14	were	be	AUX
ejpam-6540	115	15	analyzed	analyze	VERB
ejpam-6540	115	16	.	.	PUNCT
ejpam-6540	116	1	additionally	additionally	ADV
ejpam-6540	116	2	,	,	PUNCT
ejpam-6540	116	3	researchers	researcher	NOUN
ejpam-6540	116	4	have	have	AUX
ejpam-6540	116	5	investigated	investigate	VERB
ejpam-6540	116	6	graph	graph	NOUN
ejpam-6540	116	7	operations	operation	NOUN
ejpam-6540	116	8	such	such	ADJ
ejpam-6540	116	9	as	as	ADP
ejpam-6540	116	10	join	join	NOUN
ejpam-6540	116	11	of	of	ADP
ejpam-6540	116	12	graph	graph	NOUN
ejpam-6540	116	13	networks	network	NOUN
ejpam-6540	116	14	,	,	PUNCT
ejpam-6540	116	15	lexicographic	lexicographic	ADJ
ejpam-6540	116	16	product	product	NOUN
ejpam-6540	116	17	and	and	CCONJ
ejpam-6540	116	18	corona	corona	NOUN
ejpam-6540	116	19	product	product	NOUN
ejpam-6540	116	20	[	[	X
ejpam-6540	116	21	67	67	NUM
ejpam-6540	116	22	]	]	X
ejpam-6540	116	23	,	,	PUNCT
ejpam-6540	116	24	as	as	ADV
ejpam-6540	116	25	well	well	ADV
ejpam-6540	116	26	as	as	ADP
ejpam-6540	116	27	hierarchical	hierarchical	ADJ
ejpam-6540	116	28	products	product	NOUN
ejpam-6540	116	29	across	across	ADP
ejpam-6540	116	30	various	various	ADJ
ejpam-6540	116	31	graph	graph	NOUN
ejpam-6540	116	32	classes	class	NOUN
ejpam-6540	116	33	[	[	X
ejpam-6540	116	34	68	68	NUM
ejpam-6540	116	35	]	]	PUNCT
ejpam-6540	116	36	.	.	PUNCT
ejpam-6540	117	1	recently	recently	ADV
ejpam-6540	117	2	,	,	PUNCT
ejpam-6540	117	3	increasing	increase	VERB
ejpam-6540	117	4	attention	attention	NOUN
ejpam-6540	117	5	has	have	AUX
ejpam-6540	117	6	been	be	AUX
ejpam-6540	117	7	given	give	VERB
ejpam-6540	117	8	to	to	ADP
ejpam-6540	117	9	identifying	identify	VERB
ejpam-6540	117	10	graphs	graph	NOUN
ejpam-6540	117	11	where	where	SCONJ
ejpam-6540	117	12	dime	dime	NOUN
ejpam-6540	117	13	<	<	X
ejpam-6540	117	14	dim	dim	PROPN
ejpam-6540	117	15	[	[	X
ejpam-6540	117	16	69	69	NUM
ejpam-6540	117	17	,	,	PUNCT
ejpam-6540	117	18	70	70	NUM
ejpam-6540	117	19	]	]	PUNCT
ejpam-6540	117	20	.	.	PUNCT
ejpam-6540	118	1	a	a	DET
ejpam-6540	118	2	subset	subset	NOUN
ejpam-6540	118	3	f	f	PROPN
ejpam-6540	118	4	⊆	⊆	NUM
ejpam-6540	118	5	v(γ	v(γ	NOUN
ejpam-6540	118	6	)	)	PUNCT
ejpam-6540	118	7	is	be	AUX
ejpam-6540	118	8	said	say	VERB
ejpam-6540	118	9	to	to	PART
ejpam-6540	118	10	be	be	AUX
ejpam-6540	118	11	a	a	DET
ejpam-6540	118	12	fault	fault	NOUN
ejpam-6540	118	13	-	-	PUNCT
ejpam-6540	118	14	tolerant	tolerant	ADJ
ejpam-6540	118	15	edge	edge	NOUN
ejpam-6540	118	16	resolving	resolve	VERB
ejpam-6540	118	17	set	set	VERB
ejpam-6540	118	18	if	if	SCONJ
ejpam-6540	118	19	,	,	PUNCT
ejpam-6540	118	20	for	for	ADP
ejpam-6540	118	21	every	every	DET
ejpam-6540	118	22	vertex	vertex	NOUN
ejpam-6540	118	23	u	u	NOUN
ejpam-6540	118	24	∈	∈	PROPN
ejpam-6540	118	25	f	f	PROPN
ejpam-6540	118	26	,	,	PUNCT
ejpam-6540	118	27	the	the	DET
ejpam-6540	118	28	set	set	NOUN
ejpam-6540	118	29	f	f	PROPN
ejpam-6540	118	30	\	\	PROPN
ejpam-6540	118	31	{	{	PUNCT
ejpam-6540	118	32	u	u	NOUN
ejpam-6540	118	33	}	}	PUNCT
ejpam-6540	118	34	remains	remain	VERB
ejpam-6540	118	35	an	an	DET
ejpam-6540	118	36	edge	edge	NOUN
ejpam-6540	118	37	resolving	resolve	VERB
ejpam-6540	118	38	set	set	NOUN
ejpam-6540	118	39	of	of	ADP
ejpam-6540	118	40	γ	γ	PROPN
ejpam-6540	118	41	.	.	PROPN
ejpam-6540	119	1	among	among	ADP
ejpam-6540	119	2	all	all	DET
ejpam-6540	119	3	such	such	ADJ
ejpam-6540	119	4	subsets	subset	NOUN
ejpam-6540	119	5	,	,	PUNCT
ejpam-6540	119	6	one	one	NUM
ejpam-6540	119	7	with	with	ADP
ejpam-6540	119	8	the	the	DET
ejpam-6540	119	9	smallest	small	ADJ
ejpam-6540	119	10	possible	possible	ADJ
ejpam-6540	119	11	size	size	NOUN
ejpam-6540	119	12	is	be	AUX
ejpam-6540	119	13	called	call	VERB
ejpam-6540	119	14	a	a	DET
ejpam-6540	119	15	fault	fault	NOUN
ejpam-6540	119	16	-	-	PUNCT
ejpam-6540	119	17	tolerant	tolerant	ADJ
ejpam-6540	119	18	edge	edge	NOUN
ejpam-6540	119	19	metric	metric	ADJ
ejpam-6540	119	20	basis	basis	NOUN
ejpam-6540	119	21	.	.	PUNCT
ejpam-6540	120	1	the	the	DET
ejpam-6540	120	2	cardinality	cardinality	NOUN
ejpam-6540	120	3	of	of	ADP
ejpam-6540	120	4	a	a	DET
ejpam-6540	120	5	fault	fault	NOUN
ejpam-6540	120	6	-	-	PUNCT
ejpam-6540	120	7	tolerant	tolerant	ADJ
ejpam-6540	120	8	edge	edge	NOUN
ejpam-6540	120	9	metric	metric	ADJ
ejpam-6540	120	10	basis	basis	NOUN
ejpam-6540	120	11	is	be	AUX
ejpam-6540	120	12	referred	refer	VERB
ejpam-6540	120	13	to	to	ADP
ejpam-6540	120	14	as	as	ADP
ejpam-6540	120	15	the	the	DET
ejpam-6540	120	16	fault	fault	NOUN
ejpam-6540	120	17	-	-	PUNCT
ejpam-6540	120	18	tolerant	tolerant	ADJ
ejpam-6540	120	19	edge	edge	NOUN
ejpam-6540	120	20	metric	metric	ADJ
ejpam-6540	120	21	dimension	dimension	NOUN
ejpam-6540	120	22	of	of	ADP
ejpam-6540	120	23	γ	γ	PROPN
ejpam-6540	120	24	,	,	PUNCT
ejpam-6540	120	25	denoted	denote	VERB
ejpam-6540	120	26	by	by	ADP
ejpam-6540	120	27	dime′(γ	dime′(γ	PROPN
ejpam-6540	120	28	)	)	PUNCT
ejpam-6540	120	29	.	.	PUNCT
ejpam-6540	121	1	k.	k.	PROPN
ejpam-6540	121	2	b.	b.	PROPN
ejpam-6540	121	3	dharan	dharan	PROPN
ejpam-6540	121	4	,	,	PUNCT
ejpam-6540	121	5	s.	s.	PROPN
ejpam-6540	121	6	radha	radha	PROPN
ejpam-6540	121	7	/	/	PUNCT
ejpam-6540	121	8	eur	eur	PROPN
ejpam-6540	121	9	.	.	PUNCT
ejpam-6540	122	1	j.	j.	PROPN
ejpam-6540	122	2	pure	pure	PROPN
ejpam-6540	122	3	appl	appl	PROPN
ejpam-6540	122	4	.	.	PROPN
ejpam-6540	122	5	math	math	PROPN
ejpam-6540	122	6	,	,	PUNCT
ejpam-6540	122	7	18	18	NUM
ejpam-6540	122	8	(	(	PUNCT
ejpam-6540	122	9	3	3	NUM
ejpam-6540	122	10	)	)	PUNCT
ejpam-6540	122	11	(	(	PUNCT
ejpam-6540	122	12	2025	2025	NUM
ejpam-6540	122	13	)	)	PUNCT
ejpam-6540	122	14	,	,	PUNCT
ejpam-6540	122	15	6540	6540	NUM
ejpam-6540	122	16	7	7	NUM
ejpam-6540	122	17	of	of	ADP
ejpam-6540	122	18	17	17	NUM
ejpam-6540	122	19	figure	figure	NOUN
ejpam-6540	122	20	4	4	NUM
ejpam-6540	122	21	:	:	PUNCT
ejpam-6540	122	22	edge	edge	NOUN
ejpam-6540	122	23	representation	representation	NOUN
ejpam-6540	122	24	of	of	ADP
ejpam-6540	122	25	each	each	DET
ejpam-6540	122	26	edge	edge	NOUN
ejpam-6540	122	27	with	with	ADP
ejpam-6540	122	28	respect	respect	NOUN
ejpam-6540	122	29	to	to	ADP
ejpam-6540	122	30	the	the	DET
ejpam-6540	122	31	set	set	NOUN
ejpam-6540	122	32	w	w	PROPN
ejpam-6540	122	33	=	=	PUNCT
ejpam-6540	122	34	{	{	PUNCT
ejpam-6540	122	35	02	02	NUM
ejpam-6540	122	36	,	,	PUNCT
ejpam-6540	122	37	20	20	NUM
ejpam-6540	122	38	}	}	PUNCT
ejpam-6540	122	39	in	in	ADP
ejpam-6540	122	40	s2	s2	PROPN
ejpam-6540	122	41	c5	c5	PROPN
ejpam-6540	122	42	from	from	ADP
ejpam-6540	122	43	figure	figure	NOUN
ejpam-6540	122	44	4	4	NUM
ejpam-6540	122	45	,	,	PUNCT
ejpam-6540	122	46	we	we	PRON
ejpam-6540	122	47	can	can	AUX
ejpam-6540	122	48	easily	easily	ADV
ejpam-6540	122	49	conclude	conclude	VERB
ejpam-6540	122	50	that	that	SCONJ
ejpam-6540	122	51	dime(s	dime(	VERB
ejpam-6540	122	52	2	2	NUM
ejpam-6540	122	53	c5	c5	PROPN
ejpam-6540	122	54	)	)	PUNCT
ejpam-6540	123	1	=	=	SYM
ejpam-6540	123	2	2	2	NUM
ejpam-6540	123	3	,	,	PUNCT
ejpam-6540	123	4	and	and	CCONJ
ejpam-6540	123	5	it	it	PRON
ejpam-6540	123	6	is	be	AUX
ejpam-6540	123	7	easy	easy	ADJ
ejpam-6540	123	8	to	to	PART
ejpam-6540	123	9	verify	verify	VERB
ejpam-6540	123	10	that	that	SCONJ
ejpam-6540	123	11	the	the	DET
ejpam-6540	123	12	fault	fault	NOUN
ejpam-6540	123	13	-	-	PUNCT
ejpam-6540	123	14	tolerant	tolerant	ADJ
ejpam-6540	123	15	edge	edge	NOUN
ejpam-6540	123	16	metric	metric	ADJ
ejpam-6540	123	17	dimension	dimension	NOUN
ejpam-6540	123	18	of	of	ADP
ejpam-6540	123	19	s2	s2	PROPN
ejpam-6540	123	20	c5	c5	PROPN
ejpam-6540	123	21	is	be	AUX
ejpam-6540	123	22	equal	equal	ADJ
ejpam-6540	123	23	to	to	ADP
ejpam-6540	123	24	4	4	NUM
ejpam-6540	123	25	,	,	PUNCT
ejpam-6540	123	26	where	where	SCONJ
ejpam-6540	123	27	{	{	PUNCT
ejpam-6540	123	28	02	02	NUM
ejpam-6540	123	29	,	,	PUNCT
ejpam-6540	123	30	20	20	NUM
ejpam-6540	123	31	,	,	PUNCT
ejpam-6540	123	32	03	03	NUM
ejpam-6540	123	33	,	,	PUNCT
ejpam-6540	123	34	30	30	NUM
ejpam-6540	123	35	}	}	PUNCT
ejpam-6540	123	36	is	be	AUX
ejpam-6540	123	37	the	the	DET
ejpam-6540	123	38	faulttolerant	faulttolerant	ADJ
ejpam-6540	123	39	metric	metric	ADJ
ejpam-6540	123	40	basis	basis	NOUN
ejpam-6540	123	41	.	.	PUNCT
ejpam-6540	124	1	in	in	ADP
ejpam-6540	124	2	this	this	DET
ejpam-6540	124	3	paper	paper	NOUN
ejpam-6540	124	4	,	,	PUNCT
ejpam-6540	124	5	we	we	PRON
ejpam-6540	124	6	use	use	VERB
ejpam-6540	124	7	the	the	DET
ejpam-6540	124	8	following	follow	VERB
ejpam-6540	124	9	notations	notation	NOUN
ejpam-6540	124	10	to	to	PART
ejpam-6540	124	11	represent	represent	VERB
ejpam-6540	124	12	various	various	ADJ
ejpam-6540	124	13	parameters	parameter	NOUN
ejpam-6540	124	14	:	:	PUNCT
ejpam-6540	124	15	rs	rs	ADJ
ejpam-6540	124	16	for	for	ADP
ejpam-6540	124	17	metric	metric	ADJ
ejpam-6540	124	18	resolving	resolving	NOUN
ejpam-6540	124	19	set	set	NOUN
ejpam-6540	124	20	,	,	PUNCT
ejpam-6540	124	21	mb	mb	ADP
ejpam-6540	124	22	for	for	ADP
ejpam-6540	124	23	metric	metric	ADJ
ejpam-6540	124	24	basis	basis	NOUN
ejpam-6540	124	25	,	,	PUNCT
ejpam-6540	124	26	dim	dim	VERB
ejpam-6540	124	27	for	for	ADP
ejpam-6540	124	28	metric	metric	ADJ
ejpam-6540	124	29	dimension	dimension	NOUN
ejpam-6540	124	30	,	,	PUNCT
ejpam-6540	124	31	ftrs	ftr	VERB
ejpam-6540	124	32	for	for	ADP
ejpam-6540	124	33	fault	fault	NOUN
ejpam-6540	124	34	-	-	PUNCT
ejpam-6540	124	35	tolerant	tolerant	ADJ
ejpam-6540	124	36	metric	metric	ADJ
ejpam-6540	124	37	resolving	resolving	NOUN
ejpam-6540	124	38	set	set	NOUN
ejpam-6540	124	39	,	,	PUNCT
ejpam-6540	124	40	ftmb	ftmb	VERB
ejpam-6540	124	41	for	for	ADP
ejpam-6540	124	42	fault	fault	NOUN
ejpam-6540	124	43	-	-	PUNCT
ejpam-6540	124	44	tolerant	tolerant	ADJ
ejpam-6540	124	45	metric	metric	ADJ
ejpam-6540	124	46	basis	basis	NOUN
ejpam-6540	124	47	,	,	PUNCT
ejpam-6540	124	48	dim′	dim′	VERB
ejpam-6540	124	49	for	for	ADP
ejpam-6540	124	50	fault	fault	NOUN
ejpam-6540	124	51	-	-	PUNCT
ejpam-6540	124	52	tolerant	tolerant	ADJ
ejpam-6540	124	53	metric	metric	ADJ
ejpam-6540	124	54	dimension	dimension	NOUN
ejpam-6540	124	55	,	,	PUNCT
ejpam-6540	124	56	ers	er	NOUN
ejpam-6540	124	57	for	for	ADP
ejpam-6540	124	58	edge	edge	NOUN
ejpam-6540	124	59	resolving	resolve	VERB
ejpam-6540	124	60	set	set	NOUN
ejpam-6540	124	61	,	,	PUNCT
ejpam-6540	124	62	emb	emb	VERB
ejpam-6540	124	63	for	for	ADP
ejpam-6540	124	64	edge	edge	NOUN
ejpam-6540	124	65	metric	metric	ADJ
ejpam-6540	124	66	basis	basis	NOUN
ejpam-6540	124	67	,	,	PUNCT
ejpam-6540	124	68	dime	dime	NOUN
ejpam-6540	124	69	for	for	ADP
ejpam-6540	124	70	edge	edge	NOUN
ejpam-6540	124	71	metric	metric	ADJ
ejpam-6540	124	72	dimension	dimension	NOUN
ejpam-6540	124	73	,	,	PUNCT
ejpam-6540	124	74	fters	fter	NOUN
ejpam-6540	124	75	for	for	ADP
ejpam-6540	124	76	fault	fault	NOUN
ejpam-6540	124	77	-	-	PUNCT
ejpam-6540	124	78	tolerant	tolerant	ADJ
ejpam-6540	124	79	edge	edge	NOUN
ejpam-6540	124	80	resolving	resolve	VERB
ejpam-6540	124	81	set	set	NOUN
ejpam-6540	124	82	,	,	PUNCT
ejpam-6540	124	83	ftemb	ftemb	NOUN
ejpam-6540	124	84	for	for	ADP
ejpam-6540	124	85	fault	fault	NOUN
ejpam-6540	124	86	-	-	PUNCT
ejpam-6540	124	87	tolerant	tolerant	ADJ
ejpam-6540	124	88	edge	edge	NOUN
ejpam-6540	124	89	metric	metric	ADJ
ejpam-6540	124	90	basis	basis	NOUN
ejpam-6540	124	91	,	,	PUNCT
ejpam-6540	124	92	and	and	CCONJ
ejpam-6540	124	93	dim′	dim′	VERB
ejpam-6540	124	94	e	e	NOUN
ejpam-6540	124	95	for	for	ADP
ejpam-6540	124	96	fault	fault	NOUN
ejpam-6540	124	97	-	-	PUNCT
ejpam-6540	124	98	tolerant	tolerant	ADJ
ejpam-6540	124	99	edge	edge	NOUN
ejpam-6540	124	100	metric	metric	ADJ
ejpam-6540	124	101	dimension	dimension	NOUN
ejpam-6540	124	102	.	.	PUNCT
ejpam-6540	125	1	3	3	X
ejpam-6540	125	2	.	.	X
ejpam-6540	125	3	main	main	ADJ
ejpam-6540	125	4	results	result	NOUN
ejpam-6540	125	5	in	in	ADP
ejpam-6540	125	6	this	this	DET
ejpam-6540	125	7	section	section	NOUN
ejpam-6540	125	8	,	,	PUNCT
ejpam-6540	125	9	we	we	PRON
ejpam-6540	125	10	present	present	VERB
ejpam-6540	125	11	results	result	NOUN
ejpam-6540	125	12	pertaining	pertain	VERB
ejpam-6540	125	13	to	to	ADP
ejpam-6540	125	14	the	the	DET
ejpam-6540	125	15	exact	exact	ADJ
ejpam-6540	125	16	values	value	NOUN
ejpam-6540	125	17	of	of	ADP
ejpam-6540	125	18	both	both	CCONJ
ejpam-6540	125	19	the	the	DET
ejpam-6540	125	20	dim(γ	dim(γ	NOUN
ejpam-6540	125	21	)	)	PUNCT
ejpam-6540	125	22	and	and	CCONJ
ejpam-6540	125	23	the	the	DET
ejpam-6540	125	24	dim′(γ)s	dim′(γ)	NOUN
ejpam-6540	125	25	,	,	PUNCT
ejpam-6540	125	26	as	as	SCONJ
ejpam-6540	125	27	outlined	outline	VERB
ejpam-6540	125	28	in	in	ADP
ejpam-6540	125	29	subsection	subsection	NOUN
ejpam-6540	125	30	3.1	3.1	NUM
ejpam-6540	125	31	.	.	PUNCT
ejpam-6540	126	1	subsequently	subsequently	ADV
ejpam-6540	126	2	,	,	PUNCT
ejpam-6540	126	3	subsection	subsection	NOUN
ejpam-6540	126	4	3.2	3.2	NUM
ejpam-6540	126	5	addresses	address	NOUN
ejpam-6540	126	6	the	the	DET
ejpam-6540	126	7	corresponding	corresponding	ADJ
ejpam-6540	126	8	results	result	NOUN
ejpam-6540	126	9	for	for	ADP
ejpam-6540	126	10	the	the	DET
ejpam-6540	126	11	dime(γ	dime(γ	PROPN
ejpam-6540	126	12	)	)	PUNCT
ejpam-6540	126	13	and	and	CCONJ
ejpam-6540	126	14	the	the	DET
ejpam-6540	126	15	dim′	dim′	NOUN
ejpam-6540	126	16	e(γ	e(γ	NOUN
ejpam-6540	126	17	)	)	PUNCT
ejpam-6540	126	18	.	.	PUNCT
ejpam-6540	127	1	to	to	PART
ejpam-6540	127	2	support	support	VERB
ejpam-6540	127	3	the	the	DET
ejpam-6540	127	4	upcoming	upcoming	ADJ
ejpam-6540	127	5	theorems	theorem	NOUN
ejpam-6540	127	6	,	,	PUNCT
ejpam-6540	127	7	we	we	PRON
ejpam-6540	127	8	introduce	introduce	VERB
ejpam-6540	127	9	a	a	DET
ejpam-6540	127	10	particular	particular	ADJ
ejpam-6540	127	11	subset	subset	NOUN
ejpam-6540	127	12	of	of	ADP
ejpam-6540	127	13	vertices	vertex	NOUN
ejpam-6540	127	14	that	that	PRON
ejpam-6540	127	15	will	will	AUX
ejpam-6540	127	16	be	be	AUX
ejpam-6540	127	17	instrumental	instrumental	ADJ
ejpam-6540	127	18	in	in	ADP
ejpam-6540	127	19	the	the	DET
ejpam-6540	127	20	analysis	analysis	NOUN
ejpam-6540	127	21	.	.	PUNCT
ejpam-6540	128	1	let	let	VERB
ejpam-6540	128	2	γ′	γ′	PRON
ejpam-6540	128	3	be	be	AUX
ejpam-6540	128	4	an	an	DET
ejpam-6540	128	5	induced	induced	ADJ
ejpam-6540	128	6	subgraph	subgraph	NOUN
ejpam-6540	128	7	of	of	ADP
ejpam-6540	128	8	sh	sh	PROPN
ejpam-6540	128	9	c5	c5	PROPN
ejpam-6540	128	10	,	,	PUNCT
ejpam-6540	128	11	and	and	CCONJ
ejpam-6540	128	12	let	let	VERB
ejpam-6540	128	13	w	w	PART
ejpam-6540	128	14	denote	denote	VERB
ejpam-6540	128	15	a	a	DET
ejpam-6540	128	16	resolving	resolving	NOUN
ejpam-6540	128	17	set	set	VERB
ejpam-6540	128	18	for	for	ADP
ejpam-6540	128	19	sh	sh	PROPN
ejpam-6540	128	20	c5	c5	PROPN
ejpam-6540	128	21	with	with	ADP
ejpam-6540	128	22	h	h	PROPN
ejpam-6540	128	23	≥	≥	PROPN
ejpam-6540	128	24	3	3	NUM
ejpam-6540	128	25	.	.	PUNCT
ejpam-6540	129	1	a	a	DET
ejpam-6540	129	2	vertex	vertex	NOUN
ejpam-6540	129	3	v	v	ADP
ejpam-6540	129	4	∈	∈	PROPN
ejpam-6540	129	5	v(γ′	v(γ′	NOUN
ejpam-6540	129	6	)	)	PUNCT
ejpam-6540	129	7	is	be	AUX
ejpam-6540	129	8	referred	refer	VERB
ejpam-6540	129	9	to	to	ADP
ejpam-6540	129	10	as	as	ADP
ejpam-6540	129	11	a	a	DET
ejpam-6540	129	12	pseudo	pseudo	NOUN
ejpam-6540	129	13	resolver	resolver	NOUN
ejpam-6540	129	14	for	for	ADP
ejpam-6540	129	15	γ′	γ′	PROPN
ejpam-6540	129	16	if	if	SCONJ
ejpam-6540	129	17	there	there	PRON
ejpam-6540	129	18	exists	exist	VERB
ejpam-6540	129	19	a	a	DET
ejpam-6540	129	20	vertex	vertex	NOUN
ejpam-6540	129	21	u	u	NOUN
ejpam-6540	129	22	∈	∈	PROPN
ejpam-6540	129	23	w	w	NOUN
ejpam-6540	129	24	\	\	PROPN
ejpam-6540	129	25	v(γ′	v(γ′	NOUN
ejpam-6540	129	26	)	)	PUNCT
ejpam-6540	129	27	such	such	ADJ
ejpam-6540	129	28	that	that	SCONJ
ejpam-6540	129	29	,	,	PUNCT
ejpam-6540	129	30	∀x	∀x	X
ejpam-6540	129	31	∈	∈	PROPN
ejpam-6540	129	32	v(γ′	v(γ′	NOUN
ejpam-6540	129	33	)	)	PUNCT
ejpam-6540	129	34	,	,	PUNCT
ejpam-6540	129	35	the	the	DET
ejpam-6540	129	36	equality	equality	NOUN
ejpam-6540	129	37	dγ(x	dγ(x	ADJ
ejpam-6540	129	38	,	,	PUNCT
ejpam-6540	129	39	u	u	NOUN
ejpam-6540	129	40	)	)	PUNCT
ejpam-6540	129	41	=	=	SYM
ejpam-6540	129	42	dγ(x	dγ(x	X
ejpam-6540	129	43	,	,	PUNCT
ejpam-6540	129	44	v	v	NOUN
ejpam-6540	129	45	)	)	PUNCT
ejpam-6540	129	46	+	+	CCONJ
ejpam-6540	129	47	dγ(v	dγ(v	NOUN
ejpam-6540	129	48	,	,	PUNCT
ejpam-6540	129	49	u	u	NOUN
ejpam-6540	129	50	)	)	PUNCT
ejpam-6540	129	51	holds	hold	VERB
ejpam-6540	129	52	.	.	PUNCT
ejpam-6540	130	1	this	this	PRON
ejpam-6540	130	2	implies	imply	VERB
ejpam-6540	130	3	that	that	SCONJ
ejpam-6540	130	4	replacing	replace	VERB
ejpam-6540	130	5	u	u	NOUN
ejpam-6540	130	6	in	in	ADP
ejpam-6540	130	7	w	w	ADP
ejpam-6540	130	8	with	with	ADP
ejpam-6540	130	9	v	v	NOUN
ejpam-6540	130	10	results	result	NOUN
ejpam-6540	130	11	in	in	ADP
ejpam-6540	130	12	a	a	DET
ejpam-6540	130	13	set	set	NOUN
ejpam-6540	130	14	that	that	PRON
ejpam-6540	130	15	still	still	ADV
ejpam-6540	130	16	resolves	resolve	VERB
ejpam-6540	130	17	γ′	γ′	PROPN
ejpam-6540	130	18	,	,	PUNCT
ejpam-6540	130	19	that	that	ADV
ejpam-6540	130	20	is	be	AUX
ejpam-6540	130	21	,	,	PUNCT
ejpam-6540	130	22	r(x|(w	r(x|(w	NOUN
ejpam-6540	130	23	\	\	NOUN
ejpam-6540	130	24	{	{	PUNCT
ejpam-6540	130	25	u	u	NOUN
ejpam-6540	130	26	}	}	PUNCT
ejpam-6540	130	27	)	)	PUNCT
ejpam-6540	130	28	∪	∪	ADP
ejpam-6540	130	29	{	{	PUNCT
ejpam-6540	130	30	v	v	NOUN
ejpam-6540	130	31	}	}	PUNCT
ejpam-6540	130	32	)	)	PUNCT
ejpam-6540	131	1	̸=	̸=	PROPN
ejpam-6540	131	2	r(y|(w	r(y|(w	NUM
ejpam-6540	131	3	\	\	NOUN
ejpam-6540	131	4	{	{	PUNCT
ejpam-6540	131	5	u	u	NOUN
ejpam-6540	131	6	}	}	PUNCT
ejpam-6540	131	7	)	)	PUNCT
ejpam-6540	131	8	∪	∪	ADP
ejpam-6540	131	9	{	{	PUNCT
ejpam-6540	131	10	v	v	NOUN
ejpam-6540	131	11	}	}	PUNCT
ejpam-6540	131	12	)	)	PUNCT
ejpam-6540	131	13	for	for	ADP
ejpam-6540	131	14	all	all	DET
ejpam-6540	131	15	distinct	distinct	ADJ
ejpam-6540	131	16	x	x	NOUN
ejpam-6540	131	17	,	,	PUNCT
ejpam-6540	131	18	y	y	PROPN
ejpam-6540	131	19	∈	∈	PROPN
ejpam-6540	131	20	v(γ′	v(γ′	NOUN
ejpam-6540	131	21	)	)	PUNCT
ejpam-6540	131	22	.	.	PUNCT
ejpam-6540	132	1	figure	figure	NOUN
ejpam-6540	132	2	5	5	NUM
ejpam-6540	132	3	illustrates	illustrate	VERB
ejpam-6540	132	4	the	the	DET
ejpam-6540	132	5	collection	collection	NOUN
ejpam-6540	132	6	of	of	ADP
ejpam-6540	132	7	pseudo	pseudo	NOUN
ejpam-6540	132	8	resolver	resolver	NOUN
ejpam-6540	132	9	vertices	vertex	NOUN
ejpam-6540	132	10	for	for	ADP
ejpam-6540	132	11	each	each	DET
ejpam-6540	132	12	induced	induce	VERB
ejpam-6540	132	13	subgraph	subgraph	PROPN
ejpam-6540	132	14	is2	is2	PROPN
ejpam-6540	132	15	c5	c5	PROPN
ejpam-6540	132	16	,	,	PUNCT
ejpam-6540	132	17	where	where	SCONJ
ejpam-6540	132	18	i	i	PRON
ejpam-6540	132	19	∈	∈	PROPN
ejpam-6540	132	20	z5	z5	PROPN
ejpam-6540	132	21	,	,	PUNCT
ejpam-6540	132	22	within	within	ADP
ejpam-6540	132	23	the	the	DET
ejpam-6540	132	24	graph	graph	NOUN
ejpam-6540	132	25	s3	s3	PROPN
ejpam-6540	132	26	c5	c5	PROPN
ejpam-6540	132	27	.	.	PUNCT
ejpam-6540	133	1	k.	k.	PROPN
ejpam-6540	133	2	b.	b.	PROPN
ejpam-6540	133	3	dharan	dharan	PROPN
ejpam-6540	133	4	,	,	PUNCT
ejpam-6540	133	5	s.	s.	PROPN
ejpam-6540	133	6	radha	radha	PROPN
ejpam-6540	133	7	/	/	PUNCT
ejpam-6540	133	8	eur	eur	PROPN
ejpam-6540	133	9	.	.	PUNCT
ejpam-6540	134	1	j.	j.	PROPN
ejpam-6540	134	2	pure	pure	PROPN
ejpam-6540	134	3	appl	appl	PROPN
ejpam-6540	134	4	.	.	PROPN
ejpam-6540	134	5	math	math	PROPN
ejpam-6540	134	6	,	,	PUNCT
ejpam-6540	134	7	18	18	NUM
ejpam-6540	134	8	(	(	PUNCT
ejpam-6540	134	9	3	3	NUM
ejpam-6540	134	10	)	)	PUNCT
ejpam-6540	134	11	(	(	PUNCT
ejpam-6540	134	12	2025	2025	NUM
ejpam-6540	134	13	)	)	PUNCT
ejpam-6540	134	14	,	,	PUNCT
ejpam-6540	134	15	6540	6540	NUM
ejpam-6540	134	16	8	8	NUM
ejpam-6540	134	17	of	of	ADP
ejpam-6540	134	18	17	17	NUM
ejpam-6540	134	19	000	000	NUM
ejpam-6540	134	20	001	001	NUM
ejpam-6540	134	21	002003	002003	NUM
ejpam-6540	134	22	004	004	NUM
ejpam-6540	134	23	010	010	NUM
ejpam-6540	134	24	011	011	NUM
ejpam-6540	134	25	012013	012013	NUM
ejpam-6540	134	26	014	014	NUM
ejpam-6540	134	27	020	020	NUM
ejpam-6540	134	28	021	021	NUM
ejpam-6540	134	29	000	000	NUM
ejpam-6540	134	30	001	001	NUM
ejpam-6540	134	31	002003	002003	NUM
ejpam-6540	134	32	004	004	NUM
ejpam-6540	134	33	010	010	NUM
ejpam-6540	134	34	011	011	NUM
ejpam-6540	134	35	012013	012013	NUM
ejpam-6540	134	36	014	014	NUM
ejpam-6540	134	37	022	022	NUM
ejpam-6540	134	38	023	023	NUM
ejpam-6540	134	39	024	024	NUM
ejpam-6540	134	40	030	030	NUM
ejpam-6540	134	41	031	031	NUM
ejpam-6540	134	42	032	032	NUM
ejpam-6540	134	43	033	033	NUM
ejpam-6540	134	44	034	034	NUM
ejpam-6540	134	45	040	040	NUM
ejpam-6540	134	46	041	041	NUM
ejpam-6540	134	47	042	042	NUM
ejpam-6540	134	48	043	043	NUM
ejpam-6540	134	49	044	044	NUM
ejpam-6540	134	50	120	120	NUM
ejpam-6540	134	51	121	121	NUM
ejpam-6540	134	52	100	100	NUM
ejpam-6540	134	53	101	101	NUM
ejpam-6540	134	54	102103	102103	NUM
ejpam-6540	134	55	104	104	NUM
ejpam-6540	134	56	110	110	NUM
ejpam-6540	134	57	111	111	NUM
ejpam-6540	134	58	112113	112113	NUM
ejpam-6540	134	59	114	114	NUM
ejpam-6540	134	60	122	122	NUM
ejpam-6540	134	61	124	124	NUM
ejpam-6540	134	62	130	130	NUM
ejpam-6540	134	63	131	131	NUM
ejpam-6540	134	64	132	132	NUM
ejpam-6540	134	65	134	134	NUM
ejpam-6540	134	66	140	140	NUM
ejpam-6540	134	67	141	141	NUM
ejpam-6540	134	68	142143	142143	NUM
ejpam-6540	134	69	144	144	NUM
ejpam-6540	134	70	420	420	NUM
ejpam-6540	134	71	421	421	NUM
ejpam-6540	134	72	400	400	NUM
ejpam-6540	134	73	401	401	NUM
ejpam-6540	134	74	402403	402403	NUM
ejpam-6540	134	75	404	404	NUM
ejpam-6540	135	1	410	410	NUM
ejpam-6540	136	1	411	411	NUM
ejpam-6540	136	2	412	412	NUM
ejpam-6540	136	3	413	413	NUM
ejpam-6540	136	4	414	414	NUM
ejpam-6540	136	5	422	422	NUM
ejpam-6540	136	6	424	424	NUM
ejpam-6540	136	7	430	430	NUM
ejpam-6540	136	8	431	431	NUM
ejpam-6540	136	9	432	432	NUM
ejpam-6540	136	10	434	434	NUM
ejpam-6540	136	11	440	440	NUM
ejpam-6540	136	12	441	441	NUM
ejpam-6540	136	13	442	442	NUM
ejpam-6540	136	14	443	443	NUM
ejpam-6540	136	15	444	444	NUM
ejpam-6540	136	16	320	320	NUM
ejpam-6540	136	17	321	321	NUM
ejpam-6540	136	18	300	300	NUM
ejpam-6540	136	19	301	301	NUM
ejpam-6540	136	20	302	302	NUM
ejpam-6540	136	21	303	303	NUM
ejpam-6540	136	22	304	304	NUM
ejpam-6540	136	23	310	310	NUM
ejpam-6540	136	24	311	311	NUM
ejpam-6540	136	25	312313	312313	NUM
ejpam-6540	136	26	314	314	NUM
ejpam-6540	136	27	322	322	NUM
ejpam-6540	136	28	324	324	NUM
ejpam-6540	136	29	330	330	NUM
ejpam-6540	136	30	332	332	NUM
ejpam-6540	136	31	332	332	NUM
ejpam-6540	136	32	334	334	NUM
ejpam-6540	136	33	340	340	NUM
ejpam-6540	136	34	341	341	NUM
ejpam-6540	136	35	342	342	NUM
ejpam-6540	136	36	343	343	NUM
ejpam-6540	136	37	344	344	NUM
ejpam-6540	136	38	220	220	NUM
ejpam-6540	136	39	221	221	NUM
ejpam-6540	136	40	200	200	NUM
ejpam-6540	136	41	201	201	NUM
ejpam-6540	136	42	202	202	NUM
ejpam-6540	136	43	203	203	NUM
ejpam-6540	136	44	204	204	NUM
ejpam-6540	136	45	210	210	NUM
ejpam-6540	136	46	211	211	NUM
ejpam-6540	136	47	212213	212213	NUM
ejpam-6540	136	48	214	214	NUM
ejpam-6540	136	49	222	222	NUM
ejpam-6540	136	50	224	224	NUM
ejpam-6540	136	51	230	230	NUM
ejpam-6540	136	52	231	231	NUM
ejpam-6540	136	53	232	232	NUM
ejpam-6540	136	54	234	234	NUM
ejpam-6540	136	55	240	240	NUM
ejpam-6540	136	56	241	241	NUM
ejpam-6540	136	57	242	242	NUM
ejpam-6540	136	58	243	243	NUM
ejpam-6540	136	59	244	244	NUM
ejpam-6540	136	60	123	123	NUM
ejpam-6540	136	61	133	133	NUM
ejpam-6540	136	62	223233323333	223233323333	NUM
ejpam-6540	136	63	423	423	NUM
ejpam-6540	136	64	433	433	NUM
ejpam-6540	136	65	figure	figure	NOUN
ejpam-6540	136	66	5	5	NUM
ejpam-6540	136	67	:	:	PUNCT
ejpam-6540	136	68	s3	s3	PROPN
ejpam-6540	136	69	c5	c5	PROPN
ejpam-6540	136	70	with	with	ADP
ejpam-6540	136	71	vertices	vertex	NOUN
ejpam-6540	136	72	of	of	ADP
ejpam-6540	136	73	the	the	DET
ejpam-6540	136	74	resolving	resolving	NOUN
ejpam-6540	136	75	set	set	NOUN
ejpam-6540	136	76	encircled	encircle	VERB
ejpam-6540	136	77	with	with	ADP
ejpam-6540	136	78	green	green	ADJ
ejpam-6540	136	79	color	color	NOUN
ejpam-6540	136	80	and	and	CCONJ
ejpam-6540	136	81	pseudo	pseudo	NOUN
ejpam-6540	136	82	resolvers	resolver	NOUN
ejpam-6540	136	83	for	for	ADP
ejpam-6540	136	84	each	each	DET
ejpam-6540	136	85	s2	s2	PROPN
ejpam-6540	136	86	c5	c5	PROPN
ejpam-6540	136	87	encircled	encircle	VERB
ejpam-6540	136	88	with	with	ADP
ejpam-6540	136	89	violet	violet	ADJ
ejpam-6540	136	90	color	color	NOUN
ejpam-6540	136	91	3.1	3.1	NUM
ejpam-6540	136	92	.	.	PUNCT
ejpam-6540	137	1	metric	metric	ADJ
ejpam-6540	137	2	dimension	dimension	NOUN
ejpam-6540	137	3	of	of	ADP
ejpam-6540	137	4	generalized	generalized	ADJ
ejpam-6540	137	5	sierpiński	sierpiński	ADJ
ejpam-6540	137	6	networks	network	NOUN
ejpam-6540	137	7	over	over	ADP
ejpam-6540	137	8	cycle	cycle	NOUN
ejpam-6540	137	9	of	of	ADP
ejpam-6540	137	10	length	length	NOUN
ejpam-6540	137	11	five	five	NUM
ejpam-6540	137	12	we	we	PRON
ejpam-6540	137	13	can	can	AUX
ejpam-6540	137	14	easily	easily	ADV
ejpam-6540	137	15	say	say	VERB
ejpam-6540	137	16	that	that	SCONJ
ejpam-6540	137	17	dim(s1	dim(s1	PROPN
ejpam-6540	137	18	cn	cn	PROPN
ejpam-6540	137	19	)	)	PUNCT
ejpam-6540	137	20	=	=	SYM
ejpam-6540	137	21	2	2	NUM
ejpam-6540	137	22	as	as	SCONJ
ejpam-6540	137	23	s1	s1	PROPN
ejpam-6540	137	24	cn	cn	PROPN
ejpam-6540	137	25	is	be	AUX
ejpam-6540	137	26	isomorphic	isomorphic	ADJ
ejpam-6540	137	27	to	to	ADP
ejpam-6540	137	28	cn	cn	PROPN
ejpam-6540	137	29	.	.	PUNCT
ejpam-6540	138	1	then	then	ADV
ejpam-6540	138	2	,	,	PUNCT
ejpam-6540	138	3	dim(s2	dim(s2	PROPN
ejpam-6540	138	4	c5	c5	PROPN
ejpam-6540	138	5	)	)	PUNCT
ejpam-6540	139	1	=	=	SYM
ejpam-6540	139	2	2	2	NUM
ejpam-6540	139	3	from	from	ADP
ejpam-6540	139	4	the	the	DET
ejpam-6540	139	5	section	section	NOUN
ejpam-6540	139	6	2.1	2.1	NUM
ejpam-6540	139	7	.	.	PUNCT
ejpam-6540	140	1	consider	consider	VERB
ejpam-6540	140	2	the	the	DET
ejpam-6540	140	3	graph	graph	NOUN
ejpam-6540	140	4	s3	s3	PROPN
ejpam-6540	140	5	c5	c5	PROPN
ejpam-6540	140	6	.	.	PUNCT
ejpam-6540	141	1	it	it	PRON
ejpam-6540	141	2	has	have	AUX
ejpam-6540	141	3	exactly	exactly	ADV
ejpam-6540	141	4	5	5	NUM
ejpam-6540	141	5	induced	induced	ADJ
ejpam-6540	141	6	subgraphs	subgraph	NOUN
ejpam-6540	141	7	as	as	SCONJ
ejpam-6540	141	8	s2	s2	PROPN
ejpam-6540	141	9	c5	c5	PROPN
ejpam-6540	141	10	the	the	DET
ejpam-6540	141	11	dim	dim	NOUN
ejpam-6540	141	12	of	of	ADP
ejpam-6540	141	13	those	those	DET
ejpam-6540	141	14	induced	induce	VERB
ejpam-6540	141	15	subgraphs	subgraph	NOUN
ejpam-6540	141	16	is	be	AUX
ejpam-6540	141	17	2	2	NUM
ejpam-6540	141	18	.	.	PUNCT
ejpam-6540	141	19	then	then	ADV
ejpam-6540	141	20	let	let	VERB
ejpam-6540	141	21	us	we	PRON
ejpam-6540	141	22	consider	consider	VERB
ejpam-6540	141	23	the	the	DET
ejpam-6540	141	24	subset	subset	NOUN
ejpam-6540	141	25	w	w	NOUN
ejpam-6540	142	1	=	=	PUNCT
ejpam-6540	142	2	{	{	PUNCT
ejpam-6540	143	1	[	[	X
ejpam-6540	143	2	x]3	x]3	PROPN
ejpam-6540	143	3	:	:	PUNCT
ejpam-6540	143	4	x	x	X
ejpam-6540	143	5	∈	∈	PROPN
ejpam-6540	143	6	z5	z5	PROPN
ejpam-6540	143	7	}	}	PUNCT
ejpam-6540	143	8	of	of	ADP
ejpam-6540	143	9	s3	s3	PROPN
ejpam-6540	143	10	c5	c5	PROPN
ejpam-6540	143	11	.	.	PUNCT
ejpam-6540	144	1	then	then	ADV
ejpam-6540	144	2	for	for	ADP
ejpam-6540	144	3	each	each	DET
ejpam-6540	144	4	induced	induce	VERB
ejpam-6540	144	5	subgraph	subgraph	NOUN
ejpam-6540	144	6	s2	s2	PROPN
ejpam-6540	144	7	c5	c5	PROPN
ejpam-6540	144	8	there	there	PRON
ejpam-6540	144	9	are	be	VERB
ejpam-6540	144	10	exactly	exactly	ADV
ejpam-6540	144	11	two	two	NUM
ejpam-6540	144	12	pseudo	pseudo	NOUN
ejpam-6540	144	13	resolvers	resolver	NOUN
ejpam-6540	144	14	in	in	ADP
ejpam-6540	144	15	the	the	DET
ejpam-6540	144	16	subset	subset	NOUN
ejpam-6540	144	17	{	{	PUNCT
ejpam-6540	144	18	i1i22	i1i22	NOUN
ejpam-6540	144	19	:	:	PUNCT
ejpam-6540	144	20	i2	i2	PROPN
ejpam-6540	144	21	≡	≡	PROPN
ejpam-6540	144	22	(	(	PUNCT
ejpam-6540	144	23	i1±	i1±	PROPN
ejpam-6540	144	24	1)mod	1)mod	NUM
ejpam-6540	144	25	5	5	NUM
ejpam-6540	144	26	}	}	PUNCT
ejpam-6540	144	27	⊂	⊂	PROPN
ejpam-6540	144	28	v(i1s2	v(i1s2	ADV
ejpam-6540	144	29	c5	c5	PROPN
ejpam-6540	144	30	)	)	PUNCT
ejpam-6540	144	31	.	.	PUNCT
ejpam-6540	145	1	these	these	DET
ejpam-6540	145	2	pseudo	pseudo	NOUN
ejpam-6540	145	3	resolvers	resolver	NOUN
ejpam-6540	145	4	serve	serve	VERB
ejpam-6540	145	5	a	a	DET
ejpam-6540	145	6	crucial	crucial	ADJ
ejpam-6540	145	7	role	role	NOUN
ejpam-6540	145	8	:	:	PUNCT
ejpam-6540	145	9	although	although	SCONJ
ejpam-6540	145	10	they	they	PRON
ejpam-6540	145	11	are	be	AUX
ejpam-6540	145	12	not	not	PART
ejpam-6540	145	13	part	part	NOUN
ejpam-6540	145	14	of	of	ADP
ejpam-6540	145	15	w	w	NOUN
ejpam-6540	145	16	,	,	PUNCT
ejpam-6540	145	17	but	but	CCONJ
ejpam-6540	145	18	due	due	ADP
ejpam-6540	145	19	to	to	ADP
ejpam-6540	145	20	their	their	PRON
ejpam-6540	145	21	property	property	NOUN
ejpam-6540	145	22	(	(	PUNCT
ejpam-6540	145	23	given	give	VERB
ejpam-6540	145	24	in	in	ADP
ejpam-6540	145	25	definition	definition	NOUN
ejpam-6540	145	26	of	of	ADP
ejpam-6540	145	27	pseudo	pseudo	NOUN
ejpam-6540	145	28	resolvers	resolver	NOUN
ejpam-6540	145	29	)	)	PUNCT
ejpam-6540	145	30	,	,	PUNCT
ejpam-6540	145	31	their	their	PRON
ejpam-6540	145	32	relative	relative	ADJ
ejpam-6540	145	33	positions	position	NOUN
ejpam-6540	145	34	with	with	ADP
ejpam-6540	145	35	respect	respect	NOUN
ejpam-6540	145	36	to	to	ADP
ejpam-6540	145	37	the	the	DET
ejpam-6540	145	38	remaining	remain	VERB
ejpam-6540	145	39	vertices	vertex	NOUN
ejpam-6540	145	40	in	in	ADP
ejpam-6540	145	41	w	w	AUX
ejpam-6540	145	42	allow	allow	VERB
ejpam-6540	145	43	them	they	PRON
ejpam-6540	145	44	to	to	PART
ejpam-6540	145	45	replace	replace	VERB
ejpam-6540	145	46	the	the	DET
ejpam-6540	145	47	resolvers	resolver	NOUN
ejpam-6540	145	48	that	that	PRON
ejpam-6540	145	49	would	would	AUX
ejpam-6540	145	50	belong	belong	VERB
ejpam-6540	145	51	to	to	ADP
ejpam-6540	145	52	the	the	DET
ejpam-6540	145	53	subgraph	subgraph	NOUN
ejpam-6540	145	54	i1s	i1	NOUN
ejpam-6540	145	55	2	2	NUM
ejpam-6540	145	56	c5	c5	PROPN
ejpam-6540	145	57	.	.	PUNCT
ejpam-6540	146	1	this	this	PRON
ejpam-6540	146	2	implies	imply	VERB
ejpam-6540	146	3	that	that	SCONJ
ejpam-6540	146	4	the	the	DET
ejpam-6540	146	5	every	every	DET
ejpam-6540	146	6	pseudo	pseudo	NOUN
ejpam-6540	146	7	resolvers	resolver	NOUN
ejpam-6540	146	8	of	of	ADP
ejpam-6540	146	9	i2s	i2s	NOUN
ejpam-6540	146	10	2	2	NUM
ejpam-6540	146	11	c5	c5	PROPN
ejpam-6540	146	12	along	along	ADP
ejpam-6540	146	13	with	with	ADP
ejpam-6540	146	14	the	the	DET
ejpam-6540	146	15	vertices	vertex	NOUN
ejpam-6540	146	16	in	in	ADP
ejpam-6540	146	17	i1s	i1	NOUN
ejpam-6540	146	18	2	2	NUM
ejpam-6540	146	19	c5	c5	PROPN
ejpam-6540	146	20	∩w	∩w	NOUN
ejpam-6540	146	21	are	be	AUX
ejpam-6540	146	22	enough	enough	ADJ
ejpam-6540	146	23	to	to	PART
ejpam-6540	146	24	resolve	resolve	VERB
ejpam-6540	146	25	all	all	DET
ejpam-6540	146	26	the	the	DET
ejpam-6540	146	27	vertices	vertex	NOUN
ejpam-6540	146	28	of	of	ADP
ejpam-6540	146	29	i1s	i1	NOUN
ejpam-6540	146	30	2	2	NUM
ejpam-6540	146	31	c5	c5	PROPN
ejpam-6540	146	32	,	,	PUNCT
ejpam-6540	146	33	i1	i1	PROPN
ejpam-6540	146	34	∈	∈	PROPN
ejpam-6540	146	35	z5	z5	PROPN
ejpam-6540	146	36	.	.	PUNCT
ejpam-6540	147	1	this	this	PRON
ejpam-6540	147	2	implies	imply	VERB
ejpam-6540	147	3	w	w	NOUN
ejpam-6540	147	4	is	be	AUX
ejpam-6540	147	5	enough	enough	ADJ
ejpam-6540	147	6	to	to	PART
ejpam-6540	147	7	resolve	resolve	VERB
ejpam-6540	147	8	all	all	DET
ejpam-6540	147	9	the	the	DET
ejpam-6540	147	10	vertices	vertex	NOUN
ejpam-6540	147	11	of	of	ADP
ejpam-6540	147	12	s3	s3	PROPN
ejpam-6540	147	13	c5	c5	PROPN
ejpam-6540	147	14	.	.	PUNCT
ejpam-6540	148	1	so	so	ADV
ejpam-6540	148	2	that	that	SCONJ
ejpam-6540	148	3	,	,	PUNCT
ejpam-6540	148	4	dim(s3	dim(s3	PROPN
ejpam-6540	148	5	c5	c5	PROPN
ejpam-6540	148	6	)	)	PUNCT
ejpam-6540	148	7	≤	≤	ADV
ejpam-6540	148	8	5	5	NUM
ejpam-6540	148	9	.	.	PUNCT
ejpam-6540	148	10	suppose	suppose	VERB
ejpam-6540	148	11	that	that	SCONJ
ejpam-6540	148	12	dim(s3	dim(s3	PROPN
ejpam-6540	148	13	c5	c5	PROPN
ejpam-6540	148	14	)	)	PUNCT
ejpam-6540	148	15	=	=	PUNCT
ejpam-6540	149	1	4	4	X
ejpam-6540	149	2	.	.	PUNCT
ejpam-6540	149	3	by	by	ADP
ejpam-6540	149	4	the	the	DET
ejpam-6540	149	5	pigeonhole	pigeonhole	NOUN
ejpam-6540	149	6	principle	principle	NOUN
ejpam-6540	149	7	,	,	PUNCT
ejpam-6540	149	8	there	there	PRON
ejpam-6540	149	9	exist	exist	VERB
ejpam-6540	149	10	at	at	ADV
ejpam-6540	149	11	least	least	ADV
ejpam-6540	149	12	one	one	NUM
ejpam-6540	149	13	induced	induced	ADJ
ejpam-6540	149	14	subgraph	subgraph	NOUN
ejpam-6540	149	15	s2	s2	PROPN
ejpam-6540	149	16	c5	c5	PROPN
ejpam-6540	149	17	that	that	PRON
ejpam-6540	149	18	do	do	AUX
ejpam-6540	149	19	not	not	PART
ejpam-6540	149	20	contain	contain	VERB
ejpam-6540	149	21	any	any	DET
ejpam-6540	149	22	vertex	vertex	NOUN
ejpam-6540	149	23	from	from	ADP
ejpam-6540	149	24	w	w	PROPN
ejpam-6540	149	25	.	.	PUNCT
ejpam-6540	150	1	then	then	ADV
ejpam-6540	150	2	there	there	PRON
ejpam-6540	150	3	exists	exist	VERB
ejpam-6540	150	4	at	at	ADP
ejpam-6540	150	5	least	least	ADV
ejpam-6540	150	6	two	two	NUM
ejpam-6540	150	7	vertices	vertex	NOUN
ejpam-6540	150	8	that	that	PRON
ejpam-6540	150	9	have	have	VERB
ejpam-6540	150	10	the	the	DET
ejpam-6540	150	11	same	same	ADJ
ejpam-6540	150	12	representation	representation	NOUN
ejpam-6540	150	13	,	,	PUNCT
ejpam-6540	150	14	a	a	DET
ejpam-6540	150	15	contradiction	contradiction	NOUN
ejpam-6540	150	16	.	.	PUNCT
ejpam-6540	151	1	this	this	PRON
ejpam-6540	151	2	implies	imply	VERB
ejpam-6540	151	3	that	that	SCONJ
ejpam-6540	151	4	dim(s3	dim(s3	PROPN
ejpam-6540	151	5	c5	c5	PROPN
ejpam-6540	151	6	)	)	PUNCT
ejpam-6540	151	7	≥	≥	PROPN
ejpam-6540	151	8	5	5	NUM
ejpam-6540	151	9	.	.	PUNCT
ejpam-6540	151	10	then	then	ADV
ejpam-6540	151	11	dim(s3	dim(s3	PROPN
ejpam-6540	151	12	c5	c5	PROPN
ejpam-6540	151	13	)	)	PUNCT
ejpam-6540	151	14	=	=	PUNCT
ejpam-6540	152	1	5	5	X
ejpam-6540	152	2	.	.	PUNCT
ejpam-6540	153	1	the	the	DET
ejpam-6540	153	2	following	follow	VERB
ejpam-6540	153	3	theorem	theorem	NOUN
ejpam-6540	153	4	gives	give	VERB
ejpam-6540	153	5	the	the	DET
ejpam-6540	153	6	k.	k.	PROPN
ejpam-6540	153	7	b.	b.	PROPN
ejpam-6540	153	8	dharan	dharan	PROPN
ejpam-6540	153	9	,	,	PUNCT
ejpam-6540	153	10	s.	s.	PROPN
ejpam-6540	153	11	radha	radha	PROPN
ejpam-6540	153	12	/	/	PUNCT
ejpam-6540	153	13	eur	eur	PROPN
ejpam-6540	153	14	.	.	PUNCT
ejpam-6540	154	1	j.	j.	PROPN
ejpam-6540	154	2	pure	pure	PROPN
ejpam-6540	154	3	appl	appl	PROPN
ejpam-6540	154	4	.	.	PROPN
ejpam-6540	154	5	math	math	PROPN
ejpam-6540	154	6	,	,	PUNCT
ejpam-6540	154	7	18	18	NUM
ejpam-6540	154	8	(	(	PUNCT
ejpam-6540	154	9	3	3	NUM
ejpam-6540	154	10	)	)	PUNCT
ejpam-6540	154	11	(	(	PUNCT
ejpam-6540	154	12	2025	2025	NUM
ejpam-6540	154	13	)	)	PUNCT
ejpam-6540	154	14	,	,	PUNCT
ejpam-6540	154	15	6540	6540	NUM
ejpam-6540	154	16	9	9	NUM
ejpam-6540	154	17	of	of	ADP
ejpam-6540	154	18	17	17	NUM
ejpam-6540	154	19	value	value	NOUN
ejpam-6540	154	20	of	of	ADP
ejpam-6540	154	21	dim(sh	dim(sh	PROPN
ejpam-6540	154	22	c5	c5	PROPN
ejpam-6540	154	23	)	)	PUNCT
ejpam-6540	155	1	for	for	ADP
ejpam-6540	155	2	any	any	DET
ejpam-6540	155	3	h	h	NOUN
ejpam-6540	155	4	≥	≥	NOUN
ejpam-6540	155	5	3	3	NUM
ejpam-6540	155	6	.	.	PUNCT
ejpam-6540	155	7	theorem	theorem	NOUN
ejpam-6540	155	8	1	1	NUM
ejpam-6540	155	9	.	.	PUNCT
ejpam-6540	156	1	if	if	SCONJ
ejpam-6540	156	2	h	h	PROPN
ejpam-6540	156	3	≥	≥	NOUN
ejpam-6540	156	4	3	3	NUM
ejpam-6540	156	5	,	,	PUNCT
ejpam-6540	156	6	then	then	ADV
ejpam-6540	156	7	dim(sh	dim(sh	X
ejpam-6540	156	8	c5	c5	PROPN
ejpam-6540	156	9	)	)	PUNCT
ejpam-6540	157	1	=	=	PUNCT
ejpam-6540	158	1	5(1	5(1	NUM
ejpam-6540	158	2	+	+	NUM
ejpam-6540	158	3	5h−3	5h−3	NUM
ejpam-6540	158	4	)	)	PUNCT
ejpam-6540	158	5	2	2	NUM
ejpam-6540	158	6	.	.	PUNCT
ejpam-6540	159	1	proof	proof	NOUN
ejpam-6540	159	2	.	.	PUNCT
ejpam-6540	160	1	let	let	VERB
ejpam-6540	160	2	w3	w3	PROPN
ejpam-6540	160	3	=	=	PUNCT
ejpam-6540	160	4	{	{	PUNCT
ejpam-6540	160	5	x3	x3	ADV
ejpam-6540	160	6	:	:	PUNCT
ejpam-6540	160	7	x	x	SYM
ejpam-6540	160	8	∈	∈	PROPN
ejpam-6540	160	9	z5	z5	X
ejpam-6540	160	10	}	}	PUNCT
ejpam-6540	160	11	and	and	CCONJ
ejpam-6540	160	12	for	for	ADP
ejpam-6540	160	13	h	h	PROPN
ejpam-6540	160	14	≥	≥	NOUN
ejpam-6540	160	15	4	4	NUM
ejpam-6540	160	16	,	,	PUNCT
ejpam-6540	160	17	wh	wh	VERB
ejpam-6540	160	18	=	=	SYM
ejpam-6540	160	19	4⋃	4⋃	NUM
ejpam-6540	160	20	i=0	i=0	PROPN
ejpam-6540	160	21	iwh−1	iwh−1	X
ejpam-6540	160	22	\	\	NOUN
ejpam-6540	160	23	{	{	PUNCT
ejpam-6540	161	1	i((i−	i((i−	PROPN
ejpam-6540	161	2	1)mod	1)mod	NUM
ejpam-6540	161	3	5)h−1	5)h−1	NUM
ejpam-6540	161	4	,	,	PUNCT
ejpam-6540	161	5	i((i+	i((i+	VERB
ejpam-6540	161	6	1)mod	1)mod	NUM
ejpam-6540	161	7	5)h−1	5)h−1	NUM
ejpam-6540	161	8	}	}	PUNCT
ejpam-6540	161	9	.	.	PUNCT
ejpam-6540	162	1	we	we	PRON
ejpam-6540	162	2	claim	claim	VERB
ejpam-6540	162	3	that	that	SCONJ
ejpam-6540	162	4	wh	wh	NOUN
ejpam-6540	162	5	is	be	AUX
ejpam-6540	162	6	a	a	DET
ejpam-6540	162	7	rs	rs	NOUN
ejpam-6540	162	8	of	of	ADP
ejpam-6540	162	9	sh	sh	PROPN
ejpam-6540	162	10	c5	c5	PROPN
ejpam-6540	162	11	,	,	PUNCT
ejpam-6540	162	12	h	h	PROPN
ejpam-6540	162	13	≥	≥	NOUN
ejpam-6540	162	14	4	4	NUM
ejpam-6540	162	15	and	and	CCONJ
ejpam-6540	162	16	proceed	procee	VERB
ejpam-6540	162	17	by	by	ADP
ejpam-6540	162	18	induction	induction	NOUN
ejpam-6540	162	19	on	on	ADP
ejpam-6540	162	20	h.	h.	PROPN
ejpam-6540	162	21	already	already	ADV
ejpam-6540	162	22	we	we	PRON
ejpam-6540	162	23	know	know	VERB
ejpam-6540	162	24	that	that	SCONJ
ejpam-6540	162	25	the	the	DET
ejpam-6540	162	26	claim	claim	NOUN
ejpam-6540	162	27	is	be	AUX
ejpam-6540	162	28	true	true	ADJ
ejpam-6540	162	29	for	for	ADP
ejpam-6540	162	30	h	h	NOUN
ejpam-6540	162	31	=	=	SYM
ejpam-6540	162	32	3	3	X
ejpam-6540	162	33	.	.	PUNCT
ejpam-6540	163	1	so	so	ADV
ejpam-6540	163	2	it	it	PRON
ejpam-6540	163	3	remains	remain	VERB
ejpam-6540	163	4	to	to	PART
ejpam-6540	163	5	verify	verify	VERB
ejpam-6540	163	6	that	that	SCONJ
ejpam-6540	163	7	,	,	PUNCT
ejpam-6540	163	8	wh+1	wh+1	PROPN
ejpam-6540	163	9	is	be	AUX
ejpam-6540	163	10	rs	rs	NOUN
ejpam-6540	163	11	of	of	ADP
ejpam-6540	163	12	sh+1	sh+1	PROPN
ejpam-6540	163	13	c5	c5	PROPN
ejpam-6540	163	14	,	,	PUNCT
ejpam-6540	163	15	h	h	PROPN
ejpam-6540	163	16	≥	≥	NOUN
ejpam-6540	163	17	4	4	NUM
ejpam-6540	163	18	.	.	PUNCT
ejpam-6540	163	19	consider	consider	VERB
ejpam-6540	163	20	any	any	DET
ejpam-6540	163	21	two	two	NUM
ejpam-6540	163	22	arbitrary	arbitrary	ADJ
ejpam-6540	163	23	vertices	vertex	NOUN
ejpam-6540	163	24	u	u	NOUN
ejpam-6540	163	25	=	=	X
ejpam-6540	163	26	u1u2	u1u2	X
ejpam-6540	163	27	.	.	PUNCT
ejpam-6540	163	28	.	.	PUNCT
ejpam-6540	163	29	.	.	PUNCT
ejpam-6540	164	1	uh+1	uh+1	PROPN
ejpam-6540	164	2	and	and	CCONJ
ejpam-6540	164	3	v	v	NOUN
ejpam-6540	164	4	=	=	PUNCT
ejpam-6540	164	5	v1v2	v1v2	X
ejpam-6540	164	6	.	.	PUNCT
ejpam-6540	164	7	.	.	PUNCT
ejpam-6540	165	1	.	.	PUNCT
ejpam-6540	166	1	vh+1	vh+1	NUM
ejpam-6540	166	2	of	of	ADP
ejpam-6540	166	3	sh+1	sh+1	PROPN
ejpam-6540	166	4	c5	c5	PROPN
ejpam-6540	166	5	.	.	PUNCT
ejpam-6540	167	1	case	case	NOUN
ejpam-6540	167	2	1	1	NUM
ejpam-6540	167	3	:	:	PUNCT
ejpam-6540	167	4	u1	u1	NOUN
ejpam-6540	167	5	−	−	PROPN
ejpam-6540	167	6	v1	v1	PROPN
ejpam-6540	167	7	≡	≡	PROPN
ejpam-6540	167	8	±1	±1	VERB
ejpam-6540	167	9	mod	mod	PROPN
ejpam-6540	167	10	5	5	NUM
ejpam-6540	167	11	suppose	suppose	VERB
ejpam-6540	167	12	there	there	PRON
ejpam-6540	167	13	exists	exist	VERB
ejpam-6540	167	14	some	some	DET
ejpam-6540	167	15	vertices	vertex	NOUN
ejpam-6540	167	16	x	x	X
ejpam-6540	167	17	∈	∈	PROPN
ejpam-6540	167	18	u1s	u1s	PROPN
ejpam-6540	167	19	h	h	NOUN
ejpam-6540	167	20	c5	c5	PROPN
ejpam-6540	167	21	and	and	CCONJ
ejpam-6540	167	22	y	y	PROPN
ejpam-6540	167	23	∈	∈	PROPN
ejpam-6540	168	1	v1s	v1s	NOUN
ejpam-6540	168	2	h	h	NOUN
ejpam-6540	168	3	c5	c5	PROPN
ejpam-6540	168	4	such	such	ADJ
ejpam-6540	168	5	that	that	SCONJ
ejpam-6540	168	6	r(x|wh+1	r(x|wh+1	PROPN
ejpam-6540	168	7	∩	∩	NOUN
ejpam-6540	168	8	u1s	u1s	ADJ
ejpam-6540	168	9	h	h	NOUN
ejpam-6540	168	10	c5	c5	PROPN
ejpam-6540	168	11	)	)	PUNCT
ejpam-6540	169	1	=	=	PUNCT
ejpam-6540	169	2	r(y|wh+1	r(y|wh+1	PROPN
ejpam-6540	169	3	∩	∩	ADJ
ejpam-6540	169	4	u1s	u1s	NOUN
ejpam-6540	169	5	h	h	NOUN
ejpam-6540	169	6	c5	c5	PROPN
ejpam-6540	169	7	)	)	PUNCT
ejpam-6540	169	8	but	but	CCONJ
ejpam-6540	169	9	there	there	PRON
ejpam-6540	169	10	exists	exist	VERB
ejpam-6540	169	11	t	t	PROPN
ejpam-6540	169	12	∈	∈	PROPN
ejpam-6540	169	13	wh+1	wh+1	PROPN
ejpam-6540	169	14	∩	∩	NOUN
ejpam-6540	169	15	(	(	PUNCT
ejpam-6540	169	16	(	(	PUNCT
ejpam-6540	169	17	v1	v1	VERB
ejpam-6540	169	18	+	+	CCONJ
ejpam-6540	169	19	1	1	X
ejpam-6540	169	20	)	)	PUNCT
ejpam-6540	169	21	mod	mod	NOUN
ejpam-6540	170	1	5)sh	5)sh	PROPN
ejpam-6540	170	2	c5	c5	PROPN
ejpam-6540	170	3	such	such	ADJ
ejpam-6540	170	4	that	that	SCONJ
ejpam-6540	170	5	dsh+1	dsh+1	PROPN
ejpam-6540	170	6	c5	c5	PROPN
ejpam-6540	170	7	(	(	PUNCT
ejpam-6540	170	8	x	x	PROPN
ejpam-6540	170	9	,	,	PUNCT
ejpam-6540	170	10	t	t	PROPN
ejpam-6540	170	11	)	)	PUNCT
ejpam-6540	170	12	̸=	̸=	PROPN
ejpam-6540	170	13	dsh+1	dsh+1	NOUN
ejpam-6540	170	14	c5	c5	PROPN
ejpam-6540	170	15	(	(	PUNCT
ejpam-6540	170	16	y	y	PROPN
ejpam-6540	170	17	,	,	PUNCT
ejpam-6540	170	18	t	t	PROPN
ejpam-6540	170	19	)	)	PUNCT
ejpam-6540	170	20	when	when	SCONJ
ejpam-6540	170	21	u1	u1	NOUN
ejpam-6540	170	22	<	<	X
ejpam-6540	170	23	v1	v1	PROPN
ejpam-6540	170	24	or	or	CCONJ
ejpam-6540	170	25	there	there	ADV
ejpam-6540	170	26	exists	exist	VERB
ejpam-6540	170	27	t	t	PROPN
ejpam-6540	170	28	∈	∈	PROPN
ejpam-6540	170	29	wh+1∩	wh+1∩	ADP
ejpam-6540	170	30	(	(	PUNCT
ejpam-6540	170	31	(	(	PUNCT
ejpam-6540	170	32	u1	u1	VERB
ejpam-6540	170	33	+	+	NOUN
ejpam-6540	170	34	1	1	NUM
ejpam-6540	170	35	)	)	PUNCT
ejpam-6540	170	36	mod	mod	NOUN
ejpam-6540	171	1	5)sh	5)sh	PROPN
ejpam-6540	171	2	c5	c5	PROPN
ejpam-6540	171	3	such	such	ADJ
ejpam-6540	171	4	that	that	SCONJ
ejpam-6540	171	5	dsh+1	dsh+1	PROPN
ejpam-6540	171	6	c5	c5	PROPN
ejpam-6540	171	7	(	(	PUNCT
ejpam-6540	171	8	x	x	PROPN
ejpam-6540	171	9	,	,	PUNCT
ejpam-6540	171	10	t	t	PROPN
ejpam-6540	171	11	)	)	PUNCT
ejpam-6540	171	12	̸=	̸=	PROPN
ejpam-6540	171	13	dsh+1	dsh+1	NOUN
ejpam-6540	171	14	c5	c5	PROPN
ejpam-6540	171	15	(	(	PUNCT
ejpam-6540	171	16	y	y	PROPN
ejpam-6540	171	17	,	,	PUNCT
ejpam-6540	171	18	t	t	PROPN
ejpam-6540	171	19	)	)	PUNCT
ejpam-6540	171	20	when	when	SCONJ
ejpam-6540	171	21	u1	u1	NOUN
ejpam-6540	171	22	>	>	X
ejpam-6540	171	23	v1	v1	PROPN
ejpam-6540	171	24	.	.	PUNCT
ejpam-6540	172	1	this	this	PRON
ejpam-6540	172	2	implies	imply	VERB
ejpam-6540	172	3	that	that	SCONJ
ejpam-6540	172	4	r(x|wh+1	r(x|wh+1	NOUN
ejpam-6540	172	5	)	)	PUNCT
ejpam-6540	172	6	̸=	̸=	PROPN
ejpam-6540	172	7	r(y|wh+1	r(y|wh+1	PROPN
ejpam-6540	172	8	)	)	PUNCT
ejpam-6540	172	9	for	for	ADP
ejpam-6540	172	10	all	all	DET
ejpam-6540	172	11	x	x	SYM
ejpam-6540	172	12	∈	∈	PROPN
ejpam-6540	172	13	u1s	u1s	PROPN
ejpam-6540	172	14	h	h	NOUN
ejpam-6540	172	15	c5	c5	PROPN
ejpam-6540	172	16	and	and	CCONJ
ejpam-6540	172	17	y	y	PROPN
ejpam-6540	172	18	∈	∈	PROPN
ejpam-6540	172	19	v1s	v1s	NOUN
ejpam-6540	172	20	h	h	NOUN
ejpam-6540	172	21	c5	c5	PROPN
ejpam-6540	172	22	.	.	PUNCT
ejpam-6540	173	1	then	then	ADV
ejpam-6540	173	2	u	u	PROPN
ejpam-6540	173	3	and	and	CCONJ
ejpam-6540	173	4	v	v	NOUN
ejpam-6540	173	5	have	have	VERB
ejpam-6540	173	6	distinct	distinct	ADJ
ejpam-6540	173	7	representation	representation	NOUN
ejpam-6540	173	8	with	with	ADP
ejpam-6540	173	9	respect	respect	NOUN
ejpam-6540	173	10	to	to	ADP
ejpam-6540	173	11	wh+1	wh+1	PRON
ejpam-6540	173	12	when	when	SCONJ
ejpam-6540	173	13	u1	u1	NOUN
ejpam-6540	173	14	−	−	PROPN
ejpam-6540	173	15	v1	v1	PROPN
ejpam-6540	173	16	≡	≡	PROPN
ejpam-6540	173	17	±1(mod	±1(mod	PROPN
ejpam-6540	173	18	5	5	NUM
ejpam-6540	173	19	)	)	PUNCT
ejpam-6540	173	20	.	.	PUNCT
ejpam-6540	174	1	case	case	NOUN
ejpam-6540	174	2	2	2	NUM
ejpam-6540	174	3	:	:	PUNCT
ejpam-6540	174	4	u1	u1	NOUN
ejpam-6540	174	5	−	−	PROPN
ejpam-6540	174	6	v1	v1	PROPN
ejpam-6540	174	7	̸≡	̸≡	X
ejpam-6540	174	8	±1(mod	±1(mod	PROPN
ejpam-6540	174	9	5	5	NUM
ejpam-6540	174	10	)	)	PUNCT
ejpam-6540	174	11	in	in	ADP
ejpam-6540	174	12	this	this	DET
ejpam-6540	174	13	case	case	NOUN
ejpam-6540	174	14	,	,	PUNCT
ejpam-6540	174	15	we	we	PRON
ejpam-6540	174	16	have	have	VERB
ejpam-6540	174	17	dsh+1	dsh+1	NOUN
ejpam-6540	174	18	c5	c5	PROPN
ejpam-6540	174	19	(	(	PUNCT
ejpam-6540	174	20	u	u	PROPN
ejpam-6540	174	21	,	,	PUNCT
ejpam-6540	174	22	t	t	PROPN
ejpam-6540	174	23	)	)	PUNCT
ejpam-6540	174	24	<	<	X
ejpam-6540	174	25	dsh+1	dsh+1	PROPN
ejpam-6540	174	26	c5	c5	PROPN
ejpam-6540	174	27	(	(	PUNCT
ejpam-6540	174	28	v	v	PROPN
ejpam-6540	174	29	,	,	PUNCT
ejpam-6540	174	30	t	t	PROPN
ejpam-6540	174	31	)	)	PUNCT
ejpam-6540	174	32	for	for	ADP
ejpam-6540	174	33	all	all	DET
ejpam-6540	174	34	t	t	NOUN
ejpam-6540	174	35	∈	∈	PRON
ejpam-6540	174	36	wh+1	wh+1	PROPN
ejpam-6540	174	37	∩	∩	ADJ
ejpam-6540	174	38	u1s	u1s	PROPN
ejpam-6540	174	39	h	h	PROPN
ejpam-6540	174	40	c5	c5	PROPN
ejpam-6540	174	41	.	.	PUNCT
ejpam-6540	175	1	thus	thus	ADV
ejpam-6540	175	2	,	,	PUNCT
ejpam-6540	175	3	u	u	NOUN
ejpam-6540	175	4	and	and	CCONJ
ejpam-6540	175	5	v	v	NOUN
ejpam-6540	175	6	have	have	VERB
ejpam-6540	175	7	distinct	distinct	ADJ
ejpam-6540	175	8	representation	representation	NOUN
ejpam-6540	175	9	with	with	ADP
ejpam-6540	175	10	respect	respect	NOUN
ejpam-6540	175	11	to	to	ADP
ejpam-6540	175	12	wh+1	wh+1	PRON
ejpam-6540	175	13	when	when	SCONJ
ejpam-6540	175	14	u1	u1	NOUN
ejpam-6540	175	15	<	<	X
ejpam-6540	175	16	v1	v1	PROPN
ejpam-6540	175	17	and	and	CCONJ
ejpam-6540	175	18	u1	u1	NOUN
ejpam-6540	175	19	−	−	PROPN
ejpam-6540	175	20	v1	v1	PROPN
ejpam-6540	175	21	̸≡	̸≡	NOUN
ejpam-6540	175	22	1(mod	1(mod	NUM
ejpam-6540	175	23	5	5	NUM
ejpam-6540	175	24	)	)	PUNCT
ejpam-6540	175	25	.	.	PUNCT
ejpam-6540	176	1	case	case	NOUN
ejpam-6540	176	2	3	3	NUM
ejpam-6540	176	3	:	:	PUNCT
ejpam-6540	176	4	u1	u1	NOUN
ejpam-6540	176	5	=	=	SYM
ejpam-6540	176	6	v1	v1	PROPN
ejpam-6540	176	7	we	we	PRON
ejpam-6540	176	8	may	may	AUX
ejpam-6540	176	9	assume	assume	VERB
ejpam-6540	176	10	that	that	SCONJ
ejpam-6540	176	11	u1	u1	NOUN
ejpam-6540	176	12	=	=	SYM
ejpam-6540	176	13	v1	v1	PROPN
ejpam-6540	176	14	=	=	SYM
ejpam-6540	176	15	0	0	NUM
ejpam-6540	176	16	.	.	PUNCT
ejpam-6540	177	1	by	by	ADP
ejpam-6540	177	2	induction	induction	NOUN
ejpam-6540	177	3	and	and	CCONJ
ejpam-6540	177	4	the	the	DET
ejpam-6540	177	5	structure	structure	NOUN
ejpam-6540	177	6	of	of	ADP
ejpam-6540	177	7	sh+1	sh+1	PROPN
ejpam-6540	177	8	c5	c5	PROPN
ejpam-6540	177	9	,	,	PUNCT
ejpam-6540	177	10	the	the	DET
ejpam-6540	177	11	set	set	NOUN
ejpam-6540	177	12	0wh	0wh	ADJ
ejpam-6540	177	13	resolves	resolve	NOUN
ejpam-6540	177	14	all	all	DET
ejpam-6540	177	15	the	the	DET
ejpam-6540	177	16	vertices	vertex	NOUN
ejpam-6540	177	17	in	in	ADP
ejpam-6540	177	18	v	v	NOUN
ejpam-6540	177	19	(	(	PUNCT
ejpam-6540	177	20	0sh	0sh	ADJ
ejpam-6540	177	21	c5	c5	PROPN
ejpam-6540	177	22	)	)	PUNCT
ejpam-6540	177	23	.	.	PUNCT
ejpam-6540	178	1	by	by	ADP
ejpam-6540	178	2	the	the	DET
ejpam-6540	178	3	construction	construction	NOUN
ejpam-6540	178	4	,	,	PUNCT
ejpam-6540	178	5	01h	01h	NOUN
ejpam-6540	178	6	,	,	PUNCT
ejpam-6540	178	7	04h	04h	NOUN
ejpam-6540	178	8	∈	∈	PROPN
ejpam-6540	178	9	0wh	0wh	NOUN
ejpam-6540	178	10	but	but	CCONJ
ejpam-6540	178	11	these	these	DET
ejpam-6540	178	12	vertices	vertex	NOUN
ejpam-6540	178	13	becomes	become	VERB
ejpam-6540	178	14	pseudo	pseudo	NOUN
ejpam-6540	178	15	resolvers	resolver	NOUN
ejpam-6540	178	16	for	for	ADP
ejpam-6540	178	17	0sh	0sh	ADJ
ejpam-6540	178	18	c5	c5	PROPN
ejpam-6540	178	19	as	as	ADP
ejpam-6540	178	20	for	for	ADP
ejpam-6540	178	21	every	every	DET
ejpam-6540	178	22	x	x	SYM
ejpam-6540	178	23	∈	∈	PROPN
ejpam-6540	178	24	0sh	0sh	NOUN
ejpam-6540	178	25	c5	c5	PROPN
ejpam-6540	178	26	,	,	PUNCT
ejpam-6540	178	27	we	we	PRON
ejpam-6540	178	28	have	have	VERB
ejpam-6540	178	29	dsh+1	dsh+1	NOUN
ejpam-6540	178	30	c5	c5	PROPN
ejpam-6540	178	31	(	(	PUNCT
ejpam-6540	178	32	x	x	PROPN
ejpam-6540	178	33	,	,	PUNCT
ejpam-6540	178	34	t	t	PROPN
ejpam-6540	178	35	)	)	PUNCT
ejpam-6540	178	36	=	=	PUNCT
ejpam-6540	178	37	dsh+1	dsh+1	NOUN
ejpam-6540	178	38	c5	c5	PROPN
ejpam-6540	178	39	(	(	PUNCT
ejpam-6540	178	40	x	x	X
ejpam-6540	178	41	,	,	PUNCT
ejpam-6540	178	42	01h	01h	NUM
ejpam-6540	178	43	)	)	PUNCT
ejpam-6540	179	1	+	+	CCONJ
ejpam-6540	179	2	dsh+1	dsh+1	NOUN
ejpam-6540	179	3	c5	c5	PROPN
ejpam-6540	179	4	(	(	PUNCT
ejpam-6540	179	5	01h	01h	NOUN
ejpam-6540	179	6	,	,	PUNCT
ejpam-6540	179	7	t	t	PROPN
ejpam-6540	179	8	)	)	PUNCT
ejpam-6540	179	9	,	,	PUNCT
ejpam-6540	179	10	for	for	ADP
ejpam-6540	179	11	t	t	PROPN
ejpam-6540	179	12	∈	∈	PROPN
ejpam-6540	179	13	wh+1	wh+1	PRON
ejpam-6540	179	14	∩	∩	PROPN
ejpam-6540	179	15	2sh	2sh	ADJ
ejpam-6540	179	16	c5	c5	PROPN
ejpam-6540	179	17	and	and	CCONJ
ejpam-6540	179	18	dsh+1	dsh+1	PROPN
ejpam-6540	179	19	c5	c5	PROPN
ejpam-6540	179	20	(	(	PUNCT
ejpam-6540	179	21	x	x	PROPN
ejpam-6540	179	22	,	,	PUNCT
ejpam-6540	179	23	t	t	PROPN
ejpam-6540	179	24	)	)	PUNCT
ejpam-6540	179	25	=	=	PUNCT
ejpam-6540	179	26	dsh+1	dsh+1	NOUN
ejpam-6540	179	27	c5	c5	PROPN
ejpam-6540	179	28	(	(	PUNCT
ejpam-6540	179	29	x	x	X
ejpam-6540	179	30	,	,	PUNCT
ejpam-6540	179	31	04h	04h	NOUN
ejpam-6540	179	32	)	)	PUNCT
ejpam-6540	179	33	+	+	NUM
ejpam-6540	179	34	dsh+1	dsh+1	NOUN
ejpam-6540	179	35	c5	c5	PROPN
ejpam-6540	179	36	(	(	PUNCT
ejpam-6540	179	37	04h	04h	X
ejpam-6540	179	38	,	,	PUNCT
ejpam-6540	179	39	t	t	PROPN
ejpam-6540	179	40	)	)	PUNCT
ejpam-6540	179	41	,	,	PUNCT
ejpam-6540	179	42	for	for	ADP
ejpam-6540	179	43	t	t	PROPN
ejpam-6540	179	44	∈	∈	PROPN
ejpam-6540	179	45	wh+1∩3sh	wh+1∩3sh	PROPN
ejpam-6540	179	46	c5	c5	PROPN
ejpam-6540	179	47	.	.	PUNCT
ejpam-6540	180	1	this	this	PRON
ejpam-6540	180	2	implies	imply	VERB
ejpam-6540	180	3	that	that	SCONJ
ejpam-6540	180	4	r(u|w	r(u|w	PROPN
ejpam-6540	180	5	h+1	h+1	NOUN
ejpam-6540	180	6	)	)	PUNCT
ejpam-6540	180	7	̸=	̸=	PROPN
ejpam-6540	180	8	r(v|w	r(v|w	VERB
ejpam-6540	180	9	h+1	h+1	VERB
ejpam-6540	180	10	)	)	PUNCT
ejpam-6540	180	11	for	for	ADP
ejpam-6540	180	12	u	u	NOUN
ejpam-6540	180	13	̸=	̸=	PROPN
ejpam-6540	180	14	v	v	NOUN
ejpam-6540	180	15	and	and	CCONJ
ejpam-6540	180	16	u1	u1	NOUN
ejpam-6540	180	17	=	=	SYM
ejpam-6540	180	18	v1	v1	NOUN
ejpam-6540	180	19	.	.	PUNCT
ejpam-6540	181	1	thus	thus	ADV
ejpam-6540	181	2	,	,	PUNCT
ejpam-6540	181	3	we	we	PRON
ejpam-6540	181	4	conclude	conclude	VERB
ejpam-6540	181	5	that	that	SCONJ
ejpam-6540	181	6	wh+1	wh+1	PROPN
ejpam-6540	181	7	is	be	AUX
ejpam-6540	181	8	a	a	DET
ejpam-6540	181	9	rs	rs	NOUN
ejpam-6540	181	10	of	of	ADP
ejpam-6540	181	11	sh+1	sh+1	PROPN
ejpam-6540	181	12	c5	c5	PROPN
ejpam-6540	181	13	.	.	PUNCT
ejpam-6540	182	1	for	for	ADP
ejpam-6540	182	2	h	h	PROPN
ejpam-6540	182	3	≥	≥	NOUN
ejpam-6540	182	4	4	4	NUM
ejpam-6540	182	5	,	,	PUNCT
ejpam-6540	182	6	|wh|	|wh|	PROPN
ejpam-6540	182	7	=	=	SYM
ejpam-6540	183	1	5(|wh−1|	5(|wh−1|	NUM
ejpam-6540	183	2	−	−	NOUN
ejpam-6540	183	3	2	2	NUM
ejpam-6540	183	4	)	)	PUNCT
ejpam-6540	183	5	,	,	PUNCT
ejpam-6540	183	6	where	where	SCONJ
ejpam-6540	183	7	|w3|	|w3|	NOUN
ejpam-6540	183	8	=	=	NOUN
ejpam-6540	183	9	5	5	X
ejpam-6540	183	10	.	.	PUNCT
ejpam-6540	184	1	solving	solve	VERB
ejpam-6540	184	2	this	this	DET
ejpam-6540	184	3	recurrence	recurrence	NOUN
ejpam-6540	184	4	relation	relation	NOUN
ejpam-6540	184	5	,	,	PUNCT
ejpam-6540	184	6	we	we	PRON
ejpam-6540	184	7	get	get	VERB
ejpam-6540	184	8	|wh|	|wh|	NUM
ejpam-6540	184	9	=	=	SYM
ejpam-6540	184	10	5(1	5(1	PROPN
ejpam-6540	184	11	+	+	NUM
ejpam-6540	184	12	5h−3	5h−3	NUM
ejpam-6540	184	13	)	)	PUNCT
ejpam-6540	184	14	2	2	NUM
ejpam-6540	184	15	for	for	ADP
ejpam-6540	184	16	h	h	PROPN
ejpam-6540	184	17	≥	≥	NOUN
ejpam-6540	184	18	3	3	NUM
ejpam-6540	184	19	.	.	PUNCT
ejpam-6540	185	1	thus	thus	ADV
ejpam-6540	185	2	dim(sh	dim(sh	X
ejpam-6540	185	3	c5	c5	PROPN
ejpam-6540	185	4	)	)	PUNCT
ejpam-6540	185	5	≤	≤	ADV
ejpam-6540	186	1	5(1	5(1	NUM
ejpam-6540	186	2	+	+	SYM
ejpam-6540	186	3	5h−3	5h−3	NUM
ejpam-6540	186	4	)	)	PUNCT
ejpam-6540	186	5	2	2	NUM
ejpam-6540	186	6	.	.	PUNCT
ejpam-6540	187	1	to	to	PART
ejpam-6540	187	2	prove	prove	VERB
ejpam-6540	187	3	that	that	SCONJ
ejpam-6540	187	4	dim(sh	dim(sh	PROPN
ejpam-6540	187	5	c5	c5	PROPN
ejpam-6540	187	6	)	)	PUNCT
ejpam-6540	187	7	≥	≥	NOUN
ejpam-6540	187	8	5(1	5(1	NUM
ejpam-6540	187	9	+	+	NOUN
ejpam-6540	187	10	5h−3	5h−3	NUM
ejpam-6540	187	11	)	)	PUNCT
ejpam-6540	187	12	2	2	NUM
ejpam-6540	187	13	,	,	PUNCT
ejpam-6540	187	14	let	let	VERB
ejpam-6540	187	15	us	we	PRON
ejpam-6540	187	16	assume	assume	VERB
ejpam-6540	187	17	that	that	SCONJ
ejpam-6540	187	18	there	there	PRON
ejpam-6540	187	19	exist	exist	VERB
ejpam-6540	187	20	a	a	DET
ejpam-6540	187	21	resolving	resolving	NOUN
ejpam-6540	187	22	set	set	VERB
ejpam-6540	187	23	w	w	ADP
ejpam-6540	187	24	,	,	PUNCT
ejpam-6540	187	25	such	such	ADJ
ejpam-6540	187	26	that	that	SCONJ
ejpam-6540	187	27	|w	|w	NOUN
ejpam-6540	187	28	|	|	NOUN
ejpam-6540	188	1	=	=	PUNCT
ejpam-6540	188	2	5(1	5(1	NUM
ejpam-6540	188	3	+	+	NUM
ejpam-6540	188	4	5h−3	5h−3	NUM
ejpam-6540	188	5	)	)	PUNCT
ejpam-6540	188	6	2	2	NUM
ejpam-6540	188	7	−	−	NOUN
ejpam-6540	188	8	1	1	NUM
ejpam-6540	188	9	.	.	PUNCT
ejpam-6540	189	1	then	then	ADV
ejpam-6540	189	2	by	by	ADP
ejpam-6540	189	3	pigeonhole	pigeonhole	NOUN
ejpam-6540	189	4	principle	principle	NOUN
ejpam-6540	189	5	,	,	PUNCT
ejpam-6540	189	6	there	there	PRON
ejpam-6540	189	7	exist	exist	VERB
ejpam-6540	189	8	at	at	ADV
ejpam-6540	189	9	least	least	ADV
ejpam-6540	189	10	one	one	NUM
ejpam-6540	189	11	induced	induced	ADJ
ejpam-6540	189	12	subgraph	subgraph	NOUN
ejpam-6540	189	13	i1i2	i1i2	PROPN
ejpam-6540	189	14	.	.	PUNCT
ejpam-6540	189	15	.	.	PUNCT
ejpam-6540	189	16	.	.	PUNCT
ejpam-6540	190	1	ih−2s	ih−2s	INTJ
ejpam-6540	190	2	2	2	NUM
ejpam-6540	190	3	c5	c5	PROPN
ejpam-6540	190	4	with	with	ADP
ejpam-6540	190	5	only	only	ADV
ejpam-6540	190	6	two	two	NUM
ejpam-6540	190	7	pseudo	pseudo	NOUN
ejpam-6540	190	8	resolvers	resolver	NOUN
ejpam-6540	190	9	u	u	NOUN
ejpam-6540	190	10	,	,	PUNCT
ejpam-6540	190	11	v	v	PROPN
ejpam-6540	190	12	∈	∈	PROPN
ejpam-6540	191	1	i1i2	i1i2	PUNCT
ejpam-6540	191	2	.	.	PUNCT
ejpam-6540	191	3	.	.	PUNCT
ejpam-6540	191	4	.	.	PUNCT
ejpam-6540	192	1	ih−2s	ih−2s	INTJ
ejpam-6540	192	2	2	2	NUM
ejpam-6540	192	3	c5	c5	PROPN
ejpam-6540	192	4	such	such	ADJ
ejpam-6540	192	5	that	that	SCONJ
ejpam-6540	192	6	uh	uh	INTJ
ejpam-6540	192	7	=	=	SYM
ejpam-6540	192	8	uh−1	uh−1	PROPN
ejpam-6540	192	9	=	=	PUNCT
ejpam-6540	192	10	uh−2	uh−2	PROPN
ejpam-6540	192	11	±	±	PROPN
ejpam-6540	192	12	1	1	NUM
ejpam-6540	192	13	(	(	PUNCT
ejpam-6540	192	14	mod	mod	NOUN
ejpam-6540	192	15	5	5	NUM
ejpam-6540	192	16	)	)	PUNCT
ejpam-6540	192	17	and	and	CCONJ
ejpam-6540	192	18	v(i1i2	v(i1i2	NOUN
ejpam-6540	192	19	.	.	PUNCT
ejpam-6540	192	20	.	.	PUNCT
ejpam-6540	192	21	.	.	PUNCT
ejpam-6540	193	1	ih−2s	ih−2s	PROPN
ejpam-6540	193	2	2	2	NUM
ejpam-6540	193	3	c5	c5	PROPN
ejpam-6540	193	4	)	)	PUNCT
ejpam-6540	193	5	∩w	∩w	PUNCT
ejpam-6540	194	1	=	=	PUNCT
ejpam-6540	194	2	∅.	∅.	VERB
ejpam-6540	194	3	then	then	ADV
ejpam-6540	194	4	we	we	PRON
ejpam-6540	194	5	have	have	AUX
ejpam-6540	194	6	either	either	PRON
ejpam-6540	194	7	r(i1	r(i1	VERB
ejpam-6540	194	8	.	.	PUNCT
ejpam-6540	194	9	.	.	PUNCT
ejpam-6540	194	10	.	.	PUNCT
ejpam-6540	195	1	ih−2(ih−2	ih−2(ih−2	PROPN
ejpam-6540	195	2	−	−	PROPN
ejpam-6540	196	1	1)(ih−2	1)(ih−2	NUM
ejpam-6540	196	2	+	+	CCONJ
ejpam-6540	196	3	2)|w	2)|w	NUM
ejpam-6540	196	4	)	)	PUNCT
ejpam-6540	197	1	=	=	NOUN
ejpam-6540	197	2	r(i1	r(i1	NOUN
ejpam-6540	197	3	.	.	PUNCT
ejpam-6540	197	4	.	.	PUNCT
ejpam-6540	197	5	.	.	PUNCT
ejpam-6540	198	1	ih−2(ih−2	ih−2(ih−2	PROPN
ejpam-6540	198	2	−	−	PROPN
ejpam-6540	199	1	2)(ih−2	2)(ih−2	NUM
ejpam-6540	199	2	−	−	PROPN
ejpam-6540	199	3	1)|w	1)|w	NUM
ejpam-6540	199	4	)	)	PUNCT
ejpam-6540	199	5	or	or	CCONJ
ejpam-6540	199	6	r(i1	r(i1	VERB
ejpam-6540	199	7	.	.	PUNCT
ejpam-6540	199	8	.	.	PUNCT
ejpam-6540	199	9	.	.	PUNCT
ejpam-6540	200	1	ih−2(ih−2	ih−2(ih−2	PROPN
ejpam-6540	200	2	+	+	CCONJ
ejpam-6540	201	1	1)(ih−2	1)(ih−2	NUM
ejpam-6540	201	2	−	−	NOUN
ejpam-6540	201	3	2)|w	2)|w	NUM
ejpam-6540	201	4	)	)	PUNCT
ejpam-6540	201	5	=	=	NOUN
ejpam-6540	201	6	r(i1	r(i1	NOUN
ejpam-6540	201	7	.	.	PUNCT
ejpam-6540	201	8	.	.	PUNCT
ejpam-6540	201	9	.	.	PUNCT
ejpam-6540	202	1	ih−2(ih−2	ih−2(ih−2	PROPN
ejpam-6540	202	2	+	+	CCONJ
ejpam-6540	202	3	2)(ih−2	2)(ih−2	NUM
ejpam-6540	203	1	+	+	NUM
ejpam-6540	203	2	1)|w	1)|w	NUM
ejpam-6540	203	3	)	)	PUNCT
ejpam-6540	203	4	,	,	PUNCT
ejpam-6540	203	5	k.	k.	PROPN
ejpam-6540	203	6	b.	b.	PROPN
ejpam-6540	203	7	dharan	dharan	PROPN
ejpam-6540	203	8	,	,	PUNCT
ejpam-6540	203	9	s.	s.	PROPN
ejpam-6540	203	10	radha	radha	PROPN
ejpam-6540	203	11	/	/	PUNCT
ejpam-6540	203	12	eur	eur	PROPN
ejpam-6540	203	13	.	.	PUNCT
ejpam-6540	204	1	j.	j.	PROPN
ejpam-6540	204	2	pure	pure	PROPN
ejpam-6540	204	3	appl	appl	PROPN
ejpam-6540	204	4	.	.	PROPN
ejpam-6540	204	5	math	math	PROPN
ejpam-6540	204	6	,	,	PUNCT
ejpam-6540	204	7	18	18	NUM
ejpam-6540	204	8	(	(	PUNCT
ejpam-6540	204	9	3	3	NUM
ejpam-6540	204	10	)	)	PUNCT
ejpam-6540	204	11	(	(	PUNCT
ejpam-6540	204	12	2025	2025	NUM
ejpam-6540	204	13	)	)	PUNCT
ejpam-6540	204	14	,	,	PUNCT
ejpam-6540	204	15	6540	6540	NUM
ejpam-6540	204	16	10	10	NUM
ejpam-6540	204	17	of	of	ADP
ejpam-6540	204	18	17	17	NUM
ejpam-6540	204	19	a	a	DET
ejpam-6540	204	20	contradiction	contradiction	NOUN
ejpam-6540	204	21	.	.	PUNCT
ejpam-6540	205	1	this	this	PRON
ejpam-6540	205	2	leads	lead	VERB
ejpam-6540	205	3	to	to	ADP
ejpam-6540	205	4	dim(sh	dim(sh	PROPN
ejpam-6540	205	5	c5	c5	PROPN
ejpam-6540	205	6	)	)	PUNCT
ejpam-6540	205	7	≥	≥	NOUN
ejpam-6540	205	8	5(1	5(1	NUM
ejpam-6540	205	9	+	+	NOUN
ejpam-6540	205	10	5h−3	5h−3	NUM
ejpam-6540	205	11	)	)	PUNCT
ejpam-6540	205	12	2	2	NUM
ejpam-6540	205	13	.	.	PUNCT
ejpam-6540	206	1	hence	hence	ADV
ejpam-6540	206	2	,	,	PUNCT
ejpam-6540	206	3	dim(sh	dim(sh	X
ejpam-6540	206	4	c5	c5	PROPN
ejpam-6540	206	5	)	)	PUNCT
ejpam-6540	207	1	=	=	PUNCT
ejpam-6540	208	1	5(1	5(1	NUM
ejpam-6540	208	2	+	+	NUM
ejpam-6540	208	3	5h−3	5h−3	NUM
ejpam-6540	208	4	)	)	PUNCT
ejpam-6540	208	5	2	2	NUM
ejpam-6540	208	6	for	for	ADP
ejpam-6540	208	7	h	h	PROPN
ejpam-6540	208	8	≥	≥	NOUN
ejpam-6540	208	9	3	3	NUM
ejpam-6540	208	10	.	.	PUNCT
ejpam-6540	208	11	lemma	lemma	PROPN
ejpam-6540	208	12	1	1	X
ejpam-6540	208	13	.	.	PUNCT
ejpam-6540	209	1	let	let	VERB
ejpam-6540	209	2	r3	r3	PROPN
ejpam-6540	209	3	=	=	SYM
ejpam-6540	209	4	{	{	PUNCT
ejpam-6540	209	5	x((x+	x((x+	PROPN
ejpam-6540	209	6	2)mod	2)mod	NUM
ejpam-6540	209	7	5)2	5)2	NUM
ejpam-6540	209	8	:	:	PUNCT
ejpam-6540	209	9	x	x	SYM
ejpam-6540	209	10	∈	∈	NOUN
ejpam-6540	209	11	z5	z5	X
ejpam-6540	209	12	}	}	PUNCT
ejpam-6540	209	13	.	.	PUNCT
ejpam-6540	210	1	for	for	ADP
ejpam-6540	210	2	h	h	PROPN
ejpam-6540	210	3	≥	≥	NOUN
ejpam-6540	210	4	4	4	NUM
ejpam-6540	210	5	,	,	PUNCT
ejpam-6540	210	6	rh	rh	PROPN
ejpam-6540	210	7	=	=	PUNCT
ejpam-6540	210	8	⋃4	⋃4	PROPN
ejpam-6540	210	9	i=0	i=0	PROPN
ejpam-6540	210	10	irh−1	irh−1	PROPN
ejpam-6540	210	11	\	\	PROPN
ejpam-6540	210	12	{	{	PUNCT
ejpam-6540	210	13	i((i+	i((i+	NUM
ejpam-6540	210	14	1)mod	1)mod	NUM
ejpam-6540	210	15	5)h−2((i+	5)h−2((i+	NUM
ejpam-6540	210	16	3)mod	3)mod	NUM
ejpam-6540	210	17	5	5	NUM
ejpam-6540	210	18	)	)	PUNCT
ejpam-6540	210	19	,	,	PUNCT
ejpam-6540	210	20	i((i−	i((i−	PROPN
ejpam-6540	210	21	1)mod	1)mod	NUM
ejpam-6540	210	22	5)h−2((i−	5)h−2((i−	NUM
ejpam-6540	210	23	3)mod	3)mod	NUM
ejpam-6540	210	24	5	5	NUM
ejpam-6540	210	25	)	)	PUNCT
ejpam-6540	210	26	}	}	PUNCT
ejpam-6540	210	27	is	be	AUX
ejpam-6540	210	28	a	a	DET
ejpam-6540	210	29	rs	rs	NOUN
ejpam-6540	210	30	for	for	ADP
ejpam-6540	210	31	sh	sh	PROPN
ejpam-6540	210	32	c5	c5	PROPN
ejpam-6540	210	33	.	.	PUNCT
ejpam-6540	211	1	proof	proof	NOUN
ejpam-6540	211	2	.	.	PUNCT
ejpam-6540	212	1	the	the	DET
ejpam-6540	212	2	case	case	NOUN
ejpam-6540	212	3	h	h	NOUN
ejpam-6540	212	4	=	=	NOUN
ejpam-6540	212	5	3	3	NUM
ejpam-6540	212	6	can	can	AUX
ejpam-6540	212	7	be	be	AUX
ejpam-6540	212	8	verified	verify	VERB
ejpam-6540	212	9	directly	directly	ADV
ejpam-6540	212	10	.	.	PUNCT
ejpam-6540	213	1	assume	assume	VERB
ejpam-6540	213	2	,	,	PUNCT
ejpam-6540	213	3	as	as	ADP
ejpam-6540	213	4	the	the	DET
ejpam-6540	213	5	induction	induction	NOUN
ejpam-6540	213	6	hypothesis	hypothesis	NOUN
ejpam-6540	213	7	,	,	PUNCT
ejpam-6540	213	8	that	that	SCONJ
ejpam-6540	213	9	the	the	DET
ejpam-6540	213	10	claim	claim	NOUN
ejpam-6540	213	11	holds	hold	VERB
ejpam-6540	213	12	for	for	ADP
ejpam-6540	213	13	h	h	PRON
ejpam-6540	213	14	≥	≥	NOUN
ejpam-6540	213	15	4	4	NUM
ejpam-6540	213	16	.	.	PUNCT
ejpam-6540	214	1	we	we	PRON
ejpam-6540	214	2	proceed	proceed	VERB
ejpam-6540	214	3	to	to	PART
ejpam-6540	214	4	verify	verify	VERB
ejpam-6540	214	5	the	the	DET
ejpam-6540	214	6	claim	claim	NOUN
ejpam-6540	214	7	for	for	ADP
ejpam-6540	214	8	h	h	NOUN
ejpam-6540	214	9	+	+	NOUN
ejpam-6540	214	10	1	1	X
ejpam-6540	214	11	.	.	PUNCT
ejpam-6540	214	12	let	let	VERB
ejpam-6540	214	13	p	p	NOUN
ejpam-6540	214	14	=	=	X
ejpam-6540	214	15	p1p2	p1p2	PROPN
ejpam-6540	214	16	.	.	PUNCT
ejpam-6540	214	17	.	.	PUNCT
ejpam-6540	214	18	.	.	PUNCT
ejpam-6540	215	1	ph+1	ph+1	PROPN
ejpam-6540	215	2	and	and	CCONJ
ejpam-6540	215	3	q	q	NOUN
ejpam-6540	215	4	=	=	SYM
ejpam-6540	215	5	q1q2	q1q2	PROPN
ejpam-6540	215	6	.	.	PUNCT
ejpam-6540	215	7	.	.	PUNCT
ejpam-6540	216	1	.	.	PUNCT
ejpam-6540	217	1	qh+1	qh+1	INTJ
ejpam-6540	217	2	be	be	AUX
ejpam-6540	217	3	two	two	NUM
ejpam-6540	217	4	arbitrary	arbitrary	ADJ
ejpam-6540	217	5	vertices	vertex	NOUN
ejpam-6540	217	6	of	of	ADP
ejpam-6540	217	7	sh+1	sh+1	PROPN
ejpam-6540	217	8	c5	c5	PROPN
ejpam-6540	217	9	.	.	PUNCT
ejpam-6540	218	1	case	case	NOUN
ejpam-6540	218	2	1	1	NUM
ejpam-6540	218	3	:	:	PUNCT
ejpam-6540	218	4	p1	p1	PROPN
ejpam-6540	218	5	−	−	PROPN
ejpam-6540	218	6	q1	q1	PROPN
ejpam-6540	218	7	≡	≡	PROPN
ejpam-6540	218	8	±1	±1	VERB
ejpam-6540	218	9	mod	mod	PROPN
ejpam-6540	218	10	5	5	NUM
ejpam-6540	218	11	suppose	suppose	VERB
ejpam-6540	218	12	there	there	PRON
ejpam-6540	218	13	exists	exist	VERB
ejpam-6540	218	14	some	some	DET
ejpam-6540	218	15	vertices	vertex	NOUN
ejpam-6540	218	16	x	x	X
ejpam-6540	218	17	∈	∈	NOUN
ejpam-6540	218	18	p1s	p1	NOUN
ejpam-6540	218	19	h	h	NOUN
ejpam-6540	218	20	c5	c5	PROPN
ejpam-6540	218	21	and	and	CCONJ
ejpam-6540	218	22	y	y	PROPN
ejpam-6540	218	23	∈	∈	PROPN
ejpam-6540	218	24	q1s	q1s	NOUN
ejpam-6540	218	25	h	h	NOUN
ejpam-6540	218	26	c5	c5	PROPN
ejpam-6540	218	27	such	such	ADJ
ejpam-6540	218	28	that	that	SCONJ
ejpam-6540	218	29	r(x|rh+1∩p1sh	r(x|rh+1∩p1sh	PROPN
ejpam-6540	218	30	c5	c5	PROPN
ejpam-6540	218	31	)	)	PUNCT
ejpam-6540	219	1	=	=	PUNCT
ejpam-6540	219	2	r(y|rh+1	r(y|rh+1	PROPN
ejpam-6540	219	3	∩	∩	NOUN
ejpam-6540	219	4	p1s	p1s	PUNCT
ejpam-6540	219	5	h	h	NOUN
ejpam-6540	219	6	c5	c5	PROPN
ejpam-6540	219	7	)	)	PUNCT
ejpam-6540	220	1	but	but	CCONJ
ejpam-6540	220	2	there	there	PRON
ejpam-6540	220	3	exists	exist	VERB
ejpam-6540	220	4	t	t	PROPN
ejpam-6540	220	5	∈	∈	PROPN
ejpam-6540	220	6	rh+1	rh+1	NOUN
ejpam-6540	220	7	∩	∩	NOUN
ejpam-6540	220	8	(	(	PUNCT
ejpam-6540	220	9	(	(	PUNCT
ejpam-6540	220	10	q1	q1	NOUN
ejpam-6540	220	11	+	+	CCONJ
ejpam-6540	220	12	1	1	NUM
ejpam-6540	220	13	)	)	PUNCT
ejpam-6540	220	14	mod	mod	NOUN
ejpam-6540	221	1	5)sh	5)sh	PROPN
ejpam-6540	221	2	c5	c5	PROPN
ejpam-6540	221	3	such	such	ADJ
ejpam-6540	221	4	that	that	SCONJ
ejpam-6540	221	5	dsh	dsh	PROPN
ejpam-6540	221	6	c5	c5	PROPN
ejpam-6540	221	7	(	(	PUNCT
ejpam-6540	221	8	x	x	PROPN
ejpam-6540	221	9	,	,	PUNCT
ejpam-6540	221	10	t	t	PROPN
ejpam-6540	221	11	)	)	PUNCT
ejpam-6540	221	12	̸=	̸=	PROPN
ejpam-6540	221	13	dsh	dsh	PROPN
ejpam-6540	221	14	c5	c5	PROPN
ejpam-6540	221	15	(	(	PUNCT
ejpam-6540	221	16	y	y	PROPN
ejpam-6540	221	17	,	,	PUNCT
ejpam-6540	221	18	t	t	PROPN
ejpam-6540	221	19	)	)	PUNCT
ejpam-6540	221	20	when	when	SCONJ
ejpam-6540	221	21	p1	p1	PROPN
ejpam-6540	221	22	<	<	X
ejpam-6540	221	23	q1	q1	PROPN
ejpam-6540	221	24	or	or	CCONJ
ejpam-6540	221	25	there	there	ADV
ejpam-6540	221	26	exists	exist	VERB
ejpam-6540	221	27	t	t	PROPN
ejpam-6540	221	28	∈	∈	PROPN
ejpam-6540	221	29	rh+1∩((p1	rh+1∩((p1	PROPN
ejpam-6540	221	30	+	+	PROPN
ejpam-6540	221	31	1	1	NUM
ejpam-6540	221	32	)	)	PUNCT
ejpam-6540	221	33	mod	mod	NOUN
ejpam-6540	222	1	5)sh	5)sh	PROPN
ejpam-6540	222	2	c5	c5	PROPN
ejpam-6540	222	3	such	such	ADJ
ejpam-6540	222	4	that	that	SCONJ
ejpam-6540	222	5	dsh	dsh	PROPN
ejpam-6540	222	6	c5	c5	PROPN
ejpam-6540	222	7	(	(	PUNCT
ejpam-6540	222	8	x	x	PROPN
ejpam-6540	222	9	,	,	PUNCT
ejpam-6540	222	10	t	t	PROPN
ejpam-6540	222	11	)	)	PUNCT
ejpam-6540	222	12	̸=	̸=	PROPN
ejpam-6540	222	13	dsh	dsh	PROPN
ejpam-6540	222	14	c5	c5	PROPN
ejpam-6540	222	15	(	(	PUNCT
ejpam-6540	222	16	y	y	PROPN
ejpam-6540	222	17	,	,	PUNCT
ejpam-6540	222	18	t	t	PROPN
ejpam-6540	222	19	)	)	PUNCT
ejpam-6540	222	20	when	when	SCONJ
ejpam-6540	222	21	p1	p1	PROPN
ejpam-6540	222	22	>	>	X
ejpam-6540	222	23	q1	q1	PROPN
ejpam-6540	222	24	.	.	PUNCT
ejpam-6540	223	1	this	this	PRON
ejpam-6540	223	2	implies	imply	VERB
ejpam-6540	223	3	that	that	SCONJ
ejpam-6540	223	4	r(x|rh+1	r(x|rh+1	NOUN
ejpam-6540	223	5	)	)	PUNCT
ejpam-6540	223	6	̸=	̸=	PROPN
ejpam-6540	223	7	r(y|rh+1	r(y|rh+1	PROPN
ejpam-6540	223	8	)	)	PUNCT
ejpam-6540	223	9	for	for	ADP
ejpam-6540	223	10	all	all	PRON
ejpam-6540	223	11	x	x	SYM
ejpam-6540	223	12	∈	∈	PROPN
ejpam-6540	223	13	p1s	p1	NOUN
ejpam-6540	223	14	h	h	NOUN
ejpam-6540	223	15	c5	c5	PROPN
ejpam-6540	223	16	and	and	CCONJ
ejpam-6540	223	17	y	y	PROPN
ejpam-6540	223	18	∈	∈	PROPN
ejpam-6540	223	19	q1s	q1s	NOUN
ejpam-6540	223	20	h	h	NOUN
ejpam-6540	223	21	c5	c5	PROPN
ejpam-6540	223	22	.	.	PUNCT
ejpam-6540	224	1	then	then	ADV
ejpam-6540	224	2	p	p	PROPN
ejpam-6540	224	3	and	and	CCONJ
ejpam-6540	224	4	q	q	NOUN
ejpam-6540	224	5	have	have	VERB
ejpam-6540	224	6	distinct	distinct	ADJ
ejpam-6540	224	7	representation	representation	NOUN
ejpam-6540	224	8	with	with	ADP
ejpam-6540	224	9	respect	respect	NOUN
ejpam-6540	224	10	to	to	ADP
ejpam-6540	224	11	rh+1	rh+1	NOUN
ejpam-6540	224	12	when	when	SCONJ
ejpam-6540	224	13	p1	p1	PROPN
ejpam-6540	224	14	−	−	PROPN
ejpam-6540	224	15	q1	q1	PROPN
ejpam-6540	224	16	≡	≡	PROPN
ejpam-6540	224	17	±1(mod	±1(mod	PROPN
ejpam-6540	224	18	5	5	NUM
ejpam-6540	224	19	)	)	PUNCT
ejpam-6540	224	20	.	.	PUNCT
ejpam-6540	225	1	case	case	NOUN
ejpam-6540	225	2	2	2	NUM
ejpam-6540	225	3	:	:	PUNCT
ejpam-6540	225	4	p1	p1	PROPN
ejpam-6540	225	5	−	−	PROPN
ejpam-6540	225	6	q1	q1	PROPN
ejpam-6540	225	7	̸≡	̸≡	X
ejpam-6540	225	8	±1(mod	±1(mod	PROPN
ejpam-6540	225	9	5	5	NUM
ejpam-6540	225	10	)	)	PUNCT
ejpam-6540	225	11	in	in	ADP
ejpam-6540	225	12	this	this	DET
ejpam-6540	225	13	case	case	NOUN
ejpam-6540	225	14	,	,	PUNCT
ejpam-6540	225	15	we	we	PRON
ejpam-6540	225	16	have	have	VERB
ejpam-6540	225	17	dsh+1	dsh+1	NOUN
ejpam-6540	225	18	c5	c5	PROPN
ejpam-6540	225	19	(	(	PUNCT
ejpam-6540	225	20	p	p	PROPN
ejpam-6540	225	21	,	,	PUNCT
ejpam-6540	225	22	t	t	PROPN
ejpam-6540	225	23	)	)	PUNCT
ejpam-6540	225	24	<	<	X
ejpam-6540	225	25	dsh+1	dsh+1	PROPN
ejpam-6540	225	26	c5	c5	PROPN
ejpam-6540	225	27	(	(	PUNCT
ejpam-6540	225	28	q	q	PROPN
ejpam-6540	225	29	,	,	PUNCT
ejpam-6540	225	30	t	t	PROPN
ejpam-6540	225	31	)	)	PUNCT
ejpam-6540	225	32	for	for	ADP
ejpam-6540	225	33	all	all	DET
ejpam-6540	225	34	t	t	NOUN
ejpam-6540	225	35	∈	∈	NOUN
ejpam-6540	225	36	rh+1	rh+1	NOUN
ejpam-6540	225	37	∩	∩	NOUN
ejpam-6540	225	38	p1s	p1s	PUNCT
ejpam-6540	225	39	h	h	NOUN
ejpam-6540	225	40	c5	c5	PROPN
ejpam-6540	225	41	.	.	PUNCT
ejpam-6540	226	1	so	so	ADV
ejpam-6540	226	2	p	p	PROPN
ejpam-6540	226	3	and	and	CCONJ
ejpam-6540	226	4	q	q	NOUN
ejpam-6540	226	5	have	have	VERB
ejpam-6540	226	6	distinct	distinct	ADJ
ejpam-6540	226	7	representation	representation	NOUN
ejpam-6540	226	8	with	with	ADP
ejpam-6540	226	9	respect	respect	NOUN
ejpam-6540	226	10	to	to	ADP
ejpam-6540	226	11	rh+1	rh+1	NOUN
ejpam-6540	226	12	when	when	SCONJ
ejpam-6540	226	13	p1	p1	PROPN
ejpam-6540	226	14	<	<	X
ejpam-6540	226	15	q1	q1	PROPN
ejpam-6540	226	16	and	and	CCONJ
ejpam-6540	226	17	p1	p1	PROPN
ejpam-6540	226	18	−	−	PROPN
ejpam-6540	226	19	q1	q1	PROPN
ejpam-6540	226	20	̸≡	̸≡	PROPN
ejpam-6540	226	21	1(mod	1(mod	NUM
ejpam-6540	226	22	5	5	NUM
ejpam-6540	226	23	)	)	PUNCT
ejpam-6540	226	24	.	.	PUNCT
ejpam-6540	227	1	case	case	NOUN
ejpam-6540	227	2	3	3	NUM
ejpam-6540	227	3	:	:	PUNCT
ejpam-6540	227	4	p1	p1	PROPN
ejpam-6540	227	5	=	=	PROPN
ejpam-6540	227	6	q1	q1	PROPN
ejpam-6540	227	7	now	now	ADV
ejpam-6540	227	8	assume	assume	VERB
ejpam-6540	227	9	that	that	SCONJ
ejpam-6540	227	10	p1	p1	PROPN
ejpam-6540	227	11	=	=	PROPN
ejpam-6540	227	12	q1	q1	PROPN
ejpam-6540	227	13	.	.	PUNCT
ejpam-6540	228	1	we	we	PRON
ejpam-6540	228	2	may	may	AUX
ejpam-6540	228	3	assume	assume	VERB
ejpam-6540	228	4	that	that	SCONJ
ejpam-6540	228	5	p1	p1	PROPN
ejpam-6540	228	6	=	=	PROPN
ejpam-6540	228	7	q1	q1	PROPN
ejpam-6540	228	8	=	=	SYM
ejpam-6540	228	9	0	0	NUM
ejpam-6540	228	10	.	.	PUNCT
ejpam-6540	229	1	by	by	ADP
ejpam-6540	229	2	induction	induction	NOUN
ejpam-6540	229	3	and	and	CCONJ
ejpam-6540	229	4	the	the	DET
ejpam-6540	229	5	structure	structure	NOUN
ejpam-6540	229	6	of	of	ADP
ejpam-6540	229	7	sh+1	sh+1	PROPN
ejpam-6540	229	8	c5	c5	PROPN
ejpam-6540	229	9	,	,	PUNCT
ejpam-6540	229	10	the	the	DET
ejpam-6540	229	11	set	set	NOUN
ejpam-6540	229	12	0rh	0rh	NOUN
ejpam-6540	229	13	resolves	resolve	VERB
ejpam-6540	229	14	all	all	DET
ejpam-6540	229	15	the	the	DET
ejpam-6540	229	16	vertices	vertex	NOUN
ejpam-6540	229	17	in	in	ADP
ejpam-6540	229	18	v	v	NOUN
ejpam-6540	229	19	(	(	PUNCT
ejpam-6540	229	20	0sh	0sh	ADJ
ejpam-6540	229	21	c5	c5	PROPN
ejpam-6540	229	22	)	)	PUNCT
ejpam-6540	229	23	.	.	PUNCT
ejpam-6540	230	1	by	by	ADP
ejpam-6540	230	2	the	the	DET
ejpam-6540	230	3	construction	construction	NOUN
ejpam-6540	230	4	,	,	PUNCT
ejpam-6540	230	5	01h	01h	NOUN
ejpam-6540	230	6	,	,	PUNCT
ejpam-6540	230	7	04h	04h	NOUN
ejpam-6540	230	8	∈	∈	PROPN
ejpam-6540	230	9	0rh	0rh	NOUN
ejpam-6540	230	10	but	but	CCONJ
ejpam-6540	230	11	these	these	DET
ejpam-6540	230	12	vertices	vertex	NOUN
ejpam-6540	230	13	becomes	become	VERB
ejpam-6540	230	14	pseudo	pseudo	NOUN
ejpam-6540	230	15	resolvers	resolver	NOUN
ejpam-6540	230	16	for	for	ADP
ejpam-6540	230	17	0sh	0sh	ADJ
ejpam-6540	230	18	c5	c5	PROPN
ejpam-6540	230	19	as	as	ADP
ejpam-6540	230	20	for	for	ADP
ejpam-6540	230	21	every	every	DET
ejpam-6540	230	22	x	x	SYM
ejpam-6540	230	23	∈	∈	PROPN
ejpam-6540	230	24	0sh	0sh	NOUN
ejpam-6540	230	25	c5	c5	PROPN
ejpam-6540	230	26	,	,	PUNCT
ejpam-6540	230	27	we	we	PRON
ejpam-6540	230	28	have	have	VERB
ejpam-6540	230	29	dsh+1	dsh+1	NOUN
ejpam-6540	230	30	c5	c5	PROPN
ejpam-6540	230	31	(	(	PUNCT
ejpam-6540	230	32	x	x	PROPN
ejpam-6540	230	33	,	,	PUNCT
ejpam-6540	230	34	t	t	PROPN
ejpam-6540	230	35	)	)	PUNCT
ejpam-6540	230	36	=	=	PUNCT
ejpam-6540	230	37	dsh+1	dsh+1	NOUN
ejpam-6540	230	38	c5	c5	PROPN
ejpam-6540	230	39	(	(	PUNCT
ejpam-6540	230	40	x	x	X
ejpam-6540	230	41	,	,	PUNCT
ejpam-6540	230	42	01h	01h	NUM
ejpam-6540	230	43	)	)	PUNCT
ejpam-6540	231	1	+	+	CCONJ
ejpam-6540	231	2	dsh+1	dsh+1	NOUN
ejpam-6540	231	3	c5	c5	PROPN
ejpam-6540	231	4	(	(	PUNCT
ejpam-6540	231	5	01h	01h	NOUN
ejpam-6540	231	6	,	,	PUNCT
ejpam-6540	231	7	t	t	PROPN
ejpam-6540	231	8	)	)	PUNCT
ejpam-6540	231	9	,	,	PUNCT
ejpam-6540	231	10	for	for	ADP
ejpam-6540	231	11	t	t	PROPN
ejpam-6540	231	12	∈	∈	PROPN
ejpam-6540	231	13	rh+1	rh+1	NOUN
ejpam-6540	231	14	∩	∩	PROPN
ejpam-6540	231	15	2sh	2sh	ADJ
ejpam-6540	231	16	c5	c5	PROPN
ejpam-6540	231	17	and	and	CCONJ
ejpam-6540	231	18	dsh+1	dsh+1	PROPN
ejpam-6540	231	19	c5	c5	PROPN
ejpam-6540	231	20	(	(	PUNCT
ejpam-6540	231	21	x	x	PROPN
ejpam-6540	231	22	,	,	PUNCT
ejpam-6540	231	23	t	t	PROPN
ejpam-6540	231	24	)	)	PUNCT
ejpam-6540	231	25	=	=	PUNCT
ejpam-6540	231	26	dsh+1	dsh+1	NOUN
ejpam-6540	231	27	c5	c5	PROPN
ejpam-6540	231	28	(	(	PUNCT
ejpam-6540	231	29	x	x	X
ejpam-6540	231	30	,	,	PUNCT
ejpam-6540	231	31	04h)+dsh+1	04h)+dsh+1	NUM
ejpam-6540	231	32	c5	c5	PROPN
ejpam-6540	231	33	(	(	PUNCT
ejpam-6540	231	34	04h	04h	X
ejpam-6540	231	35	,	,	PUNCT
ejpam-6540	231	36	t	t	PROPN
ejpam-6540	231	37	)	)	PUNCT
ejpam-6540	231	38	,	,	PUNCT
ejpam-6540	231	39	for	for	ADP
ejpam-6540	231	40	t	t	PROPN
ejpam-6540	231	41	∈	∈	PROPN
ejpam-6540	231	42	rh+1∩3sh	rh+1∩3sh	PROPN
ejpam-6540	231	43	c5	c5	PROPN
ejpam-6540	231	44	.	.	PUNCT
ejpam-6540	232	1	this	this	PRON
ejpam-6540	232	2	implies	imply	VERB
ejpam-6540	232	3	that	that	SCONJ
ejpam-6540	232	4	r(p|rh+1	r(p|rh+1	PROPN
ejpam-6540	232	5	)	)	PUNCT
ejpam-6540	232	6	̸=	̸=	PROPN
ejpam-6540	232	7	r(q|rh+1	r(q|rh+1	PROPN
ejpam-6540	232	8	)	)	PUNCT
ejpam-6540	232	9	for	for	ADP
ejpam-6540	232	10	p	p	PROPN
ejpam-6540	232	11	̸=	̸=	PROPN
ejpam-6540	232	12	q	q	PROPN
ejpam-6540	232	13	and	and	CCONJ
ejpam-6540	232	14	p1	p1	PROPN
ejpam-6540	232	15	=	=	PROPN
ejpam-6540	232	16	q1	q1	PROPN
ejpam-6540	232	17	.	.	PUNCT
ejpam-6540	233	1	thus	thus	ADV
ejpam-6540	233	2	,	,	PUNCT
ejpam-6540	233	3	we	we	PRON
ejpam-6540	233	4	conclude	conclude	VERB
ejpam-6540	233	5	that	that	SCONJ
ejpam-6540	233	6	rh+1	rh+1	NOUN
ejpam-6540	233	7	is	be	AUX
ejpam-6540	233	8	a	a	DET
ejpam-6540	233	9	rs	rs	NOUN
ejpam-6540	233	10	of	of	ADP
ejpam-6540	233	11	sh+1	sh+1	PROPN
ejpam-6540	233	12	c5	c5	PROPN
ejpam-6540	233	13	.	.	PUNCT
ejpam-6540	234	1	to	to	PART
ejpam-6540	234	2	prove	prove	VERB
ejpam-6540	234	3	the	the	DET
ejpam-6540	234	4	dim′	dim′	NOUN
ejpam-6540	234	5	of	of	ADP
ejpam-6540	234	6	sh	sh	PROPN
ejpam-6540	234	7	c5	c5	PROPN
ejpam-6540	234	8	for	for	ADP
ejpam-6540	234	9	h	h	PROPN
ejpam-6540	234	10	≥	≥	PROPN
ejpam-6540	234	11	3	3	NUM
ejpam-6540	234	12	,	,	PUNCT
ejpam-6540	234	13	we	we	PRON
ejpam-6540	234	14	defined	define	VERB
ejpam-6540	234	15	a	a	DET
ejpam-6540	234	16	mb	mb	NOUN
ejpam-6540	234	17	rh	rh	PROPN
ejpam-6540	234	18	in	in	ADP
ejpam-6540	234	19	the	the	DET
ejpam-6540	234	20	lemma	lemma	PROPN
ejpam-6540	234	21	1	1	NUM
ejpam-6540	234	22	,	,	PUNCT
ejpam-6540	234	23	such	such	ADJ
ejpam-6540	234	24	that	that	SCONJ
ejpam-6540	234	25	rh	rh	PROPN
ejpam-6540	234	26	∩	∩	NOUN
ejpam-6540	234	27	wh	wh	AUX
ejpam-6540	234	28	=	=	PUNCT
ejpam-6540	234	29	∅.	∅.	NOUN
ejpam-6540	234	30	then	then	ADV
ejpam-6540	234	31	w	w	NOUN
ejpam-6540	235	1	′	′	NUM
ejpam-6540	236	1	h	h	NOUN
ejpam-6540	237	1	=	=	SYM
ejpam-6540	237	2	rh	rh	PROPN
ejpam-6540	237	3	∪	∪	X
ejpam-6540	237	4	wh	wh	NOUN
ejpam-6540	237	5	is	be	AUX
ejpam-6540	237	6	also	also	ADV
ejpam-6540	237	7	a	a	DET
ejpam-6540	237	8	rs	rs	NOUN
ejpam-6540	237	9	and	and	CCONJ
ejpam-6540	237	10	w	w	NOUN
ejpam-6540	237	11	′	′	NUM
ejpam-6540	237	12	h	h	NOUN
ejpam-6540	237	13	is	be	AUX
ejpam-6540	237	14	obviously	obviously	ADV
ejpam-6540	237	15	a	a	DET
ejpam-6540	237	16	ftrs	ftrs	NOUN
ejpam-6540	237	17	for	for	ADP
ejpam-6540	237	18	sh	sh	PROPN
ejpam-6540	237	19	c5	c5	PROPN
ejpam-6540	237	20	,	,	PUNCT
ejpam-6540	237	21	when	when	SCONJ
ejpam-6540	237	22	h	h	PROPN
ejpam-6540	237	23	≥	≥	VERB
ejpam-6540	237	24	3	3	NUM
ejpam-6540	237	25	and	and	CCONJ
ejpam-6540	237	26	the	the	DET
ejpam-6540	237	27	proof	proof	NOUN
ejpam-6540	237	28	for	for	ADP
ejpam-6540	237	29	w	w	PROPN
ejpam-6540	237	30	′	′	NUM
ejpam-6540	237	31	h	h	NOUN
ejpam-6540	237	32	to	to	PART
ejpam-6540	237	33	be	be	AUX
ejpam-6540	237	34	a	a	DET
ejpam-6540	237	35	ftb	ftb	NOUN
ejpam-6540	237	36	is	be	AUX
ejpam-6540	237	37	given	give	VERB
ejpam-6540	237	38	in	in	ADP
ejpam-6540	237	39	the	the	DET
ejpam-6540	237	40	following	follow	VERB
ejpam-6540	237	41	theorem	theorem	NOUN
ejpam-6540	237	42	.	.	PUNCT
ejpam-6540	238	1	theorem	theorem	NOUN
ejpam-6540	238	2	2	2	NUM
ejpam-6540	238	3	.	.	X
ejpam-6540	239	1	for	for	ADP
ejpam-6540	239	2	h	h	PROPN
ejpam-6540	239	3	≥	≥	PROPN
ejpam-6540	239	4	3	3	NUM
ejpam-6540	239	5	,	,	PUNCT
ejpam-6540	239	6	dim′(sh	dim′(sh	PROPN
ejpam-6540	239	7	c5	c5	PROPN
ejpam-6540	239	8	)	)	PUNCT
ejpam-6540	240	1	=	=	PUNCT
ejpam-6540	241	1	5(1	5(1	NUM
ejpam-6540	241	2	+	+	NUM
ejpam-6540	241	3	5h−3	5h−3	NUM
ejpam-6540	241	4	)	)	PUNCT
ejpam-6540	241	5	.	.	PUNCT
ejpam-6540	242	1	proof	proof	NOUN
ejpam-6540	242	2	.	.	PUNCT
ejpam-6540	243	1	we	we	PRON
ejpam-6540	243	2	know	know	VERB
ejpam-6540	243	3	that	that	PRON
ejpam-6540	243	4	w	w	ADP
ejpam-6540	244	1	′	′	NUM
ejpam-6540	244	2	h	h	NOUN
ejpam-6540	245	1	=	=	SYM
ejpam-6540	245	2	rh	rh	PROPN
ejpam-6540	245	3	∪	∪	X
ejpam-6540	245	4	wh	wh	NOUN
ejpam-6540	245	5	is	be	AUX
ejpam-6540	245	6	a	a	DET
ejpam-6540	245	7	ftrs	ftrs	NOUN
ejpam-6540	245	8	for	for	ADP
ejpam-6540	245	9	sh	sh	PROPN
ejpam-6540	245	10	c5	c5	PROPN
ejpam-6540	245	11	,	,	PUNCT
ejpam-6540	245	12	when	when	SCONJ
ejpam-6540	245	13	h	h	PROPN
ejpam-6540	245	14	≥	≥	NOUN
ejpam-6540	245	15	3	3	X
ejpam-6540	245	16	.	.	PUNCT
ejpam-6540	246	1	this	this	PRON
ejpam-6540	246	2	implies	imply	VERB
ejpam-6540	246	3	that	that	PRON
ejpam-6540	246	4	dim′(sh	dim′(sh	PROPN
ejpam-6540	246	5	c5	c5	PROPN
ejpam-6540	246	6	)	)	PUNCT
ejpam-6540	246	7	≤	≤	ADV
ejpam-6540	247	1	5(1	5(1	NUM
ejpam-6540	247	2	+	+	SYM
ejpam-6540	247	3	5h−3	5h−3	NUM
ejpam-6540	247	4	)	)	PUNCT
ejpam-6540	247	5	,	,	PUNCT
ejpam-6540	247	6	for	for	ADP
ejpam-6540	247	7	h	h	PROPN
ejpam-6540	247	8	≥	≥	NOUN
ejpam-6540	247	9	3	3	NUM
ejpam-6540	247	10	.	.	PUNCT
ejpam-6540	248	1	now	now	ADV
ejpam-6540	248	2	,	,	PUNCT
ejpam-6540	248	3	we	we	PRON
ejpam-6540	248	4	need	need	VERB
ejpam-6540	248	5	to	to	PART
ejpam-6540	248	6	prove	prove	VERB
ejpam-6540	248	7	that	that	SCONJ
ejpam-6540	248	8	dim′(sh	dim′(sh	PROPN
ejpam-6540	248	9	c5	c5	PROPN
ejpam-6540	248	10	)	)	PUNCT
ejpam-6540	248	11	≥	≥	NOUN
ejpam-6540	248	12	5(1	5(1	NUM
ejpam-6540	248	13	+	+	CCONJ
ejpam-6540	248	14	5h−3	5h−3	NUM
ejpam-6540	248	15	)	)	PUNCT
ejpam-6540	248	16	.	.	PUNCT
ejpam-6540	249	1	suppose	suppose	VERB
ejpam-6540	249	2	that	that	SCONJ
ejpam-6540	249	3	there	there	PRON
ejpam-6540	249	4	exist	exist	VERB
ejpam-6540	249	5	a	a	DET
ejpam-6540	249	6	ftrs	ftrs	NOUN
ejpam-6540	249	7	w	w	PROPN
ejpam-6540	249	8	′	′	NOUN
ejpam-6540	249	9	,	,	PUNCT
ejpam-6540	249	10	such	such	ADJ
ejpam-6540	249	11	that	that	SCONJ
ejpam-6540	249	12	|w	|w	ADJ
ejpam-6540	249	13	′|	′|	NUM
ejpam-6540	249	14	=	=	SYM
ejpam-6540	249	15	5(1	5(1	NUM
ejpam-6540	249	16	+	+	SYM
ejpam-6540	249	17	5h−3	5h−3	NUM
ejpam-6540	249	18	)	)	PUNCT
ejpam-6540	249	19	−	−	PROPN
ejpam-6540	249	20	1	1	X
ejpam-6540	249	21	.	.	PUNCT
ejpam-6540	249	22	then	then	ADV
ejpam-6540	249	23	by	by	ADP
ejpam-6540	249	24	pigeonhole	pigeonhole	NOUN
ejpam-6540	249	25	principle	principle	NOUN
ejpam-6540	249	26	,	,	PUNCT
ejpam-6540	249	27	there	there	PRON
ejpam-6540	249	28	exists	exist	VERB
ejpam-6540	249	29	i1	i1	PROPN
ejpam-6540	249	30	,	,	PUNCT
ejpam-6540	249	31	i2	i2	PROPN
ejpam-6540	249	32	,	,	PUNCT
ejpam-6540	249	33	.	.	PUNCT
ejpam-6540	249	34	.	.	PUNCT
ejpam-6540	250	1	.	.	PUNCT
ejpam-6540	251	1	,	,	PUNCT
ejpam-6540	251	2	ih−2	ih−2	PROPN
ejpam-6540	251	3	∈	∈	PROPN
ejpam-6540	251	4	z5	z5	PROPN
ejpam-6540	251	5	,	,	PUNCT
ejpam-6540	251	6	such	such	ADJ
ejpam-6540	251	7	that	that	DET
ejpam-6540	251	8	|i1i2	|i1i2	NOUN
ejpam-6540	251	9	.	.	PUNCT
ejpam-6540	251	10	.	.	PUNCT
ejpam-6540	251	11	.	.	PUNCT
ejpam-6540	252	1	ih−2s	ih−2s	INTJ
ejpam-6540	252	2	2	2	NUM
ejpam-6540	252	3	c5	c5	PROPN
ejpam-6540	252	4	∩	∩	PROPN
ejpam-6540	252	5	w	w	ADP
ejpam-6540	252	6	′|	′|	NUM
ejpam-6540	252	7	=	=	SYM
ejpam-6540	252	8	1	1	NUM
ejpam-6540	252	9	with	with	ADP
ejpam-6540	252	10	two	two	NUM
ejpam-6540	252	11	pseudo	pseudo	NOUN
ejpam-6540	252	12	resolvers	resolver	NOUN
ejpam-6540	252	13	,	,	PUNCT
ejpam-6540	252	14	that	that	PRON
ejpam-6540	252	15	is	be	AUX
ejpam-6540	252	16	not	not	PART
ejpam-6540	252	17	sufficient	sufficient	ADJ
ejpam-6540	252	18	to	to	PART
ejpam-6540	252	19	fault	fault	AUX
ejpam-6540	252	20	-	-	PUNCT
ejpam-6540	252	21	tolerantly	tolerantly	ADV
ejpam-6540	252	22	resolve	resolve	VERB
ejpam-6540	252	23	all	all	DET
ejpam-6540	252	24	the	the	DET
ejpam-6540	252	25	vertices	vertex	NOUN
ejpam-6540	252	26	of	of	ADP
ejpam-6540	252	27	the	the	DET
ejpam-6540	252	28	induced	induced	ADJ
ejpam-6540	252	29	subgraph	subgraph	NOUN
ejpam-6540	252	30	i1i2	i1i2	PROPN
ejpam-6540	252	31	.	.	PUNCT
ejpam-6540	252	32	.	.	PUNCT
ejpam-6540	252	33	.	.	PUNCT
ejpam-6540	253	1	ih−2s	ih−2s	INTJ
ejpam-6540	253	2	2	2	NUM
ejpam-6540	253	3	c5	c5	PROPN
ejpam-6540	253	4	,	,	PUNCT
ejpam-6540	253	5	a	a	DET
ejpam-6540	253	6	contradiction	contradiction	NOUN
ejpam-6540	253	7	.	.	PUNCT
ejpam-6540	254	1	so	so	ADV
ejpam-6540	254	2	,	,	PUNCT
ejpam-6540	254	3	for	for	ADP
ejpam-6540	254	4	h	h	PROPN
ejpam-6540	254	5	≥	≥	NOUN
ejpam-6540	254	6	3	3	NUM
ejpam-6540	254	7	,	,	PUNCT
ejpam-6540	254	8	dim′(s2	dim′(s2	X
ejpam-6540	254	9	ch	ch	NOUN
ejpam-6540	254	10	)	)	PUNCT
ejpam-6540	254	11	≥	≥	NOUN
ejpam-6540	254	12	5(1	5(1	NUM
ejpam-6540	254	13	+	+	NOUN
ejpam-6540	254	14	5h−3	5h−3	NUM
ejpam-6540	254	15	)	)	PUNCT
ejpam-6540	254	16	,	,	PUNCT
ejpam-6540	254	17	implies	imply	VERB
ejpam-6540	254	18	dim′(s2	dim′(s2	PRON
ejpam-6540	254	19	ch	ch	NOUN
ejpam-6540	254	20	)	)	PUNCT
ejpam-6540	255	1	=	=	PUNCT
ejpam-6540	256	1	5(1	5(1	NUM
ejpam-6540	256	2	+	+	NUM
ejpam-6540	256	3	5h−3	5h−3	NUM
ejpam-6540	256	4	)	)	PUNCT
ejpam-6540	256	5	.	.	PUNCT
ejpam-6540	257	1	k.	k.	PROPN
ejpam-6540	257	2	b.	b.	PROPN
ejpam-6540	257	3	dharan	dharan	PROPN
ejpam-6540	257	4	,	,	PUNCT
ejpam-6540	257	5	s.	s.	PROPN
ejpam-6540	257	6	radha	radha	PROPN
ejpam-6540	257	7	/	/	PUNCT
ejpam-6540	257	8	eur	eur	PROPN
ejpam-6540	257	9	.	.	PUNCT
ejpam-6540	258	1	j.	j.	PROPN
ejpam-6540	258	2	pure	pure	PROPN
ejpam-6540	258	3	appl	appl	PROPN
ejpam-6540	258	4	.	.	PROPN
ejpam-6540	258	5	math	math	PROPN
ejpam-6540	258	6	,	,	PUNCT
ejpam-6540	258	7	18	18	NUM
ejpam-6540	258	8	(	(	PUNCT
ejpam-6540	258	9	3	3	NUM
ejpam-6540	258	10	)	)	PUNCT
ejpam-6540	258	11	(	(	PUNCT
ejpam-6540	258	12	2025	2025	NUM
ejpam-6540	258	13	)	)	PUNCT
ejpam-6540	258	14	,	,	PUNCT
ejpam-6540	258	15	6540	6540	NUM
ejpam-6540	258	16	11	11	NUM
ejpam-6540	258	17	of	of	ADP
ejpam-6540	258	18	17	17	NUM
ejpam-6540	258	19	3.2	3.2	NUM
ejpam-6540	258	20	.	.	PUNCT
ejpam-6540	259	1	edge	edge	VERB
ejpam-6540	259	2	metric	metric	ADJ
ejpam-6540	259	3	dimension	dimension	NOUN
ejpam-6540	259	4	of	of	ADP
ejpam-6540	259	5	generalized	generalized	ADJ
ejpam-6540	259	6	sierpiński	sierpiński	ADJ
ejpam-6540	259	7	networks	network	NOUN
ejpam-6540	259	8	over	over	ADP
ejpam-6540	259	9	cycle	cycle	NOUN
ejpam-6540	259	10	of	of	ADP
ejpam-6540	259	11	length	length	NOUN
ejpam-6540	259	12	five	five	NUM
ejpam-6540	260	1	we	we	PRON
ejpam-6540	260	2	can	can	AUX
ejpam-6540	260	3	easilty	easilty	PROPN
ejpam-6540	260	4	say	say	VERB
ejpam-6540	260	5	that	that	SCONJ
ejpam-6540	260	6	dime(s	dime(	VERB
ejpam-6540	260	7	1	1	NUM
ejpam-6540	260	8	c5	c5	PROPN
ejpam-6540	260	9	)	)	PUNCT
ejpam-6540	261	1	=	=	SYM
ejpam-6540	261	2	2	2	NUM
ejpam-6540	261	3	as	as	SCONJ
ejpam-6540	261	4	s1	s1	PROPN
ejpam-6540	261	5	cn	cn	PROPN
ejpam-6540	261	6	is	be	AUX
ejpam-6540	261	7	isomorphic	isomorphic	ADJ
ejpam-6540	261	8	to	to	ADP
ejpam-6540	261	9	cn	cn	PROPN
ejpam-6540	261	10	.	.	PROPN
ejpam-6540	262	1	for	for	ADP
ejpam-6540	262	2	s2	s2	PROPN
ejpam-6540	262	3	c5	c5	PROPN
ejpam-6540	262	4	,	,	PUNCT
ejpam-6540	262	5	let	let	VERB
ejpam-6540	262	6	w2	w2	NOUN
ejpam-6540	262	7	=	=	PRON
ejpam-6540	262	8	{	{	PUNCT
ejpam-6540	262	9	02	02	NUM
ejpam-6540	262	10	,	,	PUNCT
ejpam-6540	262	11	20	20	NUM
ejpam-6540	262	12	}	}	PUNCT
ejpam-6540	262	13	be	be	AUX
ejpam-6540	262	14	the	the	DET
ejpam-6540	262	15	subset	subset	NOUN
ejpam-6540	262	16	of	of	ADP
ejpam-6540	262	17	v(s2	v(s2	PROPN
ejpam-6540	262	18	c5	c5	PROPN
ejpam-6540	262	19	)	)	PUNCT
ejpam-6540	262	20	.	.	PUNCT
ejpam-6540	263	1	from	from	ADP
ejpam-6540	263	2	figure	figure	NOUN
ejpam-6540	263	3	4	4	NUM
ejpam-6540	263	4	,	,	PUNCT
ejpam-6540	263	5	we	we	PRON
ejpam-6540	263	6	can	can	AUX
ejpam-6540	263	7	easily	easily	ADV
ejpam-6540	263	8	verify	verify	VERB
ejpam-6540	263	9	that	that	SCONJ
ejpam-6540	263	10	each	each	DET
ejpam-6540	263	11	edges	edge	NOUN
ejpam-6540	263	12	having	have	VERB
ejpam-6540	263	13	unique	unique	ADJ
ejpam-6540	263	14	representation	representation	NOUN
ejpam-6540	263	15	with	with	ADP
ejpam-6540	263	16	respect	respect	NOUN
ejpam-6540	263	17	to	to	ADP
ejpam-6540	263	18	w2	w2	NOUN
ejpam-6540	263	19	and	and	CCONJ
ejpam-6540	263	20	dime(s	dime(	VERB
ejpam-6540	263	21	2	2	NUM
ejpam-6540	263	22	c5	c5	PROPN
ejpam-6540	263	23	)	)	PUNCT
ejpam-6540	263	24	can	can	AUX
ejpam-6540	263	25	not	not	PART
ejpam-6540	263	26	be	be	AUX
ejpam-6540	263	27	less	less	ADJ
ejpam-6540	263	28	than	than	ADP
ejpam-6540	263	29	2	2	NUM
ejpam-6540	263	30	as	as	SCONJ
ejpam-6540	263	31	it	it	PRON
ejpam-6540	263	32	is	be	AUX
ejpam-6540	263	33	not	not	PART
ejpam-6540	263	34	isomorphic	isomorphic	ADJ
ejpam-6540	263	35	to	to	ADP
ejpam-6540	263	36	path	path	NOUN
ejpam-6540	263	37	graph	graph	NOUN
ejpam-6540	263	38	.	.	PUNCT
ejpam-6540	264	1	for	for	ADP
ejpam-6540	264	2	s3	s3	PROPN
ejpam-6540	264	3	c5	c5	PROPN
ejpam-6540	264	4	,	,	PUNCT
ejpam-6540	264	5	let	let	VERB
ejpam-6540	264	6	w3	w3	PROPN
ejpam-6540	264	7	=	=	SYM
ejpam-6540	264	8	{	{	PUNCT
ejpam-6540	264	9	022	022	PROPN
ejpam-6540	264	10	,	,	PUNCT
ejpam-6540	264	11	133	133	NUM
ejpam-6540	264	12	,	,	PUNCT
ejpam-6540	264	13	244	244	NUM
ejpam-6540	264	14	,	,	PUNCT
ejpam-6540	264	15	300	300	NUM
ejpam-6540	264	16	,	,	PUNCT
ejpam-6540	264	17	411	411	NUM
ejpam-6540	264	18	}	}	PUNCT
ejpam-6540	264	19	be	be	AUX
ejpam-6540	264	20	the	the	DET
ejpam-6540	264	21	subset	subset	NOUN
ejpam-6540	264	22	of	of	ADP
ejpam-6540	264	23	v	v	NOUN
ejpam-6540	264	24	(	(	PUNCT
ejpam-6540	264	25	s3	s3	PROPN
ejpam-6540	264	26	c5	c5	PROPN
ejpam-6540	264	27	)	)	PUNCT
ejpam-6540	264	28	.	.	PUNCT
ejpam-6540	265	1	then	then	ADV
ejpam-6540	265	2	each	each	DET
ejpam-6540	265	3	edge	edge	NOUN
ejpam-6540	265	4	incident	incident	NOUN
ejpam-6540	265	5	to	to	ADP
ejpam-6540	265	6	v(0s2	v(0s2	PROPN
ejpam-6540	265	7	c5	c5	PROPN
ejpam-6540	265	8	)	)	PUNCT
ejpam-6540	265	9	is	be	AUX
ejpam-6540	265	10	resolved	resolve	VERB
ejpam-6540	265	11	by	by	ADP
ejpam-6540	265	12	the	the	DET
ejpam-6540	265	13	vertices	vertex	NOUN
ejpam-6540	265	14	in	in	ADP
ejpam-6540	265	15	{	{	PUNCT
ejpam-6540	265	16	022	022	PROPN
ejpam-6540	265	17	,	,	PUNCT
ejpam-6540	265	18	133	133	NUM
ejpam-6540	265	19	,	,	PUNCT
ejpam-6540	265	20	411	411	NUM
ejpam-6540	265	21	}	}	PUNCT
ejpam-6540	265	22	where	where	SCONJ
ejpam-6540	265	23	the	the	DET
ejpam-6540	265	24	vertices	vertex	NOUN
ejpam-6540	265	25	011	011	NUM
ejpam-6540	265	26	,	,	PUNCT
ejpam-6540	265	27	044	044	NUM
ejpam-6540	265	28	acts	act	NOUN
ejpam-6540	265	29	as	as	ADP
ejpam-6540	265	30	an	an	DET
ejpam-6540	265	31	pseudo	pseudo	NOUN
ejpam-6540	265	32	resolver	resolver	NOUN
ejpam-6540	265	33	for	for	ADP
ejpam-6540	265	34	the	the	DET
ejpam-6540	265	35	edges	edge	NOUN
ejpam-6540	265	36	incident	incident	NOUN
ejpam-6540	265	37	with	with	ADP
ejpam-6540	265	38	v(0s2	v(0s2	PROPN
ejpam-6540	265	39	c5	c5	PROPN
ejpam-6540	265	40	)	)	PUNCT
ejpam-6540	265	41	.	.	PUNCT
ejpam-6540	266	1	now	now	ADV
ejpam-6540	266	2	,	,	PUNCT
ejpam-6540	266	3	suppose	suppose	VERB
ejpam-6540	266	4	that	that	SCONJ
ejpam-6540	266	5	there	there	PRON
ejpam-6540	266	6	exists	exist	VERB
ejpam-6540	266	7	two	two	NUM
ejpam-6540	266	8	edges	edge	NOUN
ejpam-6540	266	9	etu	etu	PROPN
ejpam-6540	266	10	(	(	PUNCT
ejpam-6540	266	11	t	t	PROPN
ejpam-6540	266	12	,	,	PUNCT
ejpam-6540	266	13	u	u	PROPN
ejpam-6540	266	14	∈	∈	NOUN
ejpam-6540	266	15	v(0s2	v(0s2	X
ejpam-6540	266	16	c5	c5	PROPN
ejpam-6540	266	17	)	)	PUNCT
ejpam-6540	266	18	)	)	PUNCT
ejpam-6540	266	19	and	and	CCONJ
ejpam-6540	266	20	evw	evw	PRON
ejpam-6540	266	21	(	(	PUNCT
ejpam-6540	266	22	v	v	NOUN
ejpam-6540	266	23	∈	∈	PROPN
ejpam-6540	266	24	v(is2	v(is2	PROPN
ejpam-6540	266	25	c5	c5	PROPN
ejpam-6540	266	26	)	)	PUNCT
ejpam-6540	266	27	or	or	CCONJ
ejpam-6540	266	28	w	w	PROPN
ejpam-6540	266	29	∈	∈	PROPN
ejpam-6540	266	30	v(is2	v(is2	PROPN
ejpam-6540	266	31	c5	c5	PROPN
ejpam-6540	266	32	)	)	PUNCT
ejpam-6540	266	33	,	,	PUNCT
ejpam-6540	266	34	i	i	PRON
ejpam-6540	266	35	>	>	X
ejpam-6540	266	36	0	0	NUM
ejpam-6540	266	37	)	)	PUNCT
ejpam-6540	266	38	,	,	PUNCT
ejpam-6540	266	39	such	such	ADJ
ejpam-6540	266	40	that	that	SCONJ
ejpam-6540	266	41	ds3	ds3	PROPN
ejpam-6540	266	42	c5	c5	PROPN
ejpam-6540	266	43	(	(	PUNCT
ejpam-6540	266	44	etu	etu	PROPN
ejpam-6540	266	45	,	,	PUNCT
ejpam-6540	266	46	022	022	NUM
ejpam-6540	266	47	)	)	PUNCT
ejpam-6540	266	48	=	=	SYM
ejpam-6540	266	49	ds3	ds3	PROPN
ejpam-6540	266	50	c5	c5	PROPN
ejpam-6540	266	51	(	(	PUNCT
ejpam-6540	266	52	evw	evw	PROPN
ejpam-6540	266	53	,	,	PUNCT
ejpam-6540	266	54	022	022	NUM
ejpam-6540	266	55	)	)	PUNCT
ejpam-6540	266	56	,	,	PUNCT
ejpam-6540	266	57	then	then	ADV
ejpam-6540	266	58	we	we	PRON
ejpam-6540	266	59	have	have	VERB
ejpam-6540	266	60	ds3	ds3	PROPN
ejpam-6540	266	61	c5	c5	PROPN
ejpam-6540	266	62	(	(	PUNCT
ejpam-6540	266	63	etu	etu	PROPN
ejpam-6540	266	64	,	,	PUNCT
ejpam-6540	266	65	i(i+2)2	i(i+2)2	PROPN
ejpam-6540	266	66	)	)	PUNCT
ejpam-6540	266	67	≥	≥	PROPN
ejpam-6540	266	68	ds3	ds3	PROPN
ejpam-6540	266	69	c5	c5	PROPN
ejpam-6540	266	70	(	(	PUNCT
ejpam-6540	266	71	evw	evw	PROPN
ejpam-6540	266	72	,	,	PUNCT
ejpam-6540	266	73	i(i+2)2)+1	i(i+2)2)+1	PROPN
ejpam-6540	266	74	.	.	PUNCT
ejpam-6540	267	1	this	this	PRON
ejpam-6540	267	2	implies	imply	VERB
ejpam-6540	267	3	that	that	SCONJ
ejpam-6540	267	4	edges	edge	VERB
ejpam-6540	267	5	incident	incident	NOUN
ejpam-6540	267	6	to	to	ADP
ejpam-6540	267	7	the	the	DET
ejpam-6540	267	8	vertices	vertex	NOUN
ejpam-6540	267	9	in	in	ADP
ejpam-6540	267	10	v(0s2	v(0s2	PROPN
ejpam-6540	267	11	c5	c5	PROPN
ejpam-6540	267	12	)	)	PUNCT
ejpam-6540	267	13	have	have	VERB
ejpam-6540	267	14	distinct	distinct	ADJ
ejpam-6540	267	15	representation	representation	NOUN
ejpam-6540	267	16	in	in	ADP
ejpam-6540	267	17	e(s3	e(s3	PROPN
ejpam-6540	267	18	c5	c5	PROPN
ejpam-6540	267	19	)	)	PUNCT
ejpam-6540	267	20	.	.	PUNCT
ejpam-6540	268	1	thus	thus	ADV
ejpam-6540	268	2	,	,	PUNCT
ejpam-6540	268	3	dime(s	dime(	VERB
ejpam-6540	268	4	3	3	NUM
ejpam-6540	268	5	c5	c5	PROPN
ejpam-6540	268	6	)	)	PUNCT
ejpam-6540	268	7	≤	≤	ADV
ejpam-6540	268	8	5	5	NUM
ejpam-6540	268	9	.	.	PUNCT
ejpam-6540	268	10	due	due	ADP
ejpam-6540	268	11	to	to	ADP
ejpam-6540	268	12	symmetrical	symmetrical	ADJ
ejpam-6540	268	13	property	property	NOUN
ejpam-6540	268	14	,	,	PUNCT
ejpam-6540	268	15	all	all	DET
ejpam-6540	268	16	the	the	DET
ejpam-6540	268	17	edges	edge	NOUN
ejpam-6540	268	18	in	in	ADP
ejpam-6540	268	19	s3	s3	PROPN
ejpam-6540	268	20	c5	c5	PROPN
ejpam-6540	268	21	have	have	VERB
ejpam-6540	268	22	unique	unique	ADJ
ejpam-6540	268	23	representation	representation	NOUN
ejpam-6540	268	24	with	with	ADP
ejpam-6540	268	25	respect	respect	NOUN
ejpam-6540	268	26	to	to	ADP
ejpam-6540	268	27	w3	w3	PROPN
ejpam-6540	268	28	.	.	PUNCT
ejpam-6540	269	1	this	this	PRON
ejpam-6540	269	2	implies	imply	VERB
ejpam-6540	269	3	dime(s	dime(	VERB
ejpam-6540	269	4	3	3	NUM
ejpam-6540	269	5	c5	c5	PROPN
ejpam-6540	269	6	)	)	PUNCT
ejpam-6540	269	7	≤	≤	ADV
ejpam-6540	269	8	5	5	NUM
ejpam-6540	269	9	.	.	PUNCT
ejpam-6540	269	10	suppose	suppose	VERB
ejpam-6540	269	11	that	that	SCONJ
ejpam-6540	269	12	there	there	PRON
ejpam-6540	269	13	exists	exist	VERB
ejpam-6540	269	14	an	an	DET
ejpam-6540	269	15	ers	er	NOUN
ejpam-6540	269	16	u	u	NOUN
ejpam-6540	269	17	with	with	ADP
ejpam-6540	269	18	cardinality	cardinality	NOUN
ejpam-6540	269	19	4	4	NUM
ejpam-6540	269	20	.	.	PUNCT
ejpam-6540	269	21	then	then	ADV
ejpam-6540	269	22	by	by	ADP
ejpam-6540	269	23	pigeonhole	pigeonhole	NOUN
ejpam-6540	269	24	principle	principle	NOUN
ejpam-6540	269	25	,	,	PUNCT
ejpam-6540	269	26	there	there	PRON
ejpam-6540	269	27	exists	exist	VERB
ejpam-6540	269	28	i	i	PRON
ejpam-6540	269	29	∈	∈	PROPN
ejpam-6540	269	30	z5	z5	PROPN
ejpam-6540	269	31	,	,	PUNCT
ejpam-6540	269	32	such	such	ADJ
ejpam-6540	269	33	that	that	SCONJ
ejpam-6540	269	34	v(is2	v(is2	PROPN
ejpam-6540	269	35	c5	c5	PROPN
ejpam-6540	269	36	)	)	PUNCT
ejpam-6540	269	37	∩	∩	PROPN
ejpam-6540	269	38	u	u	NOUN
ejpam-6540	269	39	=	=	PUNCT
ejpam-6540	269	40	∅.	∅.	PROPN
ejpam-6540	269	41	then	then	ADV
ejpam-6540	269	42	there	there	PRON
ejpam-6540	269	43	exists	exist	VERB
ejpam-6540	269	44	two	two	NUM
ejpam-6540	269	45	edges	edge	NOUN
ejpam-6540	269	46	etu	etu	PROPN
ejpam-6540	269	47	and	and	CCONJ
ejpam-6540	269	48	evw	evw	PROPN
ejpam-6540	269	49	(	(	PUNCT
ejpam-6540	269	50	t	t	NOUN
ejpam-6540	269	51	=	=	SYM
ejpam-6540	269	52	i((i	i((i	NOUN
ejpam-6540	269	53	+	+	CCONJ
ejpam-6540	269	54	2)mod	2)mod	NUM
ejpam-6540	269	55	5)2	5)2	NUM
ejpam-6540	269	56	,	,	PUNCT
ejpam-6540	269	57	u	u	NOUN
ejpam-6540	269	58	=	=	NOUN
ejpam-6540	269	59	i((i	i((i	NOUN
ejpam-6540	269	60	+	+	CCONJ
ejpam-6540	269	61	2)mod	2)mod	NUM
ejpam-6540	269	62	5)((i	5)((i	NUM
ejpam-6540	270	1	+	+	CCONJ
ejpam-6540	270	2	1)mod	1)mod	NUM
ejpam-6540	270	3	5	5	NUM
ejpam-6540	270	4	)	)	PUNCT
ejpam-6540	270	5	,	,	PUNCT
ejpam-6540	270	6	v	v	NOUN
ejpam-6540	270	7	=	=	SYM
ejpam-6540	270	8	i((i	i((i	NOUN
ejpam-6540	270	9	+	+	CCONJ
ejpam-6540	270	10	1)mod	1)mod	NUM
ejpam-6540	270	11	5)((i	5)((i	NUM
ejpam-6540	270	12	−	−	NOUN
ejpam-6540	270	13	2)mod	2)mod	NUM
ejpam-6540	270	14	5	5	NUM
ejpam-6540	270	15	)	)	PUNCT
ejpam-6540	270	16	and	and	CCONJ
ejpam-6540	270	17	w	w	NOUN
ejpam-6540	270	18	=	=	PUNCT
ejpam-6540	270	19	i((i	i((i	NOUN
ejpam-6540	271	1	+	+	CCONJ
ejpam-6540	271	2	1)mod	1)mod	NUM
ejpam-6540	272	1	5)((i	5)((i	NUM
ejpam-6540	272	2	−	−	NOUN
ejpam-6540	272	3	1)mod	1)mod	NUM
ejpam-6540	272	4	5	5	NUM
ejpam-6540	272	5	)	)	PUNCT
ejpam-6540	272	6	)	)	PUNCT
ejpam-6540	272	7	in	in	ADP
ejpam-6540	272	8	an	an	DET
ejpam-6540	272	9	induced	induced	ADJ
ejpam-6540	272	10	subgraph	subgraph	NOUN
ejpam-6540	272	11	is2	is2	PROPN
ejpam-6540	272	12	c5	c5	PROPN
ejpam-6540	272	13	,	,	PUNCT
ejpam-6540	272	14	whose	whose	DET
ejpam-6540	272	15	edge	edge	NOUN
ejpam-6540	272	16	representations	representation	NOUN
ejpam-6540	272	17	with	with	ADP
ejpam-6540	272	18	respect	respect	NOUN
ejpam-6540	272	19	to	to	ADP
ejpam-6540	272	20	u	u	PRON
ejpam-6540	272	21	are	be	AUX
ejpam-6540	272	22	same	same	ADJ
ejpam-6540	272	23	,	,	PUNCT
ejpam-6540	272	24	which	which	PRON
ejpam-6540	272	25	is	be	AUX
ejpam-6540	272	26	a	a	DET
ejpam-6540	272	27	contradiction	contradiction	NOUN
ejpam-6540	272	28	and	and	CCONJ
ejpam-6540	272	29	implies	imply	VERB
ejpam-6540	272	30	that	that	SCONJ
ejpam-6540	272	31	dim(s3	dim(s3	PROPN
ejpam-6540	272	32	c5	c5	PROPN
ejpam-6540	272	33	)	)	PUNCT
ejpam-6540	272	34	≥	≥	PROPN
ejpam-6540	272	35	5	5	NUM
ejpam-6540	272	36	.	.	PUNCT
ejpam-6540	273	1	hence	hence	ADV
ejpam-6540	273	2	dim(s3	dim(s3	PROPN
ejpam-6540	273	3	c5	c5	PROPN
ejpam-6540	273	4	)	)	PUNCT
ejpam-6540	274	1	=	=	SYM
ejpam-6540	274	2	5	5	X
ejpam-6540	274	3	.	.	PUNCT
ejpam-6540	274	4	theorem	theorem	NOUN
ejpam-6540	274	5	3	3	NUM
ejpam-6540	274	6	.	.	X
ejpam-6540	274	7	for	for	ADP
ejpam-6540	274	8	h	h	PROPN
ejpam-6540	274	9	≥	≥	NOUN
ejpam-6540	274	10	3	3	NUM
ejpam-6540	274	11	,	,	PUNCT
ejpam-6540	274	12	dime(s	dime(	VERB
ejpam-6540	274	13	h	h	NOUN
ejpam-6540	274	14	c5	c5	PROPN
ejpam-6540	274	15	)	)	PUNCT
ejpam-6540	275	1	=	=	PUNCT
ejpam-6540	275	2	5h−2	5h−2	X
ejpam-6540	275	3	.	.	PUNCT
ejpam-6540	276	1	proof	proof	NOUN
ejpam-6540	276	2	.	.	PUNCT
ejpam-6540	277	1	let	let	VERB
ejpam-6540	277	2	w3	w3	PROPN
ejpam-6540	277	3	=	=	PUNCT
ejpam-6540	277	4	{	{	PUNCT
ejpam-6540	277	5	x(x+	x(x+	PROPN
ejpam-6540	277	6	2)2	2)2	NUM
ejpam-6540	277	7	:	:	PUNCT
ejpam-6540	277	8	x	x	SYM
ejpam-6540	277	9	∈	∈	PROPN
ejpam-6540	277	10	z5	z5	X
ejpam-6540	277	11	}	}	PUNCT
ejpam-6540	277	12	and	and	CCONJ
ejpam-6540	277	13	for	for	ADP
ejpam-6540	277	14	h	h	PROPN
ejpam-6540	277	15	≥	≥	NOUN
ejpam-6540	277	16	4	4	NUM
ejpam-6540	277	17	,	,	PUNCT
ejpam-6540	277	18	let	let	VERB
ejpam-6540	277	19	wh	wh	VERB
ejpam-6540	277	20	=	=	NOUN
ejpam-6540	277	21	4⋃	4⋃	NUM
ejpam-6540	277	22	i=0	i=0	PUNCT
ejpam-6540	277	23	iwh−1	iwh−1	NOUN
ejpam-6540	277	24	we	we	PRON
ejpam-6540	277	25	claim	claim	VERB
ejpam-6540	277	26	that	that	SCONJ
ejpam-6540	277	27	wh	wh	NOUN
ejpam-6540	277	28	is	be	AUX
ejpam-6540	277	29	a	a	DET
ejpam-6540	277	30	ers	er	NOUN
ejpam-6540	277	31	for	for	ADP
ejpam-6540	277	32	sh	sh	PROPN
ejpam-6540	277	33	c5	c5	PROPN
ejpam-6540	277	34	,	,	PUNCT
ejpam-6540	277	35	h	h	PROPN
ejpam-6540	277	36	≥	≥	NOUN
ejpam-6540	277	37	4	4	NUM
ejpam-6540	277	38	and	and	CCONJ
ejpam-6540	277	39	prove	prove	VERB
ejpam-6540	277	40	this	this	PRON
ejpam-6540	277	41	by	by	ADP
ejpam-6540	277	42	induction	induction	NOUN
ejpam-6540	277	43	on	on	ADP
ejpam-6540	277	44	h.	h.	PROPN
ejpam-6540	277	45	we	we	PRON
ejpam-6540	277	46	know	know	VERB
ejpam-6540	277	47	that	that	SCONJ
ejpam-6540	277	48	the	the	DET
ejpam-6540	277	49	claim	claim	NOUN
ejpam-6540	277	50	is	be	AUX
ejpam-6540	277	51	true	true	ADJ
ejpam-6540	277	52	for	for	ADP
ejpam-6540	277	53	h	h	NOUN
ejpam-6540	277	54	=	=	SYM
ejpam-6540	277	55	3	3	NUM
ejpam-6540	277	56	.	.	PUNCT
ejpam-6540	278	1	thus	thus	ADV
ejpam-6540	278	2	,	,	PUNCT
ejpam-6540	278	3	it	it	PRON
ejpam-6540	278	4	needs	need	VERB
ejpam-6540	278	5	to	to	PART
ejpam-6540	278	6	verify	verify	VERB
ejpam-6540	278	7	that	that	SCONJ
ejpam-6540	278	8	wh+1	wh+1	ADJ
ejpam-6540	278	9	,	,	PUNCT
ejpam-6540	278	10	h	h	NOUN
ejpam-6540	278	11	≥	≥	NOUN
ejpam-6540	278	12	4	4	NUM
ejpam-6540	278	13	,	,	PUNCT
ejpam-6540	278	14	is	be	AUX
ejpam-6540	278	15	a	a	DET
ejpam-6540	278	16	ers	er	NOUN
ejpam-6540	278	17	of	of	ADP
ejpam-6540	278	18	sh+1	sh+1	PROPN
ejpam-6540	278	19	c5	c5	PROPN
ejpam-6540	278	20	.	.	PUNCT
ejpam-6540	279	1	for	for	ADP
ejpam-6540	279	2	any	any	DET
ejpam-6540	279	3	etu	etu	PROPN
ejpam-6540	279	4	,	,	PUNCT
ejpam-6540	279	5	evw	evw	PROPN
ejpam-6540	279	6	∈	∈	PROPN
ejpam-6540	279	7	e(sh+1	e(sh+1	PROPN
ejpam-6540	279	8	c5	c5	PROPN
ejpam-6540	279	9	)	)	PUNCT
ejpam-6540	279	10	,	,	PUNCT
ejpam-6540	279	11	the	the	DET
ejpam-6540	279	12	following	follow	VERB
ejpam-6540	279	13	cases	case	NOUN
ejpam-6540	279	14	will	will	AUX
ejpam-6540	279	15	occur	occur	VERB
ejpam-6540	279	16	.	.	PUNCT
ejpam-6540	280	1	case	case	NOUN
ejpam-6540	280	2	1	1	NUM
ejpam-6540	280	3	:	:	PUNCT
ejpam-6540	280	4	t	t	PROPN
ejpam-6540	280	5	,	,	PUNCT
ejpam-6540	280	6	u	u	NOUN
ejpam-6540	280	7	,	,	PUNCT
ejpam-6540	280	8	v	v	NOUN
ejpam-6540	280	9	,	,	PUNCT
ejpam-6540	280	10	w	w	PROPN
ejpam-6540	280	11	∈	∈	PROPN
ejpam-6540	280	12	v(0sh	v(0sh	NOUN
ejpam-6540	280	13	c5	c5	PROPN
ejpam-6540	280	14	)	)	PUNCT
ejpam-6540	280	15	by	by	ADP
ejpam-6540	280	16	the	the	DET
ejpam-6540	280	17	construction	construction	NOUN
ejpam-6540	280	18	of	of	ADP
ejpam-6540	280	19	sh+1	sh+1	PROPN
ejpam-6540	280	20	c5	c5	PROPN
ejpam-6540	280	21	and	and	CCONJ
ejpam-6540	280	22	erswh+1	erswh+1	PROPN
ejpam-6540	280	23	,	,	PUNCT
ejpam-6540	280	24	we	we	PRON
ejpam-6540	280	25	have	have	VERB
ejpam-6540	280	26	r(etu|wh+1∩v	r(etu|wh+1∩v	PROPN
ejpam-6540	280	27	(	(	PUNCT
ejpam-6540	280	28	0sh	0sh	ADJ
ejpam-6540	280	29	c5	c5	PROPN
ejpam-6540	280	30	)	)	PUNCT
ejpam-6540	280	31	)	)	PUNCT
ejpam-6540	281	1	̸=	̸=	PROPN
ejpam-6540	281	2	r(evw|wh+1∩	r(evw|wh+1∩	ADP
ejpam-6540	281	3	v	v	NOUN
ejpam-6540	281	4	(	(	PUNCT
ejpam-6540	281	5	0sh	0sh	ADJ
ejpam-6540	281	6	c5	c5	PROPN
ejpam-6540	281	7	)	)	PUNCT
ejpam-6540	281	8	)	)	PUNCT
ejpam-6540	281	9	for	for	ADP
ejpam-6540	281	10	all	all	DET
ejpam-6540	281	11	t	t	PROPN
ejpam-6540	281	12	,	,	PUNCT
ejpam-6540	281	13	u	u	NOUN
ejpam-6540	281	14	,	,	PUNCT
ejpam-6540	281	15	v	v	NOUN
ejpam-6540	281	16	,	,	PUNCT
ejpam-6540	281	17	w	w	PROPN
ejpam-6540	281	18	∈	∈	PROPN
ejpam-6540	281	19	v(0sh	v(0sh	NOUN
ejpam-6540	281	20	c5	c5	PROPN
ejpam-6540	281	21	)	)	PUNCT
ejpam-6540	281	22	.	.	PUNCT
ejpam-6540	282	1	this	this	PRON
ejpam-6540	282	2	implies	imply	VERB
ejpam-6540	282	3	that	that	SCONJ
ejpam-6540	282	4	no	no	DET
ejpam-6540	282	5	two	two	NUM
ejpam-6540	282	6	edges	edge	NOUN
ejpam-6540	282	7	incident	incident	NOUN
ejpam-6540	282	8	only	only	ADV
ejpam-6540	282	9	with	with	ADP
ejpam-6540	282	10	the	the	DET
ejpam-6540	282	11	vertices	vertex	NOUN
ejpam-6540	282	12	in	in	ADP
ejpam-6540	282	13	v(0sh	v(0sh	NOUN
ejpam-6540	282	14	c5	c5	PROPN
ejpam-6540	282	15	)	)	PUNCT
ejpam-6540	282	16	have	have	VERB
ejpam-6540	282	17	same	same	ADJ
ejpam-6540	282	18	edge	edge	NOUN
ejpam-6540	282	19	representation	representation	NOUN
ejpam-6540	282	20	.	.	PUNCT
ejpam-6540	283	1	case	case	NOUN
ejpam-6540	283	2	2	2	NUM
ejpam-6540	283	3	:	:	PUNCT
ejpam-6540	283	4	t	t	PROPN
ejpam-6540	283	5	,	,	PUNCT
ejpam-6540	283	6	u	u	PROPN
ejpam-6540	283	7	∈	∈	PROPN
ejpam-6540	283	8	v(0sh	v(0sh	NOUN
ejpam-6540	283	9	c5	c5	PROPN
ejpam-6540	283	10	)	)	PUNCT
ejpam-6540	283	11	and	and	CCONJ
ejpam-6540	283	12	v	v	NOUN
ejpam-6540	283	13	,	,	PUNCT
ejpam-6540	283	14	w	w	PROPN
ejpam-6540	283	15	̸∈	̸∈	PROPN
ejpam-6540	283	16	v(0sh	v(0sh	PROPN
ejpam-6540	283	17	c5	c5	PROPN
ejpam-6540	283	18	)	)	PUNCT
ejpam-6540	283	19	in	in	ADP
ejpam-6540	283	20	this	this	DET
ejpam-6540	283	21	case	case	NOUN
ejpam-6540	283	22	,	,	PUNCT
ejpam-6540	283	23	there	there	PRON
ejpam-6540	283	24	exists	exist	VERB
ejpam-6540	283	25	atleast	atleast	ADV
ejpam-6540	283	26	one	one	NUM
ejpam-6540	283	27	vertex	vertex	NOUN
ejpam-6540	283	28	x	x	X
ejpam-6540	283	29	∈	∈	NOUN
ejpam-6540	283	30	wh+1	wh+1	ADJ
ejpam-6540	283	31	∪	∪	ADJ
ejpam-6540	283	32	0sh	0sh	ADJ
ejpam-6540	283	33	c5	c5	PROPN
ejpam-6540	284	1	such	such	ADJ
ejpam-6540	284	2	that	that	SCONJ
ejpam-6540	284	3	dsh+1	dsh+1	PROPN
ejpam-6540	284	4	c5	c5	PROPN
ejpam-6540	284	5	(	(	PUNCT
ejpam-6540	284	6	etu	etu	PROPN
ejpam-6540	284	7	,	,	PUNCT
ejpam-6540	284	8	x	x	NOUN
ejpam-6540	284	9	)	)	PUNCT
ejpam-6540	284	10	<	<	X
ejpam-6540	284	11	dsh+1	dsh+1	PROPN
ejpam-6540	284	12	c5	c5	PROPN
ejpam-6540	284	13	(	(	PUNCT
ejpam-6540	284	14	evw	evw	PROPN
ejpam-6540	284	15	,	,	PUNCT
ejpam-6540	284	16	x	x	NOUN
ejpam-6540	284	17	)	)	PUNCT
ejpam-6540	284	18	.	.	PUNCT
ejpam-6540	285	1	this	this	PRON
ejpam-6540	285	2	implies	imply	VERB
ejpam-6540	285	3	that	that	SCONJ
ejpam-6540	285	4	r(etu|wh+1	r(etu|wh+1	PROPN
ejpam-6540	285	5	)	)	PUNCT
ejpam-6540	285	6	̸=	̸=	PROPN
ejpam-6540	285	7	r(evw|wh+1	r(evw|wh+1	PROPN
ejpam-6540	285	8	)	)	PUNCT
ejpam-6540	285	9	for	for	ADP
ejpam-6540	285	10	t	t	PROPN
ejpam-6540	285	11	,	,	PUNCT
ejpam-6540	285	12	u	u	PROPN
ejpam-6540	285	13	∈	∈	PROPN
ejpam-6540	285	14	v(0sh	v(0sh	NOUN
ejpam-6540	285	15	c5	c5	PROPN
ejpam-6540	285	16	)	)	PUNCT
ejpam-6540	285	17	and	and	CCONJ
ejpam-6540	285	18	v	v	NOUN
ejpam-6540	285	19	,	,	PUNCT
ejpam-6540	285	20	w	w	PROPN
ejpam-6540	285	21	̸∈	̸∈	PROPN
ejpam-6540	285	22	v(0sh	v(0sh	PROPN
ejpam-6540	285	23	c5	c5	PROPN
ejpam-6540	285	24	)	)	PUNCT
ejpam-6540	285	25	.	.	PUNCT
ejpam-6540	286	1	case	case	NOUN
ejpam-6540	286	2	3	3	NUM
ejpam-6540	286	3	:	:	PUNCT
ejpam-6540	286	4	t	t	PROPN
ejpam-6540	286	5	,	,	PUNCT
ejpam-6540	286	6	u	u	NOUN
ejpam-6540	286	7	,	,	PUNCT
ejpam-6540	286	8	v	v	NOUN
ejpam-6540	286	9	∈	∈	PROPN
ejpam-6540	286	10	v(0sh	v(0sh	NOUN
ejpam-6540	286	11	c5	c5	PROPN
ejpam-6540	286	12	)	)	PUNCT
ejpam-6540	286	13	and	and	CCONJ
ejpam-6540	286	14	w	w	PROPN
ejpam-6540	286	15	̸∈	̸∈	PROPN
ejpam-6540	286	16	v(0sh	v(0sh	PROPN
ejpam-6540	286	17	c5	c5	PROPN
ejpam-6540	286	18	)	)	PUNCT
ejpam-6540	286	19	in	in	ADP
ejpam-6540	286	20	this	this	DET
ejpam-6540	286	21	case	case	NOUN
ejpam-6540	286	22	,	,	PUNCT
ejpam-6540	286	23	there	there	PRON
ejpam-6540	286	24	exists	exist	VERB
ejpam-6540	286	25	some	some	DET
ejpam-6540	286	26	edges	edge	NOUN
ejpam-6540	286	27	etu	etu	PROPN
ejpam-6540	286	28	such	such	ADJ
ejpam-6540	286	29	that	that	SCONJ
ejpam-6540	286	30	r(etu|wh+1∪0sh	r(etu|wh+1∪0sh	NOUN
ejpam-6540	286	31	c5	c5	PROPN
ejpam-6540	286	32	)	)	PUNCT
ejpam-6540	287	1	=	=	PUNCT
ejpam-6540	287	2	r(evw|wh+1∪0sh	r(evw|wh+1∪0sh	X
ejpam-6540	287	3	c5	c5	PROPN
ejpam-6540	287	4	)	)	PUNCT
ejpam-6540	287	5	.	.	PUNCT
ejpam-6540	288	1	but	but	CCONJ
ejpam-6540	288	2	,	,	PUNCT
ejpam-6540	288	3	there	there	PRON
ejpam-6540	288	4	exists	exist	VERB
ejpam-6540	288	5	some	some	PRON
ejpam-6540	288	6	x	x	SYM
ejpam-6540	288	7	∈	∈	PROPN
ejpam-6540	288	8	wh+1	wh+1	PROPN
ejpam-6540	288	9	\	\	PROPN
ejpam-6540	289	1	v(0sh+1	v(0sh+1	PROPN
ejpam-6540	289	2	c5	c5	PROPN
ejpam-6540	289	3	)	)	PUNCT
ejpam-6540	289	4	,	,	PUNCT
ejpam-6540	289	5	we	we	PRON
ejpam-6540	289	6	have	have	VERB
ejpam-6540	289	7	dsh+1	dsh+1	NOUN
ejpam-6540	289	8	c5	c5	PROPN
ejpam-6540	289	9	(	(	PUNCT
ejpam-6540	289	10	etu	etu	PROPN
ejpam-6540	289	11	,	,	PUNCT
ejpam-6540	289	12	x	x	NOUN
ejpam-6540	289	13	)	)	PUNCT
ejpam-6540	289	14	>	>	X
ejpam-6540	289	15	dsh+1	dsh+1	PROPN
ejpam-6540	289	16	c5	c5	PROPN
ejpam-6540	289	17	(	(	PUNCT
ejpam-6540	289	18	evw	evw	PROPN
ejpam-6540	289	19	,	,	PUNCT
ejpam-6540	289	20	x	x	NOUN
ejpam-6540	289	21	)	)	PUNCT
ejpam-6540	289	22	.	.	PUNCT
ejpam-6540	290	1	k.	k.	PROPN
ejpam-6540	290	2	b.	b.	PROPN
ejpam-6540	290	3	dharan	dharan	PROPN
ejpam-6540	290	4	,	,	PUNCT
ejpam-6540	290	5	s.	s.	PROPN
ejpam-6540	290	6	radha	radha	PROPN
ejpam-6540	290	7	/	/	PUNCT
ejpam-6540	290	8	eur	eur	PROPN
ejpam-6540	290	9	.	.	PUNCT
ejpam-6540	291	1	j.	j.	PROPN
ejpam-6540	291	2	pure	pure	PROPN
ejpam-6540	291	3	appl	appl	PROPN
ejpam-6540	291	4	.	.	PROPN
ejpam-6540	291	5	math	math	PROPN
ejpam-6540	291	6	,	,	PUNCT
ejpam-6540	291	7	18	18	NUM
ejpam-6540	291	8	(	(	PUNCT
ejpam-6540	291	9	3	3	NUM
ejpam-6540	291	10	)	)	PUNCT
ejpam-6540	291	11	(	(	PUNCT
ejpam-6540	291	12	2025	2025	NUM
ejpam-6540	291	13	)	)	PUNCT
ejpam-6540	291	14	,	,	PUNCT
ejpam-6540	291	15	6540	6540	NUM
ejpam-6540	291	16	12	12	NUM
ejpam-6540	291	17	of	of	ADP
ejpam-6540	291	18	17	17	NUM
ejpam-6540	291	19	from	from	ADP
ejpam-6540	291	20	the	the	DET
ejpam-6540	291	21	above	above	ADJ
ejpam-6540	291	22	cases	case	NOUN
ejpam-6540	291	23	,	,	PUNCT
ejpam-6540	291	24	we	we	PRON
ejpam-6540	291	25	can	can	AUX
ejpam-6540	291	26	say	say	VERB
ejpam-6540	291	27	that	that	SCONJ
ejpam-6540	291	28	every	every	DET
ejpam-6540	291	29	edge	edge	NOUN
ejpam-6540	291	30	incident	incident	NOUN
ejpam-6540	291	31	to	to	PART
ejpam-6540	291	32	v(0sh	v(0sh	VERB
ejpam-6540	291	33	c5	c5	PROPN
ejpam-6540	291	34	)	)	PUNCT
ejpam-6540	291	35	have	have	VERB
ejpam-6540	291	36	distinct	distinct	ADJ
ejpam-6540	291	37	representations	representation	NOUN
ejpam-6540	291	38	.	.	PUNCT
ejpam-6540	292	1	due	due	ADP
ejpam-6540	292	2	to	to	ADP
ejpam-6540	292	3	the	the	DET
ejpam-6540	292	4	symmetrical	symmetrical	ADJ
ejpam-6540	292	5	structure	structure	NOUN
ejpam-6540	292	6	of	of	ADP
ejpam-6540	292	7	sh+1	sh+1	PROPN
ejpam-6540	292	8	c5	c5	PROPN
ejpam-6540	292	9	,	,	PUNCT
ejpam-6540	292	10	all	all	DET
ejpam-6540	292	11	the	the	DET
ejpam-6540	292	12	edges	edge	NOUN
ejpam-6540	292	13	in	in	ADP
ejpam-6540	292	14	sh+1	sh+1	PROPN
ejpam-6540	292	15	c5	c5	PROPN
ejpam-6540	292	16	have	have	VERB
ejpam-6540	292	17	distinct	distinct	ADJ
ejpam-6540	292	18	edge	edge	NOUN
ejpam-6540	292	19	representations	representation	NOUN
ejpam-6540	292	20	.	.	PUNCT
ejpam-6540	293	1	this	this	PRON
ejpam-6540	293	2	implies	imply	VERB
ejpam-6540	293	3	that	that	SCONJ
ejpam-6540	293	4	wh+1	wh+1	PROPN
ejpam-6540	293	5	is	be	AUX
ejpam-6540	293	6	an	an	DET
ejpam-6540	293	7	ers	er	NOUN
ejpam-6540	293	8	of	of	ADP
ejpam-6540	293	9	sh+1	sh+1	PROPN
ejpam-6540	293	10	c5	c5	PROPN
ejpam-6540	293	11	.	.	PUNCT
ejpam-6540	294	1	so	so	ADV
ejpam-6540	294	2	that	that	SCONJ
ejpam-6540	294	3	for	for	ADP
ejpam-6540	294	4	h	h	PROPN
ejpam-6540	294	5	≥	≥	NOUN
ejpam-6540	294	6	4	4	NUM
ejpam-6540	294	7	,	,	PUNCT
ejpam-6540	294	8	|wh|	|wh|	PROPN
ejpam-6540	294	9	=	=	SYM
ejpam-6540	294	10	5(|wh−1|	5(|wh−1|	NUM
ejpam-6540	294	11	)	)	PUNCT
ejpam-6540	294	12	.	.	PUNCT
ejpam-6540	295	1	solving	solve	VERB
ejpam-6540	295	2	this	this	DET
ejpam-6540	295	3	recurrence	recurrence	NOUN
ejpam-6540	295	4	relation	relation	NOUN
ejpam-6540	295	5	,	,	PUNCT
ejpam-6540	295	6	we	we	PRON
ejpam-6540	295	7	get	get	VERB
ejpam-6540	295	8	|wh|	|wh|	NOUN
ejpam-6540	295	9	=	=	SYM
ejpam-6540	295	10	5h−2	5h−2	PROPN
ejpam-6540	295	11	for	for	ADP
ejpam-6540	295	12	h	h	PROPN
ejpam-6540	295	13	≥	≥	NOUN
ejpam-6540	295	14	4	4	NUM
ejpam-6540	295	15	,	,	PUNCT
ejpam-6540	295	16	which	which	PRON
ejpam-6540	295	17	implies	imply	VERB
ejpam-6540	295	18	that	that	SCONJ
ejpam-6540	295	19	dime(s	dime(	VERB
ejpam-6540	295	20	h	h	NOUN
ejpam-6540	295	21	c5	c5	PROPN
ejpam-6540	295	22	)	)	PUNCT
ejpam-6540	295	23	≤	≤	PROPN
ejpam-6540	296	1	5h−2	5h−2	PROPN
ejpam-6540	296	2	.	.	PUNCT
ejpam-6540	297	1	now	now	ADV
ejpam-6540	297	2	to	to	PART
ejpam-6540	297	3	prove	prove	VERB
ejpam-6540	297	4	that	that	SCONJ
ejpam-6540	297	5	dime(s	dime(	VERB
ejpam-6540	297	6	h	h	NOUN
ejpam-6540	297	7	c5	c5	PROPN
ejpam-6540	297	8	)	)	PUNCT
ejpam-6540	297	9	≥	≥	PROPN
ejpam-6540	297	10	5h−2	5h−2	NUM
ejpam-6540	297	11	,	,	PUNCT
ejpam-6540	297	12	let	let	VERB
ejpam-6540	297	13	us	we	PRON
ejpam-6540	297	14	suppose	suppose	VERB
ejpam-6540	297	15	that	that	SCONJ
ejpam-6540	297	16	there	there	PRON
ejpam-6540	297	17	exist	exist	VERB
ejpam-6540	297	18	a	a	DET
ejpam-6540	297	19	resolving	resolving	NOUN
ejpam-6540	297	20	set	set	VERB
ejpam-6540	297	21	w	w	NOUN
ejpam-6540	297	22	with	with	ADP
ejpam-6540	297	23	cardinality	cardinality	NOUN
ejpam-6540	297	24	less	less	ADV
ejpam-6540	297	25	that	that	SCONJ
ejpam-6540	297	26	5h−2	5h−2	VERB
ejpam-6540	297	27	.	.	PUNCT
ejpam-6540	298	1	let	let	VERB
ejpam-6540	298	2	us	we	PRON
ejpam-6540	298	3	assume	assume	VERB
ejpam-6540	298	4	that	that	SCONJ
ejpam-6540	298	5	dime(s	dime(	VERB
ejpam-6540	298	6	h	h	NOUN
ejpam-6540	298	7	c5	c5	PROPN
ejpam-6540	298	8	)	)	PUNCT
ejpam-6540	299	1	=	=	PUNCT
ejpam-6540	300	1	5h−2	5h−2	NOUN
ejpam-6540	300	2	−	−	NOUN
ejpam-6540	301	1	1	1	NUM
ejpam-6540	301	2	.	.	PUNCT
ejpam-6540	301	3	then	then	ADV
ejpam-6540	301	4	by	by	ADP
ejpam-6540	301	5	pigeonhole	pigeonhole	NOUN
ejpam-6540	301	6	principle	principle	NOUN
ejpam-6540	301	7	,	,	PUNCT
ejpam-6540	301	8	there	there	PRON
ejpam-6540	301	9	exist	exist	VERB
ejpam-6540	301	10	at	at	ADV
ejpam-6540	301	11	least	least	ADV
ejpam-6540	301	12	one	one	NUM
ejpam-6540	301	13	induced	induced	ADJ
ejpam-6540	301	14	subgraph	subgraph	NOUN
ejpam-6540	301	15	i1i2	i1i2	PROPN
ejpam-6540	301	16	.	.	PUNCT
ejpam-6540	301	17	.	.	PUNCT
ejpam-6540	301	18	.	.	PUNCT
ejpam-6540	302	1	ih−2s	ih−2s	INTJ
ejpam-6540	302	2	2	2	NUM
ejpam-6540	302	3	c5	c5	PROPN
ejpam-6540	302	4	(	(	PUNCT
ejpam-6540	302	5	i1	i1	PROPN
ejpam-6540	302	6	,	,	PUNCT
ejpam-6540	302	7	i2	i2	PROPN
ejpam-6540	302	8	,	,	PUNCT
ejpam-6540	302	9	.	.	PUNCT
ejpam-6540	302	10	.	.	PUNCT
ejpam-6540	302	11	.	.	PUNCT
ejpam-6540	303	1	,	,	PUNCT
ejpam-6540	303	2	ih−2	ih−2	PROPN
ejpam-6540	303	3	∈	∈	PROPN
ejpam-6540	303	4	z5	z5	PROPN
ejpam-6540	303	5	)	)	PUNCT
ejpam-6540	303	6	with	with	ADP
ejpam-6540	303	7	only	only	ADV
ejpam-6540	303	8	two	two	NUM
ejpam-6540	303	9	pseudo	pseudo	NOUN
ejpam-6540	303	10	resolvers	resolver	NOUN
ejpam-6540	303	11	u	u	NOUN
ejpam-6540	303	12	,	,	PUNCT
ejpam-6540	303	13	v	v	PROPN
ejpam-6540	303	14	∈	∈	PROPN
ejpam-6540	303	15	i1i2	i1i2	PUNCT
ejpam-6540	303	16	.	.	PUNCT
ejpam-6540	303	17	.	.	PUNCT
ejpam-6540	303	18	.	.	PUNCT
ejpam-6540	304	1	ih−2s	ih−2s	INTJ
ejpam-6540	304	2	2	2	NUM
ejpam-6540	304	3	c5	c5	PROPN
ejpam-6540	304	4	such	such	ADJ
ejpam-6540	304	5	that	that	SCONJ
ejpam-6540	304	6	uh	uh	INTJ
ejpam-6540	304	7	=	=	SYM
ejpam-6540	304	8	uh−1	uh−1	PROPN
ejpam-6540	304	9	=	=	PUNCT
ejpam-6540	304	10	uh−2	uh−2	VERB
ejpam-6540	304	11	±	±	NOUN
ejpam-6540	304	12	1	1	NUM
ejpam-6540	304	13	and	and	CCONJ
ejpam-6540	304	14	v(i1i2	v(i1i2	NOUN
ejpam-6540	304	15	.	.	PUNCT
ejpam-6540	304	16	.	.	PUNCT
ejpam-6540	304	17	.	.	PUNCT
ejpam-6540	305	1	ih−2s	ih−2s	PROPN
ejpam-6540	305	2	2	2	NUM
ejpam-6540	305	3	c5	c5	PROPN
ejpam-6540	305	4	)	)	PUNCT
ejpam-6540	305	5	∩	∩	PROPN
ejpam-6540	305	6	w	w	NOUN
ejpam-6540	305	7	=	=	PUNCT
ejpam-6540	305	8	∅.	∅.	NOUN
ejpam-6540	305	9	then	then	ADV
ejpam-6540	305	10	there	there	PRON
ejpam-6540	305	11	exists	exist	VERB
ejpam-6540	305	12	two	two	NUM
ejpam-6540	305	13	edges	edge	NOUN
ejpam-6540	305	14	etu	etu	PROPN
ejpam-6540	305	15	,	,	PUNCT
ejpam-6540	305	16	evw	evw	PROPN
ejpam-6540	305	17	∈	∈	PROPN
ejpam-6540	305	18	e(s2	e(s2	PROPN
ejpam-6540	305	19	c5	c5	PROPN
ejpam-6540	305	20	)	)	PUNCT
ejpam-6540	306	1	(	(	PUNCT
ejpam-6540	306	2	t	t	PROPN
ejpam-6540	306	3	=	=	PROPN
ejpam-6540	306	4	i1	i1	PROPN
ejpam-6540	306	5	.	.	PUNCT
ejpam-6540	306	6	.	.	PUNCT
ejpam-6540	306	7	.	.	PUNCT
ejpam-6540	307	1	ih−2((ih−2	ih−2((ih−2	X
ejpam-6540	308	1	+	+	NOUN
ejpam-6540	308	2	2)mod	2)mod	NUM
ejpam-6540	308	3	5)2	5)2	NUM
ejpam-6540	308	4	,	,	PUNCT
ejpam-6540	308	5	u	u	NOUN
ejpam-6540	308	6	=	=	PROPN
ejpam-6540	308	7	i1	i1	PROPN
ejpam-6540	308	8	.	.	PUNCT
ejpam-6540	308	9	.	.	PUNCT
ejpam-6540	308	10	.	.	PUNCT
ejpam-6540	309	1	ih−2((ih−2	ih−2((ih−2	X
ejpam-6540	310	1	+	+	PROPN
ejpam-6540	310	2	2)mod	2)mod	NUM
ejpam-6540	310	3	5)((ih−2	5)((ih−2	NUM
ejpam-6540	310	4	+	+	NOUN
ejpam-6540	310	5	1)mod	1)mod	NUM
ejpam-6540	310	6	5	5	NUM
ejpam-6540	310	7	)	)	PUNCT
ejpam-6540	310	8	,	,	PUNCT
ejpam-6540	310	9	v	v	X
ejpam-6540	310	10	=	=	PROPN
ejpam-6540	310	11	i1	i1	PROPN
ejpam-6540	310	12	.	.	PUNCT
ejpam-6540	310	13	.	.	PUNCT
ejpam-6540	310	14	.	.	PUNCT
ejpam-6540	311	1	ih−2((ih−2	ih−2((ih−2	PART
ejpam-6540	312	1	+	+	CCONJ
ejpam-6540	312	2	1)mod	1)mod	NUM
ejpam-6540	312	3	5)((ih−2	5)((ih−2	NUM
ejpam-6540	312	4	−	−	NOUN
ejpam-6540	312	5	2)mod	2)mod	NUM
ejpam-6540	312	6	5	5	NUM
ejpam-6540	312	7	)	)	PUNCT
ejpam-6540	312	8	and	and	CCONJ
ejpam-6540	312	9	w	w	PROPN
ejpam-6540	312	10	=	=	PROPN
ejpam-6540	312	11	i1	i1	PROPN
ejpam-6540	312	12	.	.	PUNCT
ejpam-6540	313	1	.	.	PUNCT
ejpam-6540	313	2	.	.	PUNCT
ejpam-6540	314	1	ih−2((ih−2	ih−2((ih−2	PART
ejpam-6540	315	1	+	+	CCONJ
ejpam-6540	315	2	1)mod	1)mod	NUM
ejpam-6540	315	3	5)((ih−2−1)mod	5)((ih−2−1)mod	NUM
ejpam-6540	315	4	5	5	NUM
ejpam-6540	315	5	)	)	PUNCT
ejpam-6540	315	6	)	)	PUNCT
ejpam-6540	315	7	have	have	VERB
ejpam-6540	315	8	the	the	DET
ejpam-6540	315	9	same	same	ADJ
ejpam-6540	315	10	representation	representation	NOUN
ejpam-6540	315	11	with	with	ADP
ejpam-6540	315	12	respect	respect	NOUN
ejpam-6540	315	13	to	to	ADP
ejpam-6540	315	14	w	w	PROPN
ejpam-6540	315	15	,	,	PUNCT
ejpam-6540	315	16	a	a	DET
ejpam-6540	315	17	contradiction	contradiction	NOUN
ejpam-6540	315	18	.	.	PUNCT
ejpam-6540	316	1	this	this	PRON
ejpam-6540	316	2	leads	lead	VERB
ejpam-6540	316	3	to	to	AUX
ejpam-6540	316	4	dime(s	dime(s	VERB
ejpam-6540	316	5	h	h	NOUN
ejpam-6540	316	6	c5	c5	PROPN
ejpam-6540	316	7	)	)	PUNCT
ejpam-6540	316	8	≥	≥	PROPN
ejpam-6540	316	9	5h−2	5h−2	NOUN
ejpam-6540	316	10	.	.	PUNCT
ejpam-6540	317	1	hence	hence	ADV
ejpam-6540	317	2	,	,	PUNCT
ejpam-6540	317	3	dime(s	dime(	VERB
ejpam-6540	317	4	h	h	NOUN
ejpam-6540	317	5	c5	c5	PROPN
ejpam-6540	317	6	)	)	PUNCT
ejpam-6540	318	1	=	=	PUNCT
ejpam-6540	318	2	5h−2	5h−2	X
ejpam-6540	318	3	.	.	PUNCT
ejpam-6540	319	1	lemma	lemma	PROPN
ejpam-6540	319	2	2	2	X
ejpam-6540	319	3	.	.	PUNCT
ejpam-6540	319	4	let	let	VERB
ejpam-6540	319	5	u3	u3	PROPN
ejpam-6540	319	6	=	=	SYM
ejpam-6540	319	7	{	{	PUNCT
ejpam-6540	319	8	033	033	NUM
ejpam-6540	319	9	,	,	PUNCT
ejpam-6540	319	10	144	144	NUM
ejpam-6540	319	11	,	,	PUNCT
ejpam-6540	319	12	200	200	NUM
ejpam-6540	319	13	,	,	PUNCT
ejpam-6540	319	14	311	311	NUM
ejpam-6540	319	15	,	,	PUNCT
ejpam-6540	319	16	422	422	NUM
ejpam-6540	319	17	}	}	PUNCT
ejpam-6540	319	18	.	.	PUNCT
ejpam-6540	320	1	for	for	ADP
ejpam-6540	320	2	h	h	PROPN
ejpam-6540	320	3	≥	≥	NOUN
ejpam-6540	320	4	4	4	NUM
ejpam-6540	320	5	,	,	PUNCT
ejpam-6540	320	6	uh	uh	INTJ
ejpam-6540	320	7	=	=	SYM
ejpam-6540	320	8	⋃4	⋃4	NOUN
ejpam-6540	320	9	i=0	i=0	PROPN
ejpam-6540	320	10	iuh−1	iuh−1	PROPN
ejpam-6540	320	11	is	be	AUX
ejpam-6540	320	12	an	an	DET
ejpam-6540	320	13	emb	emb	NOUN
ejpam-6540	320	14	for	for	ADP
ejpam-6540	320	15	sh	sh	PROPN
ejpam-6540	320	16	c5	c5	PROPN
ejpam-6540	320	17	.	.	PUNCT
ejpam-6540	321	1	the	the	DET
ejpam-6540	321	2	proof	proof	NOUN
ejpam-6540	321	3	of	of	ADP
ejpam-6540	321	4	the	the	DET
ejpam-6540	321	5	above	above	ADJ
ejpam-6540	321	6	lemma	lemma	PROPN
ejpam-6540	321	7	is	be	AUX
ejpam-6540	321	8	similar	similar	ADJ
ejpam-6540	321	9	to	to	ADP
ejpam-6540	321	10	the	the	DET
ejpam-6540	321	11	proof	proof	NOUN
ejpam-6540	321	12	of	of	ADP
ejpam-6540	321	13	theorem	theorem	NOUN
ejpam-6540	321	14	3	3	NUM
ejpam-6540	321	15	,	,	PUNCT
ejpam-6540	321	16	due	due	ADP
ejpam-6540	321	17	to	to	ADP
ejpam-6540	321	18	the	the	DET
ejpam-6540	321	19	reflexive	reflexive	ADJ
ejpam-6540	321	20	property	property	NOUN
ejpam-6540	321	21	of	of	ADP
ejpam-6540	321	22	sh	sh	PROPN
ejpam-6540	321	23	c5	c5	PROPN
ejpam-6540	321	24	.	.	PUNCT
ejpam-6540	322	1	to	to	PART
ejpam-6540	322	2	prove	prove	VERB
ejpam-6540	322	3	the	the	DET
ejpam-6540	322	4	dime′	dime′	NOUN
ejpam-6540	322	5	of	of	ADP
ejpam-6540	322	6	sh	sh	PROPN
ejpam-6540	322	7	c5	c5	PROPN
ejpam-6540	322	8	for	for	ADP
ejpam-6540	322	9	h	h	PROPN
ejpam-6540	322	10	≥	≥	PROPN
ejpam-6540	322	11	3	3	NUM
ejpam-6540	322	12	,	,	PUNCT
ejpam-6540	322	13	we	we	PRON
ejpam-6540	322	14	defined	define	VERB
ejpam-6540	322	15	a	a	DET
ejpam-6540	322	16	emb	emb	NOUN
ejpam-6540	322	17	uh	uh	INTJ
ejpam-6540	322	18	in	in	ADP
ejpam-6540	322	19	the	the	DET
ejpam-6540	322	20	lemma	lemma	PROPN
ejpam-6540	322	21	2	2	NUM
ejpam-6540	322	22	,	,	PUNCT
ejpam-6540	322	23	such	such	ADJ
ejpam-6540	322	24	that	that	SCONJ
ejpam-6540	322	25	uh	uh	INTJ
ejpam-6540	322	26	∩wh	∩wh	NOUN
ejpam-6540	322	27	=	=	PROPN
ejpam-6540	322	28	∅.	∅.	NOUN
ejpam-6540	322	29	then	then	ADV
ejpam-6540	322	30	w	w	NOUN
ejpam-6540	322	31	′	′	NUM
ejpam-6540	323	1	h	h	NOUN
ejpam-6540	324	1	=	=	NOUN
ejpam-6540	325	1	uh	uh	INTJ
ejpam-6540	325	2	∪wh	∪wh	NOUN
ejpam-6540	325	3	is	be	AUX
ejpam-6540	325	4	also	also	ADV
ejpam-6540	325	5	an	an	DET
ejpam-6540	325	6	ers	er	NOUN
ejpam-6540	325	7	and	and	CCONJ
ejpam-6540	325	8	w	w	NOUN
ejpam-6540	325	9	′	′	NUM
ejpam-6540	325	10	h	h	NOUN
ejpam-6540	325	11	is	be	AUX
ejpam-6540	325	12	obviously	obviously	ADV
ejpam-6540	325	13	a	a	DET
ejpam-6540	325	14	fters	fter	NOUN
ejpam-6540	325	15	for	for	ADP
ejpam-6540	325	16	sh	sh	PROPN
ejpam-6540	325	17	c5	c5	PROPN
ejpam-6540	325	18	,	,	PUNCT
ejpam-6540	325	19	when	when	SCONJ
ejpam-6540	325	20	h	h	PROPN
ejpam-6540	325	21	≥	≥	VERB
ejpam-6540	325	22	3	3	NUM
ejpam-6540	325	23	and	and	CCONJ
ejpam-6540	325	24	the	the	DET
ejpam-6540	325	25	proof	proof	NOUN
ejpam-6540	325	26	for	for	ADP
ejpam-6540	325	27	w	w	PROPN
ejpam-6540	325	28	′	′	NUM
ejpam-6540	325	29	h	h	NOUN
ejpam-6540	325	30	to	to	PART
ejpam-6540	325	31	be	be	AUX
ejpam-6540	325	32	a	a	DET
ejpam-6540	325	33	fteb	fteb	NOUN
ejpam-6540	325	34	is	be	AUX
ejpam-6540	325	35	given	give	VERB
ejpam-6540	325	36	in	in	ADP
ejpam-6540	325	37	the	the	DET
ejpam-6540	325	38	following	follow	VERB
ejpam-6540	325	39	theorem	theorem	NOUN
ejpam-6540	325	40	.	.	PUNCT
ejpam-6540	326	1	theorem	theorem	NOUN
ejpam-6540	326	2	4	4	NUM
ejpam-6540	326	3	.	.	PUNCT
ejpam-6540	327	1	for	for	ADP
ejpam-6540	327	2	h	h	PROPN
ejpam-6540	327	3	≥	≥	PROPN
ejpam-6540	327	4	3	3	NUM
ejpam-6540	327	5	,	,	PUNCT
ejpam-6540	327	6	dime′(sh	dime′(sh	CCONJ
ejpam-6540	327	7	c5	c5	PROPN
ejpam-6540	327	8	)	)	PUNCT
ejpam-6540	327	9	=	=	SYM
ejpam-6540	327	10	2	2	X
ejpam-6540	327	11	·	·	SYM
ejpam-6540	327	12	5h−2	5h−2	NOUN
ejpam-6540	327	13	.	.	PUNCT
ejpam-6540	327	14	proof	proof	NOUN
ejpam-6540	327	15	.	.	PUNCT
ejpam-6540	328	1	let	let	VERB
ejpam-6540	328	2	u3	u3	PROPN
ejpam-6540	328	3	and	and	CCONJ
ejpam-6540	328	4	w3	w3	PROPN
ejpam-6540	328	5	be	be	VERB
ejpam-6540	328	6	the	the	DET
ejpam-6540	328	7	distinct	distinct	ADJ
ejpam-6540	328	8	ers	er	NOUN
ejpam-6540	328	9	of	of	ADP
ejpam-6540	328	10	s3	s3	PROPN
ejpam-6540	328	11	c5	c5	PROPN
ejpam-6540	328	12	,	,	PUNCT
ejpam-6540	328	13	such	such	ADJ
ejpam-6540	328	14	that	that	SCONJ
ejpam-6540	328	15	u3	u3	NOUN
ejpam-6540	328	16	∩w3	∩w3	NOUN
ejpam-6540	328	17	=	=	PUNCT
ejpam-6540	328	18	∅.	∅.	NOUN
ejpam-6540	328	19	obviously	obviously	ADV
ejpam-6540	328	20	,	,	PUNCT
ejpam-6540	328	21	the	the	DET
ejpam-6540	328	22	set	set	ADJ
ejpam-6540	328	23	u3	u3	NOUN
ejpam-6540	328	24	∪	∪	NOUN
ejpam-6540	328	25	w3	w3	PROPN
ejpam-6540	328	26	will	will	AUX
ejpam-6540	328	27	be	be	AUX
ejpam-6540	328	28	the	the	DET
ejpam-6540	328	29	fters	fter	NOUN
ejpam-6540	328	30	for	for	ADP
ejpam-6540	328	31	s3	s3	PROPN
ejpam-6540	328	32	c5	c5	PROPN
ejpam-6540	328	33	,	,	PUNCT
ejpam-6540	328	34	proving	prove	VERB
ejpam-6540	328	35	that	that	SCONJ
ejpam-6540	328	36	dime′(s3	dime′(s3	PROPN
ejpam-6540	328	37	c5	c5	PROPN
ejpam-6540	328	38	)	)	PUNCT
ejpam-6540	328	39	≤	≤	ADV
ejpam-6540	328	40	10	10	NUM
ejpam-6540	328	41	.	.	PUNCT
ejpam-6540	329	1	to	to	PART
ejpam-6540	329	2	prove	prove	VERB
ejpam-6540	329	3	the	the	DET
ejpam-6540	329	4	sufficient	sufficient	ADJ
ejpam-6540	329	5	part	part	NOUN
ejpam-6540	329	6	,	,	PUNCT
ejpam-6540	329	7	let	let	VERB
ejpam-6540	329	8	us	we	PRON
ejpam-6540	329	9	assume	assume	VERB
ejpam-6540	329	10	that	that	SCONJ
ejpam-6540	329	11	there	there	PRON
ejpam-6540	329	12	exist	exist	VERB
ejpam-6540	329	13	a	a	DET
ejpam-6540	329	14	fters	fter	NOUN
ejpam-6540	329	15	s	s	NOUN
ejpam-6540	329	16	,	,	PUNCT
ejpam-6540	329	17	such	such	ADJ
ejpam-6540	329	18	that	that	SCONJ
ejpam-6540	329	19	|s|	|s|	VERB
ejpam-6540	329	20	<	<	X
ejpam-6540	329	21	10	10	NUM
ejpam-6540	329	22	.	.	PUNCT
ejpam-6540	330	1	let	let	VERB
ejpam-6540	330	2	us	we	PRON
ejpam-6540	330	3	assume	assume	VERB
ejpam-6540	330	4	that	that	SCONJ
ejpam-6540	330	5	|s|	|s|	VERB
ejpam-6540	330	6	=	=	SYM
ejpam-6540	330	7	9	9	NUM
ejpam-6540	330	8	.	.	PUNCT
ejpam-6540	331	1	then	then	ADV
ejpam-6540	331	2	,	,	PUNCT
ejpam-6540	331	3	by	by	ADP
ejpam-6540	331	4	pigeonhole	pigeonhole	NOUN
ejpam-6540	331	5	principle	principle	NOUN
ejpam-6540	331	6	,	,	PUNCT
ejpam-6540	331	7	there	there	PRON
ejpam-6540	331	8	exist	exist	VERB
ejpam-6540	331	9	i	i	PROPN
ejpam-6540	331	10	∈	∈	PROPN
ejpam-6540	331	11	z5	z5	PROPN
ejpam-6540	331	12	,	,	PUNCT
ejpam-6540	331	13	such	such	ADJ
ejpam-6540	331	14	that	that	SCONJ
ejpam-6540	331	15	v(is2	v(is2	PROPN
ejpam-6540	331	16	c5	c5	PROPN
ejpam-6540	331	17	)	)	PUNCT
ejpam-6540	331	18	∩	∩	PROPN
ejpam-6540	331	19	w	w	NOUN
ejpam-6540	332	1	′	′	NOUN
ejpam-6540	332	2	<	<	X
ejpam-6540	332	3	2	2	NUM
ejpam-6540	332	4	with	with	ADP
ejpam-6540	332	5	only	only	ADV
ejpam-6540	332	6	two	two	NUM
ejpam-6540	332	7	pseudo	pseudo	NOUN
ejpam-6540	332	8	resolvers	resolver	NOUN
ejpam-6540	332	9	{	{	PUNCT
ejpam-6540	332	10	i(i	i(i	PROPN
ejpam-6540	332	11	+	+	PROPN
ejpam-6540	332	12	1)2	1)2	NUM
ejpam-6540	332	13	,	,	PUNCT
ejpam-6540	332	14	i(i	i(i	PROPN
ejpam-6540	332	15	−	−	PROPN
ejpam-6540	333	1	1)2	1)2	NUM
ejpam-6540	333	2	}	}	PUNCT
ejpam-6540	333	3	.	.	PUNCT
ejpam-6540	334	1	when	when	SCONJ
ejpam-6540	334	2	removing	remove	VERB
ejpam-6540	334	3	that	that	DET
ejpam-6540	334	4	one	one	NUM
ejpam-6540	334	5	vertex	vertex	NOUN
ejpam-6540	334	6	in	in	ADP
ejpam-6540	334	7	v(is2	v(is2	PROPN
ejpam-6540	334	8	c5	c5	PROPN
ejpam-6540	334	9	)	)	PUNCT
ejpam-6540	334	10	∩	∩	PROPN
ejpam-6540	334	11	s	s	X
ejpam-6540	334	12	,	,	PUNCT
ejpam-6540	334	13	there	there	PRON
ejpam-6540	334	14	exists	exist	VERB
ejpam-6540	334	15	two	two	NUM
ejpam-6540	334	16	edges	edge	NOUN
ejpam-6540	334	17	incident	incident	NOUN
ejpam-6540	334	18	to	to	ADP
ejpam-6540	334	19	the	the	DET
ejpam-6540	334	20	vertices	vertex	NOUN
ejpam-6540	334	21	in	in	ADP
ejpam-6540	334	22	v(is2	v(is2	PROPN
ejpam-6540	334	23	c5	c5	PROPN
ejpam-6540	334	24	)	)	PUNCT
ejpam-6540	334	25	that	that	PRON
ejpam-6540	334	26	have	have	VERB
ejpam-6540	334	27	the	the	DET
ejpam-6540	334	28	same	same	ADJ
ejpam-6540	334	29	edge	edge	NOUN
ejpam-6540	334	30	representation	representation	NOUN
ejpam-6540	334	31	,	,	PUNCT
ejpam-6540	334	32	which	which	PRON
ejpam-6540	334	33	implies	imply	VERB
ejpam-6540	334	34	that	that	SCONJ
ejpam-6540	334	35	any	any	DET
ejpam-6540	334	36	subset	subset	NOUN
ejpam-6540	334	37	w	w	ADP
ejpam-6540	334	38	′	′	NOUN
ejpam-6540	334	39	with	with	ADP
ejpam-6540	334	40	cardinality	cardinality	NOUN
ejpam-6540	334	41	less	less	ADJ
ejpam-6540	334	42	than	than	ADP
ejpam-6540	334	43	10	10	NUM
ejpam-6540	334	44	can	can	AUX
ejpam-6540	334	45	not	not	PART
ejpam-6540	334	46	be	be	AUX
ejpam-6540	334	47	a	a	DET
ejpam-6540	334	48	fters	fter	NOUN
ejpam-6540	334	49	for	for	ADP
ejpam-6540	334	50	s3	s3	PROPN
ejpam-6540	334	51	c5	c5	PROPN
ejpam-6540	334	52	.	.	PUNCT
ejpam-6540	335	1	for	for	ADP
ejpam-6540	335	2	h	h	PROPN
ejpam-6540	335	3	≥	≥	NOUN
ejpam-6540	335	4	4	4	NUM
ejpam-6540	335	5	,	,	PUNCT
ejpam-6540	335	6	let	let	VERB
ejpam-6540	335	7	w	w	NOUN
ejpam-6540	335	8	′	′	NUM
ejpam-6540	335	9	h	h	NOUN
ejpam-6540	336	1	=	=	PUNCT
ejpam-6540	336	2	wh	wh	NOUN
ejpam-6540	336	3	∪	∪	NOUN
ejpam-6540	336	4	uh	uh	INTJ
ejpam-6540	336	5	,	,	PUNCT
ejpam-6540	336	6	where	where	SCONJ
ejpam-6540	336	7	wh	wh	AUX
ejpam-6540	336	8	=	=	SYM
ejpam-6540	336	9	⋃4	⋃4	NOUN
ejpam-6540	336	10	i=0	i=0	VERB
ejpam-6540	336	11	iwh−1	iwh−1	PROPN
ejpam-6540	336	12	and	and	CCONJ
ejpam-6540	336	13	uh	uh	INTJ
ejpam-6540	336	14	=	=	SYM
ejpam-6540	336	15	⋃4	⋃4	PROPN
ejpam-6540	336	16	i=0	i=0	PROPN
ejpam-6540	336	17	iuh−1	iuh−1	PROPN
ejpam-6540	336	18	.	.	PUNCT
ejpam-6540	337	1	we	we	PRON
ejpam-6540	337	2	know	know	VERB
ejpam-6540	337	3	that	that	SCONJ
ejpam-6540	337	4	wh	wh	VERB
ejpam-6540	337	5	and	and	CCONJ
ejpam-6540	337	6	uh	uh	INTJ
ejpam-6540	337	7	are	be	AUX
ejpam-6540	337	8	the	the	DET
ejpam-6540	337	9	ers	er	NOUN
ejpam-6540	337	10	for	for	ADP
ejpam-6540	337	11	sh	sh	PROPN
ejpam-6540	337	12	c5	c5	PROPN
ejpam-6540	337	13	for	for	ADP
ejpam-6540	337	14	any	any	DET
ejpam-6540	337	15	h	h	NOUN
ejpam-6540	337	16	≥	≥	NOUN
ejpam-6540	337	17	2	2	NUM
ejpam-6540	337	18	and	and	CCONJ
ejpam-6540	337	19	wh	wh	VERB
ejpam-6540	337	20	∩	∩	NOUN
ejpam-6540	337	21	uh	uh	INTJ
ejpam-6540	337	22	=	=	PUNCT
ejpam-6540	337	23	∅.	∅.	NOUN
ejpam-6540	337	24	then	then	ADV
ejpam-6540	337	25	w	w	NOUN
ejpam-6540	337	26	′	′	NUM
ejpam-6540	337	27	h	h	NOUN
ejpam-6540	337	28	be	be	VERB
ejpam-6540	337	29	the	the	DET
ejpam-6540	337	30	fters	fter	NOUN
ejpam-6540	337	31	for	for	ADP
ejpam-6540	337	32	sh	sh	PROPN
ejpam-6540	337	33	c5	c5	PROPN
ejpam-6540	337	34	,	,	PUNCT
ejpam-6540	337	35	∀h	∀h	X
ejpam-6540	337	36	≥	≥	NUM
ejpam-6540	337	37	4	4	NUM
ejpam-6540	337	38	.	.	PUNCT
ejpam-6540	338	1	we	we	PRON
ejpam-6540	338	2	have	have	VERB
ejpam-6540	338	3	|w	|w	ADJ
ejpam-6540	338	4	′	′	NUM
ejpam-6540	338	5	h|	h|	ADJ
ejpam-6540	338	6	=	=	SYM
ejpam-6540	338	7	5	5	X
ejpam-6540	338	8	·	·	PUNCT
ejpam-6540	338	9	|w	|w	ADJ
ejpam-6540	338	10	′	′	NUM
ejpam-6540	338	11	h−1|	h−1|	NOUN
ejpam-6540	338	12	.	.	PUNCT
ejpam-6540	339	1	solving	solve	VERB
ejpam-6540	339	2	this	this	DET
ejpam-6540	339	3	recurrence	recurrence	NOUN
ejpam-6540	339	4	relation	relation	NOUN
ejpam-6540	339	5	,	,	PUNCT
ejpam-6540	339	6	we	we	PRON
ejpam-6540	339	7	get	get	VERB
ejpam-6540	339	8	|w	|w	ADJ
ejpam-6540	339	9	′	′	PUNCT
ejpam-6540	340	1	h|	h|	ADJ
ejpam-6540	340	2	=	=	SYM
ejpam-6540	340	3	2	2	NUM
ejpam-6540	340	4	·	·	PUNCT
ejpam-6540	340	5	5h−2	5h−2	NOUN
ejpam-6540	340	6	.	.	PUNCT
ejpam-6540	341	1	this	this	PRON
ejpam-6540	341	2	implies	imply	VERB
ejpam-6540	341	3	that	that	SCONJ
ejpam-6540	341	4	dime′(sh	dime′(sh	PROPN
ejpam-6540	341	5	c5	c5	PROPN
ejpam-6540	341	6	)	)	PUNCT
ejpam-6540	341	7	≤	≤	ADV
ejpam-6540	341	8	2	2	NUM
ejpam-6540	341	9	·	·	SYM
ejpam-6540	341	10	5h−2	5h−2	NOUN
ejpam-6540	341	11	.	.	PUNCT
ejpam-6540	342	1	now	now	ADV
ejpam-6540	342	2	we	we	PRON
ejpam-6540	342	3	need	need	VERB
ejpam-6540	342	4	to	to	PART
ejpam-6540	342	5	prove	prove	VERB
ejpam-6540	342	6	that	that	SCONJ
ejpam-6540	342	7	dime′(sh	dime′(sh	PROPN
ejpam-6540	342	8	c5	c5	PROPN
ejpam-6540	342	9	)	)	PUNCT
ejpam-6540	342	10	≥	≥	PROPN
ejpam-6540	342	11	2·5h−1	2·5h−1	NUM
ejpam-6540	342	12	.	.	PUNCT
ejpam-6540	343	1	let	let	VERB
ejpam-6540	343	2	us	we	PRON
ejpam-6540	343	3	assume	assume	VERB
ejpam-6540	343	4	the	the	DET
ejpam-6540	343	5	contrary	contrary	NOUN
ejpam-6540	343	6	that	that	SCONJ
ejpam-6540	343	7	there	there	PRON
ejpam-6540	343	8	exist	exist	VERB
ejpam-6540	343	9	a	a	DET
ejpam-6540	343	10	ftersw	ftersw	NOUN
ejpam-6540	343	11	′	′	NUM
ejpam-6540	343	12	h	h	NOUN
ejpam-6540	343	13	,	,	PUNCT
ejpam-6540	344	1	such	such	ADJ
ejpam-6540	344	2	that	that	SCONJ
ejpam-6540	344	3	|w	|w	NOUN
ejpam-6540	344	4	′	′	NUM
ejpam-6540	344	5	h|	h|	PROPN
ejpam-6540	345	1	=	=	SYM
ejpam-6540	346	1	2·5h−2−1	2·5h−2−1	PROPN
ejpam-6540	346	2	.	.	PUNCT
ejpam-6540	347	1	then	then	ADV
ejpam-6540	347	2	,	,	PUNCT
ejpam-6540	347	3	there	there	PRON
ejpam-6540	347	4	exist	exist	VERB
ejpam-6540	347	5	i1	i1	PROPN
ejpam-6540	347	6	,	,	PUNCT
ejpam-6540	347	7	i2	i2	PROPN
ejpam-6540	347	8	,	,	PUNCT
ejpam-6540	347	9	.	.	PUNCT
ejpam-6540	347	10	.	.	PUNCT
ejpam-6540	348	1	.	.	PUNCT
ejpam-6540	349	1	,	,	PUNCT
ejpam-6540	349	2	ih−2	ih−2	PROPN
ejpam-6540	349	3	∈	∈	PROPN
ejpam-6540	349	4	z5	z5	PROPN
ejpam-6540	349	5	such	such	PROPN
ejpam-6540	349	6	k.	k.	PROPN
ejpam-6540	349	7	b.	b.	PROPN
ejpam-6540	349	8	dharan	dharan	PROPN
ejpam-6540	349	9	,	,	PUNCT
ejpam-6540	349	10	s.	s.	PROPN
ejpam-6540	349	11	radha	radha	PROPN
ejpam-6540	349	12	/	/	PUNCT
ejpam-6540	349	13	eur	eur	PROPN
ejpam-6540	349	14	.	.	PUNCT
ejpam-6540	350	1	j.	j.	PROPN
ejpam-6540	350	2	pure	pure	PROPN
ejpam-6540	350	3	appl	appl	PROPN
ejpam-6540	350	4	.	.	PROPN
ejpam-6540	350	5	math	math	PROPN
ejpam-6540	350	6	,	,	PUNCT
ejpam-6540	350	7	18	18	NUM
ejpam-6540	350	8	(	(	PUNCT
ejpam-6540	350	9	3	3	NUM
ejpam-6540	350	10	)	)	PUNCT
ejpam-6540	350	11	(	(	PUNCT
ejpam-6540	350	12	2025	2025	NUM
ejpam-6540	350	13	)	)	PUNCT
ejpam-6540	350	14	,	,	PUNCT
ejpam-6540	350	15	6540	6540	NUM
ejpam-6540	350	16	13	13	NUM
ejpam-6540	350	17	of	of	ADP
ejpam-6540	350	18	17	17	NUM
ejpam-6540	350	19	that	that	PRON
ejpam-6540	350	20	v(i1i2	v(i1i2	NOUN
ejpam-6540	350	21	.	.	PUNCT
ejpam-6540	350	22	.	.	PUNCT
ejpam-6540	350	23	.	.	PUNCT
ejpam-6540	351	1	ih−2s	ih−2s	PROPN
ejpam-6540	351	2	2	2	NUM
ejpam-6540	351	3	c5	c5	PROPN
ejpam-6540	351	4	)	)	PUNCT
ejpam-6540	351	5	∩w	∩w	NOUN
ejpam-6540	352	1	′	′	NUM
ejpam-6540	352	2	h	h	NOUN
ejpam-6540	352	3	<	<	X
ejpam-6540	352	4	2	2	NUM
ejpam-6540	352	5	with	with	ADP
ejpam-6540	352	6	two	two	NUM
ejpam-6540	352	7	pseudo	pseudo	NOUN
ejpam-6540	352	8	resolvers	resolver	NOUN
ejpam-6540	352	9	i1i2	i1i2	X
ejpam-6540	352	10	.	.	PUNCT
ejpam-6540	352	11	.	.	PUNCT
ejpam-6540	352	12	.	.	PUNCT
ejpam-6540	353	1	ih−2((ih−2	ih−2((ih−2	X
ejpam-6540	354	1	+	+	NOUN
ejpam-6540	354	2	1)mod	1)mod	PROPN
ejpam-6540	354	3	5)2	5)2	NUM
ejpam-6540	354	4	and	and	CCONJ
ejpam-6540	354	5	i1i2	i1i2	PROPN
ejpam-6540	354	6	.	.	PUNCT
ejpam-6540	354	7	.	.	PUNCT
ejpam-6540	354	8	.	.	PUNCT
ejpam-6540	355	1	ih−2((ih−2−1)mod	ih−2((ih−2−1)mod	ADJ
ejpam-6540	355	2	5)2	5)2	NUM
ejpam-6540	355	3	,	,	PUNCT
ejpam-6540	355	4	where	where	SCONJ
ejpam-6540	355	5	these	these	DET
ejpam-6540	355	6	vertices	vertex	NOUN
ejpam-6540	355	7	are	be	AUX
ejpam-6540	355	8	not	not	PART
ejpam-6540	355	9	enough	enough	ADJ
ejpam-6540	355	10	to	to	PART
ejpam-6540	355	11	fault	fault	AUX
ejpam-6540	355	12	-	-	PUNCT
ejpam-6540	355	13	tolerantly	tolerantly	ADV
ejpam-6540	355	14	resolve	resolve	VERB
ejpam-6540	355	15	the	the	DET
ejpam-6540	355	16	edges	edge	NOUN
ejpam-6540	355	17	incident	incident	NOUN
ejpam-6540	355	18	to	to	ADP
ejpam-6540	355	19	the	the	DET
ejpam-6540	355	20	vertices	vertex	NOUN
ejpam-6540	355	21	in	in	ADP
ejpam-6540	355	22	v(i1i2	v(i1i2	NOUN
ejpam-6540	355	23	.	.	PUNCT
ejpam-6540	355	24	.	.	PUNCT
ejpam-6540	355	25	.	.	PUNCT
ejpam-6540	356	1	ih−2s	ih−2s	PROPN
ejpam-6540	356	2	2	2	NUM
ejpam-6540	356	3	c5	c5	PROPN
ejpam-6540	356	4	)	)	PUNCT
ejpam-6540	356	5	,	,	PUNCT
ejpam-6540	356	6	a	a	DET
ejpam-6540	356	7	contradiction	contradiction	NOUN
ejpam-6540	356	8	.	.	PUNCT
ejpam-6540	357	1	so	so	ADV
ejpam-6540	357	2	,	,	PUNCT
ejpam-6540	357	3	we	we	PRON
ejpam-6540	357	4	conclude	conclude	VERB
ejpam-6540	357	5	that	that	SCONJ
ejpam-6540	357	6	dime′(sh	dime′(sh	PROPN
ejpam-6540	357	7	c5	c5	PROPN
ejpam-6540	357	8	)	)	PUNCT
ejpam-6540	357	9	≥	≥	PROPN
ejpam-6540	357	10	2	2	NUM
ejpam-6540	357	11	·	·	SYM
ejpam-6540	357	12	5h−2	5h−2	NUM
ejpam-6540	357	13	,	,	PUNCT
ejpam-6540	357	14	∀h	∀h	X
ejpam-6540	357	15	≥	≥	NUM
ejpam-6540	357	16	3	3	NUM
ejpam-6540	357	17	.	.	PUNCT
ejpam-6540	358	1	then	then	ADV
ejpam-6540	358	2	dime′(sh	dime′(sh	PROPN
ejpam-6540	358	3	c5	c5	PROPN
ejpam-6540	358	4	)	)	PUNCT
ejpam-6540	359	1	=	=	SYM
ejpam-6540	359	2	2	2	X
ejpam-6540	359	3	·	·	SYM
ejpam-6540	359	4	5h−2	5h−2	NUM
ejpam-6540	359	5	.	.	NOUN
ejpam-6540	360	1	4	4	X
ejpam-6540	360	2	.	.	X
ejpam-6540	360	3	conclusion	conclusion	NOUN
ejpam-6540	360	4	in	in	ADP
ejpam-6540	360	5	this	this	DET
ejpam-6540	360	6	study	study	NOUN
ejpam-6540	360	7	,	,	PUNCT
ejpam-6540	360	8	we	we	PRON
ejpam-6540	360	9	analyzed	analyze	VERB
ejpam-6540	360	10	dim	dim	NOUN
ejpam-6540	360	11	,	,	PUNCT
ejpam-6540	360	12	dim′	dim′	NOUN
ejpam-6540	360	13	,	,	PUNCT
ejpam-6540	360	14	dime	dime	NOUN
ejpam-6540	360	15	,	,	PUNCT
ejpam-6540	360	16	and	and	CCONJ
ejpam-6540	360	17	dime′	dime′	ADV
ejpam-6540	360	18	of	of	ADP
ejpam-6540	360	19	generalized	generalized	ADJ
ejpam-6540	360	20	sierpiński	sierpiński	ADJ
ejpam-6540	360	21	networks	network	NOUN
ejpam-6540	360	22	over	over	ADP
ejpam-6540	360	23	c5	c5	PROPN
ejpam-6540	360	24	.	.	PUNCT
ejpam-6540	361	1	our	our	PRON
ejpam-6540	361	2	findings	finding	NOUN
ejpam-6540	361	3	reveal	reveal	VERB
ejpam-6540	361	4	that	that	SCONJ
ejpam-6540	361	5	the	the	DET
ejpam-6540	361	6	fault	fault	NOUN
ejpam-6540	361	7	-	-	PUNCT
ejpam-6540	361	8	tolerant	tolerant	ADJ
ejpam-6540	361	9	(	(	PUNCT
ejpam-6540	361	10	edge	edge	NOUN
ejpam-6540	361	11	)	)	PUNCT
ejpam-6540	361	12	metric	metric	ADJ
ejpam-6540	361	13	dimension	dimension	NOUN
ejpam-6540	361	14	is	be	AUX
ejpam-6540	361	15	directly	directly	ADV
ejpam-6540	361	16	proportional	proportional	ADJ
ejpam-6540	361	17	to	to	ADP
ejpam-6540	361	18	the	the	DET
ejpam-6540	361	19	(	(	PUNCT
ejpam-6540	361	20	edge	edge	NOUN
ejpam-6540	361	21	)	)	PUNCT
ejpam-6540	361	22	metric	metric	ADJ
ejpam-6540	361	23	dimension	dimension	NOUN
ejpam-6540	361	24	with	with	ADP
ejpam-6540	361	25	proportionality	proportionality	NOUN
ejpam-6540	361	26	constant	constant	ADJ
ejpam-6540	361	27	2	2	NUM
ejpam-6540	361	28	,	,	PUNCT
ejpam-6540	361	29	for	for	ADP
ejpam-6540	361	30	this	this	DET
ejpam-6540	361	31	graph	graph	NOUN
ejpam-6540	361	32	family	family	NOUN
ejpam-6540	361	33	.	.	PUNCT
ejpam-6540	362	1	this	this	DET
ejpam-6540	362	2	relationship	relationship	NOUN
ejpam-6540	362	3	highlights	highlight	VERB
ejpam-6540	362	4	the	the	DET
ejpam-6540	362	5	structural	structural	ADJ
ejpam-6540	362	6	consistency	consistency	NOUN
ejpam-6540	362	7	of	of	ADP
ejpam-6540	362	8	these	these	DET
ejpam-6540	362	9	graphs	graph	NOUN
ejpam-6540	362	10	and	and	CCONJ
ejpam-6540	362	11	provides	provide	VERB
ejpam-6540	362	12	a	a	DET
ejpam-6540	362	13	fundamental	fundamental	ADJ
ejpam-6540	362	14	insight	insight	NOUN
ejpam-6540	362	15	into	into	ADP
ejpam-6540	362	16	their	their	PRON
ejpam-6540	362	17	resolvability	resolvability	NOUN
ejpam-6540	362	18	and	and	CCONJ
ejpam-6540	362	19	robustness	robustness	NOUN
ejpam-6540	362	20	in	in	ADP
ejpam-6540	362	21	network	network	NOUN
ejpam-6540	362	22	applications	application	NOUN
ejpam-6540	362	23	.	.	PUNCT
ejpam-6540	363	1	the	the	DET
ejpam-6540	363	2	proportionality	proportionality	NOUN
ejpam-6540	363	3	observed	observe	VERB
ejpam-6540	363	4	in	in	ADP
ejpam-6540	363	5	our	our	PRON
ejpam-6540	363	6	results	result	NOUN
ejpam-6540	363	7	has	have	VERB
ejpam-6540	363	8	practical	practical	ADJ
ejpam-6540	363	9	significance	significance	NOUN
ejpam-6540	363	10	in	in	ADP
ejpam-6540	363	11	fault	fault	NOUN
ejpam-6540	363	12	-	-	PUNCT
ejpam-6540	363	13	tolerant	tolerant	ADJ
ejpam-6540	363	14	network	network	NOUN
ejpam-6540	363	15	design	design	NOUN
ejpam-6540	363	16	,	,	PUNCT
ejpam-6540	363	17	where	where	SCONJ
ejpam-6540	363	18	ensuring	ensure	VERB
ejpam-6540	363	19	efficient	efficient	ADJ
ejpam-6540	363	20	localization	localization	NOUN
ejpam-6540	363	21	despite	despite	SCONJ
ejpam-6540	363	22	failures	failure	NOUN
ejpam-6540	363	23	is	be	AUX
ejpam-6540	363	24	crucial	crucial	ADJ
ejpam-6540	363	25	.	.	PUNCT
ejpam-6540	364	1	additionally	additionally	ADV
ejpam-6540	364	2	,	,	PUNCT
ejpam-6540	364	3	these	these	DET
ejpam-6540	364	4	findings	finding	NOUN
ejpam-6540	364	5	contribute	contribute	VERB
ejpam-6540	364	6	to	to	ADP
ejpam-6540	364	7	a	a	DET
ejpam-6540	364	8	deeper	deep	ADJ
ejpam-6540	364	9	understanding	understanding	NOUN
ejpam-6540	364	10	of	of	ADP
ejpam-6540	364	11	fractal	fractal	NOUN
ejpam-6540	364	12	-	-	PUNCT
ejpam-6540	364	13	based	base	VERB
ejpam-6540	364	14	graph	graph	NOUN
ejpam-6540	364	15	structures	structure	NOUN
ejpam-6540	364	16	,	,	PUNCT
ejpam-6540	364	17	reinforcing	reinforce	VERB
ejpam-6540	364	18	their	their	PRON
ejpam-6540	364	19	applicability	applicability	NOUN
ejpam-6540	364	20	in	in	ADP
ejpam-6540	364	21	areas	area	NOUN
ejpam-6540	364	22	such	such	ADJ
ejpam-6540	364	23	as	as	ADP
ejpam-6540	364	24	routing	routing	NOUN
ejpam-6540	364	25	,	,	PUNCT
ejpam-6540	364	26	surveillance	surveillance	NOUN
ejpam-6540	364	27	,	,	PUNCT
ejpam-6540	364	28	and	and	CCONJ
ejpam-6540	364	29	resilient	resilient	ADJ
ejpam-6540	364	30	communication	communication	NOUN
ejpam-6540	364	31	systems	system	NOUN
ejpam-6540	364	32	.	.	PUNCT
ejpam-6540	365	1	future	future	ADJ
ejpam-6540	365	2	work	work	NOUN
ejpam-6540	365	3	can	can	AUX
ejpam-6540	365	4	explore	explore	VERB
ejpam-6540	365	5	whether	whether	SCONJ
ejpam-6540	365	6	similar	similar	ADJ
ejpam-6540	365	7	proportional	proportional	ADJ
ejpam-6540	365	8	relationships	relationship	NOUN
ejpam-6540	365	9	hold	hold	VERB
ejpam-6540	365	10	for	for	ADP
ejpam-6540	365	11	other	other	ADJ
ejpam-6540	365	12	families	family	NOUN
ejpam-6540	365	13	of	of	ADP
ejpam-6540	365	14	generalized	generalized	ADJ
ejpam-6540	365	15	sierpiński	sierpiński	ADJ
ejpam-6540	365	16	networks	network	NOUN
ejpam-6540	365	17	or	or	CCONJ
ejpam-6540	365	18	different	different	ADJ
ejpam-6540	365	19	base	base	NOUN
ejpam-6540	365	20	structures	structure	NOUN
ejpam-6540	365	21	.	.	PUNCT
ejpam-6540	366	1	references	reference	NOUN
ejpam-6540	366	2	[	[	X
ejpam-6540	366	3	1	1	NUM
ejpam-6540	366	4	]	]	X
ejpam-6540	366	5	m.c	m.c	PROPN
ejpam-6540	366	6	.	.	PROPN
ejpam-6540	366	7	chen	chen	PROPN
ejpam-6540	366	8	.	.	PUNCT
ejpam-6540	367	1	a	a	DET
ejpam-6540	367	2	design	design	NOUN
ejpam-6540	367	3	methodology	methodology	NOUN
ejpam-6540	367	4	for	for	ADP
ejpam-6540	367	5	synthesizing	synthesize	VERB
ejpam-6540	367	6	parallel	parallel	ADJ
ejpam-6540	367	7	algorithms	algorithm	NOUN
ejpam-6540	367	8	and	and	CCONJ
ejpam-6540	367	9	architectueres	architectuere	NOUN
ejpam-6540	367	10	.	.	PUNCT
ejpam-6540	368	1	journal	journal	NOUN
ejpam-6540	368	2	of	of	ADP
ejpam-6540	368	3	parallel	parallel	ADJ
ejpam-6540	368	4	and	and	CCONJ
ejpam-6540	368	5	distributed	distributed	ADJ
ejpam-6540	368	6	computing	computing	NOUN
ejpam-6540	368	7	,	,	PUNCT
ejpam-6540	368	8	3(4):461–491	3(4):461–491	NUM
ejpam-6540	368	9	,	,	PUNCT
ejpam-6540	368	10	1986	1986	NUM
ejpam-6540	368	11	.	.	PUNCT
ejpam-6540	369	1	[	[	X
ejpam-6540	369	2	2	2	NUM
ejpam-6540	369	3	]	]	X
ejpam-6540	369	4	t.y	t.y	PROPN
ejpam-6540	369	5	.	.	PUNCT
ejpam-6540	369	6	chen	chen	PROPN
ejpam-6540	369	7	.	.	PUNCT
ejpam-6540	370	1	graph	graph	NOUN
ejpam-6540	370	2	traversal	traversal	NOUN
ejpam-6540	370	3	techniques	technique	NOUN
ejpam-6540	370	4	and	and	CCONJ
ejpam-6540	370	5	the	the	DET
ejpam-6540	370	6	maximum	maximum	ADJ
ejpam-6540	370	7	flow	flow	NOUN
ejpam-6540	370	8	problem	problem	NOUN
ejpam-6540	370	9	in	in	ADP
ejpam-6540	370	10	distributed	distribute	VERB
ejpam-6540	370	11	computation	computation	NOUN
ejpam-6540	370	12	.	.	PUNCT
ejpam-6540	371	1	ieee	ieee	NOUN
ejpam-6540	371	2	transactions	transaction	NOUN
ejpam-6540	371	3	on	on	ADP
ejpam-6540	371	4	software	software	NOUN
ejpam-6540	371	5	engineering	engineering	NOUN
ejpam-6540	371	6	,	,	PUNCT
ejpam-6540	371	7	se-9(4):504–512	se-9(4):504–512	ADJ
ejpam-6540	371	8	,	,	PUNCT
ejpam-6540	371	9	1983	1983	NUM
ejpam-6540	371	10	.	.	PUNCT
ejpam-6540	372	1	[	[	X
ejpam-6540	372	2	3	3	NUM
ejpam-6540	372	3	]	]	PUNCT
ejpam-6540	372	4	r.	r.	PROPN
ejpam-6540	372	5	shang	shang	PROPN
ejpam-6540	372	6	.	.	PUNCT
ejpam-6540	373	1	efficient	efficient	ADJ
ejpam-6540	373	2	task	task	PROPN
ejpam-6540	373	3	scheduling	scheduling	NOUN
ejpam-6540	373	4	for	for	ADP
ejpam-6540	373	5	large	large	ADJ
ejpam-6540	373	6	-	-	PUNCT
ejpam-6540	373	7	scale	scale	NOUN
ejpam-6540	373	8	graph	graph	NOUN
ejpam-6540	373	9	data	datum	NOUN
ejpam-6540	373	10	processing	processing	NOUN
ejpam-6540	373	11	in	in	ADP
ejpam-6540	373	12	cloud	cloud	NOUN
ejpam-6540	373	13	computing	computing	NOUN
ejpam-6540	373	14	:	:	PUNCT
ejpam-6540	373	15	a	a	DET
ejpam-6540	373	16	particle	particle	NOUN
ejpam-6540	373	17	swarm	swarm	NOUN
ejpam-6540	373	18	optimization	optimization	NOUN
ejpam-6540	373	19	approach	approach	NOUN
ejpam-6540	373	20	.	.	PUNCT
ejpam-6540	374	1	journal	journal	NOUN
ejpam-6540	374	2	of	of	ADP
ejpam-6540	374	3	combinatorial	combinatorial	ADJ
ejpam-6540	374	4	mathematics	mathematic	NOUN
ejpam-6540	374	5	and	and	CCONJ
ejpam-6540	374	6	combinatorial	combinatorial	ADJ
ejpam-6540	374	7	computing	computing	NOUN
ejpam-6540	374	8	,	,	PUNCT
ejpam-6540	374	9	122:135–148	122:135–148	NUM
ejpam-6540	374	10	,	,	PUNCT
ejpam-6540	374	11	2024	2024	NUM
ejpam-6540	374	12	.	.	PUNCT
ejpam-6540	375	1	[	[	X
ejpam-6540	375	2	4	4	X
ejpam-6540	375	3	]	]	PUNCT
ejpam-6540	375	4	h.	h.	PROPN
ejpam-6540	375	5	wang	wang	PROPN
ejpam-6540	375	6	,	,	PUNCT
ejpam-6540	375	7	w.	w.	PROPN
ejpam-6540	375	8	guo	guo	PROPN
ejpam-6540	375	9	,	,	PUNCT
ejpam-6540	375	10	and	and	CCONJ
ejpam-6540	375	11	m.	m.	PROPN
ejpam-6540	375	12	zhang	zhang	PROPN
ejpam-6540	375	13	.	.	PUNCT
ejpam-6540	376	1	performance	performance	NOUN
ejpam-6540	376	2	optimization	optimization	NOUN
ejpam-6540	376	3	of	of	ADP
ejpam-6540	376	4	heterogenious	heterogenious	ADJ
ejpam-6540	376	5	computing	computing	NOUN
ejpam-6540	376	6	for	for	ADP
ejpam-6540	376	7	large	large	ADJ
ejpam-6540	376	8	-	-	PUNCT
ejpam-6540	376	9	scale	scale	NOUN
ejpam-6540	376	10	dynamic	dynamic	ADJ
ejpam-6540	376	11	graph	graph	NOUN
ejpam-6540	376	12	data	datum	NOUN
ejpam-6540	376	13	.	.	PUNCT
ejpam-6540	377	1	the	the	DET
ejpam-6540	377	2	journal	journal	NOUN
ejpam-6540	377	3	of	of	ADP
ejpam-6540	377	4	supercomputing	supercomputing	NOUN
ejpam-6540	377	5	,	,	PUNCT
ejpam-6540	377	6	81(41	81(41	NUM
ejpam-6540	377	7	)	)	PUNCT
ejpam-6540	377	8	,	,	PUNCT
ejpam-6540	377	9	2025	2025	NUM
ejpam-6540	377	10	.	.	PUNCT
ejpam-6540	378	1	[	[	X
ejpam-6540	378	2	5	5	X
ejpam-6540	378	3	]	]	PUNCT
ejpam-6540	378	4	h.	h.	PROPN
ejpam-6540	378	5	raza	raza	PROPN
ejpam-6540	378	6	,	,	PUNCT
ejpam-6540	378	7	s.	s.	PROPN
ejpam-6540	378	8	hayat	hayat	PROPN
ejpam-6540	378	9	,	,	PUNCT
ejpam-6540	378	10	and	and	CCONJ
ejpam-6540	378	11	x.-f	x.-f	NOUN
ejpam-6540	378	12	.	.	PUNCT
ejpam-6540	379	1	pan	pan	PROPN
ejpam-6540	379	2	.	.	PROPN
ejpam-6540	380	1	on	on	ADP
ejpam-6540	380	2	the	the	DET
ejpam-6540	380	3	fault	fault	NOUN
ejpam-6540	380	4	-	-	PUNCT
ejpam-6540	380	5	tolerant	tolerant	ADJ
ejpam-6540	380	6	metric	metric	ADJ
ejpam-6540	380	7	dimension	dimension	NOUN
ejpam-6540	380	8	of	of	ADP
ejpam-6540	380	9	certain	certain	ADJ
ejpam-6540	380	10	interconnection	interconnection	NOUN
ejpam-6540	380	11	networks	network	NOUN
ejpam-6540	380	12	.	.	PUNCT
ejpam-6540	381	1	journal	journal	NOUN
ejpam-6540	381	2	of	of	ADP
ejpam-6540	381	3	applied	apply	VERB
ejpam-6540	381	4	mathematics	mathematic	NOUN
ejpam-6540	381	5	and	and	CCONJ
ejpam-6540	381	6	computing	computing	NOUN
ejpam-6540	381	7	,	,	PUNCT
ejpam-6540	381	8	60:517	60:517	NUM
ejpam-6540	381	9	–	–	PUNCT
ejpam-6540	381	10	535	535	NUM
ejpam-6540	381	11	,	,	PUNCT
ejpam-6540	381	12	2019	2019	NUM
ejpam-6540	381	13	.	.	PUNCT
ejpam-6540	382	1	[	[	X
ejpam-6540	382	2	6	6	NUM
ejpam-6540	382	3	]	]	PUNCT
ejpam-6540	382	4	s.	s.	PROPN
ejpam-6540	382	5	lagraa	lagraa	PROPN
ejpam-6540	382	6	,	,	PUNCT
ejpam-6540	382	7	m.	m.	NOUN
ejpam-6540	382	8	husák	husák	PROPN
ejpam-6540	382	9	,	,	PUNCT
ejpam-6540	382	10	h.	h.	PROPN
ejpam-6540	382	11	seba	seba	PROPN
ejpam-6540	382	12	,	,	PUNCT
ejpam-6540	382	13	s.	s.	PROPN
ejpam-6540	382	14	vuppala	vuppala	PROPN
ejpam-6540	382	15	,	,	PUNCT
ejpam-6540	382	16	r.	r.	PROPN
ejpam-6540	382	17	state	state	PROPN
ejpam-6540	382	18	,	,	PUNCT
ejpam-6540	382	19	and	and	CCONJ
ejpam-6540	382	20	m.	m.	NOUN
ejpam-6540	382	21	ouedraogo	ouedraogo	PROPN
ejpam-6540	382	22	.	.	PUNCT
ejpam-6540	383	1	a	a	DET
ejpam-6540	383	2	review	review	NOUN
ejpam-6540	383	3	on	on	ADP
ejpam-6540	383	4	graph	graph	NOUN
ejpam-6540	383	5	-	-	PUNCT
ejpam-6540	383	6	based	base	VERB
ejpam-6540	383	7	approaches	approach	NOUN
ejpam-6540	383	8	for	for	ADP
ejpam-6540	383	9	network	network	NOUN
ejpam-6540	383	10	security	security	NOUN
ejpam-6540	383	11	monitoring	monitoring	NOUN
ejpam-6540	383	12	and	and	CCONJ
ejpam-6540	383	13	botnet	botnet	NOUN
ejpam-6540	383	14	detection	detection	NOUN
ejpam-6540	383	15	.	.	PUNCT
ejpam-6540	384	1	international	international	ADJ
ejpam-6540	384	2	journal	journal	PROPN
ejpam-6540	384	3	of	of	ADP
ejpam-6540	384	4	information	information	NOUN
ejpam-6540	384	5	security	security	NOUN
ejpam-6540	384	6	,	,	PUNCT
ejpam-6540	384	7	23:119–140	23:119–140	NUM
ejpam-6540	384	8	,	,	PUNCT
ejpam-6540	384	9	2024	2024	NUM
ejpam-6540	384	10	.	.	PUNCT
ejpam-6540	385	1	[	[	X
ejpam-6540	385	2	7	7	X
ejpam-6540	385	3	]	]	X
ejpam-6540	385	4	k.t	k.t	PROPN
ejpam-6540	385	5	.	.	PROPN
ejpam-6540	385	6	min	min	PROPN
ejpam-6540	385	7	and	and	CCONJ
ejpam-6540	385	8	n.	n.	PROPN
ejpam-6540	385	9	jeyanthi	jeyanthi	PROPN
ejpam-6540	385	10	.	.	PUNCT
ejpam-6540	386	1	routing	route	VERB
ejpam-6540	386	2	performance	performance	NOUN
ejpam-6540	386	3	in	in	ADP
ejpam-6540	386	4	wireless	wireless	ADJ
ejpam-6540	386	5	sensor	sensor	NOUN
ejpam-6540	386	6	networks	network	NOUN
ejpam-6540	386	7	:	:	PUNCT
ejpam-6540	386	8	determining	determine	VERB
ejpam-6540	386	9	shortest	short	ADJ
ejpam-6540	386	10	path	path	NOUN
ejpam-6540	386	11	algorithms	algorithm	NOUN
ejpam-6540	386	12	effectiveness	effectiveness	NOUN
ejpam-6540	386	13	.	.	PUNCT
ejpam-6540	387	1	international	international	ADJ
ejpam-6540	387	2	journal	journal	PROPN
ejpam-6540	387	3	of	of	ADP
ejpam-6540	387	4	computer	computer	NOUN
ejpam-6540	387	5	networks	network	NOUN
ejpam-6540	387	6	&	&	CCONJ
ejpam-6540	387	7	communications	communication	NOUN
ejpam-6540	387	8	,	,	PUNCT
ejpam-6540	387	9	16(6	16(6	NUM
ejpam-6540	387	10	)	)	PUNCT
ejpam-6540	387	11	,	,	PUNCT
ejpam-6540	387	12	2024	2024	NUM
ejpam-6540	387	13	.	.	PUNCT
ejpam-6540	388	1	k.	k.	PROPN
ejpam-6540	388	2	b.	b.	PROPN
ejpam-6540	388	3	dharan	dharan	PROPN
ejpam-6540	388	4	,	,	PUNCT
ejpam-6540	388	5	s.	s.	PROPN
ejpam-6540	388	6	radha	radha	PROPN
ejpam-6540	388	7	/	/	PUNCT
ejpam-6540	388	8	eur	eur	PROPN
ejpam-6540	388	9	.	.	PUNCT
ejpam-6540	389	1	j.	j.	PROPN
ejpam-6540	389	2	pure	pure	PROPN
ejpam-6540	389	3	appl	appl	PROPN
ejpam-6540	389	4	.	.	PROPN
ejpam-6540	389	5	math	math	PROPN
ejpam-6540	389	6	,	,	PUNCT
ejpam-6540	389	7	18	18	NUM
ejpam-6540	389	8	(	(	PUNCT
ejpam-6540	389	9	3	3	NUM
ejpam-6540	389	10	)	)	PUNCT
ejpam-6540	389	11	(	(	PUNCT
ejpam-6540	389	12	2025	2025	NUM
ejpam-6540	389	13	)	)	PUNCT
ejpam-6540	389	14	,	,	PUNCT
ejpam-6540	389	15	6540	6540	NUM
ejpam-6540	389	16	14	14	NUM
ejpam-6540	389	17	of	of	ADP
ejpam-6540	389	18	17	17	NUM
ejpam-6540	390	1	[	[	SYM
ejpam-6540	390	2	8	8	NUM
ejpam-6540	390	3	]	]	X
ejpam-6540	390	4	y.	y.	PROPN
ejpam-6540	390	5	qi	qi	PROPN
ejpam-6540	390	6	,	,	PUNCT
ejpam-6540	390	7	y.	y.	PROPN
ejpam-6540	390	8	dong	dong	PROPN
ejpam-6540	390	9	,	,	PUNCT
ejpam-6540	390	10	z.	z.	PROPN
ejpam-6540	390	11	zhang	zhang	PROPN
ejpam-6540	390	12	,	,	PUNCT
ejpam-6540	390	13	and	and	CCONJ
ejpam-6540	390	14	z.	z.	PROPN
ejpam-6540	390	15	zhang	zhang	PROPN
ejpam-6540	390	16	.	.	PUNCT
ejpam-6540	391	1	hitting	hit	VERB
ejpam-6540	391	2	times	time	NOUN
ejpam-6540	391	3	for	for	ADP
ejpam-6540	391	4	random	random	ADJ
ejpam-6540	391	5	walks	walk	NOUN
ejpam-6540	391	6	on	on	ADP
ejpam-6540	391	7	sierpiński	sierpiński	ADJ
ejpam-6540	391	8	networks	network	NOUN
ejpam-6540	391	9	and	and	CCONJ
ejpam-6540	391	10	hierarchical	hierarchical	ADJ
ejpam-6540	391	11	graphs	graph	NOUN
ejpam-6540	391	12	.	.	PUNCT
ejpam-6540	392	1	the	the	DET
ejpam-6540	392	2	computer	computer	NOUN
ejpam-6540	392	3	journal	journal	NOUN
ejpam-6540	392	4	,	,	PUNCT
ejpam-6540	392	5	63(1):1385–1396	63(1):1385–1396	NUM
ejpam-6540	392	6	,	,	PUNCT
ejpam-6540	392	7	2020	2020	NUM
ejpam-6540	392	8	.	.	PUNCT
ejpam-6540	393	1	[	[	X
ejpam-6540	393	2	9	9	NUM
ejpam-6540	393	3	]	]	PUNCT
ejpam-6540	393	4	m.	m.	NOUN
ejpam-6540	393	5	arulperumjothi	arulperumjothi	PROPN
ejpam-6540	393	6	,	,	PUNCT
ejpam-6540	393	7	s.	s.	PROPN
ejpam-6540	393	8	klavžar	klavžar	PROPN
ejpam-6540	393	9	,	,	PUNCT
ejpam-6540	393	10	and	and	CCONJ
ejpam-6540	393	11	s.	s.	PROPN
ejpam-6540	393	12	prabhu	prabhu	PROPN
ejpam-6540	393	13	.	.	PUNCT
ejpam-6540	394	1	redefining	redefine	VERB
ejpam-6540	394	2	fractal	fractal	ADJ
ejpam-6540	394	3	cubic	cubic	ADJ
ejpam-6540	394	4	networks	network	NOUN
ejpam-6540	394	5	and	and	CCONJ
ejpam-6540	394	6	determining	determine	VERB
ejpam-6540	394	7	their	their	PRON
ejpam-6540	394	8	metric	metric	ADJ
ejpam-6540	394	9	dimension	dimension	NOUN
ejpam-6540	394	10	and	and	CCONJ
ejpam-6540	394	11	fault	fault	NOUN
ejpam-6540	394	12	-	-	PUNCT
ejpam-6540	394	13	tolerant	tolerant	ADJ
ejpam-6540	394	14	metric	metric	ADJ
ejpam-6540	394	15	dimension	dimension	NOUN
ejpam-6540	394	16	.	.	PUNCT
ejpam-6540	395	1	applied	apply	VERB
ejpam-6540	395	2	mathematics	mathematic	NOUN
ejpam-6540	395	3	and	and	CCONJ
ejpam-6540	395	4	computation	computation	NOUN
ejpam-6540	395	5	,	,	PUNCT
ejpam-6540	395	6	452:128037	452:128037	NUM
ejpam-6540	395	7	,	,	PUNCT
ejpam-6540	395	8	2023	2023	NUM
ejpam-6540	395	9	.	.	PUNCT
ejpam-6540	396	1	[	[	X
ejpam-6540	396	2	10	10	NUM
ejpam-6540	396	3	]	]	X
ejpam-6540	396	4	i.	i.	PROPN
ejpam-6540	396	5	javid	javid	PROPN
ejpam-6540	396	6	,	,	PUNCT
ejpam-6540	396	7	h.	h.	PROPN
ejpam-6540	396	8	benish	benish	PROPN
ejpam-6540	396	9	,	,	PUNCT
ejpam-6540	396	10	m.	m.	NOUN
ejpam-6540	396	11	imran	imran	PROPN
ejpam-6540	396	12	,	,	PUNCT
ejpam-6540	396	13	a.	a.	PROPN
ejpam-6540	396	14	khan	khan	PROPN
ejpam-6540	396	15	,	,	PUNCT
ejpam-6540	396	16	and	and	CCONJ
ejpam-6540	396	17	z.	z.	PROPN
ejpam-6540	396	18	ullah	ullah	PROPN
ejpam-6540	396	19	.	.	PUNCT
ejpam-6540	397	1	on	on	ADP
ejpam-6540	397	2	some	some	DET
ejpam-6540	397	3	bounds	bound	NOUN
ejpam-6540	397	4	of	of	ADP
ejpam-6540	397	5	the	the	DET
ejpam-6540	397	6	topological	topological	ADJ
ejpam-6540	397	7	indices	index	NOUN
ejpam-6540	397	8	of	of	ADP
ejpam-6540	397	9	generalized	generalized	ADJ
ejpam-6540	397	10	sierpiński	sierpiński	ADJ
ejpam-6540	397	11	and	and	CCONJ
ejpam-6540	397	12	extended	extend	VERB
ejpam-6540	397	13	sierpiński	sierpiński	ADJ
ejpam-6540	397	14	networks	network	NOUN
ejpam-6540	397	15	.	.	PUNCT
ejpam-6540	398	1	journal	journal	PROPN
ejpam-6540	398	2	of	of	ADP
ejpam-6540	398	3	inequalities	inequality	NOUN
ejpam-6540	398	4	and	and	CCONJ
ejpam-6540	398	5	applications	application	NOUN
ejpam-6540	398	6	,	,	PUNCT
ejpam-6540	398	7	2019(37	2019(37	NUM
ejpam-6540	398	8	)	)	PUNCT
ejpam-6540	398	9	,	,	PUNCT
ejpam-6540	398	10	2019	2019	NUM
ejpam-6540	398	11	.	.	PUNCT
ejpam-6540	399	1	[	[	X
ejpam-6540	399	2	11	11	NUM
ejpam-6540	399	3	]	]	PUNCT
ejpam-6540	399	4	k.	k.	PROPN
ejpam-6540	399	5	liu	liu	PROPN
ejpam-6540	399	6	and	and	CCONJ
ejpam-6540	399	7	n.	n.	PROPN
ejpam-6540	399	8	abu	abu	PROPN
ejpam-6540	399	9	-	-	PUNCT
ejpam-6540	399	10	ghazaleh	ghazaleh	PROPN
ejpam-6540	399	11	.	.	PUNCT
ejpam-6540	400	1	virtual	virtual	ADJ
ejpam-6540	400	2	coordinates	coordinate	NOUN
ejpam-6540	400	3	with	with	ADP
ejpam-6540	400	4	backtracking	backtrack	VERB
ejpam-6540	400	5	for	for	ADP
ejpam-6540	400	6	void	void	ADJ
ejpam-6540	400	7	traversal	traversal	NOUN
ejpam-6540	400	8	in	in	ADP
ejpam-6540	400	9	geographic	geographic	ADJ
ejpam-6540	400	10	routing	routing	NOUN
ejpam-6540	400	11	.	.	PUNCT
ejpam-6540	401	1	in	in	ADP
ejpam-6540	401	2	adhoc	adhoc	NOUN
ejpam-6540	401	3	-	-	PUNCT
ejpam-6540	401	4	now	now	ADV
ejpam-6540	401	5	2006	2006	NUM
ejpam-6540	401	6	,	,	PUNCT
ejpam-6540	401	7	lecture	lecture	NOUN
ejpam-6540	401	8	notes	note	NOUN
ejpam-6540	401	9	in	in	ADP
ejpam-6540	401	10	computer	computer	NOUN
ejpam-6540	401	11	science	science	NOUN
ejpam-6540	401	12	,	,	PUNCT
ejpam-6540	401	13	volume	volume	NOUN
ejpam-6540	401	14	4104	4104	NUM
ejpam-6540	401	15	,	,	PUNCT
ejpam-6540	401	16	pages	page	NOUN
ejpam-6540	401	17	45–59	45–59	NUM
ejpam-6540	401	18	,	,	PUNCT
ejpam-6540	401	19	2006	2006	NUM
ejpam-6540	401	20	.	.	PUNCT
ejpam-6540	402	1	[	[	X
ejpam-6540	402	2	12	12	NUM
ejpam-6540	402	3	]	]	PUNCT
ejpam-6540	402	4	b.	b.	PROPN
ejpam-6540	402	5	hu	hu	PROPN
ejpam-6540	402	6	,	,	PUNCT
ejpam-6540	402	7	z.	z.	PROPN
ejpam-6540	402	8	cao	cao	PROPN
ejpam-6540	402	9	,	,	PUNCT
ejpam-6540	402	10	and	and	CCONJ
ejpam-6540	402	11	m.	m.	PROPN
ejpam-6540	402	12	zhou	zhou	PROPN
ejpam-6540	402	13	.	.	PUNCT
ejpam-6540	403	1	energy	energy	NOUN
ejpam-6540	403	2	-	-	PUNCT
ejpam-6540	403	3	minimized	minimized	ADJ
ejpam-6540	403	4	scheduling	scheduling	NOUN
ejpam-6540	403	5	of	of	ADP
ejpam-6540	403	6	real	real	ADJ
ejpam-6540	403	7	-	-	PUNCT
ejpam-6540	403	8	time	time	NOUN
ejpam-6540	403	9	parallel	parallel	ADJ
ejpam-6540	403	10	workflows	workflow	NOUN
ejpam-6540	403	11	on	on	ADP
ejpam-6540	403	12	heterogeneous	heterogeneous	ADJ
ejpam-6540	403	13	distributed	distribute	VERB
ejpam-6540	403	14	computing	computing	NOUN
ejpam-6540	403	15	system	system	NOUN
ejpam-6540	403	16	.	.	PUNCT
ejpam-6540	404	1	ieee	ieee	NOUN
ejpam-6540	404	2	transactions	transaction	NOUN
ejpam-6540	404	3	on	on	ADP
ejpam-6540	404	4	services	service	NOUN
ejpam-6540	404	5	computing	computing	NOUN
ejpam-6540	404	6	,	,	PUNCT
ejpam-6540	404	7	15(5):2766–2779	15(5):2766–2779	PROPN
ejpam-6540	404	8	,	,	PUNCT
ejpam-6540	404	9	2022	2022	NUM
ejpam-6540	404	10	.	.	PUNCT
ejpam-6540	405	1	[	[	X
ejpam-6540	405	2	13	13	NUM
ejpam-6540	405	3	]	]	X
ejpam-6540	405	4	e.	e.	PROPN
ejpam-6540	405	5	fernández	fernández	PROPN
ejpam-6540	405	6	and	and	CCONJ
ejpam-6540	405	7	h.	h.	PROPN
ejpam-6540	405	8	f.	f.	PROPN
ejpam-6540	405	9	jelinek	jelinek	PROPN
ejpam-6540	405	10	.	.	PUNCT
ejpam-6540	406	1	use	use	NOUN
ejpam-6540	406	2	of	of	ADP
ejpam-6540	406	3	fractal	fractal	ADJ
ejpam-6540	406	4	theory	theory	NOUN
ejpam-6540	406	5	in	in	ADP
ejpam-6540	406	6	neuroscience	neuroscience	NOUN
ejpam-6540	406	7	:	:	PUNCT
ejpam-6540	406	8	methods	method	NOUN
ejpam-6540	406	9	,	,	PUNCT
ejpam-6540	406	10	advantages	advantage	NOUN
ejpam-6540	406	11	,	,	PUNCT
ejpam-6540	406	12	and	and	CCONJ
ejpam-6540	406	13	potential	potential	ADJ
ejpam-6540	406	14	problems	problem	NOUN
ejpam-6540	406	15	.	.	PUNCT
ejpam-6540	407	1	methods	method	NOUN
ejpam-6540	407	2	,	,	PUNCT
ejpam-6540	407	3	24(4):309–321	24(4):309–321	NUM
ejpam-6540	407	4	,	,	PUNCT
ejpam-6540	407	5	2001	2001	NUM
ejpam-6540	407	6	.	.	PUNCT
ejpam-6540	408	1	[	[	X
ejpam-6540	408	2	14	14	NUM
ejpam-6540	408	3	]	]	X
ejpam-6540	408	4	o.	o.	PROPN
ejpam-6540	408	5	lópez	lópez	PROPN
ejpam-6540	408	6	-	-	PUNCT
ejpam-6540	408	7	ortega	ortega	PROPN
ejpam-6540	408	8	and	and	CCONJ
ejpam-6540	408	9	s.i	s.i	PROPN
ejpam-6540	408	10	.	.	PROPN
ejpam-6540	408	11	lópez	lópez	ADV
ejpam-6540	408	12	-	-	PUNCT
ejpam-6540	408	13	popa	popa	NOUN
ejpam-6540	408	14	.	.	PUNCT
ejpam-6540	409	1	fractals	fractal	NOUN
ejpam-6540	409	2	,	,	PUNCT
ejpam-6540	409	3	fuzzy	fuzzy	ADJ
ejpam-6540	409	4	logic	logic	NOUN
ejpam-6540	409	5	and	and	CCONJ
ejpam-6540	409	6	expert	expert	NOUN
ejpam-6540	409	7	systems	system	NOUN
ejpam-6540	409	8	to	to	PART
ejpam-6540	409	9	assist	assist	VERB
ejpam-6540	409	10	in	in	ADP
ejpam-6540	409	11	the	the	DET
ejpam-6540	409	12	construction	construction	NOUN
ejpam-6540	409	13	of	of	ADP
ejpam-6540	409	14	musical	musical	ADJ
ejpam-6540	409	15	pieces	piece	NOUN
ejpam-6540	409	16	.	.	PUNCT
ejpam-6540	410	1	expert	expert	NOUN
ejpam-6540	410	2	systems	system	NOUN
ejpam-6540	410	3	with	with	ADP
ejpam-6540	410	4	applications	application	NOUN
ejpam-6540	410	5	,	,	PUNCT
ejpam-6540	410	6	39(15):11911–11923	39(15):11911–11923	NUM
ejpam-6540	410	7	,	,	PUNCT
ejpam-6540	410	8	2012	2012	NUM
ejpam-6540	410	9	.	.	PUNCT
ejpam-6540	411	1	[	[	X
ejpam-6540	411	2	15	15	NUM
ejpam-6540	411	3	]	]	X
ejpam-6540	411	4	m.	m.	NOUN
ejpam-6540	411	5	obert	obert	NOUN
ejpam-6540	411	6	,	,	PUNCT
ejpam-6540	411	7	p.	p.	NOUN
ejpam-6540	411	8	pfeifer	pfeifer	NOUN
ejpam-6540	411	9	,	,	PUNCT
ejpam-6540	411	10	and	and	CCONJ
ejpam-6540	411	11	m.	m.	NOUN
ejpam-6540	411	12	sernetz	sernetz	NOUN
ejpam-6540	411	13	.	.	PUNCT
ejpam-6540	412	1	microbial	microbial	ADJ
ejpam-6540	412	2	growth	growth	NOUN
ejpam-6540	412	3	patterns	pattern	NOUN
ejpam-6540	412	4	described	describe	VERB
ejpam-6540	412	5	by	by	ADP
ejpam-6540	412	6	fractal	fractal	ADJ
ejpam-6540	412	7	geometry	geometry	NOUN
ejpam-6540	412	8	.	.	PUNCT
ejpam-6540	413	1	journal	journal	PROPN
ejpam-6540	413	2	of	of	ADP
ejpam-6540	413	3	bacteriology	bacteriology	NOUN
ejpam-6540	413	4	,	,	PUNCT
ejpam-6540	413	5	172(3):1180–1185	172(3):1180–1185	NUM
ejpam-6540	413	6	,	,	PUNCT
ejpam-6540	413	7	1990	1990	NUM
ejpam-6540	413	8	.	.	PUNCT
ejpam-6540	414	1	[	[	X
ejpam-6540	414	2	16	16	X
ejpam-6540	414	3	]	]	X
ejpam-6540	414	4	y.	y.	PROPN
ejpam-6540	414	5	zhao	zhao	PROPN
ejpam-6540	414	6	,	,	PUNCT
ejpam-6540	414	7	k.	k.	PROPN
ejpam-6540	414	8	yoshigoe	yoshigoe	PROPN
ejpam-6540	414	9	,	,	PUNCT
ejpam-6540	414	10	j.	j.	PROPN
ejpam-6540	414	11	bian	bian	PROPN
ejpam-6540	414	12	,	,	PUNCT
ejpam-6540	414	13	m.	m.	PROPN
ejpam-6540	414	14	xie	xie	PROPN
ejpam-6540	414	15	,	,	PUNCT
ejpam-6540	414	16	and	and	CCONJ
ejpam-6540	414	17	y.	y.	PROPN
ejpam-6540	414	18	feng	feng	PROPN
ejpam-6540	414	19	.	.	PUNCT
ejpam-6540	415	1	a	a	DET
ejpam-6540	415	2	distributed	distribute	VERB
ejpam-6540	415	3	graph	graph	NOUN
ejpam-6540	415	4	-	-	PUNCT
ejpam-6540	415	5	parallel	parallel	ADJ
ejpam-6540	415	6	computing	computing	NOUN
ejpam-6540	415	7	system	system	NOUN
ejpam-6540	415	8	with	with	ADP
ejpam-6540	415	9	lightweight	lightweight	ADJ
ejpam-6540	415	10	communication	communication	NOUN
ejpam-6540	415	11	overhead	overhead	ADV
ejpam-6540	415	12	.	.	PUNCT
ejpam-6540	416	1	ieee	ieee	NOUN
ejpam-6540	416	2	transactions	transaction	NOUN
ejpam-6540	416	3	on	on	ADP
ejpam-6540	416	4	big	big	ADJ
ejpam-6540	416	5	data	datum	NOUN
ejpam-6540	416	6	,	,	PUNCT
ejpam-6540	416	7	2(3):204–218	2(3):204–218	NUM
ejpam-6540	416	8	,	,	PUNCT
ejpam-6540	416	9	2016	2016	NUM
ejpam-6540	416	10	.	.	PUNCT
ejpam-6540	417	1	[	[	X
ejpam-6540	417	2	17	17	NUM
ejpam-6540	417	3	]	]	X
ejpam-6540	417	4	g.d	g.d	PROPN
ejpam-6540	417	5	.	.	PROPN
ejpam-6540	417	6	vecchia	vecchia	PROPN
ejpam-6540	417	7	and	and	CCONJ
ejpam-6540	417	8	c.	c.	PROPN
ejpam-6540	417	9	sanges	sange	NOUN
ejpam-6540	417	10	.	.	PUNCT
ejpam-6540	418	1	a	a	DET
ejpam-6540	418	2	recursively	recursively	ADV
ejpam-6540	418	3	scalable	scalable	ADJ
ejpam-6540	418	4	network	network	NOUN
ejpam-6540	418	5	vlsi	vlsi	NOUN
ejpam-6540	418	6	implementation	implementation	NOUN
ejpam-6540	418	7	.	.	PUNCT
ejpam-6540	419	1	future	future	ADJ
ejpam-6540	419	2	generation	generation	NOUN
ejpam-6540	419	3	computer	computer	NOUN
ejpam-6540	419	4	systems	system	NOUN
ejpam-6540	419	5	,	,	PUNCT
ejpam-6540	419	6	4(5):235–243	4(5):235–243	NOUN
ejpam-6540	419	7	,	,	PUNCT
ejpam-6540	419	8	1988	1988	NUM
ejpam-6540	419	9	.	.	PUNCT
ejpam-6540	420	1	[	[	X
ejpam-6540	420	2	18	18	NUM
ejpam-6540	420	3	]	]	X
ejpam-6540	420	4	s.	s.	PROPN
ejpam-6540	420	5	klavžar	klavžar	PROPN
ejpam-6540	420	6	and	and	CCONJ
ejpam-6540	420	7	u.	u.	VERB
ejpam-6540	420	8	milutinović.	milutinović.	PROPN
ejpam-6540	420	9	graphs	graph	NOUN
ejpam-6540	420	10	s(n	s(n	PROPN
ejpam-6540	420	11	,	,	PUNCT
ejpam-6540	420	12	k	k	NOUN
ejpam-6540	420	13	)	)	PUNCT
ejpam-6540	420	14	and	and	CCONJ
ejpam-6540	420	15	a	a	DET
ejpam-6540	420	16	variant	variant	NOUN
ejpam-6540	420	17	of	of	ADP
ejpam-6540	420	18	the	the	DET
ejpam-6540	420	19	tower	tower	NOUN
ejpam-6540	420	20	of	of	ADP
ejpam-6540	420	21	hanoi	hanoi	PROPN
ejpam-6540	420	22	problem	problem	NOUN
ejpam-6540	420	23	.	.	PUNCT
ejpam-6540	421	1	czechoslovak	czechoslovak	ADJ
ejpam-6540	421	2	mathematical	mathematical	PROPN
ejpam-6540	421	3	journal	journal	PROPN
ejpam-6540	421	4	,	,	PUNCT
ejpam-6540	421	5	47(1):95–104	47(1):95–104	PROPN
ejpam-6540	421	6	,	,	PUNCT
ejpam-6540	421	7	1997	1997	NUM
ejpam-6540	421	8	.	.	PUNCT
ejpam-6540	422	1	[	[	X
ejpam-6540	422	2	19	19	NUM
ejpam-6540	422	3	]	]	PUNCT
ejpam-6540	422	4	a.m.	a.m.	PROPN
ejpam-6540	422	5	hinz	hinz	PROPN
ejpam-6540	422	6	,	,	PUNCT
ejpam-6540	422	7	s.	s.	PROPN
ejpam-6540	422	8	klavžar	klavžar	PROPN
ejpam-6540	422	9	,	,	PUNCT
ejpam-6540	422	10	and	and	CCONJ
ejpam-6540	422	11	s.s	s.s	PROPN
ejpam-6540	422	12	.	.	PROPN
ejpam-6540	422	13	zemljič.	zemljič.	PROPN
ejpam-6540	422	14	a	a	DET
ejpam-6540	422	15	survey	survey	NOUN
ejpam-6540	422	16	and	and	CCONJ
ejpam-6540	422	17	classification	classification	NOUN
ejpam-6540	422	18	of	of	ADP
ejpam-6540	422	19	sierpiński	sierpiński	ADJ
ejpam-6540	422	20	-	-	PUNCT
ejpam-6540	422	21	type	type	NOUN
ejpam-6540	422	22	graphs	graph	NOUN
ejpam-6540	422	23	.	.	PUNCT
ejpam-6540	423	1	discrete	discrete	ADJ
ejpam-6540	423	2	applied	apply	VERB
ejpam-6540	423	3	mathematics	mathematic	NOUN
ejpam-6540	423	4	,	,	PUNCT
ejpam-6540	423	5	217:565–600	217:565–600	NUM
ejpam-6540	423	6	,	,	PUNCT
ejpam-6540	423	7	2017	2017	NUM
ejpam-6540	423	8	.	.	PUNCT
ejpam-6540	424	1	[	[	X
ejpam-6540	424	2	20	20	NUM
ejpam-6540	424	3	]	]	X
ejpam-6540	424	4	j.a	j.a	PROPN
ejpam-6540	424	5	.	.	PROPN
ejpam-6540	424	6	rodŕıguez	rodŕıguez	PROPN
ejpam-6540	424	7	-	-	NOUN
ejpam-6540	424	8	velázquez	velázquez	PROPN
ejpam-6540	424	9	,	,	PUNCT
ejpam-6540	424	10	e.d	e.d	PROPN
ejpam-6540	424	11	.	.	PUNCT
ejpam-6540	424	12	rodŕıquez	rodŕıquez	NOUN
ejpam-6540	424	13	-	-	PUNCT
ejpam-6540	424	14	bazán	bazán	ADJ
ejpam-6540	424	15	,	,	PUNCT
ejpam-6540	424	16	and	and	CCONJ
ejpam-6540	424	17	a.	a.	PROPN
ejpam-6540	424	18	estrada	estrada	PROPN
ejpam-6540	424	19	-	-	PUNCT
ejpam-6540	424	20	moreno	moreno	PROPN
ejpam-6540	424	21	.	.	PUNCT
ejpam-6540	425	1	on	on	ADP
ejpam-6540	425	2	generalized	generalized	ADJ
ejpam-6540	425	3	sierpiński	sierpiński	ADJ
ejpam-6540	425	4	networks	network	NOUN
ejpam-6540	425	5	.	.	PUNCT
ejpam-6540	426	1	discussiones	discussione	NOUN
ejpam-6540	426	2	mathematicae	mathematicae	PROPN
ejpam-6540	426	3	graph	graph	NOUN
ejpam-6540	426	4	theory	theory	NOUN
ejpam-6540	426	5	,	,	PUNCT
ejpam-6540	426	6	37(3):547–560	37(3):547–560	PROPN
ejpam-6540	426	7	,	,	PUNCT
ejpam-6540	426	8	2017	2017	NUM
ejpam-6540	426	9	.	.	PUNCT
ejpam-6540	427	1	[	[	X
ejpam-6540	427	2	21	21	NUM
ejpam-6540	427	3	]	]	PUNCT
ejpam-6540	427	4	k.	k.	PROPN
ejpam-6540	427	5	balakrishnan	balakrishnan	PROPN
ejpam-6540	427	6	,	,	PUNCT
ejpam-6540	427	7	m.	m.	NOUN
ejpam-6540	427	8	changat	changat	PROPN
ejpam-6540	427	9	,	,	PUNCT
ejpam-6540	427	10	a.m.	a.m.	PROPN
ejpam-6540	427	11	hinz	hinz	PROPN
ejpam-6540	427	12	,	,	PUNCT
ejpam-6540	427	13	and	and	CCONJ
ejpam-6540	427	14	d.s	d.s	PROPN
ejpam-6540	427	15	.	.	PROPN
ejpam-6540	427	16	lekha	lekha	PROPN
ejpam-6540	427	17	.	.	PUNCT
ejpam-6540	428	1	the	the	DET
ejpam-6540	428	2	median	median	NOUN
ejpam-6540	428	3	of	of	ADP
ejpam-6540	428	4	sierpiński	sierpiński	PROPN
ejpam-6540	428	5	networks	network	NOUN
ejpam-6540	428	6	.	.	PUNCT
ejpam-6540	429	1	discrete	discrete	ADJ
ejpam-6540	429	2	applied	apply	VERB
ejpam-6540	429	3	mathematics	mathematic	NOUN
ejpam-6540	429	4	,	,	PUNCT
ejpam-6540	429	5	319:159–170	319:159–170	NUM
ejpam-6540	429	6	,	,	PUNCT
ejpam-6540	429	7	2022	2022	NUM
ejpam-6540	429	8	.	.	PUNCT
ejpam-6540	430	1	[	[	X
ejpam-6540	430	2	22	22	NUM
ejpam-6540	430	3	]	]	PUNCT
ejpam-6540	430	4	a.m.	a.m.	PROPN
ejpam-6540	431	1	hinz	hinz	PROPN
ejpam-6540	431	2	and	and	CCONJ
ejpam-6540	431	3	d.	d.	PROPN
ejpam-6540	431	4	parisse	parisse	PROPN
ejpam-6540	431	5	.	.	PUNCT
ejpam-6540	432	1	the	the	DET
ejpam-6540	432	2	average	average	ADJ
ejpam-6540	432	3	eccentricity	eccentricity	NOUN
ejpam-6540	432	4	of	of	ADP
ejpam-6540	432	5	sierpiński	sierpiński	ADJ
ejpam-6540	432	6	networks	network	NOUN
ejpam-6540	432	7	.	.	PUNCT
ejpam-6540	433	1	graphs	graph	NOUN
ejpam-6540	433	2	and	and	CCONJ
ejpam-6540	433	3	combinatorics	combinatoric	NOUN
ejpam-6540	433	4	,	,	PUNCT
ejpam-6540	433	5	28(5):671–686	28(5):671–686	PROPN
ejpam-6540	433	6	,	,	PUNCT
ejpam-6540	433	7	2012	2012	NUM
ejpam-6540	433	8	.	.	PUNCT
ejpam-6540	434	1	[	[	X
ejpam-6540	434	2	23	23	NUM
ejpam-6540	434	3	]	]	X
ejpam-6540	434	4	s.	s.	PROPN
ejpam-6540	434	5	klavžar	klavžar	PROPN
ejpam-6540	434	6	and	and	CCONJ
ejpam-6540	434	7	s.s	s.s	PROPN
ejpam-6540	434	8	.	.	PROPN
ejpam-6540	434	9	zemljič.	zemljič.	PROPN
ejpam-6540	434	10	connectivity	connectivity	NOUN
ejpam-6540	434	11	and	and	CCONJ
ejpam-6540	434	12	some	some	DET
ejpam-6540	434	13	other	other	ADJ
ejpam-6540	434	14	properties	property	NOUN
ejpam-6540	434	15	of	of	ADP
ejpam-6540	434	16	generalized	generalized	ADJ
ejpam-6540	434	17	sierpiński	sierpiński	ADJ
ejpam-6540	434	18	networks	network	NOUN
ejpam-6540	434	19	.	.	PUNCT
ejpam-6540	435	1	applicable	applicable	ADJ
ejpam-6540	435	2	analysis	analysis	NOUN
ejpam-6540	435	3	and	and	CCONJ
ejpam-6540	435	4	discrete	discrete	ADJ
ejpam-6540	435	5	mathematics	mathematic	NOUN
ejpam-6540	435	6	,	,	PUNCT
ejpam-6540	435	7	12(2):401–412	12(2):401–412	PROPN
ejpam-6540	435	8	,	,	PUNCT
ejpam-6540	435	9	2018	2018	NUM
ejpam-6540	435	10	.	.	PUNCT
ejpam-6540	436	1	[	[	X
ejpam-6540	436	2	24	24	NUM
ejpam-6540	436	3	]	]	PUNCT
ejpam-6540	436	4	m.	m.	NOUN
ejpam-6540	436	5	imran	imran	PROPN
ejpam-6540	436	6	,	,	PUNCT
ejpam-6540	436	7	sabeel	sabeel	PROPN
ejpam-6540	436	8	e	e	PROPN
ejpam-6540	436	9	hafi	hafi	PROPN
ejpam-6540	436	10	,	,	PUNCT
ejpam-6540	436	11	w.	w.	PROPN
ejpam-6540	436	12	gao	gao	PROPN
ejpam-6540	436	13	,	,	PUNCT
ejpam-6540	436	14	and	and	CCONJ
ejpam-6540	436	15	m.r	m.r	PROPN
ejpam-6540	436	16	.	.	PROPN
ejpam-6540	436	17	farahani	farahani	PROPN
ejpam-6540	436	18	.	.	PUNCT
ejpam-6540	437	1	on	on	ADP
ejpam-6540	437	2	the	the	DET
ejpam-6540	437	3	topological	topological	ADJ
ejpam-6540	437	4	properties	property	NOUN
ejpam-6540	437	5	of	of	ADP
ejpam-6540	437	6	sierpiński	sierpiński	ADJ
ejpam-6540	437	7	networks	network	NOUN
ejpam-6540	437	8	.	.	PUNCT
ejpam-6540	438	1	chaos	chaos	NOUN
ejpam-6540	438	2	,	,	PUNCT
ejpam-6540	438	3	solitons	soliton	NOUN
ejpam-6540	438	4	&	&	CCONJ
ejpam-6540	438	5	fractals	fractal	NOUN
ejpam-6540	438	6	,	,	PUNCT
ejpam-6540	438	7	98:199–204	98:199–204	NUM
ejpam-6540	438	8	,	,	PUNCT
ejpam-6540	438	9	2017	2017	NUM
ejpam-6540	438	10	.	.	PUNCT
ejpam-6540	439	1	[	[	X
ejpam-6540	439	2	25	25	NUM
ejpam-6540	439	3	]	]	PUNCT
ejpam-6540	439	4	a.m.	a.m.	PROPN
ejpam-6540	440	1	hinz	hinz	PROPN
ejpam-6540	440	2	and	and	CCONJ
ejpam-6540	440	3	c.h	c.h	PROPN
ejpam-6540	440	4	.	.	PROPN
ejpam-6540	440	5	auf	auf	PROPN
ejpam-6540	440	6	der	der	PROPN
ejpam-6540	440	7	heide	heide	PROPN
ejpam-6540	440	8	.	.	PUNCT
ejpam-6540	441	1	an	an	DET
ejpam-6540	441	2	efficient	efficient	ADJ
ejpam-6540	441	3	algorithm	algorithm	NOUN
ejpam-6540	441	4	to	to	PART
ejpam-6540	441	5	determine	determine	VERB
ejpam-6540	441	6	all	all	PRON
ejpam-6540	441	7	shortest	short	ADJ
ejpam-6540	441	8	k.	k.	PROPN
ejpam-6540	441	9	b.	b.	PROPN
ejpam-6540	441	10	dharan	dharan	PROPN
ejpam-6540	441	11	,	,	PUNCT
ejpam-6540	441	12	s.	s.	PROPN
ejpam-6540	441	13	radha	radha	PROPN
ejpam-6540	441	14	/	/	PUNCT
ejpam-6540	441	15	eur	eur	PROPN
ejpam-6540	441	16	.	.	PUNCT
ejpam-6540	442	1	j.	j.	PROPN
ejpam-6540	442	2	pure	pure	PROPN
ejpam-6540	442	3	appl	appl	PROPN
ejpam-6540	442	4	.	.	PROPN
ejpam-6540	442	5	math	math	PROPN
ejpam-6540	442	6	,	,	PUNCT
ejpam-6540	442	7	18	18	NUM
ejpam-6540	442	8	(	(	PUNCT
ejpam-6540	442	9	3	3	NUM
ejpam-6540	442	10	)	)	PUNCT
ejpam-6540	442	11	(	(	PUNCT
ejpam-6540	442	12	2025	2025	NUM
ejpam-6540	442	13	)	)	PUNCT
ejpam-6540	442	14	,	,	PUNCT
ejpam-6540	442	15	6540	6540	NUM
ejpam-6540	442	16	15	15	NUM
ejpam-6540	442	17	of	of	ADP
ejpam-6540	442	18	17	17	NUM
ejpam-6540	442	19	paths	path	NOUN
ejpam-6540	442	20	in	in	ADP
ejpam-6540	442	21	sierpiński	sierpiński	ADJ
ejpam-6540	442	22	networks	network	NOUN
ejpam-6540	442	23	.	.	PUNCT
ejpam-6540	443	1	discrete	discrete	ADJ
ejpam-6540	443	2	applied	apply	VERB
ejpam-6540	443	3	mathematics	mathematic	NOUN
ejpam-6540	443	4	,	,	PUNCT
ejpam-6540	443	5	177:111–120	177:111–120	NUM
ejpam-6540	443	6	,	,	PUNCT
ejpam-6540	443	7	2014	2014	NUM
ejpam-6540	443	8	.	.	PUNCT
ejpam-6540	444	1	[	[	X
ejpam-6540	444	2	26	26	NUM
ejpam-6540	444	3	]	]	X
ejpam-6540	444	4	m.a	m.a	PROPN
ejpam-6540	444	5	.	.	PROPN
ejpam-6540	444	6	henning	henning	PROPN
ejpam-6540	444	7	,	,	PUNCT
ejpam-6540	444	8	s.	s.	PROPN
ejpam-6540	444	9	klavžar	klavžar	PROPN
ejpam-6540	444	10	,	,	PUNCT
ejpam-6540	444	11	and	and	CCONJ
ejpam-6540	444	12	i.g	i.g	PROPN
ejpam-6540	444	13	.	.	PROPN
ejpam-6540	444	14	yero	yero	PROPN
ejpam-6540	444	15	.	.	PUNCT
ejpam-6540	445	1	resolvability	resolvability	PROPN
ejpam-6540	445	2	and	and	CCONJ
ejpam-6540	445	3	convexity	convexity	NOUN
ejpam-6540	445	4	properties	property	NOUN
ejpam-6540	445	5	in	in	ADP
ejpam-6540	445	6	the	the	DET
ejpam-6540	445	7	sierpiński	sierpiński	ADJ
ejpam-6540	445	8	product	product	NOUN
ejpam-6540	445	9	of	of	ADP
ejpam-6540	445	10	graphs	graph	NOUN
ejpam-6540	445	11	.	.	PUNCT
ejpam-6540	446	1	mediterranean	mediterranean	PROPN
ejpam-6540	446	2	journal	journal	PROPN
ejpam-6540	446	3	of	of	ADP
ejpam-6540	446	4	mathematics	mathematic	NOUN
ejpam-6540	446	5	,	,	PUNCT
ejpam-6540	446	6	21(3	21(3	NUM
ejpam-6540	446	7	)	)	PUNCT
ejpam-6540	446	8	,	,	PUNCT
ejpam-6540	446	9	2024	2024	NUM
ejpam-6540	446	10	.	.	PUNCT
ejpam-6540	447	1	[	[	X
ejpam-6540	447	2	27	27	NUM
ejpam-6540	447	3	]	]	PUNCT
ejpam-6540	447	4	s.	s.	PROPN
ejpam-6540	447	5	prabhu	prabhu	PROPN
ejpam-6540	447	6	,	,	PUNCT
ejpam-6540	447	7	t.j	t.j	PROPN
ejpam-6540	447	8	.	.	PROPN
ejpam-6540	447	9	janany	janany	PROPN
ejpam-6540	447	10	,	,	PUNCT
ejpam-6540	447	11	and	and	CCONJ
ejpam-6540	447	12	p.	p.	NOUN
ejpam-6540	447	13	manuel	manuel	NOUN
ejpam-6540	447	14	.	.	PUNCT
ejpam-6540	448	1	an	an	DET
ejpam-6540	448	2	efficient	efficient	ADJ
ejpam-6540	448	3	way	way	NOUN
ejpam-6540	448	4	to	to	PART
ejpam-6540	448	5	represent	represent	VERB
ejpam-6540	448	6	the	the	DET
ejpam-6540	448	7	processors	processor	NOUN
ejpam-6540	448	8	and	and	CCONJ
ejpam-6540	448	9	their	their	PRON
ejpam-6540	448	10	connections	connection	NOUN
ejpam-6540	448	11	in	in	ADP
ejpam-6540	448	12	omega	omega	NOUN
ejpam-6540	448	13	networks	network	NOUN
ejpam-6540	448	14	.	.	PUNCT
ejpam-6540	449	1	ain	ain	PROPN
ejpam-6540	449	2	shams	sham	VERB
ejpam-6540	449	3	engineering	engineering	NOUN
ejpam-6540	449	4	journal	journal	NOUN
ejpam-6540	449	5	,	,	PUNCT
ejpam-6540	449	6	16(3):103287	16(3):103287	NUM
ejpam-6540	449	7	,	,	PUNCT
ejpam-6540	449	8	2025	2025	NUM
ejpam-6540	449	9	.	.	PUNCT
ejpam-6540	450	1	[	[	X
ejpam-6540	450	2	28	28	NUM
ejpam-6540	450	3	]	]	X
ejpam-6540	450	4	s.	s.	PROPN
ejpam-6540	450	5	prabhu	prabhu	PROPN
ejpam-6540	450	6	,	,	PUNCT
ejpam-6540	450	7	d.	d.	PROPN
ejpam-6540	450	8	jeba	jeba	PROPN
ejpam-6540	450	9	,	,	PUNCT
ejpam-6540	450	10	p.	p.	NOUN
ejpam-6540	450	11	manuel	manuel	NOUN
ejpam-6540	450	12	,	,	PUNCT
ejpam-6540	450	13	and	and	CCONJ
ejpam-6540	450	14	a.	a.	NOUN
ejpam-6540	450	15	davoodi	davoodi	PROPN
ejpam-6540	450	16	.	.	PUNCT
ejpam-6540	451	1	metric	metric	ADJ
ejpam-6540	451	2	dimension	dimension	NOUN
ejpam-6540	451	3	of	of	ADP
ejpam-6540	451	4	villarceau	villarceau	PROPN
ejpam-6540	451	5	grids	grid	NOUN
ejpam-6540	451	6	.	.	PUNCT
ejpam-6540	452	1	arxiv	arxiv	PROPN
ejpam-6540	452	2	preprint	preprint	PROPN
ejpam-6540	452	3	,	,	PUNCT
ejpam-6540	452	4	2024	2024	NUM
ejpam-6540	452	5	.	.	PUNCT
ejpam-6540	453	1	[	[	X
ejpam-6540	453	2	29	29	NUM
ejpam-6540	453	3	]	]	X
ejpam-6540	453	4	b.	b.	PROPN
ejpam-6540	453	5	rajan	rajan	PROPN
ejpam-6540	453	6	,	,	PUNCT
ejpam-6540	453	7	i.	i.	PROPN
ejpam-6540	453	8	rajasingh	rajasingh	PROPN
ejpam-6540	453	9	,	,	PUNCT
ejpam-6540	453	10	j.a	j.a	PROPN
ejpam-6540	453	11	.	.	PROPN
ejpam-6540	453	12	cynthia	cynthia	PROPN
ejpam-6540	453	13	,	,	PUNCT
ejpam-6540	453	14	and	and	CCONJ
ejpam-6540	453	15	p.	p.	NOUN
ejpam-6540	453	16	manuel	manuel	NOUN
ejpam-6540	453	17	.	.	PUNCT
ejpam-6540	454	1	metric	metric	ADJ
ejpam-6540	454	2	dimension	dimension	NOUN
ejpam-6540	454	3	of	of	ADP
ejpam-6540	454	4	directed	direct	VERB
ejpam-6540	454	5	graphs	graph	NOUN
ejpam-6540	454	6	.	.	PUNCT
ejpam-6540	455	1	international	international	ADJ
ejpam-6540	455	2	journal	journal	NOUN
ejpam-6540	455	3	of	of	ADP
ejpam-6540	455	4	computer	computer	NOUN
ejpam-6540	455	5	mathematics	mathematic	NOUN
ejpam-6540	455	6	,	,	PUNCT
ejpam-6540	455	7	91(7):1397–1406	91(7):1397–1406	NUM
ejpam-6540	455	8	,	,	PUNCT
ejpam-6540	455	9	2014	2014	NUM
ejpam-6540	455	10	.	.	PUNCT
ejpam-6540	456	1	[	[	X
ejpam-6540	456	2	30	30	NUM
ejpam-6540	456	3	]	]	PUNCT
ejpam-6540	456	4	p.	p.	NOUN
ejpam-6540	456	5	manuel	manuel	PROPN
ejpam-6540	456	6	and	and	CCONJ
ejpam-6540	456	7	i.	i.	PROPN
ejpam-6540	456	8	rajasingh	rajasingh	PROPN
ejpam-6540	456	9	.	.	PUNCT
ejpam-6540	457	1	minimum	minimum	ADJ
ejpam-6540	457	2	metric	metric	ADJ
ejpam-6540	457	3	dimension	dimension	NOUN
ejpam-6540	457	4	of	of	ADP
ejpam-6540	457	5	silicate	silicate	ADJ
ejpam-6540	457	6	networks	network	NOUN
ejpam-6540	457	7	.	.	PUNCT
ejpam-6540	458	1	ars	ars	PROPN
ejpam-6540	458	2	combinatoria	combinatoria	PROPN
ejpam-6540	458	3	,	,	PUNCT
ejpam-6540	458	4	98:501–510	98:501–510	NUM
ejpam-6540	458	5	,	,	PUNCT
ejpam-6540	458	6	2011	2011	NUM
ejpam-6540	458	7	.	.	PUNCT
ejpam-6540	459	1	[	[	X
ejpam-6540	459	2	31	31	NUM
ejpam-6540	459	3	]	]	PUNCT
ejpam-6540	459	4	p.	p.	NOUN
ejpam-6540	459	5	manuel	manuel	PROPN
ejpam-6540	459	6	,	,	PUNCT
ejpam-6540	459	7	b.	b.	PROPN
ejpam-6540	459	8	rajan	rajan	PROPN
ejpam-6540	459	9	,	,	PUNCT
ejpam-6540	459	10	i.	i.	PROPN
ejpam-6540	459	11	rajasingh	rajasingh	PROPN
ejpam-6540	459	12	,	,	PUNCT
ejpam-6540	459	13	and	and	CCONJ
ejpam-6540	459	14	m.m	m.m	PROPN
ejpam-6540	459	15	.	.	PROPN
ejpam-6540	459	16	chris	chris	PROPN
ejpam-6540	459	17	.	.	PUNCT
ejpam-6540	460	1	landmarks	landmark	NOUN
ejpam-6540	460	2	in	in	ADP
ejpam-6540	460	3	binary	binary	ADJ
ejpam-6540	460	4	tree	tree	NOUN
ejpam-6540	460	5	derived	derive	VERB
ejpam-6540	460	6	architectures	architecture	NOUN
ejpam-6540	460	7	.	.	PUNCT
ejpam-6540	461	1	ars	ars	PROPN
ejpam-6540	461	2	combinatoria	combinatoria	PROPN
ejpam-6540	461	3	,	,	PUNCT
ejpam-6540	461	4	99:473–486	99:473–486	PROPN
ejpam-6540	461	5	,	,	PUNCT
ejpam-6540	461	6	2011	2011	NUM
ejpam-6540	461	7	.	.	PUNCT
ejpam-6540	462	1	[	[	X
ejpam-6540	462	2	32	32	NUM
ejpam-6540	462	3	]	]	PUNCT
ejpam-6540	462	4	p.	p.	NOUN
ejpam-6540	462	5	manuel	manuel	PROPN
ejpam-6540	462	6	,	,	PUNCT
ejpam-6540	462	7	b.	b.	PROPN
ejpam-6540	462	8	rajan	rajan	PROPN
ejpam-6540	462	9	,	,	PUNCT
ejpam-6540	462	10	i.	i.	PROPN
ejpam-6540	462	11	rajasingh	rajasingh	PROPN
ejpam-6540	462	12	,	,	PUNCT
ejpam-6540	462	13	and	and	CCONJ
ejpam-6540	462	14	m.c	m.c	PROPN
ejpam-6540	462	15	.	.	PROPN
ejpam-6540	462	16	monica	monica	PROPN
ejpam-6540	462	17	.	.	PUNCT
ejpam-6540	463	1	landmarks	landmark	NOUN
ejpam-6540	463	2	in	in	ADP
ejpam-6540	463	3	torus	torus	PROPN
ejpam-6540	463	4	networks	network	NOUN
ejpam-6540	463	5	.	.	PUNCT
ejpam-6540	464	1	journal	journal	NOUN
ejpam-6540	464	2	of	of	ADP
ejpam-6540	464	3	discrete	discrete	ADJ
ejpam-6540	464	4	mathematical	mathematical	ADJ
ejpam-6540	464	5	sciences	science	NOUN
ejpam-6540	464	6	and	and	CCONJ
ejpam-6540	464	7	cryptography	cryptography	NOUN
ejpam-6540	464	8	,	,	PUNCT
ejpam-6540	464	9	9(2):263–271	9(2):263–271	NOUN
ejpam-6540	464	10	,	,	PUNCT
ejpam-6540	464	11	2006	2006	NUM
ejpam-6540	464	12	.	.	PUNCT
ejpam-6540	465	1	[	[	X
ejpam-6540	465	2	33	33	NUM
ejpam-6540	465	3	]	]	PUNCT
ejpam-6540	465	4	s.	s.	PROPN
ejpam-6540	465	5	prabhu	prabhu	PROPN
ejpam-6540	465	6	,	,	PUNCT
ejpam-6540	465	7	t.j	t.j	PROPN
ejpam-6540	465	8	.	.	PROPN
ejpam-6540	465	9	janany	janany	PROPN
ejpam-6540	465	10	,	,	PUNCT
ejpam-6540	465	11	and	and	CCONJ
ejpam-6540	465	12	s.	s.	PROPN
ejpam-6540	465	13	klavžar	klavžar	PROPN
ejpam-6540	465	14	.	.	PUNCT
ejpam-6540	466	1	metric	metric	ADJ
ejpam-6540	466	2	dimensions	dimension	NOUN
ejpam-6540	466	3	of	of	ADP
ejpam-6540	466	4	generalized	generalized	ADJ
ejpam-6540	466	5	sierpiński	sierpiński	ADJ
ejpam-6540	466	6	networks	network	NOUN
ejpam-6540	466	7	over	over	ADP
ejpam-6540	466	8	squares	square	NOUN
ejpam-6540	466	9	.	.	PUNCT
ejpam-6540	467	1	applied	apply	VERB
ejpam-6540	467	2	mathematics	mathematic	NOUN
ejpam-6540	467	3	and	and	CCONJ
ejpam-6540	467	4	computation	computation	NOUN
ejpam-6540	467	5	,	,	PUNCT
ejpam-6540	467	6	505:129528	505:129528	NUM
ejpam-6540	467	7	,	,	PUNCT
ejpam-6540	467	8	2025	2025	NUM
ejpam-6540	467	9	.	.	PUNCT
ejpam-6540	468	1	[	[	X
ejpam-6540	468	2	34	34	NUM
ejpam-6540	468	3	]	]	X
ejpam-6540	468	4	a.	a.	PROPN
ejpam-6540	468	5	estrada	estrada	PROPN
ejpam-6540	468	6	-	-	PUNCT
ejpam-6540	468	7	moreno	moreno	PROPN
ejpam-6540	468	8	and	and	CCONJ
ejpam-6540	468	9	j.a	j.a	PROPN
ejpam-6540	468	10	.	.	PROPN
ejpam-6540	468	11	rodŕıguez	rodŕıguez	PROPN
ejpam-6540	468	12	-	-	NOUN
ejpam-6540	468	13	velázquez	velázquez	NOUN
ejpam-6540	468	14	.	.	PUNCT
ejpam-6540	469	1	on	on	ADP
ejpam-6540	469	2	the	the	DET
ejpam-6540	469	3	general	general	ADJ
ejpam-6540	469	4	randić	randić	NOUN
ejpam-6540	469	5	index	index	NOUN
ejpam-6540	469	6	of	of	ADP
ejpam-6540	469	7	polymeric	polymeric	ADJ
ejpam-6540	469	8	networks	network	NOUN
ejpam-6540	469	9	modelled	model	VERB
ejpam-6540	469	10	by	by	ADP
ejpam-6540	469	11	generalized	generalized	ADJ
ejpam-6540	469	12	sierpiński	sierpiński	ADJ
ejpam-6540	469	13	networks	network	NOUN
ejpam-6540	469	14	.	.	PUNCT
ejpam-6540	470	1	discrete	discrete	ADJ
ejpam-6540	470	2	applied	apply	VERB
ejpam-6540	470	3	mathematics	mathematic	NOUN
ejpam-6540	470	4	,	,	PUNCT
ejpam-6540	470	5	263:140–151	263:140–151	NUM
ejpam-6540	470	6	,	,	PUNCT
ejpam-6540	470	7	2019	2019	NUM
ejpam-6540	470	8	.	.	PUNCT
ejpam-6540	471	1	[	[	X
ejpam-6540	471	2	35	35	NUM
ejpam-6540	471	3	]	]	X
ejpam-6540	471	4	f.	f.	PROPN
ejpam-6540	471	5	ramezani	ramezani	PROPN
ejpam-6540	471	6	,	,	PUNCT
ejpam-6540	471	7	e.d	e.d	PROPN
ejpam-6540	471	8	.	.	PROPN
ejpam-6540	471	9	rodŕıquex	rodŕıquex	PROPN
ejpam-6540	471	10	-	-	PUNCT
ejpam-6540	471	11	bazán	bazán	NOUN
ejpam-6540	471	12	,	,	PUNCT
ejpam-6540	471	13	and	and	CCONJ
ejpam-6540	472	1	j.a	j.a	PROPN
ejpam-6540	472	2	.	.	PROPN
ejpam-6540	472	3	rodŕıguez	rodŕıguez	PROPN
ejpam-6540	472	4	-	-	NOUN
ejpam-6540	472	5	velázquez	velázquez	NOUN
ejpam-6540	472	6	.	.	PUNCT
ejpam-6540	473	1	on	on	ADP
ejpam-6540	473	2	the	the	DET
ejpam-6540	473	3	roman	roman	ADJ
ejpam-6540	473	4	domination	domination	NOUN
ejpam-6540	473	5	number	number	NOUN
ejpam-6540	473	6	of	of	ADP
ejpam-6540	473	7	generalized	generalized	ADJ
ejpam-6540	473	8	sierpiński	sierpiński	ADJ
ejpam-6540	473	9	networks	network	NOUN
ejpam-6540	473	10	.	.	PUNCT
ejpam-6540	474	1	filomat	filomat	NOUN
ejpam-6540	474	2	,	,	PUNCT
ejpam-6540	474	3	31(20):6515–6528	31(20):6515–6528	NUM
ejpam-6540	474	4	,	,	PUNCT
ejpam-6540	474	5	2017	2017	NUM
ejpam-6540	474	6	.	.	PUNCT
ejpam-6540	475	1	[	[	X
ejpam-6540	475	2	36	36	NUM
ejpam-6540	475	3	]	]	X
ejpam-6540	475	4	e.	e.	PROPN
ejpam-6540	475	5	estaji	estaji	PROPN
ejpam-6540	475	6	and	and	CCONJ
ejpam-6540	475	7	j.a	j.a	PROPN
ejpam-6540	475	8	.	.	PROPN
ejpam-6540	475	9	rodŕıguez	rodŕıguez	PROPN
ejpam-6540	475	10	-	-	NOUN
ejpam-6540	475	11	velázquez	velázquez	NOUN
ejpam-6540	475	12	.	.	PUNCT
ejpam-6540	476	1	the	the	DET
ejpam-6540	476	2	strong	strong	ADJ
ejpam-6540	476	3	metric	metric	ADJ
ejpam-6540	476	4	dimension	dimension	NOUN
ejpam-6540	476	5	of	of	ADP
ejpam-6540	476	6	generalized	generalized	ADJ
ejpam-6540	476	7	sierpiński	sierpiński	ADJ
ejpam-6540	476	8	networks	network	NOUN
ejpam-6540	476	9	with	with	ADP
ejpam-6540	476	10	pendant	pendant	ADJ
ejpam-6540	476	11	vertices	vertex	NOUN
ejpam-6540	476	12	.	.	PUNCT
ejpam-6540	477	1	ars	ars	PROPN
ejpam-6540	477	2	mathematica	mathematica	PROPN
ejpam-6540	477	3	contemporanea	contemporanea	PROPN
ejpam-6540	477	4	,	,	PUNCT
ejpam-6540	477	5	12:127	12:127	NUM
ejpam-6540	477	6	–	–	PUNCT
ejpam-6540	477	7	134	134	NUM
ejpam-6540	477	8	,	,	PUNCT
ejpam-6540	477	9	2017	2017	NUM
ejpam-6540	477	10	.	.	PUNCT
ejpam-6540	478	1	[	[	X
ejpam-6540	478	2	37	37	NUM
ejpam-6540	478	3	]	]	PUNCT
ejpam-6540	478	4	s.	s.	PROPN
ejpam-6540	478	5	khuller	khuller	PROPN
ejpam-6540	478	6	,	,	PUNCT
ejpam-6540	478	7	j.b	j.b	PROPN
ejpam-6540	478	8	.	.	PROPN
ejpam-6540	478	9	raghavachari	raghavachari	PROPN
ejpam-6540	478	10	,	,	PUNCT
ejpam-6540	478	11	and	and	CCONJ
ejpam-6540	478	12	a.	a.	NOUN
ejpam-6540	478	13	rosenfeld	rosenfeld	PROPN
ejpam-6540	478	14	.	.	PUNCT
ejpam-6540	479	1	landmarks	landmark	NOUN
ejpam-6540	479	2	in	in	ADP
ejpam-6540	479	3	graphs	graph	NOUN
ejpam-6540	479	4	.	.	PUNCT
ejpam-6540	480	1	discrete	discrete	ADJ
ejpam-6540	480	2	applied	apply	VERB
ejpam-6540	480	3	mathematics	mathematic	NOUN
ejpam-6540	480	4	,	,	PUNCT
ejpam-6540	480	5	70(3):217–229	70(3):217–229	PROPN
ejpam-6540	480	6	,	,	PUNCT
ejpam-6540	480	7	1996	1996	NUM
ejpam-6540	480	8	.	.	PUNCT
ejpam-6540	481	1	[	[	X
ejpam-6540	481	2	38	38	NUM
ejpam-6540	481	3	]	]	PUNCT
ejpam-6540	481	4	g.	g.	PROPN
ejpam-6540	481	5	chartrand	chartrand	PROPN
ejpam-6540	481	6	,	,	PUNCT
ejpam-6540	481	7	l.	l.	PROPN
ejpam-6540	481	8	eroh	eroh	PROPN
ejpam-6540	481	9	,	,	PUNCT
ejpam-6540	481	10	m.a	m.a	PROPN
ejpam-6540	481	11	.	.	PROPN
ejpam-6540	481	12	johnson	johnson	PROPN
ejpam-6540	481	13	,	,	PUNCT
ejpam-6540	481	14	and	and	CCONJ
ejpam-6540	481	15	o.r	o.r	PROPN
ejpam-6540	481	16	.	.	PROPN
ejpam-6540	481	17	oellermann	oellermann	PROPN
ejpam-6540	481	18	.	.	PUNCT
ejpam-6540	482	1	resolvability	resolvability	NOUN
ejpam-6540	482	2	in	in	ADP
ejpam-6540	482	3	graphs	graph	NOUN
ejpam-6540	482	4	and	and	CCONJ
ejpam-6540	482	5	the	the	DET
ejpam-6540	482	6	metric	metric	ADJ
ejpam-6540	482	7	dimension	dimension	NOUN
ejpam-6540	482	8	of	of	ADP
ejpam-6540	482	9	a	a	DET
ejpam-6540	482	10	graph	graph	NOUN
ejpam-6540	482	11	.	.	PUNCT
ejpam-6540	483	1	discrete	discrete	ADJ
ejpam-6540	483	2	applied	apply	VERB
ejpam-6540	483	3	mathematics	mathematic	NOUN
ejpam-6540	483	4	,	,	PUNCT
ejpam-6540	483	5	105:99–113	105:99–113	NUM
ejpam-6540	483	6	,	,	PUNCT
ejpam-6540	483	7	2000	2000	NUM
ejpam-6540	483	8	.	.	PUNCT
ejpam-6540	484	1	[	[	X
ejpam-6540	484	2	39	39	NUM
ejpam-6540	484	3	]	]	PUNCT
ejpam-6540	484	4	g.	g.	PROPN
ejpam-6540	484	5	chartrand	chartrand	PROPN
ejpam-6540	484	6	and	and	CCONJ
ejpam-6540	484	7	p.	p.	PROPN
ejpam-6540	484	8	zhang	zhang	PROPN
ejpam-6540	484	9	.	.	PUNCT
ejpam-6540	485	1	the	the	DET
ejpam-6540	485	2	theory	theory	NOUN
ejpam-6540	485	3	and	and	CCONJ
ejpam-6540	485	4	applications	application	NOUN
ejpam-6540	485	5	of	of	ADP
ejpam-6540	485	6	resolvability	resolvability	NOUN
ejpam-6540	485	7	in	in	ADP
ejpam-6540	485	8	graphs	graph	NOUN
ejpam-6540	485	9	:	:	PUNCT
ejpam-6540	485	10	a	a	DET
ejpam-6540	485	11	survey	survey	NOUN
ejpam-6540	485	12	.	.	PUNCT
ejpam-6540	486	1	congressus	congressus	PROPN
ejpam-6540	486	2	numerantium	numerantium	PROPN
ejpam-6540	486	3	,	,	PUNCT
ejpam-6540	486	4	160:47–68	160:47–68	NUM
ejpam-6540	486	5	,	,	PUNCT
ejpam-6540	486	6	2003	2003	NUM
ejpam-6540	486	7	.	.	PUNCT
ejpam-6540	487	1	[	[	X
ejpam-6540	487	2	40	40	NUM
ejpam-6540	487	3	]	]	PUNCT
ejpam-6540	487	4	f.	f.	PROPN
ejpam-6540	487	5	harary	harary	PROPN
ejpam-6540	487	6	and	and	CCONJ
ejpam-6540	487	7	r.a	r.a	PROPN
ejpam-6540	487	8	.	.	PROPN
ejpam-6540	487	9	melter	melter	NOUN
ejpam-6540	487	10	.	.	PUNCT
ejpam-6540	488	1	on	on	ADP
ejpam-6540	488	2	the	the	DET
ejpam-6540	488	3	metric	metric	ADJ
ejpam-6540	488	4	dimension	dimension	NOUN
ejpam-6540	488	5	of	of	ADP
ejpam-6540	488	6	a	a	DET
ejpam-6540	488	7	graph	graph	NOUN
ejpam-6540	488	8	.	.	PUNCT
ejpam-6540	488	9	ars	ars	PROPN
ejpam-6540	488	10	combinatoria	combinatoria	NOUN
ejpam-6540	488	11	,	,	PUNCT
ejpam-6540	488	12	2:191–195	2:191–195	NUM
ejpam-6540	488	13	,	,	PUNCT
ejpam-6540	488	14	1976	1976	NUM
ejpam-6540	488	15	.	.	PUNCT
ejpam-6540	489	1	[	[	X
ejpam-6540	489	2	41	41	NUM
ejpam-6540	489	3	]	]	X
ejpam-6540	489	4	p.j	p.j	PROPN
ejpam-6540	489	5	.	.	PROPN
ejpam-6540	489	6	slater	slater	PROPN
ejpam-6540	489	7	.	.	PUNCT
ejpam-6540	490	1	leaves	leave	NOUN
ejpam-6540	490	2	of	of	ADP
ejpam-6540	490	3	trees	tree	NOUN
ejpam-6540	490	4	.	.	PUNCT
ejpam-6540	491	1	congressus	congressus	PROPN
ejpam-6540	491	2	numerantium	numerantium	PROPN
ejpam-6540	491	3	,	,	PUNCT
ejpam-6540	491	4	14:549–559	14:549–559	NUM
ejpam-6540	491	5	,	,	PUNCT
ejpam-6540	491	6	1975	1975	NUM
ejpam-6540	491	7	.	.	PUNCT
ejpam-6540	492	1	[	[	X
ejpam-6540	492	2	42	42	NUM
ejpam-6540	492	3	]	]	X
ejpam-6540	492	4	c.	c.	PROPN
ejpam-6540	492	5	hernando	hernando	PROPN
ejpam-6540	492	6	,	,	PUNCT
ejpam-6540	492	7	m.	m.	PROPN
ejpam-6540	492	8	mora	mora	PROPN
ejpam-6540	492	9	,	,	PUNCT
ejpam-6540	492	10	i.m	i.m	PROPN
ejpam-6540	492	11	.	.	PUNCT
ejpam-6540	492	12	pelayo	pelayo	PROPN
ejpam-6540	492	13	,	,	PUNCT
ejpam-6540	492	14	c.	c.	PROPN
ejpam-6540	492	15	seara	seara	PROPN
ejpam-6540	492	16	,	,	PUNCT
ejpam-6540	492	17	and	and	CCONJ
ejpam-6540	492	18	d.r	d.r	PROPN
ejpam-6540	492	19	.	.	PROPN
ejpam-6540	492	20	wood	wood	NOUN
ejpam-6540	492	21	.	.	PUNCT
ejpam-6540	493	1	extremal	extremal	ADJ
ejpam-6540	493	2	graph	graph	NOUN
ejpam-6540	493	3	theory	theory	NOUN
ejpam-6540	493	4	for	for	ADP
ejpam-6540	493	5	metric	metric	ADJ
ejpam-6540	493	6	dimension	dimension	NOUN
ejpam-6540	493	7	and	and	CCONJ
ejpam-6540	493	8	diameter	diameter	NOUN
ejpam-6540	493	9	.	.	PUNCT
ejpam-6540	494	1	electronic	electronic	ADJ
ejpam-6540	494	2	journal	journal	NOUN
ejpam-6540	494	3	of	of	ADP
ejpam-6540	494	4	combinatorics	combinatoric	NOUN
ejpam-6540	494	5	,	,	PUNCT
ejpam-6540	494	6	17	17	NUM
ejpam-6540	494	7	:	:	PUNCT
ejpam-6540	494	8	r30	r30	PROPN
ejpam-6540	494	9	,	,	PUNCT
ejpam-6540	494	10	2010	2010	NUM
ejpam-6540	494	11	.	.	PUNCT
ejpam-6540	495	1	[	[	X
ejpam-6540	495	2	43	43	NUM
ejpam-6540	495	3	]	]	X
ejpam-6540	495	4	p.	p.	NOUN
ejpam-6540	495	5	manuel	manuel	PROPN
ejpam-6540	495	6	,	,	PUNCT
ejpam-6540	495	7	m.	m.	PROPN
ejpam-6540	495	8	i.	i.	PROPN
ejpam-6540	495	9	abd	abd	PROPN
ejpam-6540	495	10	-	-	PROPN
ejpam-6540	495	11	el	el	PROPN
ejpam-6540	495	12	-	-	PUNCT
ejpam-6540	495	13	barr	barr	PROPN
ejpam-6540	495	14	,	,	PUNCT
ejpam-6540	495	15	i.	i.	PROPN
ejpam-6540	495	16	rajasingh	rajasingh	PROPN
ejpam-6540	495	17	,	,	PUNCT
ejpam-6540	495	18	and	and	CCONJ
ejpam-6540	495	19	b.	b.	PROPN
ejpam-6540	495	20	rajan	rajan	PROPN
ejpam-6540	495	21	.	.	PUNCT
ejpam-6540	496	1	an	an	DET
ejpam-6540	496	2	efficient	efficient	ADJ
ejpam-6540	496	3	representation	representation	NOUN
ejpam-6540	496	4	of	of	ADP
ejpam-6540	496	5	benes	benes	PROPN
ejpam-6540	496	6	networks	network	NOUN
ejpam-6540	496	7	and	and	CCONJ
ejpam-6540	496	8	its	its	PRON
ejpam-6540	496	9	applications	application	NOUN
ejpam-6540	496	10	.	.	PUNCT
ejpam-6540	497	1	journal	journal	NOUN
ejpam-6540	497	2	of	of	ADP
ejpam-6540	497	3	discrete	discrete	ADJ
ejpam-6540	497	4	algorithms	algorithm	NOUN
ejpam-6540	497	5	,	,	PUNCT
ejpam-6540	497	6	6(1):11–19	6(1):11–19	NUM
ejpam-6540	497	7	,	,	PUNCT
ejpam-6540	497	8	2008	2008	NUM
ejpam-6540	497	9	.	.	PUNCT
ejpam-6540	498	1	k.	k.	PROPN
ejpam-6540	498	2	b.	b.	PROPN
ejpam-6540	498	3	dharan	dharan	PROPN
ejpam-6540	498	4	,	,	PUNCT
ejpam-6540	498	5	s.	s.	PROPN
ejpam-6540	498	6	radha	radha	PROPN
ejpam-6540	498	7	/	/	PUNCT
ejpam-6540	498	8	eur	eur	PROPN
ejpam-6540	498	9	.	.	PUNCT
ejpam-6540	499	1	j.	j.	PROPN
ejpam-6540	499	2	pure	pure	PROPN
ejpam-6540	499	3	appl	appl	PROPN
ejpam-6540	499	4	.	.	PROPN
ejpam-6540	499	5	math	math	PROPN
ejpam-6540	499	6	,	,	PUNCT
ejpam-6540	499	7	18	18	NUM
ejpam-6540	499	8	(	(	PUNCT
ejpam-6540	499	9	3	3	NUM
ejpam-6540	499	10	)	)	PUNCT
ejpam-6540	499	11	(	(	PUNCT
ejpam-6540	499	12	2025	2025	NUM
ejpam-6540	499	13	)	)	PUNCT
ejpam-6540	499	14	,	,	PUNCT
ejpam-6540	499	15	6540	6540	NUM
ejpam-6540	499	16	16	16	NUM
ejpam-6540	499	17	of	of	ADP
ejpam-6540	499	18	17	17	NUM
ejpam-6540	499	19	[	[	SYM
ejpam-6540	499	20	44	44	NUM
ejpam-6540	499	21	]	]	PUNCT
ejpam-6540	499	22	p.	p.	NOUN
ejpam-6540	499	23	manuel	manuel	PROPN
ejpam-6540	499	24	,	,	PUNCT
ejpam-6540	499	25	b.	b.	PROPN
ejpam-6540	499	26	rajan	rajan	PROPN
ejpam-6540	499	27	,	,	PUNCT
ejpam-6540	499	28	i.	i.	PROPN
ejpam-6540	499	29	rajasingh	rajasingh	PROPN
ejpam-6540	499	30	,	,	PUNCT
ejpam-6540	499	31	and	and	CCONJ
ejpam-6540	499	32	m.c	m.c	PROPN
ejpam-6540	499	33	.	.	PROPN
ejpam-6540	499	34	monica	monica	PROPN
ejpam-6540	499	35	.	.	PUNCT
ejpam-6540	500	1	on	on	ADP
ejpam-6540	500	2	minimum	minimum	ADJ
ejpam-6540	500	3	metric	metric	ADJ
ejpam-6540	500	4	dimension	dimension	NOUN
ejpam-6540	500	5	of	of	ADP
ejpam-6540	500	6	honeycomb	honeycomb	NOUN
ejpam-6540	500	7	networks	network	NOUN
ejpam-6540	500	8	.	.	PUNCT
ejpam-6540	501	1	journal	journal	NOUN
ejpam-6540	501	2	of	of	ADP
ejpam-6540	501	3	discrete	discrete	ADJ
ejpam-6540	501	4	algorithms	algorithm	NOUN
ejpam-6540	501	5	,	,	PUNCT
ejpam-6540	501	6	6:20–27	6:20–27	NUM
ejpam-6540	501	7	,	,	PUNCT
ejpam-6540	501	8	2008	2008	NUM
ejpam-6540	501	9	.	.	PUNCT
ejpam-6540	502	1	[	[	X
ejpam-6540	502	2	45	45	NUM
ejpam-6540	502	3	]	]	PUNCT
ejpam-6540	502	4	m.	m.	NOUN
ejpam-6540	502	5	basak	basak	PROPN
ejpam-6540	502	6	,	,	PUNCT
ejpam-6540	502	7	l.	l.	PROPN
ejpam-6540	502	8	saha	saha	PROPN
ejpam-6540	502	9	,	,	PUNCT
ejpam-6540	502	10	g.k	g.k	PROPN
ejpam-6540	502	11	.	.	PROPN
ejpam-6540	502	12	das	das	PROPN
ejpam-6540	502	13	,	,	PUNCT
ejpam-6540	502	14	and	and	CCONJ
ejpam-6540	502	15	k.	k.	PROPN
ejpam-6540	502	16	tiwary	tiwary	PROPN
ejpam-6540	502	17	.	.	PUNCT
ejpam-6540	503	1	fault	fault	NOUN
ejpam-6540	503	2	-	-	PUNCT
ejpam-6540	503	3	tolerant	tolerant	ADJ
ejpam-6540	503	4	metric	metric	ADJ
ejpam-6540	503	5	dimension	dimension	NOUN
ejpam-6540	503	6	of	of	ADP
ejpam-6540	503	7	circulant	circulant	ADJ
ejpam-6540	503	8	graphs	graph	NOUN
ejpam-6540	503	9	c(1	c(1	PROPN
ejpam-6540	503	10	,	,	PUNCT
ejpam-6540	503	11	2	2	NUM
ejpam-6540	503	12	,	,	PUNCT
ejpam-6540	503	13	3	3	NUM
ejpam-6540	503	14	)	)	PUNCT
ejpam-6540	503	15	.	.	PUNCT
ejpam-6540	504	1	theoretical	theoretical	ADJ
ejpam-6540	504	2	computer	computer	NOUN
ejpam-6540	504	3	science	science	NOUN
ejpam-6540	504	4	,	,	PUNCT
ejpam-6540	504	5	817:159–170	817:159–170	NUM
ejpam-6540	504	6	,	,	PUNCT
ejpam-6540	504	7	2020	2020	NUM
ejpam-6540	504	8	.	.	PUNCT
ejpam-6540	505	1	[	[	X
ejpam-6540	505	2	46	46	NUM
ejpam-6540	505	3	]	]	PUNCT
ejpam-6540	505	4	s.	s.	PROPN
ejpam-6540	505	5	kumar	kumar	PROPN
ejpam-6540	505	6	,	,	PUNCT
ejpam-6540	505	7	s.	s.	PROPN
ejpam-6540	505	8	sharma	sharma	PROPN
ejpam-6540	505	9	,	,	PUNCT
ejpam-6540	505	10	s.k	s.k	PROPN
ejpam-6540	505	11	.	.	PROPN
ejpam-6540	505	12	sharma	sharma	PROPN
ejpam-6540	505	13	,	,	PUNCT
ejpam-6540	505	14	and	and	CCONJ
ejpam-6540	505	15	v.k	v.k	PROPN
ejpam-6540	505	16	.	.	PROPN
ejpam-6540	505	17	bhat	bhat	PROPN
ejpam-6540	505	18	.	.	PUNCT
ejpam-6540	506	1	on	on	ADP
ejpam-6540	506	2	metric	metric	ADJ
ejpam-6540	506	3	dimension	dimension	NOUN
ejpam-6540	506	4	of	of	ADP
ejpam-6540	506	5	generalized	generalized	ADJ
ejpam-6540	506	6	subdivision	subdivision	NOUN
ejpam-6540	506	7	prism	prism	NOUN
ejpam-6540	506	8	graph	graph	NOUN
ejpam-6540	506	9	.	.	PUNCT
ejpam-6540	506	10	ain	ain	PROPN
ejpam-6540	506	11	shams	sham	NOUN
ejpam-6540	506	12	engineering	engineering	NOUN
ejpam-6540	506	13	journal	journal	NOUN
ejpam-6540	506	14	,	,	PUNCT
ejpam-6540	506	15	16(8):103452	16(8):103452	NUM
ejpam-6540	506	16	,	,	PUNCT
ejpam-6540	506	17	2025	2025	NUM
ejpam-6540	506	18	.	.	PUNCT
ejpam-6540	507	1	[	[	X
ejpam-6540	507	2	47	47	NUM
ejpam-6540	507	3	]	]	PUNCT
ejpam-6540	507	4	s.	s.	PROPN
ejpam-6540	507	5	prabhu	prabhu	PROPN
ejpam-6540	507	6	,	,	PUNCT
ejpam-6540	507	7	t.	t.	NOUN
ejpam-6540	507	8	flora	flora	NOUN
ejpam-6540	507	9	,	,	PUNCT
ejpam-6540	507	10	and	and	CCONJ
ejpam-6540	507	11	m.	m.	NOUN
ejpam-6540	507	12	arulperumjothi	arulperumjothi	ADV
ejpam-6540	507	13	.	.	PUNCT
ejpam-6540	508	1	on	on	ADP
ejpam-6540	508	2	independent	independent	ADJ
ejpam-6540	508	3	resolving	resolving	NOUN
ejpam-6540	508	4	number	number	NOUN
ejpam-6540	508	5	of	of	ADP
ejpam-6540	508	6	tio2[m	tio2[m	PROPN
ejpam-6540	508	7	,	,	PUNCT
ejpam-6540	508	8	n	n	CCONJ
ejpam-6540	508	9	]	]	PUNCT
ejpam-6540	508	10	nanotubes	nanotube	NOUN
ejpam-6540	508	11	.	.	PUNCT
ejpam-6540	509	1	journal	journal	NOUN
ejpam-6540	509	2	of	of	ADP
ejpam-6540	509	3	intelligent	intelligent	ADJ
ejpam-6540	509	4	&	&	CCONJ
ejpam-6540	509	5	fuzzy	fuzzy	ADJ
ejpam-6540	509	6	systems	system	NOUN
ejpam-6540	509	7	,	,	PUNCT
ejpam-6540	509	8	35(6):6421–6425	35(6):6421–6425	NUM
ejpam-6540	509	9	,	,	PUNCT
ejpam-6540	509	10	2018	2018	NUM
ejpam-6540	509	11	.	.	PUNCT
ejpam-6540	510	1	[	[	X
ejpam-6540	510	2	48	48	NUM
ejpam-6540	510	3	]	]	PUNCT
ejpam-6540	510	4	s.	s.	PROPN
ejpam-6540	510	5	prabhu	prabhu	PROPN
ejpam-6540	510	6	,	,	PUNCT
ejpam-6540	510	7	d.s.r	d.s.r	PROPN
ejpam-6540	510	8	.	.	PROPN
ejpam-6540	510	9	jeba	jeba	PROPN
ejpam-6540	510	10	,	,	PUNCT
ejpam-6540	510	11	m.	m.	NOUN
ejpam-6540	510	12	arulperumjothi	arulperumjothi	ADV
ejpam-6540	510	13	,	,	PUNCT
ejpam-6540	510	14	and	and	CCONJ
ejpam-6540	510	15	s.	s.	PROPN
ejpam-6540	510	16	klavžar	klavžar	PROPN
ejpam-6540	510	17	.	.	PUNCT
ejpam-6540	511	1	metric	metric	ADJ
ejpam-6540	511	2	dimension	dimension	NOUN
ejpam-6540	511	3	of	of	ADP
ejpam-6540	511	4	irregular	irregular	ADJ
ejpam-6540	511	5	convex	convex	NOUN
ejpam-6540	511	6	triangular	triangular	NOUN
ejpam-6540	511	7	networks	network	NOUN
ejpam-6540	511	8	.	.	PUNCT
ejpam-6540	512	1	akce	akce	PROPN
ejpam-6540	512	2	international	international	PROPN
ejpam-6540	512	3	journal	journal	NOUN
ejpam-6540	512	4	of	of	ADP
ejpam-6540	512	5	graphs	graph	NOUN
ejpam-6540	512	6	and	and	CCONJ
ejpam-6540	512	7	combinatorics	combinatoric	NOUN
ejpam-6540	512	8	,	,	PUNCT
ejpam-6540	512	9	21(3):225–231	21(3):225–231	PROPN
ejpam-6540	512	10	,	,	PUNCT
ejpam-6540	512	11	2023	2023	NUM
ejpam-6540	512	12	.	.	PUNCT
ejpam-6540	513	1	[	[	X
ejpam-6540	513	2	49	49	NUM
ejpam-6540	513	3	]	]	PUNCT
ejpam-6540	513	4	s.	s.	PROPN
ejpam-6540	513	5	prabhu	prabhu	PROPN
ejpam-6540	513	6	,	,	PUNCT
ejpam-6540	513	7	v.	v.	ADP
ejpam-6540	513	8	manimozhi	manimozhi	PROPN
ejpam-6540	513	9	,	,	PUNCT
ejpam-6540	513	10	m.	m.	NOUN
ejpam-6540	513	11	arulperumjothi	arulperumjothi	ADV
ejpam-6540	513	12	,	,	PUNCT
ejpam-6540	513	13	and	and	CCONJ
ejpam-6540	513	14	s.	s.	PROPN
ejpam-6540	513	15	klavžar	klavžar	PROPN
ejpam-6540	513	16	.	.	PUNCT
ejpam-6540	514	1	twin	twin	ADJ
ejpam-6540	514	2	vertices	vertex	NOUN
ejpam-6540	514	3	in	in	ADP
ejpam-6540	514	4	faulttolerant	faulttolerant	ADJ
ejpam-6540	514	5	metric	metric	ADJ
ejpam-6540	514	6	sets	set	NOUN
ejpam-6540	514	7	and	and	CCONJ
ejpam-6540	514	8	fault	fault	NOUN
ejpam-6540	514	9	-	-	PUNCT
ejpam-6540	514	10	tolerant	tolerant	ADJ
ejpam-6540	514	11	metric	metric	ADJ
ejpam-6540	514	12	dimension	dimension	NOUN
ejpam-6540	514	13	of	of	ADP
ejpam-6540	514	14	multistage	multistage	NOUN
ejpam-6540	514	15	interconnection	interconnection	NOUN
ejpam-6540	514	16	networks	network	NOUN
ejpam-6540	514	17	.	.	PUNCT
ejpam-6540	515	1	applied	apply	VERB
ejpam-6540	515	2	mathematics	mathematic	NOUN
ejpam-6540	515	3	and	and	CCONJ
ejpam-6540	515	4	computation	computation	NOUN
ejpam-6540	515	5	,	,	PUNCT
ejpam-6540	515	6	420:126897	420:126897	PROPN
ejpam-6540	515	7	,	,	PUNCT
ejpam-6540	515	8	2022	2022	NUM
ejpam-6540	515	9	.	.	PUNCT
ejpam-6540	516	1	[	[	X
ejpam-6540	516	2	50	50	NUM
ejpam-6540	516	3	]	]	PUNCT
ejpam-6540	516	4	s.	s.	PROPN
ejpam-6540	516	5	klavžar	klavžar	PROPN
ejpam-6540	516	6	and	and	CCONJ
ejpam-6540	516	7	s.s	s.s	PROPN
ejpam-6540	516	8	.	.	PROPN
ejpam-6540	516	9	zemljič.	zemljič.	PROPN
ejpam-6540	516	10	on	on	ADP
ejpam-6540	516	11	distances	distance	NOUN
ejpam-6540	516	12	in	in	ADP
ejpam-6540	516	13	sierpiński	sierpiński	ADJ
ejpam-6540	516	14	networks	network	NOUN
ejpam-6540	516	15	:	:	PUNCT
ejpam-6540	516	16	almost	almost	ADV
ejpam-6540	516	17	-	-	PUNCT
ejpam-6540	516	18	extreme	extreme	ADJ
ejpam-6540	516	19	vertices	vertex	NOUN
ejpam-6540	516	20	and	and	CCONJ
ejpam-6540	516	21	metric	metric	ADJ
ejpam-6540	516	22	dimension	dimension	NOUN
ejpam-6540	516	23	.	.	PUNCT
ejpam-6540	517	1	applicable	applicable	ADJ
ejpam-6540	517	2	analysis	analysis	NOUN
ejpam-6540	517	3	and	and	CCONJ
ejpam-6540	517	4	discrete	discrete	ADJ
ejpam-6540	517	5	mathematics	mathematic	NOUN
ejpam-6540	517	6	,	,	PUNCT
ejpam-6540	517	7	7:72	7:72	NUM
ejpam-6540	517	8	–	–	PUNCT
ejpam-6540	517	9	82	82	NUM
ejpam-6540	517	10	,	,	PUNCT
ejpam-6540	517	11	2013	2013	NUM
ejpam-6540	517	12	.	.	PUNCT
ejpam-6540	518	1	[	[	X
ejpam-6540	518	2	51	51	NUM
ejpam-6540	518	3	]	]	X
ejpam-6540	518	4	r.c	r.c	PROPN
ejpam-6540	518	5	.	.	PROPN
ejpam-6540	518	6	tillquist	tillquist	PROPN
ejpam-6540	518	7	,	,	PUNCT
ejpam-6540	518	8	r.m	r.m	PROPN
ejpam-6540	518	9	.	.	PROPN
ejpam-6540	518	10	frongillo	frongillo	PROPN
ejpam-6540	518	11	,	,	PUNCT
ejpam-6540	518	12	and	and	CCONJ
ejpam-6540	518	13	m.e	m.e	PROPN
ejpam-6540	518	14	.	.	PROPN
ejpam-6540	518	15	lladser	lladser	PROPN
ejpam-6540	518	16	.	.	PUNCT
ejpam-6540	519	1	getting	get	VERB
ejpam-6540	519	2	the	the	DET
ejpam-6540	519	3	lay	lay	NOUN
ejpam-6540	519	4	of	of	ADP
ejpam-6540	519	5	the	the	DET
ejpam-6540	519	6	land	land	NOUN
ejpam-6540	519	7	in	in	ADP
ejpam-6540	519	8	discrete	discrete	ADJ
ejpam-6540	519	9	space	space	NOUN
ejpam-6540	519	10	:	:	PUNCT
ejpam-6540	519	11	a	a	DET
ejpam-6540	519	12	survey	survey	NOUN
ejpam-6540	519	13	of	of	ADP
ejpam-6540	519	14	metric	metric	ADJ
ejpam-6540	519	15	dimension	dimension	NOUN
ejpam-6540	519	16	and	and	CCONJ
ejpam-6540	519	17	its	its	PRON
ejpam-6540	519	18	application	application	NOUN
ejpam-6540	519	19	.	.	PUNCT
ejpam-6540	520	1	siam	siam	PROPN
ejpam-6540	520	2	review	review	PROPN
ejpam-6540	520	3	,	,	PUNCT
ejpam-6540	520	4	65(4):919–962	65(4):919–962	PROPN
ejpam-6540	520	5	,	,	PUNCT
ejpam-6540	520	6	2023	2023	NUM
ejpam-6540	520	7	.	.	PUNCT
ejpam-6540	521	1	[	[	X
ejpam-6540	521	2	52	52	NUM
ejpam-6540	521	3	]	]	PUNCT
ejpam-6540	521	4	a.	a.	NOUN
ejpam-6540	521	5	kelenc	kelenc	PROPN
ejpam-6540	521	6	,	,	PUNCT
ejpam-6540	521	7	n.	n.	NOUN
ejpam-6540	521	8	tratnik	tratnik	PROPN
ejpam-6540	521	9	,	,	PUNCT
ejpam-6540	521	10	and	and	CCONJ
ejpam-6540	521	11	i.g	i.g	PROPN
ejpam-6540	521	12	.	.	PROPN
ejpam-6540	521	13	yero	yero	PROPN
ejpam-6540	521	14	.	.	PUNCT
ejpam-6540	522	1	uniquely	uniquely	ADV
ejpam-6540	522	2	identifying	identify	VERB
ejpam-6540	522	3	the	the	DET
ejpam-6540	522	4	edges	edge	NOUN
ejpam-6540	522	5	of	of	ADP
ejpam-6540	522	6	a	a	DET
ejpam-6540	522	7	graph	graph	NOUN
ejpam-6540	522	8	:	:	PUNCT
ejpam-6540	522	9	the	the	DET
ejpam-6540	522	10	edge	edge	NOUN
ejpam-6540	522	11	metric	metric	ADJ
ejpam-6540	522	12	dimension	dimension	NOUN
ejpam-6540	522	13	.	.	PUNCT
ejpam-6540	523	1	discrete	discrete	ADJ
ejpam-6540	523	2	applied	apply	VERB
ejpam-6540	523	3	mathematics	mathematic	NOUN
ejpam-6540	523	4	,	,	PUNCT
ejpam-6540	523	5	251:204–220	251:204–220	NUM
ejpam-6540	523	6	,	,	PUNCT
ejpam-6540	523	7	2018	2018	NUM
ejpam-6540	523	8	.	.	PUNCT
ejpam-6540	524	1	[	[	X
ejpam-6540	524	2	53	53	NUM
ejpam-6540	524	3	]	]	PUNCT
ejpam-6540	524	4	s.	s.	PROPN
ejpam-6540	524	5	klavžar	klavžar	PROPN
ejpam-6540	524	6	and	and	CCONJ
ejpam-6540	524	7	d.	d.	PROPN
ejpam-6540	524	8	kuziak	kuziak	PROPN
ejpam-6540	524	9	.	.	PUNCT
ejpam-6540	525	1	nonlocal	nonlocal	ADJ
ejpam-6540	525	2	metric	metric	ADJ
ejpam-6540	525	3	dimension	dimension	NOUN
ejpam-6540	525	4	of	of	ADP
ejpam-6540	525	5	graphs	graph	NOUN
ejpam-6540	525	6	.	.	PUNCT
ejpam-6540	526	1	bulletin	bulletin	NOUN
ejpam-6540	526	2	of	of	ADP
ejpam-6540	526	3	the	the	DET
ejpam-6540	526	4	malaysian	malaysian	PROPN
ejpam-6540	526	5	mathematical	mathematical	PROPN
ejpam-6540	526	6	sciences	sciences	PROPN
ejpam-6540	526	7	society	society	NOUN
ejpam-6540	526	8	,	,	PUNCT
ejpam-6540	526	9	46:66	46:66	NUM
ejpam-6540	526	10	,	,	PUNCT
ejpam-6540	526	11	2023	2023	NUM
ejpam-6540	526	12	.	.	PUNCT
ejpam-6540	527	1	[	[	X
ejpam-6540	527	2	54	54	NUM
ejpam-6540	527	3	]	]	PUNCT
ejpam-6540	527	4	r.umilasari	r.umilasari	NOUN
ejpam-6540	527	5	,	,	PUNCT
ejpam-6540	527	6	l.	l.	PROPN
ejpam-6540	527	7	susilowati	susilowati	PROPN
ejpam-6540	527	8	,	,	PUNCT
ejpam-6540	527	9	and	and	CCONJ
ejpam-6540	527	10	s.	s.	PROPN
ejpam-6540	527	11	prabhu	prabhu	PROPN
ejpam-6540	527	12	.	.	PUNCT
ejpam-6540	528	1	on	on	ADP
ejpam-6540	528	2	the	the	DET
ejpam-6540	528	3	dominant	dominant	ADJ
ejpam-6540	528	4	local	local	ADJ
ejpam-6540	528	5	metric	metric	ADJ
ejpam-6540	528	6	dimension	dimension	NOUN
ejpam-6540	528	7	of	of	ADP
ejpam-6540	528	8	corona	corona	NOUN
ejpam-6540	528	9	product	product	NOUN
ejpam-6540	528	10	graphs	graph	NOUN
ejpam-6540	528	11	.	.	PUNCT
ejpam-6540	529	1	iaeng	iaeng	PROPN
ejpam-6540	529	2	international	international	PROPN
ejpam-6540	529	3	journal	journal	PROPN
ejpam-6540	529	4	of	of	ADP
ejpam-6540	529	5	applied	apply	VERB
ejpam-6540	529	6	mathematics	mathematic	NOUN
ejpam-6540	529	7	,	,	PUNCT
ejpam-6540	529	8	52(4):38	52(4):38	NUM
ejpam-6540	529	9	,	,	PUNCT
ejpam-6540	529	10	2022	2022	NUM
ejpam-6540	529	11	.	.	PUNCT
ejpam-6540	530	1	[	[	X
ejpam-6540	530	2	55	55	NUM
ejpam-6540	530	3	]	]	SYM
ejpam-6540	530	4	r.umilasari	r.umilasari	NOUN
ejpam-6540	530	5	,	,	PUNCT
ejpam-6540	530	6	l.	l.	PROPN
ejpam-6540	530	7	susilowati	susilowati	PROPN
ejpam-6540	530	8	,	,	PUNCT
ejpam-6540	530	9	slamin	slamin	PROPN
ejpam-6540	530	10	,	,	PUNCT
ejpam-6540	530	11	s.	s.	PROPN
ejpam-6540	530	12	prabhu	prabhu	PROPN
ejpam-6540	530	13	,	,	PUNCT
ejpam-6540	530	14	and	and	CCONJ
ejpam-6540	530	15	o.j	o.j	PROPN
ejpam-6540	530	16	.	.	PROPN
ejpam-6540	530	17	fadekemi	fadekemi	PROPN
ejpam-6540	530	18	.	.	PUNCT
ejpam-6540	531	1	the	the	DET
ejpam-6540	531	2	local	local	ADJ
ejpam-6540	531	3	resolving	resolving	NOUN
ejpam-6540	531	4	dominating	dominating	NOUN
ejpam-6540	531	5	set	set	NOUN
ejpam-6540	531	6	of	of	ADP
ejpam-6540	531	7	comb	comb	NOUN
ejpam-6540	531	8	product	product	NOUN
ejpam-6540	531	9	graphs	graph	NOUN
ejpam-6540	531	10	.	.	PUNCT
ejpam-6540	532	1	international	international	ADJ
ejpam-6540	532	2	journal	journal	NOUN
ejpam-6540	532	3	of	of	ADP
ejpam-6540	532	4	computer	computer	NOUN
ejpam-6540	532	5	science	science	NOUN
ejpam-6540	532	6	,	,	PUNCT
ejpam-6540	532	7	51:115–120	51:115–120	NUM
ejpam-6540	532	8	,	,	PUNCT
ejpam-6540	532	9	2024	2024	NUM
ejpam-6540	532	10	.	.	PUNCT
ejpam-6540	533	1	[	[	X
ejpam-6540	533	2	56	56	NUM
ejpam-6540	533	3	]	]	X
ejpam-6540	533	4	v.j.a	v.j.a	NOUN
ejpam-6540	533	5	.	.	PUNCT
ejpam-6540	533	6	cynthia	cynthia	PROPN
ejpam-6540	533	7	,	,	PUNCT
ejpam-6540	533	8	m.	m.	NOUN
ejpam-6540	533	9	ramya	ramya	PROPN
ejpam-6540	533	10	,	,	PUNCT
ejpam-6540	533	11	and	and	CCONJ
ejpam-6540	533	12	s.	s.	PROPN
ejpam-6540	533	13	prabhu	prabhu	PROPN
ejpam-6540	533	14	.	.	PUNCT
ejpam-6540	534	1	local	local	ADJ
ejpam-6540	534	2	metric	metric	ADJ
ejpam-6540	534	3	dimension	dimension	NOUN
ejpam-6540	534	4	of	of	ADP
ejpam-6540	534	5	certain	certain	ADJ
ejpam-6540	534	6	classes	class	NOUN
ejpam-6540	534	7	of	of	ADP
ejpam-6540	534	8	circulant	circulant	ADJ
ejpam-6540	534	9	networks	network	NOUN
ejpam-6540	534	10	.	.	PUNCT
ejpam-6540	535	1	journal	journal	NOUN
ejpam-6540	535	2	of	of	ADP
ejpam-6540	535	3	advanced	advanced	ADJ
ejpam-6540	535	4	computational	computational	ADJ
ejpam-6540	535	5	intelligence	intelligence	NOUN
ejpam-6540	535	6	and	and	CCONJ
ejpam-6540	535	7	intelligent	intelligent	ADJ
ejpam-6540	535	8	informatics	informatic	NOUN
ejpam-6540	535	9	,	,	PUNCT
ejpam-6540	535	10	27(4):554–560	27(4):554–560	PROPN
ejpam-6540	535	11	,	,	PUNCT
ejpam-6540	535	12	2023	2023	NUM
ejpam-6540	535	13	.	.	PUNCT
ejpam-6540	536	1	[	[	X
ejpam-6540	536	2	57	57	NUM
ejpam-6540	536	3	]	]	PUNCT
ejpam-6540	536	4	c.	c.	PROPN
ejpam-6540	536	5	hernando	hernando	PROPN
ejpam-6540	536	6	,	,	PUNCT
ejpam-6540	536	7	m.	m.	PROPN
ejpam-6540	536	8	mora	mora	PROPN
ejpam-6540	536	9	,	,	PUNCT
ejpam-6540	536	10	p.j	p.j	PROPN
ejpam-6540	536	11	.	.	PROPN
ejpam-6540	536	12	slater	slater	PROPN
ejpam-6540	536	13	,	,	PUNCT
ejpam-6540	536	14	and	and	CCONJ
ejpam-6540	536	15	d.r	d.r	PROPN
ejpam-6540	536	16	.	.	PROPN
ejpam-6540	536	17	wood	wood	NOUN
ejpam-6540	536	18	.	.	PUNCT
ejpam-6540	537	1	fault	fault	NOUN
ejpam-6540	537	2	-	-	PUNCT
ejpam-6540	537	3	tolerant	tolerant	ADJ
ejpam-6540	537	4	metric	metric	ADJ
ejpam-6540	537	5	dimension	dimension	NOUN
ejpam-6540	537	6	of	of	ADP
ejpam-6540	537	7	graphs	graph	NOUN
ejpam-6540	537	8	.	.	PUNCT
ejpam-6540	538	1	convexity	convexity	NOUN
ejpam-6540	538	2	in	in	ADP
ejpam-6540	538	3	discrete	discrete	ADJ
ejpam-6540	538	4	structures	structure	NOUN
ejpam-6540	538	5	,	,	PUNCT
ejpam-6540	538	6	5:81–85	5:81–85	NUM
ejpam-6540	538	7	,	,	PUNCT
ejpam-6540	538	8	2008	2008	NUM
ejpam-6540	538	9	.	.	PUNCT
ejpam-6540	539	1	[	[	X
ejpam-6540	539	2	58	58	NUM
ejpam-6540	539	3	]	]	PUNCT
ejpam-6540	539	4	s.	s.	PROPN
ejpam-6540	539	5	prabhu	prabhu	PROPN
ejpam-6540	539	6	,	,	PUNCT
ejpam-6540	539	7	v.	v.	ADP
ejpam-6540	539	8	manimozhi	manimozhi	PROPN
ejpam-6540	539	9	,	,	PUNCT
ejpam-6540	539	10	a.	a.	PROPN
ejpam-6540	539	11	davoodi	davoodi	PROPN
ejpam-6540	539	12	,	,	PUNCT
ejpam-6540	539	13	and	and	CCONJ
ejpam-6540	539	14	j.l.g	j.l.g	PROPN
ejpam-6540	539	15	.	.	PROPN
ejpam-6540	539	16	guirao	guirao	PROPN
ejpam-6540	539	17	.	.	PUNCT
ejpam-6540	540	1	fault	fault	NOUN
ejpam-6540	540	2	-	-	PUNCT
ejpam-6540	540	3	tolerant	tolerant	ADJ
ejpam-6540	540	4	basis	basis	NOUN
ejpam-6540	540	5	of	of	ADP
ejpam-6540	540	6	generalized	generalized	ADJ
ejpam-6540	540	7	fat	fat	ADJ
ejpam-6540	540	8	trees	tree	NOUN
ejpam-6540	540	9	and	and	CCONJ
ejpam-6540	540	10	perfect	perfect	ADJ
ejpam-6540	540	11	binary	binary	ADJ
ejpam-6540	540	12	tree	tree	NOUN
ejpam-6540	540	13	.	.	PUNCT
ejpam-6540	541	1	the	the	DET
ejpam-6540	541	2	journal	journal	NOUN
ejpam-6540	541	3	of	of	ADP
ejpam-6540	541	4	supercomputing	supercomputing	PROPN
ejpam-6540	541	5	,	,	PUNCT
ejpam-6540	541	6	80:15783	80:15783	NUM
ejpam-6540	541	7	–	–	PUNCT
ejpam-6540	541	8	15798	15798	NUM
ejpam-6540	541	9	,	,	PUNCT
ejpam-6540	541	10	2024	2024	NUM
ejpam-6540	541	11	.	.	PUNCT
ejpam-6540	542	1	[	[	X
ejpam-6540	542	2	59	59	NUM
ejpam-6540	542	3	]	]	X
ejpam-6540	542	4	y.	y.	PROPN
ejpam-6540	542	5	zhang	zhang	PROPN
ejpam-6540	542	6	and	and	CCONJ
ejpam-6540	542	7	s.	s.	PROPN
ejpam-6540	542	8	gao	gao	PROPN
ejpam-6540	542	9	.	.	PUNCT
ejpam-6540	543	1	on	on	ADP
ejpam-6540	543	2	the	the	DET
ejpam-6540	543	3	edge	edge	NOUN
ejpam-6540	543	4	metric	metric	ADJ
ejpam-6540	543	5	dimension	dimension	NOUN
ejpam-6540	543	6	of	of	ADP
ejpam-6540	543	7	convex	convex	ADJ
ejpam-6540	543	8	polytopes	polytope	NOUN
ejpam-6540	543	9	and	and	CCONJ
ejpam-6540	543	10	its	its	PRON
ejpam-6540	543	11	related	related	ADJ
ejpam-6540	543	12	graphs	graph	NOUN
ejpam-6540	543	13	.	.	PUNCT
ejpam-6540	544	1	journal	journal	NOUN
ejpam-6540	544	2	of	of	ADP
ejpam-6540	544	3	combinatorial	combinatorial	ADJ
ejpam-6540	544	4	optimization	optimization	NOUN
ejpam-6540	544	5	,	,	PUNCT
ejpam-6540	544	6	39:334–350	39:334–350	PROPN
ejpam-6540	544	7	,	,	PUNCT
ejpam-6540	544	8	2020	2020	NUM
ejpam-6540	544	9	.	.	PUNCT
ejpam-6540	545	1	[	[	X
ejpam-6540	545	2	60	60	NUM
ejpam-6540	545	3	]	]	X
ejpam-6540	545	4	d.g.l	d.g.l	PROPN
ejpam-6540	545	5	.	.	PUNCT
ejpam-6540	546	1	wang	wang	PROPN
ejpam-6540	546	2	,	,	PUNCT
ejpam-6540	546	3	m.m.y	m.m.y	PROPN
ejpam-6540	546	4	.	.	PROPN
ejpam-6540	546	5	wang	wang	PROPN
ejpam-6540	546	6	,	,	PUNCT
ejpam-6540	546	7	and	and	CCONJ
ejpam-6540	546	8	s.	s.	PROPN
ejpam-6540	546	9	zhang	zhang	PROPN
ejpam-6540	546	10	.	.	PUNCT
ejpam-6540	547	1	determining	determine	VERB
ejpam-6540	547	2	the	the	DET
ejpam-6540	547	3	edge	edge	NOUN
ejpam-6540	547	4	metric	metric	ADJ
ejpam-6540	547	5	dimension	dimension	NOUN
ejpam-6540	547	6	of	of	ADP
ejpam-6540	547	7	the	the	DET
ejpam-6540	547	8	generalized	generalized	ADJ
ejpam-6540	547	9	petersen	petersen	NOUN
ejpam-6540	547	10	graph	graph	NOUN
ejpam-6540	547	11	p(n	p(n	PROPN
ejpam-6540	547	12	,	,	PUNCT
ejpam-6540	547	13	3	3	NUM
ejpam-6540	547	14	)	)	PUNCT
ejpam-6540	547	15	.	.	PUNCT
ejpam-6540	548	1	journal	journal	NOUN
ejpam-6540	548	2	of	of	ADP
ejpam-6540	548	3	combinatorial	combinatorial	ADJ
ejpam-6540	548	4	optimization	optimization	NOUN
ejpam-6540	548	5	,	,	PUNCT
ejpam-6540	548	6	k.	k.	PROPN
ejpam-6540	548	7	b.	b.	PROPN
ejpam-6540	548	8	dharan	dharan	PROPN
ejpam-6540	548	9	,	,	PUNCT
ejpam-6540	548	10	s.	s.	PROPN
ejpam-6540	548	11	radha	radha	PROPN
ejpam-6540	548	12	/	/	PUNCT
ejpam-6540	548	13	eur	eur	PROPN
ejpam-6540	548	14	.	.	PUNCT
ejpam-6540	549	1	j.	j.	PROPN
ejpam-6540	549	2	pure	pure	PROPN
ejpam-6540	549	3	appl	appl	PROPN
ejpam-6540	549	4	.	.	PROPN
ejpam-6540	549	5	math	math	PROPN
ejpam-6540	549	6	,	,	PUNCT
ejpam-6540	549	7	18	18	NUM
ejpam-6540	549	8	(	(	PUNCT
ejpam-6540	549	9	3	3	NUM
ejpam-6540	549	10	)	)	PUNCT
ejpam-6540	549	11	(	(	PUNCT
ejpam-6540	549	12	2025	2025	NUM
ejpam-6540	549	13	)	)	PUNCT
ejpam-6540	549	14	,	,	PUNCT
ejpam-6540	549	15	6540	6540	NUM
ejpam-6540	549	16	17	17	NUM
ejpam-6540	549	17	of	of	ADP
ejpam-6540	549	18	17	17	NUM
ejpam-6540	549	19	43:460–496	43:460–496	NUM
ejpam-6540	549	20	,	,	PUNCT
ejpam-6540	549	21	2022	2022	NUM
ejpam-6540	549	22	.	.	PUNCT
ejpam-6540	550	1	[	[	X
ejpam-6540	550	2	61	61	NUM
ejpam-6540	550	3	]	]	PUNCT
ejpam-6540	550	4	s.	s.	PROPN
ejpam-6540	550	5	prabhu	prabhu	PROPN
ejpam-6540	550	6	and	and	CCONJ
ejpam-6540	550	7	t.j	t.j	PROPN
ejpam-6540	550	8	.	.	PROPN
ejpam-6540	550	9	janany	janany	PROPN
ejpam-6540	550	10	.	.	PUNCT
ejpam-6540	551	1	edge	edge	VERB
ejpam-6540	551	2	metric	metric	ADJ
ejpam-6540	551	3	dimension	dimension	NOUN
ejpam-6540	551	4	of	of	ADP
ejpam-6540	551	5	silicate	silicate	ADJ
ejpam-6540	551	6	networks	network	NOUN
ejpam-6540	551	7	.	.	PUNCT
ejpam-6540	552	1	communications	communication	NOUN
ejpam-6540	552	2	in	in	ADP
ejpam-6540	552	3	combinatorics	combinatoric	NOUN
ejpam-6540	552	4	and	and	CCONJ
ejpam-6540	552	5	optimization	optimization	NOUN
ejpam-6540	552	6	,	,	PUNCT
ejpam-6540	552	7	2024	2024	NUM
ejpam-6540	552	8	.	.	PUNCT
ejpam-6540	553	1	[	[	X
ejpam-6540	553	2	62	62	NUM
ejpam-6540	553	3	]	]	PUNCT
ejpam-6540	553	4	n.	n.	PROPN
ejpam-6540	553	5	zublirina	zublirina	PROPN
ejpam-6540	553	6	.	.	PUNCT
ejpam-6540	554	1	asymptotic	asymptotic	ADJ
ejpam-6540	554	2	behaviour	behaviour	NOUN
ejpam-6540	554	3	of	of	ADP
ejpam-6540	554	4	the	the	DET
ejpam-6540	554	5	edge	edge	NOUN
ejpam-6540	554	6	metric	metric	ADJ
ejpam-6540	554	7	dimension	dimension	NOUN
ejpam-6540	554	8	of	of	ADP
ejpam-6540	554	9	the	the	DET
ejpam-6540	554	10	random	random	ADJ
ejpam-6540	554	11	graph	graph	NOUN
ejpam-6540	554	12	.	.	PUNCT
ejpam-6540	555	1	discussiones	discussione	NOUN
ejpam-6540	555	2	mathematicae	mathematicae	PROPN
ejpam-6540	555	3	graph	graph	NOUN
ejpam-6540	555	4	theory	theory	NOUN
ejpam-6540	555	5	,	,	PUNCT
ejpam-6540	555	6	41(2):589–599	41(2):589–599	PROPN
ejpam-6540	555	7	,	,	PUNCT
ejpam-6540	555	8	2021	2021	NUM
ejpam-6540	555	9	.	.	PUNCT
ejpam-6540	556	1	[	[	X
ejpam-6540	556	2	63	63	NUM
ejpam-6540	556	3	]	]	PUNCT
ejpam-6540	556	4	c.	c.	PROPN
ejpam-6540	556	5	wei	wei	PROPN
ejpam-6540	556	6	,	,	PUNCT
ejpam-6540	556	7	m.	m.	PROPN
ejpam-6540	556	8	salman	salman	PROPN
ejpam-6540	556	9	,	,	PUNCT
ejpam-6540	556	10	s.	s.	PROPN
ejpam-6540	556	11	shalhzaib	shalhzaib	PROPN
ejpam-6540	556	12	,	,	PUNCT
ejpam-6540	556	13	m.u	m.u	PROPN
ejpam-6540	556	14	.	.	PROPN
ejpam-6540	556	15	rehman	rehman	PROPN
ejpam-6540	556	16	,	,	PUNCT
ejpam-6540	556	17	and	and	CCONJ
ejpam-6540	556	18	j.	j.	PROPN
ejpam-6540	556	19	fang	fang	PROPN
ejpam-6540	556	20	.	.	PUNCT
ejpam-6540	556	21	classes	class	NOUN
ejpam-6540	556	22	of	of	ADP
ejpam-6540	556	23	planar	planar	ADJ
ejpam-6540	556	24	graphs	graph	NOUN
ejpam-6540	556	25	with	with	ADP
ejpam-6540	556	26	constant	constant	ADJ
ejpam-6540	556	27	edge	edge	NOUN
ejpam-6540	556	28	metric	metric	ADJ
ejpam-6540	556	29	dimension	dimension	NOUN
ejpam-6540	556	30	.	.	PUNCT
ejpam-6540	557	1	complexity	complexity	NOUN
ejpam-6540	557	2	,	,	PUNCT
ejpam-6540	557	3	2021:5599274	2021:5599274	NUM
ejpam-6540	557	4	,	,	PUNCT
ejpam-6540	557	5	2021	2021	NUM
ejpam-6540	557	6	.	.	PUNCT
ejpam-6540	558	1	[	[	X
ejpam-6540	558	2	64	64	NUM
ejpam-6540	558	3	]	]	PUNCT
ejpam-6540	558	4	n.	n.	PROPN
ejpam-6540	558	5	zubrilina	zubrilina	PROPN
ejpam-6540	558	6	.	.	PUNCT
ejpam-6540	559	1	on	on	ADP
ejpam-6540	559	2	the	the	DET
ejpam-6540	559	3	edge	edge	NOUN
ejpam-6540	559	4	dimension	dimension	NOUN
ejpam-6540	559	5	of	of	ADP
ejpam-6540	559	6	a	a	DET
ejpam-6540	559	7	graph	graph	NOUN
ejpam-6540	559	8	.	.	PUNCT
ejpam-6540	559	9	discrete	discrete	ADJ
ejpam-6540	559	10	mathematics	mathematic	NOUN
ejpam-6540	559	11	,	,	PUNCT
ejpam-6540	559	12	341:2083	341:2083	NUM
ejpam-6540	559	13	–	–	PUNCT
ejpam-6540	559	14	2088	2088	NUM
ejpam-6540	559	15	,	,	PUNCT
ejpam-6540	559	16	2018	2018	NUM
ejpam-6540	559	17	.	.	PUNCT
ejpam-6540	560	1	[	[	X
ejpam-6540	560	2	65	65	NUM
ejpam-6540	560	3	]	]	X
ejpam-6540	560	4	e.	e.	PROPN
ejpam-6540	560	5	zhu	zhu	PROPN
ejpam-6540	560	6	,	,	PUNCT
ejpam-6540	560	7	a.	a.	PROPN
ejpam-6540	560	8	taranenko	taranenko	PROPN
ejpam-6540	560	9	,	,	PUNCT
ejpam-6540	560	10	z.	z.	PROPN
ejpam-6540	560	11	shao	shao	PROPN
ejpam-6540	560	12	,	,	PUNCT
ejpam-6540	560	13	and	and	CCONJ
ejpam-6540	560	14	j.	j.	PROPN
ejpam-6540	560	15	xu	xu	PROPN
ejpam-6540	560	16	.	.	PUNCT
ejpam-6540	561	1	on	on	ADP
ejpam-6540	561	2	graphs	graph	NOUN
ejpam-6540	561	3	with	with	ADP
ejpam-6540	561	4	the	the	DET
ejpam-6540	561	5	maximum	maximum	ADJ
ejpam-6540	561	6	edge	edge	NOUN
ejpam-6540	561	7	metric	metric	ADJ
ejpam-6540	561	8	dimension	dimension	NOUN
ejpam-6540	561	9	.	.	PUNCT
ejpam-6540	562	1	discrete	discrete	ADJ
ejpam-6540	562	2	applied	apply	VERB
ejpam-6540	562	3	mathematics	mathematic	NOUN
ejpam-6540	562	4	,	,	PUNCT
ejpam-6540	562	5	257:317–324	257:317–324	NUM
ejpam-6540	562	6	,	,	PUNCT
ejpam-6540	562	7	2019	2019	NUM
ejpam-6540	562	8	.	.	PUNCT
ejpam-6540	563	1	[	[	X
ejpam-6540	563	2	66	66	NUM
ejpam-6540	563	3	]	]	PUNCT
ejpam-6540	563	4	a.	a.	NOUN
ejpam-6540	563	5	kelenc	kelenc	PROPN
ejpam-6540	563	6	,	,	PUNCT
ejpam-6540	563	7	a.t.m	a.t.m	PROPN
ejpam-6540	563	8	.	.	PUNCT
ejpam-6540	563	9	toshi	toshi	PROPN
ejpam-6540	563	10	,	,	PUNCT
ejpam-6540	563	11	r.	r.	PROPN
ejpam-6540	563	12	škrekovski	škrekovski	PROPN
ejpam-6540	563	13	,	,	PUNCT
ejpam-6540	563	14	and	and	CCONJ
ejpam-6540	563	15	i.g	i.g	PROPN
ejpam-6540	563	16	.	.	PROPN
ejpam-6540	563	17	yero	yero	PROPN
ejpam-6540	563	18	.	.	PUNCT
ejpam-6540	564	1	on	on	ADP
ejpam-6540	564	2	metric	metric	ADJ
ejpam-6540	564	3	dimension	dimension	NOUN
ejpam-6540	564	4	of	of	ADP
ejpam-6540	564	5	hypercubes	hypercube	NOUN
ejpam-6540	564	6	.	.	PUNCT
ejpam-6540	565	1	ars	ars	PROPN
ejpam-6540	565	2	mathematica	mathematica	PROPN
ejpam-6540	565	3	contemporanea	contemporanea	PROPN
ejpam-6540	565	4	,	,	PUNCT
ejpam-6540	565	5	23(2):p2.08	23(2):p2.08	NUM
ejpam-6540	565	6	,	,	PUNCT
ejpam-6540	565	7	2022	2022	NUM
ejpam-6540	565	8	.	.	PUNCT
ejpam-6540	566	1	[	[	X
ejpam-6540	566	2	67	67	NUM
ejpam-6540	566	3	]	]	PUNCT
ejpam-6540	566	4	i.	i.	PROPN
ejpam-6540	566	5	peterin	peterin	PROPN
ejpam-6540	566	6	and	and	CCONJ
ejpam-6540	566	7	i.g	i.g	PROPN
ejpam-6540	566	8	.	.	PROPN
ejpam-6540	566	9	yero	yero	PROPN
ejpam-6540	566	10	.	.	PUNCT
ejpam-6540	566	11	edge	edge	PROPN
ejpam-6540	566	12	metric	metric	ADJ
ejpam-6540	566	13	dimension	dimension	NOUN
ejpam-6540	566	14	of	of	ADP
ejpam-6540	566	15	some	some	DET
ejpam-6540	566	16	graph	graph	NOUN
ejpam-6540	566	17	operations	operation	NOUN
ejpam-6540	566	18	.	.	PUNCT
ejpam-6540	567	1	bulletin	bulletin	NOUN
ejpam-6540	567	2	of	of	ADP
ejpam-6540	567	3	the	the	DET
ejpam-6540	567	4	malaysian	malaysian	PROPN
ejpam-6540	567	5	mathematical	mathematical	PROPN
ejpam-6540	567	6	sciences	sciences	PROPN
ejpam-6540	567	7	society	society	NOUN
ejpam-6540	567	8	,	,	PUNCT
ejpam-6540	567	9	43:2465–2477	43:2465–2477	NUM
ejpam-6540	567	10	,	,	PUNCT
ejpam-6540	567	11	2020	2020	NUM
ejpam-6540	567	12	.	.	PUNCT
ejpam-6540	568	1	[	[	X
ejpam-6540	568	2	68	68	NUM
ejpam-6540	568	3	]	]	X
ejpam-6540	568	4	s.	s.	PROPN
ejpam-6540	568	5	klavžar	klavžar	PROPN
ejpam-6540	568	6	and	and	CCONJ
ejpam-6540	568	7	m.	m.	PROPN
ejpam-6540	568	8	tavakoli	tavakoli	PROPN
ejpam-6540	568	9	.	.	PUNCT
ejpam-6540	569	1	edge	edge	VERB
ejpam-6540	569	2	metric	metric	ADJ
ejpam-6540	569	3	dimension	dimension	NOUN
ejpam-6540	569	4	via	via	ADP
ejpam-6540	569	5	hierarchical	hierarchical	ADJ
ejpam-6540	569	6	product	product	NOUN
ejpam-6540	569	7	and	and	CCONJ
ejpam-6540	569	8	integer	integer	NOUN
ejpam-6540	569	9	linear	linear	PROPN
ejpam-6540	569	10	programming	programming	NOUN
ejpam-6540	569	11	.	.	PUNCT
ejpam-6540	570	1	optimization	optimization	NOUN
ejpam-6540	570	2	letters	letter	NOUN
ejpam-6540	570	3	,	,	PUNCT
ejpam-6540	570	4	15:1993–2003	15:1993–2003	NUM
ejpam-6540	570	5	,	,	PUNCT
ejpam-6540	570	6	2021	2021	NUM
ejpam-6540	570	7	.	.	PUNCT
ejpam-6540	571	1	[	[	X
ejpam-6540	571	2	69	69	NUM
ejpam-6540	571	3	]	]	PUNCT
ejpam-6540	571	4	m.	m.	NOUN
ejpam-6540	571	5	knor	knor	PROPN
ejpam-6540	571	6	,	,	PUNCT
ejpam-6540	571	7	s.	s.	PROPN
ejpam-6540	571	8	majstorović	majstorović	PROPN
ejpam-6540	571	9	,	,	PUNCT
ejpam-6540	571	10	a.t.m	a.t.m	PROPN
ejpam-6540	571	11	.	.	PUNCT
ejpam-6540	572	1	toshi	toshi	PROPN
ejpam-6540	572	2	,	,	PUNCT
ejpam-6540	572	3	r.	r.	PROPN
ejpam-6540	572	4	škrekovski	škrekovski	PROPN
ejpam-6540	572	5	,	,	PUNCT
ejpam-6540	572	6	and	and	CCONJ
ejpam-6540	572	7	i.g	i.g	PROPN
ejpam-6540	572	8	.	.	PROPN
ejpam-6540	572	9	yero	yero	PROPN
ejpam-6540	572	10	.	.	PUNCT
ejpam-6540	572	11	graphs	graph	NOUN
ejpam-6540	572	12	with	with	ADP
ejpam-6540	572	13	the	the	DET
ejpam-6540	572	14	edge	edge	NOUN
ejpam-6540	572	15	metric	metric	ADJ
ejpam-6540	572	16	dimension	dimension	NOUN
ejpam-6540	572	17	smaller	small	ADJ
ejpam-6540	572	18	than	than	ADP
ejpam-6540	572	19	the	the	DET
ejpam-6540	572	20	metric	metric	ADJ
ejpam-6540	572	21	dimension	dimension	NOUN
ejpam-6540	572	22	.	.	PUNCT
ejpam-6540	573	1	applied	apply	VERB
ejpam-6540	573	2	mathematics	mathematic	NOUN
ejpam-6540	573	3	and	and	CCONJ
ejpam-6540	573	4	computation	computation	NOUN
ejpam-6540	573	5	,	,	PUNCT
ejpam-6540	573	6	401:126076	401:126076	NUM
ejpam-6540	573	7	,	,	PUNCT
ejpam-6540	573	8	2021	2021	NUM
ejpam-6540	573	9	.	.	PUNCT
ejpam-6540	574	1	[	[	X
ejpam-6540	574	2	70	70	NUM
ejpam-6540	574	3	]	]	PUNCT
ejpam-6540	574	4	m.	m.	NOUN
ejpam-6540	574	5	knor	knor	PROPN
ejpam-6540	574	6	,	,	PUNCT
ejpam-6540	574	7	r.	r.	PROPN
ejpam-6540	574	8	škrekovski	škrekovski	PROPN
ejpam-6540	574	9	,	,	PUNCT
ejpam-6540	574	10	and	and	CCONJ
ejpam-6540	574	11	i.g	i.g	PROPN
ejpam-6540	574	12	.	.	PROPN
ejpam-6540	574	13	yero	yero	PROPN
ejpam-6540	574	14	.	.	PUNCT
ejpam-6540	575	1	a	a	DET
ejpam-6540	575	2	note	note	NOUN
ejpam-6540	575	3	on	on	ADP
ejpam-6540	575	4	the	the	DET
ejpam-6540	575	5	metric	metric	ADJ
ejpam-6540	575	6	and	and	CCONJ
ejpam-6540	575	7	edge	edge	VERB
ejpam-6540	575	8	metric	metric	ADJ
ejpam-6540	575	9	dimensions	dimension	NOUN
ejpam-6540	575	10	of	of	ADP
ejpam-6540	575	11	2	2	NUM
ejpam-6540	575	12	-	-	PUNCT
ejpam-6540	575	13	connected	connect	VERB
ejpam-6540	575	14	graphs	graph	NOUN
ejpam-6540	575	15	.	.	PUNCT
ejpam-6540	576	1	discrete	discrete	ADJ
ejpam-6540	576	2	applied	apply	VERB
ejpam-6540	576	3	mathematics	mathematic	NOUN
ejpam-6540	576	4	,	,	PUNCT
ejpam-6540	576	5	319:454–460	319:454–460	NUM
ejpam-6540	576	6	,	,	PUNCT
ejpam-6540	576	7	2022	2022	NUM
ejpam-6540	576	8	.	.	PUNCT