id	sid	tid	token	lemma	pos
ejpam-6212	1	1	european	european	PROPN
ejpam-6212	1	2	journal	journal	PROPN
ejpam-6212	1	3	of	of	ADP
ejpam-6212	1	4	pure	pure	ADJ
ejpam-6212	1	5	and	and	CCONJ
ejpam-6212	1	6	applied	applied	ADJ
ejpam-6212	1	7	mathematics	mathematic	NOUN
ejpam-6212	1	8	2025	2025	NUM
ejpam-6212	1	9	,	,	PUNCT
ejpam-6212	1	10	vol	vol	NOUN
ejpam-6212	1	11	.	.	PROPN
ejpam-6212	1	12	18	18	NUM
ejpam-6212	1	13	,	,	PUNCT
ejpam-6212	1	14	issue	issue	NOUN
ejpam-6212	1	15	4	4	NUM
ejpam-6212	1	16	,	,	PUNCT
ejpam-6212	1	17	article	article	NOUN
ejpam-6212	1	18	number	number	NOUN
ejpam-6212	1	19	6212	6212	NUM
ejpam-6212	1	20	issn	issn	VERB
ejpam-6212	1	21	1307	1307	NUM
ejpam-6212	1	22	-	-	SYM
ejpam-6212	1	23	5543	5543	NUM
ejpam-6212	1	24	–	–	PUNCT
ejpam-6212	1	25	ejpam.com	ejpam.com	X
ejpam-6212	1	26	published	publish	VERB
ejpam-6212	1	27	by	by	ADP
ejpam-6212	1	28	new	new	PROPN
ejpam-6212	1	29	york	york	PROPN
ejpam-6212	1	30	business	business	PROPN
ejpam-6212	1	31	global	global	ADJ
ejpam-6212	1	32	bounds	bound	NOUN
ejpam-6212	1	33	of	of	ADP
ejpam-6212	1	34	geodetic	geodetic	ADJ
ejpam-6212	1	35	-	-	PUNCT
ejpam-6212	1	36	wiener	wiener	NOUN
ejpam-6212	1	37	index	index	NOUN
ejpam-6212	1	38	on	on	ADP
ejpam-6212	1	39	spirocyclic	spirocyclic	ADJ
ejpam-6212	1	40	graphs	graph	NOUN
ejpam-6212	1	41	rosalio	rosalio	ADJ
ejpam-6212	1	42	g.	g.	PROPN
ejpam-6212	1	43	artes	artes	PROPN
ejpam-6212	1	44	jr.1,2	jr.1,2	PROPN
ejpam-6212	1	45	,	,	PUNCT
ejpam-6212	1	46	r.	r.	PROPN
ejpam-6212	1	47	u.	u.	PROPN
ejpam-6212	1	48	gobithaasan1,∗	gobithaasan1,∗	PROPN
ejpam-6212	1	49	,	,	PUNCT
ejpam-6212	1	50	roslan	roslan	PROPN
ejpam-6212	1	51	hasni3	hasni3	PROPN
ejpam-6212	1	52	,	,	PUNCT
ejpam-6212	1	53	nader	nader	PROPN
ejpam-6212	1	54	jafari	jafari	PROPN
ejpam-6212	1	55	rad4	rad4	PROPN
ejpam-6212	1	56	1	1	NUM
ejpam-6212	1	57	school	school	NOUN
ejpam-6212	1	58	of	of	ADP
ejpam-6212	1	59	mathematical	mathematical	ADJ
ejpam-6212	1	60	sciences	science	NOUN
ejpam-6212	1	61	,	,	PUNCT
ejpam-6212	1	62	universiti	universiti	PROPN
ejpam-6212	1	63	sains	sain	VERB
ejpam-6212	1	64	malaysia	malaysia	PROPN
ejpam-6212	1	65	,	,	PUNCT
ejpam-6212	1	66	11800	11800	NUM
ejpam-6212	1	67	usm	usm	ADJ
ejpam-6212	1	68	penang	penang	PROPN
ejpam-6212	1	69	,	,	PUNCT
ejpam-6212	1	70	malaysia	malaysia	PROPN
ejpam-6212	1	71	2	2	NUM
ejpam-6212	1	72	department	department	NOUN
ejpam-6212	1	73	of	of	ADP
ejpam-6212	1	74	mathematics	mathematic	NOUN
ejpam-6212	1	75	,	,	PUNCT
ejpam-6212	1	76	college	college	NOUN
ejpam-6212	1	77	of	of	ADP
ejpam-6212	1	78	arts	art	NOUN
ejpam-6212	1	79	and	and	CCONJ
ejpam-6212	1	80	sciences	science	NOUN
ejpam-6212	1	81	,	,	PUNCT
ejpam-6212	1	82	mindanao	mindanao	PROPN
ejpam-6212	1	83	state	state	PROPN
ejpam-6212	1	84	university	university	PROPN
ejpam-6212	1	85	tawi	tawi	PROPN
ejpam-6212	1	86	-	-	PUNCT
ejpam-6212	1	87	tawi	tawi	PROPN
ejpam-6212	1	88	college	college	PROPN
ejpam-6212	1	89	of	of	ADP
ejpam-6212	1	90	technology	technology	NOUN
ejpam-6212	1	91	and	and	CCONJ
ejpam-6212	1	92	oceanography	oceanography	NOUN
ejpam-6212	1	93	,	,	PUNCT
ejpam-6212	1	94	7500	7500	NUM
ejpam-6212	1	95	bongao	bongao	NOUN
ejpam-6212	1	96	,	,	PUNCT
ejpam-6212	1	97	tawi	tawi	NOUN
ejpam-6212	1	98	-	-	PUNCT
ejpam-6212	1	99	tawi	tawi	NOUN
ejpam-6212	1	100	,	,	PUNCT
ejpam-6212	1	101	philippines	philippine	VERB
ejpam-6212	1	102	3	3	NUM
ejpam-6212	1	103	special	special	ADJ
ejpam-6212	1	104	interest	interest	NOUN
ejpam-6212	1	105	group	group	NOUN
ejpam-6212	1	106	on	on	ADP
ejpam-6212	1	107	modelling	modelling	NOUN
ejpam-6212	1	108	and	and	CCONJ
ejpam-6212	1	109	data	datum	NOUN
ejpam-6212	1	110	analytics	analytic	NOUN
ejpam-6212	1	111	(	(	PUNCT
ejpam-6212	1	112	sigmda	sigmda	ADJ
ejpam-6212	1	113	)	)	PUNCT
ejpam-6212	1	114	,	,	PUNCT
ejpam-6212	1	115	faculty	faculty	NOUN
ejpam-6212	1	116	of	of	ADP
ejpam-6212	1	117	computer	computer	NOUN
ejpam-6212	1	118	science	science	NOUN
ejpam-6212	1	119	and	and	CCONJ
ejpam-6212	1	120	mathematics	mathematic	NOUN
ejpam-6212	1	121	,	,	PUNCT
ejpam-6212	1	122	universiti	universiti	PROPN
ejpam-6212	1	123	malaysia	malaysia	PROPN
ejpam-6212	1	124	terengganu	terengganu	PROPN
ejpam-6212	1	125	,	,	PUNCT
ejpam-6212	1	126	21030	21030	NUM
ejpam-6212	1	127	umt	umt	NOUN
ejpam-6212	1	128	kuala	kuala	PROPN
ejpam-6212	1	129	nerus	nerus	PROPN
ejpam-6212	1	130	,	,	PUNCT
ejpam-6212	1	131	terengganu	terengganu	PROPN
ejpam-6212	1	132	,	,	PUNCT
ejpam-6212	1	133	malaysia	malaysia	PROPN
ejpam-6212	1	134	4	4	NUM
ejpam-6212	1	135	department	department	NOUN
ejpam-6212	1	136	of	of	ADP
ejpam-6212	1	137	mathematics	mathematic	NOUN
ejpam-6212	1	138	,	,	PUNCT
ejpam-6212	1	139	shahed	shahed	ADJ
ejpam-6212	1	140	university	university	NOUN
ejpam-6212	1	141	,	,	PUNCT
ejpam-6212	1	142	tehran	tehran	PROPN
ejpam-6212	1	143	,	,	PUNCT
ejpam-6212	1	144	iran	iran	PROPN
ejpam-6212	1	145	abstract	abstract	NOUN
ejpam-6212	1	146	.	.	PUNCT
ejpam-6212	2	1	wiener	wiener	NOUN
ejpam-6212	2	2	index	index	NOUN
ejpam-6212	2	3	has	have	AUX
ejpam-6212	2	4	been	be	AUX
ejpam-6212	2	5	extensively	extensively	ADV
ejpam-6212	2	6	studied	study	VERB
ejpam-6212	2	7	for	for	ADP
ejpam-6212	2	8	several	several	ADJ
ejpam-6212	2	9	decades	decade	NOUN
ejpam-6212	2	10	because	because	SCONJ
ejpam-6212	2	11	of	of	ADP
ejpam-6212	2	12	its	its	PRON
ejpam-6212	2	13	applications	application	NOUN
ejpam-6212	2	14	in	in	ADP
ejpam-6212	2	15	chemistry	chemistry	NOUN
ejpam-6212	2	16	.	.	PUNCT
ejpam-6212	3	1	many	many	ADJ
ejpam-6212	3	2	variants	variant	NOUN
ejpam-6212	3	3	of	of	ADP
ejpam-6212	3	4	wiener	wiener	NOUN
ejpam-6212	3	5	index	index	NOUN
ejpam-6212	3	6	were	be	AUX
ejpam-6212	3	7	defined	define	VERB
ejpam-6212	3	8	and	and	CCONJ
ejpam-6212	3	9	their	their	PRON
ejpam-6212	3	10	corresponding	corresponding	ADJ
ejpam-6212	3	11	bounds	bound	NOUN
ejpam-6212	3	12	were	be	AUX
ejpam-6212	3	13	explored	explore	VERB
ejpam-6212	3	14	.	.	PUNCT
ejpam-6212	4	1	in	in	ADP
ejpam-6212	4	2	this	this	DET
ejpam-6212	4	3	work	work	NOUN
ejpam-6212	4	4	,	,	PUNCT
ejpam-6212	4	5	we	we	PRON
ejpam-6212	4	6	introduced	introduce	VERB
ejpam-6212	4	7	the	the	DET
ejpam-6212	4	8	concept	concept	NOUN
ejpam-6212	4	9	of	of	ADP
ejpam-6212	4	10	geodetic	geodetic	ADJ
ejpam-6212	4	11	-	-	PUNCT
ejpam-6212	4	12	wiener	wiener	NOUN
ejpam-6212	4	13	index	index	NOUN
ejpam-6212	4	14	by	by	ADP
ejpam-6212	4	15	considering	consider	VERB
ejpam-6212	4	16	the	the	DET
ejpam-6212	4	17	number	number	NOUN
ejpam-6212	4	18	of	of	ADP
ejpam-6212	4	19	geodesics	geodesic	NOUN
ejpam-6212	4	20	between	between	ADP
ejpam-6212	4	21	any	any	DET
ejpam-6212	4	22	pair	pair	NOUN
ejpam-6212	4	23	of	of	ADP
ejpam-6212	4	24	vertices	vertex	NOUN
ejpam-6212	4	25	.	.	PUNCT
ejpam-6212	5	1	we	we	PRON
ejpam-6212	5	2	used	use	VERB
ejpam-6212	5	3	the	the	DET
ejpam-6212	5	4	concept	concept	NOUN
ejpam-6212	5	5	of	of	ADP
ejpam-6212	5	6	projection	projection	NOUN
ejpam-6212	5	7	of	of	ADP
ejpam-6212	5	8	a	a	DET
ejpam-6212	5	9	vertex	vertex	NOUN
ejpam-6212	5	10	to	to	ADP
ejpam-6212	5	11	a	a	DET
ejpam-6212	5	12	subgraph	subgraph	NOUN
ejpam-6212	5	13	to	to	PART
ejpam-6212	5	14	decompose	decompose	VERB
ejpam-6212	5	15	the	the	DET
ejpam-6212	5	16	structure	structure	NOUN
ejpam-6212	5	17	into	into	ADP
ejpam-6212	5	18	subtrees	subtree	NOUN
ejpam-6212	5	19	.	.	PUNCT
ejpam-6212	6	1	simple	simple	ADJ
ejpam-6212	6	2	spirocyclic	spirocyclic	NOUN
ejpam-6212	6	3	graphs	graph	NOUN
ejpam-6212	6	4	are	be	AUX
ejpam-6212	6	5	bicyclic	bicyclic	NOUN
ejpam-6212	6	6	graphs	graph	NOUN
ejpam-6212	6	7	whose	whose	DET
ejpam-6212	6	8	cycles	cycle	NOUN
ejpam-6212	6	9	share	share	VERB
ejpam-6212	6	10	a	a	DET
ejpam-6212	6	11	common	common	ADJ
ejpam-6212	6	12	vertex	vertex	NOUN
ejpam-6212	6	13	.	.	PUNCT
ejpam-6212	7	1	using	use	VERB
ejpam-6212	7	2	the	the	DET
ejpam-6212	7	3	idea	idea	NOUN
ejpam-6212	7	4	of	of	ADP
ejpam-6212	7	5	partial	partial	ADJ
ejpam-6212	7	6	wiener	wiener	NOUN
ejpam-6212	7	7	index	index	NOUN
ejpam-6212	7	8	,	,	PUNCT
ejpam-6212	7	9	we	we	PRON
ejpam-6212	7	10	determined	determine	VERB
ejpam-6212	7	11	the	the	DET
ejpam-6212	7	12	bounds	bound	NOUN
ejpam-6212	7	13	of	of	ADP
ejpam-6212	7	14	geodetic	geodetic	ADJ
ejpam-6212	7	15	-	-	PUNCT
ejpam-6212	7	16	wiener	wiener	NOUN
ejpam-6212	7	17	index	index	NOUN
ejpam-6212	7	18	with	with	ADP
ejpam-6212	7	19	respect	respect	NOUN
ejpam-6212	7	20	to	to	ADP
ejpam-6212	7	21	other	other	ADJ
ejpam-6212	7	22	distance	distance	NOUN
ejpam-6212	7	23	-	-	PUNCT
ejpam-6212	7	24	based	base	VERB
ejpam-6212	7	25	topological	topological	ADJ
ejpam-6212	7	26	indices	index	NOUN
ejpam-6212	7	27	for	for	ADP
ejpam-6212	7	28	simple	simple	ADJ
ejpam-6212	7	29	spirocyclic	spirocyclic	NOUN
ejpam-6212	7	30	graphs	graph	NOUN
ejpam-6212	7	31	.	.	PUNCT
ejpam-6212	8	1	2020	2020	NUM
ejpam-6212	8	2	mathematics	mathematic	NOUN
ejpam-6212	8	3	subject	subject	NOUN
ejpam-6212	8	4	classifications	classification	NOUN
ejpam-6212	8	5	:	:	PUNCT
ejpam-6212	8	6	05c30	05c30	NOUN
ejpam-6212	8	7	,	,	PUNCT
ejpam-6212	8	8	05c92	05c92	X
ejpam-6212	8	9	key	key	ADJ
ejpam-6212	8	10	words	word	NOUN
ejpam-6212	8	11	and	and	CCONJ
ejpam-6212	8	12	phrases	phrase	NOUN
ejpam-6212	8	13	:	:	PUNCT
ejpam-6212	8	14	topological	topological	ADJ
ejpam-6212	8	15	index	index	NOUN
ejpam-6212	8	16	,	,	PUNCT
ejpam-6212	8	17	geodetic	geodetic	ADJ
ejpam-6212	8	18	-	-	PUNCT
ejpam-6212	8	19	wiener	wiener	NOUN
ejpam-6212	8	20	index	index	NOUN
ejpam-6212	8	21	,	,	PUNCT
ejpam-6212	8	22	spirocyclic	spirocyclic	NOUN
ejpam-6212	8	23	graphs	graph	NOUN
ejpam-6212	8	24	1	1	NUM
ejpam-6212	8	25	.	.	PUNCT
ejpam-6212	9	1	introduction	introduction	NOUN
ejpam-6212	9	2	topological	topological	ADJ
ejpam-6212	9	3	indices	index	NOUN
ejpam-6212	9	4	(	(	PUNCT
ejpam-6212	9	5	tis	tis	NOUN
ejpam-6212	9	6	)	)	PUNCT
ejpam-6212	9	7	are	be	AUX
ejpam-6212	9	8	2d	2d	NUM
ejpam-6212	9	9	descriptors	descriptor	NOUN
ejpam-6212	9	10	that	that	PRON
ejpam-6212	9	11	 	 	SPACE
ejpam-6212	9	12	consider	consider	VERB
ejpam-6212	9	13	 	 	SPACE
ejpam-6212	9	14	the	the	DET
ejpam-6212	9	15	internal	internal	ADJ
ejpam-6212	9	16	atomic	atomic	ADJ
ejpam-6212	9	17	 	 	SPACE
ejpam-6212	9	18	structure	structure	NOUN
ejpam-6212	9	19	of	of	ADP
ejpam-6212	9	20	compounds	compound	NOUN
ejpam-6212	9	21	[	[	X
ejpam-6212	9	22	1	1	NUM
ejpam-6212	9	23	]	]	PUNCT
ejpam-6212	9	24	.	.	PUNCT
ejpam-6212	9	25	 	 	SPACE
ejpam-6212	10	1	they	they	PRON
ejpam-6212	10	2	 	 	SPACE
ejpam-6212	10	3	incorporate	incorporate	VERB
ejpam-6212	10	4	 	 	SPACE
ejpam-6212	10	5	data	datum	NOUN
ejpam-6212	10	6	 	 	SPACE
ejpam-6212	10	7	on	on	ADP
ejpam-6212	10	8	 	 	SPACE
ejpam-6212	10	9	molecular	molecular	ADJ
ejpam-6212	10	10	size	size	NOUN
ejpam-6212	10	11	,	,	PUNCT
ejpam-6212	10	12	shape	shape	NOUN
ejpam-6212	10	13	,	,	PUNCT
ejpam-6212	10	14	branching	branch	VERB
ejpam-6212	10	15	,	,	PUNCT
ejpam-6212	10	16	 	 	SPACE
ejpam-6212	10	17	occurrence	occurrence	NOUN
ejpam-6212	10	18	 	 	SPACE
ejpam-6212	10	19	of	of	ADP
ejpam-6212	10	20	heteroatoms	heteroatom	NOUN
ejpam-6212	10	21	,	,	PUNCT
ejpam-6212	10	22	and	and	CCONJ
ejpam-6212	10	23	multiple	multiple	ADJ
ejpam-6212	10	24	bonds	bond	NOUN
ejpam-6212	10	25	 	 	SPACE
ejpam-6212	10	26	into	into	ADP
ejpam-6212	10	27	 	 	SPACE
ejpam-6212	10	28	numeric	numeric	ADJ
ejpam-6212	10	29	 	 	SPACE
ejpam-6212	10	30	values	value	NOUN
ejpam-6212	10	31	  	  	SPACE
ejpam-6212	11	1	[	[	X
ejpam-6212	11	2	1	1	NUM
ejpam-6212	11	3	]	]	PUNCT
ejpam-6212	11	4	.	.	PUNCT
ejpam-6212	12	1	in	in	ADP
ejpam-6212	12	2	1947	1947	NUM
ejpam-6212	12	3	,	,	PUNCT
ejpam-6212	12	4	wiener	wiener	NOUN
ejpam-6212	12	5	[	[	X
ejpam-6212	12	6	2	2	NUM
ejpam-6212	12	7	]	]	PUNCT
ejpam-6212	12	8	calculated	calculate	VERB
ejpam-6212	12	9	boiling	boiling	NOUN
ejpam-6212	12	10	point	point	NOUN
ejpam-6212	12	11	of	of	ADP
ejpam-6212	12	12	paraffin	paraffin	NOUN
ejpam-6212	12	13	by	by	ADP
ejpam-6212	12	14	using	use	VERB
ejpam-6212	12	15	a	a	DET
ejpam-6212	12	16	distance	distance	NOUN
ejpam-6212	12	17	-	-	PUNCT
ejpam-6212	12	18	based	base	VERB
ejpam-6212	12	19	ti	ti	NOUN
ejpam-6212	12	20	called	call	VERB
ejpam-6212	12	21	the	the	DET
ejpam-6212	12	22	wiener	wiener	NOUN
ejpam-6212	12	23	index	index	NOUN
ejpam-6212	12	24	,	,	PUNCT
ejpam-6212	12	25	which	which	PRON
ejpam-6212	12	26	is	be	AUX
ejpam-6212	12	27	the	the	DET
ejpam-6212	12	28	sum	sum	NOUN
ejpam-6212	12	29	of	of	ADP
ejpam-6212	12	30	distances	distance	NOUN
ejpam-6212	12	31	between	between	ADP
ejpam-6212	12	32	all	all	DET
ejpam-6212	12	33	vertex	vertex	NOUN
ejpam-6212	12	34	pairs	pair	NOUN
ejpam-6212	12	35	in	in	ADP
ejpam-6212	12	36	a	a	DET
ejpam-6212	12	37	graph	graph	NOUN
ejpam-6212	12	38	.	.	PUNCT
ejpam-6212	13	1	since	since	SCONJ
ejpam-6212	13	2	benzenoid	benzenoid	NOUN
ejpam-6212	13	3	hydrocarbons	hydrocarbon	NOUN
ejpam-6212	13	4	are	be	AUX
ejpam-6212	13	5	fascinating	fascinate	VERB
ejpam-6212	13	6	the	the	DET
ejpam-6212	13	7	huge	huge	ADJ
ejpam-6212	13	8	significance	significance	NOUN
ejpam-6212	13	9	of	of	ADP
ejpam-6212	13	10	theoretical	theoretical	ADJ
ejpam-6212	13	11	chemists	chemist	NOUN
ejpam-6212	13	12	,	,	PUNCT
ejpam-6212	13	13	the	the	DET
ejpam-6212	13	14	theory	theory	NOUN
ejpam-6212	13	15	of	of	ADP
ejpam-6212	13	16	∗corresponding	∗corresponde	VERB
ejpam-6212	13	17	author	author	NOUN
ejpam-6212	13	18	.	.	PUNCT
ejpam-6212	14	1	doi	doi	NOUN
ejpam-6212	14	2	:	:	PUNCT
ejpam-6212	14	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6212	https://doi.org/10.29020/nybg.ejpam.v18i4.6212	ADJ
ejpam-6212	14	4	email	email	NOUN
ejpam-6212	14	5	addresses	address	NOUN
ejpam-6212	14	6	:	:	PUNCT
ejpam-6212	14	7	rosalioartes@msutawi-tawi.edu.ph	rosalioartes@msutawi-tawi.edu.ph	PROPN
ejpam-6212	14	8	(	(	PUNCT
ejpam-6212	14	9	r.	r.	PROPN
ejpam-6212	14	10	g.	g.	PROPN
ejpam-6212	14	11	artes	artes	PROPN
ejpam-6212	14	12	jr	jr	PROPN
ejpam-6212	14	13	.	.	PROPN
ejpam-6212	14	14	)	)	PUNCT
ejpam-6212	14	15	,	,	PUNCT
ejpam-6212	14	16	gobithaasan@usm.my	gobithaasan@usm.my	PROPN
ejpam-6212	14	17	(	(	PUNCT
ejpam-6212	14	18	r.	r.	PROPN
ejpam-6212	14	19	u.	u.	PROPN
ejpam-6212	14	20	gobithaasan	gobithaasan	PROPN
ejpam-6212	14	21	)	)	PUNCT
ejpam-6212	14	22	,	,	PUNCT
ejpam-6212	14	23	hroslan@umt.edu.my	hroslan@umt.edu.my	PROPN
ejpam-6212	14	24	(	(	PUNCT
ejpam-6212	14	25	r.	r.	PROPN
ejpam-6212	14	26	hasni	hasni	PROPN
ejpam-6212	14	27	)	)	PUNCT
ejpam-6212	14	28	,	,	PUNCT
ejpam-6212	14	29	n.jafarirad@shahed.ac.ir	n.jafarirad@shahed.ac.ir	PROPN
ejpam-6212	14	30	(	(	PUNCT
ejpam-6212	14	31	n.	n.	PROPN
ejpam-6212	14	32	jafari	jafari	PROPN
ejpam-6212	14	33	rad	rad	PROPN
ejpam-6212	14	34	)	)	PUNCT
ejpam-6212	14	35	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6212	15	1	1	1	NUM
ejpam-6212	15	2	copyright	copyright	NOUN
ejpam-6212	15	3	:	:	PUNCT
ejpam-6212	15	4	©	©	PROPN
ejpam-6212	15	5	2025	2025	NUM
ejpam-6212	15	6	the	the	DET
ejpam-6212	15	7	author(s	author(s	NOUN
ejpam-6212	15	8	)	)	PUNCT
ejpam-6212	15	9	.	.	PUNCT
ejpam-6212	16	1	(	(	PUNCT
ejpam-6212	16	2	cc	cc	NOUN
ejpam-6212	16	3	by	by	ADP
ejpam-6212	16	4	-	-	PUNCT
ejpam-6212	16	5	nc	nc	PROPN
ejpam-6212	16	6	4.0	4.0	NUM
ejpam-6212	16	7	)	)	PUNCT
ejpam-6212	16	8	r.	r.	PROPN
ejpam-6212	16	9	g.	g.	PROPN
ejpam-6212	16	10	artes	artes	PROPN
ejpam-6212	16	11	jr	jr	PROPN
ejpam-6212	16	12	.	.	PROPN
ejpam-6212	16	13	et	et	PROPN
ejpam-6212	16	14	al	al	PROPN
ejpam-6212	16	15	.	.	PUNCT
ejpam-6212	16	16	/	/	SYM
ejpam-6212	16	17	eur	eur	PROPN
ejpam-6212	16	18	.	.	PUNCT
ejpam-6212	17	1	j.	j.	PROPN
ejpam-6212	17	2	pure	pure	PROPN
ejpam-6212	17	3	appl	appl	PROPN
ejpam-6212	17	4	.	.	PROPN
ejpam-6212	17	5	math	math	PROPN
ejpam-6212	17	6	,	,	PUNCT
ejpam-6212	17	7	18	18	NUM
ejpam-6212	17	8	(	(	PUNCT
ejpam-6212	17	9	4	4	NUM
ejpam-6212	17	10	)	)	PUNCT
ejpam-6212	17	11	(	(	PUNCT
ejpam-6212	17	12	2025	2025	NUM
ejpam-6212	17	13	)	)	PUNCT
ejpam-6212	17	14	,	,	PUNCT
ejpam-6212	17	15	6212	6212	NUM
ejpam-6212	17	16	2	2	NUM
ejpam-6212	17	17	of	of	ADP
ejpam-6212	17	18	20	20	NUM
ejpam-6212	17	19	the	the	DET
ejpam-6212	17	20	wiener	wiener	NOUN
ejpam-6212	17	21	index	index	NOUN
ejpam-6212	17	22	of	of	ADP
ejpam-6212	17	23	the	the	DET
ejpam-6212	17	24	respective	respective	ADJ
ejpam-6212	17	25	molecular	molecular	ADJ
ejpam-6212	17	26	graphs	graph	NOUN
ejpam-6212	17	27	have	have	AUX
ejpam-6212	17	28	been	be	AUX
ejpam-6212	17	29	extensively	extensively	ADV
ejpam-6212	17	30	developed	develop	VERB
ejpam-6212	17	31	in	in	ADP
ejpam-6212	17	32	the	the	DET
ejpam-6212	17	33	last	last	ADJ
ejpam-6212	17	34	three	three	NUM
ejpam-6212	17	35	decades	decade	NOUN
ejpam-6212	17	36	[	[	X
ejpam-6212	17	37	2	2	NUM
ejpam-6212	17	38	]	]	PUNCT
ejpam-6212	17	39	.	.	PUNCT
ejpam-6212	18	1	although	although	SCONJ
ejpam-6212	18	2	the	the	DET
ejpam-6212	18	3	wiener	wiener	NOUN
ejpam-6212	18	4	index	index	NOUN
ejpam-6212	18	5	is	be	AUX
ejpam-6212	18	6	the	the	DET
ejpam-6212	18	7	oldest	old	ADJ
ejpam-6212	18	8	topological	topological	ADJ
ejpam-6212	18	9	index	index	NOUN
ejpam-6212	18	10	,	,	PUNCT
ejpam-6212	18	11	later	later	ADV
ejpam-6212	18	12	on	on	ADP
ejpam-6212	18	13	some	some	DET
ejpam-6212	18	14	distance	distance	NOUN
ejpam-6212	18	15	-	-	PUNCT
ejpam-6212	18	16	based	base	VERB
ejpam-6212	18	17	topological	topological	ADJ
ejpam-6212	18	18	indices	index	NOUN
ejpam-6212	18	19	have	have	AUX
ejpam-6212	18	20	been	be	AUX
ejpam-6212	18	21	defined	define	VERB
ejpam-6212	18	22	such	such	ADJ
ejpam-6212	18	23	as	as	ADP
ejpam-6212	18	24	hyper	hyper	ADJ
ejpam-6212	18	25	-	-	ADJ
ejpam-6212	18	26	wiener	wiener	NOUN
ejpam-6212	18	27	index	index	NOUN
ejpam-6212	18	28	[	[	X
ejpam-6212	18	29	3	3	NUM
ejpam-6212	18	30	]	]	PUNCT
ejpam-6212	18	31	,	,	PUNCT
ejpam-6212	18	32	gutman	gutman	NOUN
ejpam-6212	18	33	index	index	NOUN
ejpam-6212	18	34	[	[	X
ejpam-6212	18	35	4	4	NUM
ejpam-6212	18	36	]	]	PUNCT
ejpam-6212	18	37	,	,	PUNCT
ejpam-6212	18	38	schultz	schultz	PROPN
ejpam-6212	18	39	index	index	NOUN
ejpam-6212	19	1	[	[	X
ejpam-6212	19	2	5–9	5–9	NOUN
ejpam-6212	19	3	]	]	X
ejpam-6212	19	4	,	,	PUNCT
ejpam-6212	19	5	harary	harary	NOUN
ejpam-6212	19	6	index	index	NOUN
ejpam-6212	20	1	[	[	X
ejpam-6212	20	2	10	10	NUM
ejpam-6212	20	3	,	,	PUNCT
ejpam-6212	20	4	11	11	NUM
ejpam-6212	20	5	]	]	PUNCT
ejpam-6212	20	6	,	,	PUNCT
ejpam-6212	20	7	additively	additively	ADV
ejpam-6212	20	8	weighted	weight	VERB
ejpam-6212	20	9	harary	harary	ADJ
ejpam-6212	20	10	index	index	NOUN
ejpam-6212	21	1	[	[	X
ejpam-6212	21	2	12	12	NUM
ejpam-6212	21	3	]	]	PUNCT
ejpam-6212	21	4	and	and	CCONJ
ejpam-6212	21	5	multiplicatively	multiplicatively	ADV
ejpam-6212	21	6	weighted	weight	VERB
ejpam-6212	21	7	harary	harary	ADJ
ejpam-6212	21	8	index	index	NOUN
ejpam-6212	21	9	[	[	X
ejpam-6212	21	10	13	13	NUM
ejpam-6212	21	11	]	]	PUNCT
ejpam-6212	21	12	.	.	PUNCT
ejpam-6212	22	1	the	the	DET
ejpam-6212	22	2	idea	idea	NOUN
ejpam-6212	22	3	of	of	ADP
ejpam-6212	22	4	wiener	wiener	NOUN
ejpam-6212	22	5	index	index	NOUN
ejpam-6212	22	6	was	be	AUX
ejpam-6212	22	7	introduced	introduce	VERB
ejpam-6212	22	8	by	by	ADP
ejpam-6212	22	9	harold	harold	PROPN
ejpam-6212	22	10	wiener	wiener	NOUN
ejpam-6212	22	11	in	in	ADP
ejpam-6212	22	12	1947	1947	NUM
ejpam-6212	22	13	[	[	X
ejpam-6212	22	14	2	2	NUM
ejpam-6212	22	15	]	]	PUNCT
ejpam-6212	22	16	.	.	PUNCT
ejpam-6212	23	1	the	the	DET
ejpam-6212	23	2	wiener	wiener	NOUN
ejpam-6212	23	3	index	index	NOUN
ejpam-6212	23	4	of	of	ADP
ejpam-6212	23	5	a	a	DET
ejpam-6212	23	6	connected	connected	ADJ
ejpam-6212	23	7	graph	graph	NOUN
ejpam-6212	23	8	g	g	NOUN
ejpam-6212	23	9	as	as	SCONJ
ejpam-6212	23	10	defined	define	VERB
ejpam-6212	23	11	in	in	ADP
ejpam-6212	23	12	[	[	X
ejpam-6212	23	13	2	2	NUM
ejpam-6212	23	14	]	]	PUNCT
ejpam-6212	23	15	is	be	AUX
ejpam-6212	23	16	given	give	VERB
ejpam-6212	23	17	by	by	ADP
ejpam-6212	23	18	w	w	PROPN
ejpam-6212	23	19	(	(	PUNCT
ejpam-6212	23	20	g	g	NOUN
ejpam-6212	23	21	)	)	PUNCT
ejpam-6212	23	22	=	=	PUNCT
ejpam-6212	23	23	∑	∑	PUNCT
ejpam-6212	23	24	{	{	PUNCT
ejpam-6212	23	25	u	u	NOUN
ejpam-6212	23	26	,	,	PUNCT
ejpam-6212	23	27	v}⊆v	v}⊆v	PROPN
ejpam-6212	23	28	(	(	PUNCT
ejpam-6212	23	29	g	g	NOUN
ejpam-6212	23	30	)	)	PUNCT
ejpam-6212	23	31	dg(u	dg(u	X
ejpam-6212	23	32	,	,	PUNCT
ejpam-6212	23	33	v	v	NOUN
ejpam-6212	23	34	)	)	PUNCT
ejpam-6212	23	35	.	.	PUNCT
ejpam-6212	24	1	recently	recently	ADV
ejpam-6212	24	2	,	,	PUNCT
ejpam-6212	24	3	lin	lin	PROPN
ejpam-6212	24	4	[	[	X
ejpam-6212	24	5	14	14	NUM
ejpam-6212	24	6	]	]	PUNCT
ejpam-6212	24	7	made	make	VERB
ejpam-6212	24	8	a	a	DET
ejpam-6212	24	9	survey	survey	NOUN
ejpam-6212	24	10	of	of	ADP
ejpam-6212	24	11	all	all	DET
ejpam-6212	24	12	the	the	DET
ejpam-6212	24	13	extremal	extremal	ADJ
ejpam-6212	24	14	results	result	NOUN
ejpam-6212	24	15	on	on	ADP
ejpam-6212	24	16	the	the	DET
ejpam-6212	24	17	wiener	wiener	NOUN
ejpam-6212	24	18	index	index	NOUN
ejpam-6212	24	19	of	of	ADP
ejpam-6212	24	20	trees	tree	NOUN
ejpam-6212	24	21	from	from	ADP
ejpam-6212	24	22	2014	2014	NUM
ejpam-6212	24	23	and	and	CCONJ
ejpam-6212	24	24	presented	present	VERB
ejpam-6212	24	25	some	some	DET
ejpam-6212	24	26	open	open	ADJ
ejpam-6212	24	27	problems	problem	NOUN
ejpam-6212	24	28	.	.	PUNCT
ejpam-6212	25	1	the	the	DET
ejpam-6212	25	2	generalized	generalized	ADJ
ejpam-6212	25	3	wiener	wiener	NOUN
ejpam-6212	25	4	index	index	NOUN
ejpam-6212	25	5	of	of	ADP
ejpam-6212	25	6	a	a	DET
ejpam-6212	25	7	a	a	DET
ejpam-6212	25	8	connected	connected	ADJ
ejpam-6212	25	9	graph	graph	NOUN
ejpam-6212	25	10	g	g	NOUN
ejpam-6212	25	11	was	be	AUX
ejpam-6212	25	12	introduced	introduce	VERB
ejpam-6212	25	13	by	by	ADP
ejpam-6212	25	14	martinezperez	martinezperez	PROPN
ejpam-6212	25	15	and	and	CCONJ
ejpam-6212	25	16	rodriguez	rodriguez	NOUN
ejpam-6212	26	1	[	[	X
ejpam-6212	26	2	15	15	NUM
ejpam-6212	26	3	]	]	PUNCT
ejpam-6212	26	4	and	and	CCONJ
ejpam-6212	26	5	is	be	AUX
ejpam-6212	26	6	given	give	VERB
ejpam-6212	26	7	by	by	ADP
ejpam-6212	26	8	wλ(g	wλ(g	PUNCT
ejpam-6212	26	9	)	)	PUNCT
ejpam-6212	26	10	=	=	PUNCT
ejpam-6212	26	11	∑	∑	PUNCT
ejpam-6212	26	12	{	{	PUNCT
ejpam-6212	26	13	u	u	NOUN
ejpam-6212	26	14	,	,	PUNCT
ejpam-6212	26	15	v}⊆v	v}⊆v	PROPN
ejpam-6212	26	16	(	(	PUNCT
ejpam-6212	26	17	g	g	NOUN
ejpam-6212	26	18	)	)	PUNCT
ejpam-6212	26	19	d(u	d(u	PROPN
ejpam-6212	26	20	,	,	PUNCT
ejpam-6212	26	21	v)λ	v)λ	NOUN
ejpam-6212	26	22	,	,	PUNCT
ejpam-6212	26	23	where	where	SCONJ
ejpam-6212	26	24	λ	λ	PROPN
ejpam-6212	26	25	is	be	AUX
ejpam-6212	26	26	a	a	DET
ejpam-6212	26	27	real	real	ADJ
ejpam-6212	26	28	number	number	NOUN
ejpam-6212	26	29	.	.	PUNCT
ejpam-6212	27	1	the	the	DET
ejpam-6212	27	2	study	study	NOUN
ejpam-6212	27	3	of	of	ADP
ejpam-6212	27	4	hyper	hyper	ADJ
ejpam-6212	27	5	-	-	ADJ
ejpam-6212	27	6	wiener	wiener	NOUN
ejpam-6212	27	7	index	index	NOUN
ejpam-6212	27	8	of	of	ADP
ejpam-6212	27	9	a	a	DET
ejpam-6212	27	10	connected	connected	ADJ
ejpam-6212	27	11	graph	graph	NOUN
ejpam-6212	27	12	g	g	NOUN
ejpam-6212	27	13	was	be	AUX
ejpam-6212	27	14	pioneered	pioneer	VERB
ejpam-6212	27	15	by	by	ADP
ejpam-6212	27	16	alhevaz	alhevaz	PROPN
ejpam-6212	27	17	et	et	PROPN
ejpam-6212	27	18	al	al	PROPN
ejpam-6212	27	19	.	.	PUNCT
ejpam-6212	28	1	[	[	X
ejpam-6212	28	2	16	16	NUM
ejpam-6212	28	3	]	]	PUNCT
ejpam-6212	28	4	and	and	CCONJ
ejpam-6212	28	5	is	be	AUX
ejpam-6212	28	6	given	give	VERB
ejpam-6212	28	7	by	by	ADP
ejpam-6212	28	8	ww	ww	PROPN
ejpam-6212	28	9	(	(	PUNCT
ejpam-6212	28	10	g	g	NOUN
ejpam-6212	28	11	)	)	PUNCT
ejpam-6212	28	12	=	=	PUNCT
ejpam-6212	28	13	∑	∑	PUNCT
ejpam-6212	28	14	{	{	PUNCT
ejpam-6212	28	15	u	u	NOUN
ejpam-6212	28	16	,	,	PUNCT
ejpam-6212	28	17	v}⊆v	v}⊆v	PROPN
ejpam-6212	28	18	(	(	PUNCT
ejpam-6212	28	19	g	g	NOUN
ejpam-6212	28	20	)	)	PUNCT
ejpam-6212	28	21	(	(	PUNCT
ejpam-6212	28	22	d(u	d(u	PROPN
ejpam-6212	28	23	,	,	PUNCT
ejpam-6212	28	24	v	v	NOUN
ejpam-6212	28	25	)	)	PUNCT
ejpam-6212	28	26	+	+	CCONJ
ejpam-6212	28	27	1	1	NUM
ejpam-6212	28	28	2	2	NUM
ejpam-6212	28	29	)	)	PUNCT
ejpam-6212	28	30	=	=	SYM
ejpam-6212	28	31	1	1	NUM
ejpam-6212	28	32	2	2	NUM
ejpam-6212	28	33	∑	∑	PUNCT
ejpam-6212	28	34	{	{	PUNCT
ejpam-6212	28	35	u	u	NOUN
ejpam-6212	28	36	,	,	PUNCT
ejpam-6212	28	37	v}⊆v	v}⊆v	PROPN
ejpam-6212	28	38	(	(	PUNCT
ejpam-6212	28	39	g	g	NOUN
ejpam-6212	28	40	)	)	PUNCT
ejpam-6212	29	1	[	[	X
ejpam-6212	29	2	d(u	d(u	PROPN
ejpam-6212	29	3	,	,	PUNCT
ejpam-6212	29	4	v)2	v)2	PROPN
ejpam-6212	29	5	+	+	CCONJ
ejpam-6212	29	6	d(u	d(u	PROPN
ejpam-6212	29	7	,	,	PUNCT
ejpam-6212	29	8	v	v	NOUN
ejpam-6212	29	9	)	)	PUNCT
ejpam-6212	29	10	]	]	PUNCT
ejpam-6212	29	11	.	.	PUNCT
ejpam-6212	30	1	the	the	DET
ejpam-6212	30	2	gutman	gutman	NOUN
ejpam-6212	30	3	index	index	NOUN
ejpam-6212	30	4	of	of	ADP
ejpam-6212	30	5	g	g	NOUN
ejpam-6212	30	6	,	,	PUNCT
ejpam-6212	30	7	denoted	denote	VERB
ejpam-6212	30	8	by	by	ADP
ejpam-6212	30	9	gut(g	gut(g	PROPN
ejpam-6212	30	10	)	)	PUNCT
ejpam-6212	30	11	,	,	PUNCT
ejpam-6212	30	12	which	which	PRON
ejpam-6212	30	13	was	be	AUX
ejpam-6212	30	14	introduced	introduce	VERB
ejpam-6212	30	15	by	by	ADP
ejpam-6212	30	16	ivan	ivan	PROPN
ejpam-6212	30	17	gutman	gutman	PROPN
ejpam-6212	30	18	in	in	ADP
ejpam-6212	30	19	1994	1994	NUM
ejpam-6212	31	1	[	[	X
ejpam-6212	31	2	17	17	NUM
ejpam-6212	31	3	]	]	PUNCT
ejpam-6212	31	4	,	,	PUNCT
ejpam-6212	31	5	is	be	AUX
ejpam-6212	31	6	given	give	VERB
ejpam-6212	31	7	by	by	ADP
ejpam-6212	31	8	gut(g	gut(g	NOUN
ejpam-6212	31	9	)	)	PUNCT
ejpam-6212	31	10	=	=	PUNCT
ejpam-6212	31	11	∑	∑	PUNCT
ejpam-6212	31	12	{	{	PUNCT
ejpam-6212	31	13	u	u	NOUN
ejpam-6212	31	14	,	,	PUNCT
ejpam-6212	31	15	v}⊆v	v}⊆v	PROPN
ejpam-6212	31	16	(	(	PUNCT
ejpam-6212	31	17	g	g	NOUN
ejpam-6212	31	18	)	)	PUNCT
ejpam-6212	32	1	[	[	X
ejpam-6212	32	2	dudv]d(u	dudv]d(u	X
ejpam-6212	32	3	,	,	PUNCT
ejpam-6212	32	4	v	v	NOUN
ejpam-6212	32	5	)	)	PUNCT
ejpam-6212	32	6	.	.	PUNCT
ejpam-6212	33	1	in	in	ADP
ejpam-6212	33	2	2014	2014	NUM
ejpam-6212	33	3	,	,	PUNCT
ejpam-6212	33	4	mazorodze	mazorodze	PROPN
ejpam-6212	33	5	et	et	PROPN
ejpam-6212	33	6	al	al	PROPN
ejpam-6212	33	7	.	.	PUNCT
ejpam-6212	34	1	[	[	X
ejpam-6212	34	2	18	18	NUM
ejpam-6212	34	3	]	]	PUNCT
ejpam-6212	34	4	established	establish	VERB
ejpam-6212	34	5	asymptotically	asymptotically	ADV
ejpam-6212	34	6	sharp	sharp	ADJ
ejpam-6212	34	7	bound	bind	VERB
ejpam-6212	34	8	of	of	ADP
ejpam-6212	34	9	the	the	DET
ejpam-6212	34	10	gutman	gutman	NOUN
ejpam-6212	34	11	index	index	NOUN
ejpam-6212	34	12	for	for	ADP
ejpam-6212	34	13	graphs	graph	NOUN
ejpam-6212	34	14	without	without	ADP
ejpam-6212	34	15	pendant	pendant	ADJ
ejpam-6212	34	16	vertices	vertex	NOUN
ejpam-6212	34	17	.	.	PUNCT
ejpam-6212	35	1	the	the	DET
ejpam-6212	35	2	schultz	schultz	PROPN
ejpam-6212	35	3	index	index	NOUN
ejpam-6212	35	4	of	of	ADP
ejpam-6212	35	5	g	g	PROPN
ejpam-6212	35	6	[	[	X
ejpam-6212	35	7	19	19	NUM
ejpam-6212	35	8	]	]	PUNCT
ejpam-6212	35	9	and	and	CCONJ
ejpam-6212	35	10	is	be	AUX
ejpam-6212	35	11	given	give	VERB
ejpam-6212	35	12	by	by	ADP
ejpam-6212	35	13	s(g	s(g	PROPN
ejpam-6212	35	14	)	)	PUNCT
ejpam-6212	36	1	=	=	PUNCT
ejpam-6212	36	2	∑	∑	PUNCT
ejpam-6212	36	3	{	{	PUNCT
ejpam-6212	36	4	u	u	NOUN
ejpam-6212	36	5	,	,	PUNCT
ejpam-6212	36	6	v}⊆v	v}⊆v	PROPN
ejpam-6212	36	7	(	(	PUNCT
ejpam-6212	36	8	g	g	NOUN
ejpam-6212	36	9	)	)	PUNCT
ejpam-6212	37	1	[	[	X
ejpam-6212	37	2	du	du	X
ejpam-6212	37	3	+	+	X
ejpam-6212	37	4	dv]d(u	dv]d(u	PROPN
ejpam-6212	37	5	,	,	PUNCT
ejpam-6212	37	6	v	v	NOUN
ejpam-6212	37	7	)	)	PUNCT
ejpam-6212	37	8	.	.	PUNCT
ejpam-6212	38	1	the	the	DET
ejpam-6212	38	2	harary	harary	PROPN
ejpam-6212	38	3	index	index	NOUN
ejpam-6212	38	4	of	of	ADP
ejpam-6212	38	5	g	g	PROPN
ejpam-6212	38	6	[	[	X
ejpam-6212	38	7	11	11	NUM
ejpam-6212	38	8	]	]	PUNCT
ejpam-6212	38	9	is	be	AUX
ejpam-6212	38	10	given	give	VERB
ejpam-6212	38	11	by	by	ADP
ejpam-6212	38	12	h(g	h(g	NOUN
ejpam-6212	38	13	)	)	PUNCT
ejpam-6212	38	14	=	=	PUNCT
ejpam-6212	39	1	∑	∑	PUNCT
ejpam-6212	39	2	{	{	PUNCT
ejpam-6212	39	3	u	u	NOUN
ejpam-6212	39	4	,	,	PUNCT
ejpam-6212	39	5	v}⊆v	v}⊆v	PROPN
ejpam-6212	39	6	(	(	PUNCT
ejpam-6212	39	7	g	g	NOUN
ejpam-6212	39	8	)	)	PUNCT
ejpam-6212	39	9	1	1	NUM
ejpam-6212	39	10	d(u	d(u	PROPN
ejpam-6212	39	11	,	,	PUNCT
ejpam-6212	39	12	v	v	NOUN
ejpam-6212	39	13	)	)	PUNCT
ejpam-6212	39	14	.	.	PUNCT
ejpam-6212	40	1	r.	r.	PROPN
ejpam-6212	40	2	g.	g.	PROPN
ejpam-6212	40	3	artes	artes	PROPN
ejpam-6212	40	4	jr	jr	PROPN
ejpam-6212	40	5	.	.	PROPN
ejpam-6212	40	6	et	et	PROPN
ejpam-6212	40	7	al	al	PROPN
ejpam-6212	40	8	.	.	PUNCT
ejpam-6212	40	9	/	/	SYM
ejpam-6212	40	10	eur	eur	PROPN
ejpam-6212	40	11	.	.	PUNCT
ejpam-6212	41	1	j.	j.	PROPN
ejpam-6212	41	2	pure	pure	PROPN
ejpam-6212	41	3	appl	appl	PROPN
ejpam-6212	41	4	.	.	PROPN
ejpam-6212	41	5	math	math	PROPN
ejpam-6212	41	6	,	,	PUNCT
ejpam-6212	41	7	18	18	NUM
ejpam-6212	41	8	(	(	PUNCT
ejpam-6212	41	9	4	4	NUM
ejpam-6212	41	10	)	)	PUNCT
ejpam-6212	41	11	(	(	PUNCT
ejpam-6212	41	12	2025	2025	NUM
ejpam-6212	41	13	)	)	PUNCT
ejpam-6212	41	14	,	,	PUNCT
ejpam-6212	41	15	6212	6212	NUM
ejpam-6212	41	16	3	3	NUM
ejpam-6212	41	17	of	of	ADP
ejpam-6212	41	18	20	20	NUM
ejpam-6212	41	19	the	the	DET
ejpam-6212	41	20	additively	additively	ADV
ejpam-6212	41	21	weighted	weight	VERB
ejpam-6212	41	22	harary	harary	ADJ
ejpam-6212	41	23	index	index	NOUN
ejpam-6212	41	24	of	of	ADP
ejpam-6212	41	25	g	g	PROPN
ejpam-6212	42	1	[	[	X
ejpam-6212	42	2	12	12	NUM
ejpam-6212	42	3	]	]	PUNCT
ejpam-6212	42	4	is	be	AUX
ejpam-6212	42	5	given	give	VERB
ejpam-6212	42	6	by	by	ADP
ejpam-6212	42	7	ha(g	ha(g	NOUN
ejpam-6212	42	8	)	)	PUNCT
ejpam-6212	42	9	=	=	PUNCT
ejpam-6212	42	10	∑	∑	PUNCT
ejpam-6212	42	11	{	{	PUNCT
ejpam-6212	42	12	u	u	NOUN
ejpam-6212	42	13	,	,	PUNCT
ejpam-6212	42	14	v}⊆v	v}⊆v	PROPN
ejpam-6212	42	15	(	(	PUNCT
ejpam-6212	42	16	g	g	NOUN
ejpam-6212	42	17	)	)	PUNCT
ejpam-6212	42	18	du	du	PROPN
ejpam-6212	43	1	+	+	CCONJ
ejpam-6212	43	2	dv	dv	PROPN
ejpam-6212	43	3	d(u	d(u	PROPN
ejpam-6212	43	4	,	,	PUNCT
ejpam-6212	43	5	v	v	NOUN
ejpam-6212	43	6	)	)	PUNCT
ejpam-6212	43	7	.	.	PUNCT
ejpam-6212	44	1	the	the	DET
ejpam-6212	44	2	multiplicatively	multiplicatively	ADV
ejpam-6212	44	3	weighted	weight	VERB
ejpam-6212	44	4	harary	harary	ADJ
ejpam-6212	44	5	index	index	NOUN
ejpam-6212	44	6	of	of	ADP
ejpam-6212	44	7	g	g	PROPN
ejpam-6212	44	8	was	be	AUX
ejpam-6212	44	9	also	also	ADV
ejpam-6212	44	10	proposed	propose	VERB
ejpam-6212	44	11	by	by	ADP
ejpam-6212	44	12	alizadeh	alizadeh	PROPN
ejpam-6212	44	13	et	et	PROPN
ejpam-6212	44	14	al	al	PROPN
ejpam-6212	44	15	.	.	PUNCT
ejpam-6212	45	1	[	[	X
ejpam-6212	45	2	12	12	NUM
ejpam-6212	45	3	]	]	PUNCT
ejpam-6212	45	4	as	as	ADP
ejpam-6212	45	5	a	a	DET
ejpam-6212	45	6	modification	modification	NOUN
ejpam-6212	45	7	of	of	ADP
ejpam-6212	45	8	the	the	DET
ejpam-6212	45	9	harary	harary	PROPN
ejpam-6212	45	10	index	index	NOUN
ejpam-6212	45	11	and	and	CCONJ
ejpam-6212	45	12	is	be	AUX
ejpam-6212	45	13	given	give	VERB
ejpam-6212	45	14	by	by	ADP
ejpam-6212	45	15	hm	hm	INTJ
ejpam-6212	45	16	(	(	PUNCT
ejpam-6212	45	17	g	g	NOUN
ejpam-6212	45	18	)	)	PUNCT
ejpam-6212	45	19	=	=	PUNCT
ejpam-6212	45	20	∑	∑	PUNCT
ejpam-6212	45	21	{	{	PUNCT
ejpam-6212	45	22	u	u	NOUN
ejpam-6212	45	23	,	,	PUNCT
ejpam-6212	45	24	v}⊆v	v}⊆v	PROPN
ejpam-6212	45	25	(	(	PUNCT
ejpam-6212	45	26	g	g	NOUN
ejpam-6212	45	27	)	)	PUNCT
ejpam-6212	45	28	dudv	dudv	ADP
ejpam-6212	45	29	d(u	d(u	PROPN
ejpam-6212	45	30	,	,	PUNCT
ejpam-6212	45	31	v	v	NOUN
ejpam-6212	45	32	)	)	PUNCT
ejpam-6212	45	33	.	.	PUNCT
ejpam-6212	46	1	let	let	VERB
ejpam-6212	46	2	u	u	PRON
ejpam-6212	46	3	and	and	CCONJ
ejpam-6212	46	4	u	u	NOUN
ejpam-6212	46	5	?	?	PRON
ejpam-6212	46	6	be	be	VERB
ejpam-6212	46	7	nonempty	nonempty	ADJ
ejpam-6212	46	8	subsets	subset	NOUN
ejpam-6212	46	9	of	of	ADP
ejpam-6212	46	10	v	v	NOUN
ejpam-6212	46	11	(	(	PUNCT
ejpam-6212	46	12	g	g	NOUN
ejpam-6212	46	13	)	)	PUNCT
ejpam-6212	46	14	.	.	PUNCT
ejpam-6212	47	1	the	the	DET
ejpam-6212	47	2	partial	partial	ADJ
ejpam-6212	47	3	wiener	wiener	NOUN
ejpam-6212	47	4	index	index	NOUN
ejpam-6212	47	5	of	of	ADP
ejpam-6212	47	6	g	g	PROPN
ejpam-6212	47	7	[	[	X
ejpam-6212	47	8	20	20	NUM
ejpam-6212	47	9	]	]	PUNCT
ejpam-6212	47	10	is	be	AUX
ejpam-6212	47	11	given	give	VERB
ejpam-6212	47	12	by	by	ADP
ejpam-6212	47	13	w	w	PROPN
ejpam-6212	47	14	(	(	PUNCT
ejpam-6212	47	15	u	u	NOUN
ejpam-6212	47	16	,	,	PUNCT
ejpam-6212	47	17	u?;g	u?;g	NOUN
ejpam-6212	47	18	)	)	PUNCT
ejpam-6212	47	19	=	=	PUNCT
ejpam-6212	48	1	∑	∑	PUNCT
ejpam-6212	48	2	(	(	PUNCT
ejpam-6212	48	3	u	u	NOUN
ejpam-6212	48	4	,	,	PUNCT
ejpam-6212	48	5	v)∈u×u	v)∈u×u	NOUN
ejpam-6212	48	6	?	?	PUNCT
ejpam-6212	49	1	d(u	d(u	PROPN
ejpam-6212	49	2	,	,	PUNCT
ejpam-6212	49	3	v	v	NOUN
ejpam-6212	49	4	)	)	PUNCT
ejpam-6212	49	5	.	.	PUNCT
ejpam-6212	50	1	in	in	ADP
ejpam-6212	50	2	2017	2017	NUM
ejpam-6212	50	3	,	,	PUNCT
ejpam-6212	50	4	jamil	jamil	PROPN
ejpam-6212	50	5	[	[	X
ejpam-6212	50	6	21	21	NUM
ejpam-6212	50	7	]	]	X
ejpam-6212	50	8	first	first	ADV
ejpam-6212	50	9	derive	derive	ADJ
ejpam-6212	50	10	closed	closed	ADJ
ejpam-6212	50	11	-	-	PUNCT
ejpam-6212	50	12	form	form	NOUN
ejpam-6212	50	13	formulas	formula	NOUN
ejpam-6212	50	14	for	for	ADP
ejpam-6212	50	15	some	some	DET
ejpam-6212	50	16	distance	distance	NOUN
ejpam-6212	50	17	based	base	VERB
ejpam-6212	50	18	topological	topological	ADJ
ejpam-6212	50	19	indices	index	NOUN
ejpam-6212	50	20	for	for	ADP
ejpam-6212	50	21	double	double	ADJ
ejpam-6212	50	22	graphs	graph	NOUN
ejpam-6212	50	23	in	in	ADP
ejpam-6212	50	24	terms	term	NOUN
ejpam-6212	50	25	of	of	ADP
ejpam-6212	50	26	the	the	DET
ejpam-6212	50	27	original	original	ADJ
ejpam-6212	50	28	graph	graph	NOUN
ejpam-6212	50	29	.	.	PUNCT
ejpam-6212	51	1	moreover	moreover	ADV
ejpam-6212	51	2	,	,	PUNCT
ejpam-6212	51	3	these	these	DET
ejpam-6212	51	4	formulas	formula	NOUN
ejpam-6212	51	5	are	be	AUX
ejpam-6212	51	6	applied	apply	VERB
ejpam-6212	51	7	for	for	ADP
ejpam-6212	51	8	several	several	ADJ
ejpam-6212	51	9	special	special	ADJ
ejpam-6212	51	10	kinds	kind	NOUN
ejpam-6212	51	11	of	of	ADP
ejpam-6212	51	12	graphs	graph	NOUN
ejpam-6212	51	13	,	,	PUNCT
ejpam-6212	51	14	such	such	ADJ
ejpam-6212	51	15	as	as	ADP
ejpam-6212	51	16	,	,	PUNCT
ejpam-6212	51	17	the	the	DET
ejpam-6212	51	18	complete	complete	ADJ
ejpam-6212	51	19	graph	graph	NOUN
ejpam-6212	51	20	,	,	PUNCT
ejpam-6212	51	21	the	the	DET
ejpam-6212	51	22	path	path	NOUN
ejpam-6212	51	23	and	and	CCONJ
ejpam-6212	51	24	the	the	DET
ejpam-6212	51	25	cycle	cycle	NOUN
ejpam-6212	51	26	.	.	PUNCT
ejpam-6212	52	1	in	in	ADP
ejpam-6212	52	2	2019	2019	NUM
ejpam-6212	52	3	,	,	PUNCT
ejpam-6212	52	4	dobrynin	dobrynin	PROPN
ejpam-6212	52	5	[	[	X
ejpam-6212	52	6	22	22	NUM
ejpam-6212	52	7	]	]	PUNCT
ejpam-6212	52	8	esablished	esablishe	VERB
ejpam-6212	52	9	the	the	DET
ejpam-6212	52	10	wiener	wiener	NOUN
ejpam-6212	52	11	index	index	NOUN
ejpam-6212	52	12	of	of	ADP
ejpam-6212	52	13	uniform	uniform	ADJ
ejpam-6212	52	14	hypergraphs	hypergraph	NOUN
ejpam-6212	52	15	induced	induce	VERB
ejpam-6212	52	16	by	by	ADP
ejpam-6212	52	17	trees	tree	NOUN
ejpam-6212	52	18	.	.	PUNCT
ejpam-6212	53	1	in	in	ADP
ejpam-6212	53	2	the	the	DET
ejpam-6212	53	3	following	following	ADJ
ejpam-6212	53	4	year	year	NOUN
ejpam-6212	53	5	,	,	PUNCT
ejpam-6212	53	6	dobrynin	dobrynin	PROPN
ejpam-6212	53	7	and	and	CCONJ
ejpam-6212	53	8	estaji	estaji	PROPN
ejpam-6212	54	1	[	[	X
ejpam-6212	54	2	23	23	NUM
ejpam-6212	54	3	]	]	PUNCT
ejpam-6212	54	4	investigated	investigate	VERB
ejpam-6212	54	5	the	the	DET
ejpam-6212	54	6	wiener	wiener	NOUN
ejpam-6212	54	7	index	index	NOUN
ejpam-6212	54	8	of	of	ADP
ejpam-6212	54	9	hexagonal	hexagonal	ADJ
ejpam-6212	54	10	chains	chain	NOUN
ejpam-6212	54	11	under	under	ADP
ejpam-6212	54	12	some	some	DET
ejpam-6212	54	13	operations	operation	NOUN
ejpam-6212	54	14	on	on	ADP
ejpam-6212	54	15	the	the	DET
ejpam-6212	54	16	corresponding	corresponding	ADJ
ejpam-6212	54	17	binary	binary	ADJ
ejpam-6212	54	18	vectors	vector	NOUN
ejpam-6212	54	19	.	.	PUNCT
ejpam-6212	55	1	the	the	DET
ejpam-6212	55	2	obtained	obtain	VERB
ejpam-6212	55	3	results	result	NOUN
ejpam-6212	55	4	may	may	AUX
ejpam-6212	55	5	be	be	AUX
ejpam-6212	55	6	useful	useful	ADJ
ejpam-6212	55	7	in	in	ADP
ejpam-6212	55	8	studying	study	VERB
ejpam-6212	55	9	of	of	ADP
ejpam-6212	55	10	topological	topological	ADJ
ejpam-6212	55	11	indices	index	NOUN
ejpam-6212	55	12	for	for	ADP
ejpam-6212	55	13	sets	set	NOUN
ejpam-6212	55	14	of	of	ADP
ejpam-6212	55	15	hexagonal	hexagonal	ADJ
ejpam-6212	55	16	chains	chain	NOUN
ejpam-6212	55	17	induced	induce	VERB
ejpam-6212	55	18	by	by	ADP
ejpam-6212	55	19	algebraic	algebraic	ADJ
ejpam-6212	55	20	constructions	construction	NOUN
ejpam-6212	55	21	.	.	PUNCT
ejpam-6212	56	1	2	2	X
ejpam-6212	56	2	.	.	X
ejpam-6212	56	3	spirocyclic	spirocyclic	ADJ
ejpam-6212	56	4	compounds	compound	NOUN
ejpam-6212	56	5	and	and	CCONJ
ejpam-6212	56	6	applications	application	NOUN
ejpam-6212	56	7	spiro	spiro	NOUN
ejpam-6212	56	8	compounds	compound	NOUN
ejpam-6212	56	9	are	be	AUX
ejpam-6212	56	10	organic	organic	ADJ
ejpam-6212	56	11	compounds	compound	NOUN
ejpam-6212	56	12	 	 	SPACE
ejpam-6212	56	13	that	that	PRON
ejpam-6212	56	14	 	 	SPACE
ejpam-6212	56	15	have	have	VERB
ejpam-6212	56	16	 	 	SPACE
ejpam-6212	56	17	two	two	NUM
ejpam-6212	56	18	or	or	CCONJ
ejpam-6212	56	19	more	more	ADJ
ejpam-6212	56	20	rings	ring	NOUN
ejpam-6212	56	21	 	 	SPACE
ejpam-6212	56	22	with	with	ADP
ejpam-6212	56	23	 	 	SPACE
ejpam-6212	56	24	one	one	NUM
ejpam-6212	56	25	 	 	SPACE
ejpam-6212	56	26	common	common	ADJ
ejpam-6212	56	27	 	 	SPACE
ejpam-6212	56	28	atom	atom	NOUN
ejpam-6212	56	29	,	,	PUNCT
ejpam-6212	56	30	the	the	DET
ejpam-6212	56	31	spiro	spiro	NOUN
ejpam-6212	56	32	atom	atom	NOUN
ejpam-6212	56	33	.	.	PUNCT
ejpam-6212	57	1	the	the	DET
ejpam-6212	57	2	spiro	spiro	NOUN
ejpam-6212	57	3	atom	atom	NOUN
ejpam-6212	57	4	 	 	SPACE
ejpam-6212	57	5	gives	give	VERB
ejpam-6212	57	6	 	 	SPACE
ejpam-6212	57	7	a	a	DET
ejpam-6212	57	8	 	 	SPACE
ejpam-6212	57	9	rigid	rigid	ADJ
ejpam-6212	57	10	 	 	SPACE
ejpam-6212	57	11	geometry	geometry	NOUN
ejpam-6212	57	12	to	to	ADP
ejpam-6212	57	13	the	the	DET
ejpam-6212	57	14	rings	ring	NOUN
ejpam-6212	57	15	,	,	PUNCT
ejpam-6212	57	16	which	which	PRON
ejpam-6212	57	17	can	can	AUX
ejpam-6212	57	18	 	 	SPACE
ejpam-6212	57	19	impose	impose	VERB
ejpam-6212	57	20	 	 	SPACE
ejpam-6212	57	21	shape	shape	NOUN
ejpam-6212	57	22	and	and	CCONJ
ejpam-6212	57	23	properties	property	NOUN
ejpam-6212	57	24	 	 	SPACE
ejpam-6212	57	25	on	on	ADP
ejpam-6212	57	26	 	 	SPACE
ejpam-6212	57	27	the	the	DET
ejpam-6212	57	28	molecule	molecule	NOUN
ejpam-6212	57	29	.	.	PUNCT
ejpam-6212	58	1	spirocyclic	spirocyclic	ADJ
ejpam-6212	58	2	compunds	compund	NOUN
ejpam-6212	58	3	are	be	AUX
ejpam-6212	58	4	an	an	DET
ejpam-6212	58	5	interesting	interesting	ADJ
ejpam-6212	58	6	group	group	NOUN
ejpam-6212	58	7	of	of	ADP
ejpam-6212	58	8	organic	organic	ADJ
ejpam-6212	58	9	compounds	compound	NOUN
ejpam-6212	58	10	with	with	ADP
ejpam-6212	58	11	distinct	distinct	ADJ
ejpam-6212	58	12	structural	structural	ADJ
ejpam-6212	58	13	properties	property	NOUN
ejpam-6212	58	14	,	,	PUNCT
ejpam-6212	58	15	making	make	VERB
ejpam-6212	58	16	them	they	PRON
ejpam-6212	58	17	suitable	suitable	ADJ
ejpam-6212	58	18	for	for	ADP
ejpam-6212	58	19	application	application	NOUN
ejpam-6212	58	20	in	in	ADP
ejpam-6212	58	21	many	many	ADJ
ejpam-6212	58	22	fields	field	NOUN
ejpam-6212	58	23	,	,	PUNCT
ejpam-6212	58	24	especially	especially	ADV
ejpam-6212	58	25	medicinal	medicinal	ADJ
ejpam-6212	58	26	chemistry	chemistry	NOUN
ejpam-6212	58	27	.	.	PUNCT
ejpam-6212	59	1	spirocylic	spirocylic	ADJ
ejpam-6212	59	2	graphs	graph	NOUN
ejpam-6212	59	3	represent	represent	VERB
ejpam-6212	59	4	a	a	DET
ejpam-6212	59	5	specific	specific	ADJ
ejpam-6212	59	6	class	class	NOUN
ejpam-6212	59	7	of	of	ADP
ejpam-6212	59	8	graphs	graph	NOUN
ejpam-6212	59	9	characterized	characterize	VERB
ejpam-6212	59	10	by	by	ADP
ejpam-6212	59	11	unique	unique	ADJ
ejpam-6212	59	12	structural	structural	ADJ
ejpam-6212	59	13	features	feature	NOUN
ejpam-6212	59	14	.	.	PUNCT
ejpam-6212	60	1	these	these	DET
ejpam-6212	60	2	graphs	graph	NOUN
ejpam-6212	60	3	,	,	PUNCT
ejpam-6212	60	4	 	 	SPACE
ejpam-6212	60	5	particularly	particularly	ADV
ejpam-6212	60	6	 	 	SPACE
ejpam-6212	60	7	in	in	ADP
ejpam-6212	60	8	 	 	SPACE
ejpam-6212	60	9	the	the	DET
ejpam-6212	60	10	 	 	SPACE
ejpam-6212	60	11	theory	theory	NOUN
ejpam-6212	60	12	 	 	SPACE
ejpam-6212	60	13	of	of	ADP
ejpam-6212	60	14	spiro	spiro	NOUN
ejpam-6212	60	15	compounds	compound	NOUN
ejpam-6212	60	16	in	in	ADP
ejpam-6212	60	17	organic	organic	ADJ
ejpam-6212	60	18	chemistry	chemistry	NOUN
ejpam-6212	60	19	,	,	PUNCT
ejpam-6212	60	20	are	be	AUX
ejpam-6212	60	21	 	 	SPACE
ejpam-6212	60	22	characterized	characterize	VERB
ejpam-6212	60	23	 	 	SPACE
ejpam-6212	60	24	by	by	ADP
ejpam-6212	60	25	 	 	SPACE
ejpam-6212	60	26	two	two	NUM
ejpam-6212	60	27	or	or	CCONJ
ejpam-6212	60	28	more	more	ADJ
ejpam-6212	60	29	cycles	cycle	NOUN
ejpam-6212	60	30	connected	connect	VERB
ejpam-6212	60	31	 	 	SPACE
ejpam-6212	60	32	in	in	ADP
ejpam-6212	60	33	 	 	SPACE
ejpam-6212	60	34	one	one	NUM
ejpam-6212	60	35	 	 	SPACE
ejpam-6212	60	36	common	common	ADJ
ejpam-6212	60	37	 	 	SPACE
ejpam-6212	60	38	vertex	vertex	NOUN
ejpam-6212	60	39	.	.	PUNCT
ejpam-6212	61	1	this	this	DET
ejpam-6212	61	2	particular	particular	ADJ
ejpam-6212	61	3	connectivity	connectivity	NOUN
ejpam-6212	61	4	pattern	pattern	NOUN
ejpam-6212	61	5	 	 	SPACE
ejpam-6212	61	6	imbues	imbue	VERB
ejpam-6212	61	7	 	 	SPACE
ejpam-6212	61	8	the	the	DET
ejpam-6212	61	9	 	 	SPACE
ejpam-6212	61	10	molecules	molecule	NOUN
ejpam-6212	61	11	 	 	SPACE
ejpam-6212	61	12	that	that	PRON
ejpam-6212	61	13	correspond	correspond	VERB
ejpam-6212	61	14	 	 	SPACE
ejpam-6212	61	15	to	to	PART
ejpam-6212	61	16	 	 	SPACE
ejpam-6212	61	17	it	it	PRON
ejpam-6212	61	18	 	 	SPACE
ejpam-6212	61	19	with	with	ADP
ejpam-6212	61	20	 	 	SPACE
ejpam-6212	61	21	distinctive	distinctive	ADJ
ejpam-6212	61	22	properties	property	NOUN
ejpam-6212	61	23	,	,	PUNCT
ejpam-6212	61	24	 	 	SPACE
ejpam-6212	61	25	thus	thus	ADV
ejpam-6212	61	26	 	 	SPACE
ejpam-6212	61	27	making	make	VERB
ejpam-6212	61	28	them	they	PRON
ejpam-6212	61	29	 	 	SPACE
ejpam-6212	61	30	applicable	applicable	ADJ
ejpam-6212	61	31	 	 	SPACE
ejpam-6212	61	32	to	to	ADP
ejpam-6212	61	33	 	 	SPACE
ejpam-6212	61	34	various	various	ADJ
ejpam-6212	61	35	chemical	chemical	NOUN
ejpam-6212	61	36	and	and	CCONJ
ejpam-6212	61	37	potentially	potentially	ADV
ejpam-6212	61	38	other	other	ADJ
ejpam-6212	61	39	scientific	scientific	ADJ
ejpam-6212	61	40	 	 	SPACE
ejpam-6212	61	41	purposes	purpose	NOUN
ejpam-6212	61	42	.	.	PUNCT
ejpam-6212	62	1	if	if	SCONJ
ejpam-6212	62	2	a	a	DET
ejpam-6212	62	3	graph	graph	NOUN
ejpam-6212	62	4	contains	contain	VERB
ejpam-6212	62	5	exactly	exactly	ADV
ejpam-6212	62	6	two	two	NUM
ejpam-6212	62	7	cycles	cycle	NOUN
ejpam-6212	62	8	,	,	PUNCT
ejpam-6212	62	9	then	then	ADV
ejpam-6212	62	10	we	we	PRON
ejpam-6212	62	11	call	call	VERB
ejpam-6212	62	12	it	it	PRON
ejpam-6212	62	13	simple	simple	ADJ
ejpam-6212	62	14	spirocyclic	spirocyclic	NOUN
ejpam-6212	62	15	graph	graph	NOUN
ejpam-6212	62	16	[	[	X
ejpam-6212	62	17	24	24	NUM
ejpam-6212	62	18	]	]	PUNCT
ejpam-6212	62	19	.	.	PUNCT
ejpam-6212	63	1	in	in	ADP
ejpam-6212	63	2	drug	drug	NOUN
ejpam-6212	63	3	discovery	discovery	NOUN
ejpam-6212	63	4	,	,	PUNCT
ejpam-6212	63	5	an	an	DET
ejpam-6212	63	6	essential	essential	ADJ
ejpam-6212	63	7	property	property	NOUN
ejpam-6212	63	8	of	of	ADP
ejpam-6212	63	9	spirocycles	spirocycle	NOUN
ejpam-6212	63	10	is	be	AUX
ejpam-6212	63	11	their	their	PRON
ejpam-6212	63	12	natural	natural	ADJ
ejpam-6212	63	13	capacity	capacity	NOUN
ejpam-6212	63	14	to	to	PART
ejpam-6212	63	15	project	project	VERB
ejpam-6212	63	16	functionality	functionality	NOUN
ejpam-6212	63	17	to	to	ADP
ejpam-6212	63	18	the	the	DET
ejpam-6212	63	19	third	third	ADJ
ejpam-6212	63	20	dimension	dimension	NOUN
ejpam-6212	64	1	[	[	X
ejpam-6212	64	2	25	25	NUM
ejpam-6212	64	3	]	]	PUNCT
ejpam-6212	64	4	.	.	PUNCT
ejpam-6212	65	1	this	this	DET
ejpam-6212	65	2	three	three	NUM
ejpam-6212	65	3	-	-	PUNCT
ejpam-6212	65	4	dimensional	dimensional	ADJ
ejpam-6212	65	5	nature	nature	NOUN
ejpam-6212	65	6	is	be	AUX
ejpam-6212	65	7	essential	essential	ADJ
ejpam-6212	65	8	for	for	ADP
ejpam-6212	65	9	drug	drug	NOUN
ejpam-6212	65	10	-	-	PUNCT
ejpam-6212	65	11	target	target	NOUN
ejpam-6212	65	12	interactions	interaction	NOUN
ejpam-6212	65	13	since	since	SCONJ
ejpam-6212	65	14	drugs	drug	NOUN
ejpam-6212	65	15	need	need	VERB
ejpam-6212	65	16	to	to	PART
ejpam-6212	65	17	fit	fit	VERB
ejpam-6212	65	18	physically	physically	ADV
ejpam-6212	65	19	into	into	ADP
ejpam-6212	65	20	biological	biological	ADJ
ejpam-6212	65	21	targets	target	NOUN
ejpam-6212	65	22	,	,	PUNCT
ejpam-6212	65	23	e.g.	e.g.	ADV
ejpam-6212	65	24	,	,	PUNCT
ejpam-6212	65	25	proteins	protein	NOUN
ejpam-6212	65	26	,	,	PUNCT
ejpam-6212	65	27	which	which	PRON
ejpam-6212	65	28	occur	occur	VERB
ejpam-6212	65	29	in	in	ADP
ejpam-6212	65	30	a	a	DET
ejpam-6212	65	31	much	much	ADV
ejpam-6212	65	32	more	more	ADV
ejpam-6212	65	33	specific	specific	ADJ
ejpam-6212	65	34	and	and	CCONJ
ejpam-6212	65	35	efficient	efficient	ADJ
ejpam-6212	65	36	manner	manner	NOUN
ejpam-6212	65	37	than	than	ADP
ejpam-6212	65	38	planar	planar	ADJ
ejpam-6212	65	39	sysr	sysr	NOUN
ejpam-6212	65	40	.	.	PUNCT
ejpam-6212	66	1	g.	g.	PROPN
ejpam-6212	66	2	artes	artes	PROPN
ejpam-6212	66	3	jr	jr	PROPN
ejpam-6212	66	4	.	.	PROPN
ejpam-6212	66	5	et	et	PROPN
ejpam-6212	66	6	al	al	PROPN
ejpam-6212	66	7	.	.	PUNCT
ejpam-6212	66	8	/	/	SYM
ejpam-6212	66	9	eur	eur	PROPN
ejpam-6212	66	10	.	.	PUNCT
ejpam-6212	67	1	j.	j.	PROPN
ejpam-6212	67	2	pure	pure	PROPN
ejpam-6212	67	3	appl	appl	PROPN
ejpam-6212	67	4	.	.	PROPN
ejpam-6212	67	5	math	math	PROPN
ejpam-6212	67	6	,	,	PUNCT
ejpam-6212	67	7	18	18	NUM
ejpam-6212	67	8	(	(	PUNCT
ejpam-6212	67	9	4	4	NUM
ejpam-6212	67	10	)	)	PUNCT
ejpam-6212	67	11	(	(	PUNCT
ejpam-6212	67	12	2025	2025	NUM
ejpam-6212	67	13	)	)	PUNCT
ejpam-6212	67	14	,	,	PUNCT
ejpam-6212	67	15	6212	6212	NUM
ejpam-6212	67	16	4	4	NUM
ejpam-6212	67	17	of	of	ADP
ejpam-6212	67	18	20	20	NUM
ejpam-6212	67	19	figure	figure	NOUN
ejpam-6212	67	20	1	1	NUM
ejpam-6212	67	21	:	:	PUNCT
ejpam-6212	67	22	skeletal	skeletal	ADJ
ejpam-6212	67	23	formula	formula	NOUN
ejpam-6212	67	24	and	and	CCONJ
ejpam-6212	67	25	molecular	molecular	ADJ
ejpam-6212	67	26	structure	structure	NOUN
ejpam-6212	67	27	of	of	ADP
ejpam-6212	67	28	spirobicyclohexane	spirobicyclohexane	ADJ
ejpam-6212	67	29	tems	tem	NOUN
ejpam-6212	67	30	[	[	X
ejpam-6212	67	31	25	25	NUM
ejpam-6212	67	32	]	]	PUNCT
ejpam-6212	67	33	.	.	PUNCT
ejpam-6212	68	1	an	an	DET
ejpam-6212	68	2	example	example	NOUN
ejpam-6212	68	3	of	of	ADP
ejpam-6212	68	4	a	a	DET
ejpam-6212	68	5	spiro	spiro	NOUN
ejpam-6212	68	6	compound	compound	NOUN
ejpam-6212	68	7	with	with	ADP
ejpam-6212	68	8	a	a	DET
ejpam-6212	68	9	simple	simple	ADJ
ejpam-6212	68	10	spirocyclic	spirocyclic	NOUN
ejpam-6212	68	11	structure	structure	NOUN
ejpam-6212	68	12	is	be	AUX
ejpam-6212	68	13	the	the	DET
ejpam-6212	68	14	spirobicyclohexane	spirobicyclohexane	NOUN
ejpam-6212	68	15	(	(	PUNCT
ejpam-6212	68	16	c11h20	c11h20	PROPN
ejpam-6212	68	17	)	)	PUNCT
ejpam-6212	68	18	,	,	PUNCT
ejpam-6212	68	19	with	with	ADP
ejpam-6212	68	20	skeletal	skeletal	ADJ
ejpam-6212	68	21	formula	formula	NOUN
ejpam-6212	68	22	and	and	CCONJ
ejpam-6212	68	23	molecular	molecular	ADJ
ejpam-6212	68	24	structure	structure	NOUN
ejpam-6212	68	25	[	[	X
ejpam-6212	68	26	26	26	NUM
ejpam-6212	68	27	]	]	PUNCT
ejpam-6212	68	28	shown	show	VERB
ejpam-6212	68	29	in	in	ADP
ejpam-6212	68	30	figure	figure	NOUN
ejpam-6212	68	31	1	1	NUM
ejpam-6212	68	32	.	.	PUNCT
ejpam-6212	69	1	spirobicyclohexane	spirobicyclohexane	PROPN
ejpam-6212	69	2	is	be	AUX
ejpam-6212	69	3	a	a	DET
ejpam-6212	69	4	 	 	SPACE
ejpam-6212	69	5	new	new	ADJ
ejpam-6212	69	6	 	 	SPACE
ejpam-6212	69	7	organic	organic	ADJ
ejpam-6212	69	8	compound	compound	NOUN
ejpam-6212	69	9	 	 	SPACE
ejpam-6212	69	10	whose	whose	DET
ejpam-6212	69	11	 	 	SPACE
ejpam-6212	69	12	structure	structure	NOUN
ejpam-6212	69	13	is	be	AUX
ejpam-6212	69	14	described	describe	VERB
ejpam-6212	69	15	 	 	SPACE
ejpam-6212	69	16	by	by	ADP
ejpam-6212	69	17	 	 	SPACE
ejpam-6212	69	18	a	a	DET
ejpam-6212	69	19	 	 	SPACE
ejpam-6212	69	20	bicyclic	bicyclic	NOUN
ejpam-6212	69	21	 	 	SPACE
ejpam-6212	69	22	arrangement	arrangement	NOUN
ejpam-6212	69	23	 	 	SPACE
ejpam-6212	69	24	of	of	ADP
ejpam-6212	69	25	two	two	NUM
ejpam-6212	69	26	six	six	NUM
ejpam-6212	69	27	-	-	PUNCT
ejpam-6212	69	28	membered	membere	VERB
ejpam-6212	69	29	carbon	carbon	NOUN
ejpam-6212	69	30	rings	ring	NOUN
ejpam-6212	69	31	 	 	SPACE
ejpam-6212	69	32	in	in	ADP
ejpam-6212	69	33	a	a	DET
ejpam-6212	69	34	spiro	spiro	NOUN
ejpam-6212	69	35	 	 	SPACE
ejpam-6212	69	36	orientation	orientation	NOUN
ejpam-6212	69	37	.	.	PUNCT
ejpam-6212	69	38	 	 	SPACE
ejpam-6212	70	1	the	the	DET
ejpam-6212	70	2	 	 	SPACE
ejpam-6212	70	3	implication	implication	NOUN
ejpam-6212	70	4	 	 	SPACE
ejpam-6212	70	5	is	be	AUX
ejpam-6212	70	6	that	that	SCONJ
ejpam-6212	70	7	 	 	SPACE
ejpam-6212	70	8	the	the	DET
ejpam-6212	70	9	two	two	NUM
ejpam-6212	70	10	rings	ring	NOUN
ejpam-6212	70	11	share	share	VERB
ejpam-6212	70	12	a	a	DET
ejpam-6212	70	13	common	common	ADJ
ejpam-6212	70	14	axis	axis	NOUN
ejpam-6212	70	15	,	,	PUNCT
ejpam-6212	70	16	 	 	SPACE
ejpam-6212	70	17	each	each	PRON
ejpam-6212	70	18	with	with	ADP
ejpam-6212	70	19	 	 	SPACE
ejpam-6212	70	20	three	three	NUM
ejpam-6212	70	21	carbon	carbon	NOUN
ejpam-6212	70	22	atoms	atom	NOUN
ejpam-6212	70	23	that	that	PRON
ejpam-6212	70	24	are	be	AUX
ejpam-6212	70	25	not	not	PART
ejpam-6212	70	26	directly	directly	ADV
ejpam-6212	70	27	bonded	bond	VERB
ejpam-6212	70	28	.	.	PUNCT
ejpam-6212	70	29	 	 	SPACE
ejpam-6212	71	1	spirobicyclohexane	spirobicyclohexane	NOUN
ejpam-6212	71	2	 	 	SPACE
ejpam-6212	71	3	has	have	VERB
ejpam-6212	71	4	 	 	SPACE
ejpam-6212	71	5	a	a	DET
ejpam-6212	71	6	 	 	SPACE
ejpam-6212	71	7	symmetrical	symmetrical	ADJ
ejpam-6212	71	8	 	 	SPACE
ejpam-6212	71	9	and	and	CCONJ
ejpam-6212	71	10	rigid	rigid	ADJ
ejpam-6212	71	11	 	 	SPACE
ejpam-6212	71	12	structure	structure	NOUN
ejpam-6212	71	13	,	,	PUNCT
ejpam-6212	71	14	 	 	SPACE
ejpam-6212	71	15	which	which	PRON
ejpam-6212	71	16	 	 	SPACE
ejpam-6212	71	17	can	can	AUX
ejpam-6212	71	18	 	 	SPACE
ejpam-6212	71	19	be	be	AUX
ejpam-6212	71	20	 	 	SPACE
ejpam-6212	71	21	one	one	NUM
ejpam-6212	71	22	factor	factor	NOUN
ejpam-6212	71	23	that	that	PRON
ejpam-6212	71	24	influences	influence	VERB
ejpam-6212	71	25	 	 	SPACE
ejpam-6212	71	26	its	its	PRON
ejpam-6212	71	27	physical	physical	ADJ
ejpam-6212	71	28	and	and	CCONJ
ejpam-6212	71	29	chemical	chemical	NOUN
ejpam-6212	71	30	properties	property	NOUN
ejpam-6212	71	31	.	.	PUNCT
ejpam-6212	72	1	it	it	PRON
ejpam-6212	72	2	is	be	AUX
ejpam-6212	72	3	often	often	ADV
ejpam-6212	72	4	used	use	VERB
ejpam-6212	72	5	as	as	ADP
ejpam-6212	72	6	a	a	DET
ejpam-6212	72	7	building	building	NOUN
ejpam-6212	72	8	block	block	NOUN
ejpam-6212	72	9	to	to	PART
ejpam-6212	72	10	construct	construct	VERB
ejpam-6212	72	11	 	 	SPACE
ejpam-6212	72	12	more	more	ADV
ejpam-6212	72	13	complex	complex	ADJ
ejpam-6212	72	14	organic	organic	ADJ
ejpam-6212	72	15	molecules	molecule	NOUN
ejpam-6212	72	16	.	.	PUNCT
ejpam-6212	73	1	it	it	PRON
ejpam-6212	73	2	 	 	SPACE
ejpam-6212	73	3	is	be	AUX
ejpam-6212	73	4	 	 	SPACE
ejpam-6212	73	5	used	use	VERB
ejpam-6212	73	6	 	 	SPACE
ejpam-6212	73	7	in	in	ADP
ejpam-6212	73	8	 	 	SPACE
ejpam-6212	73	9	numerous	numerous	ADJ
ejpam-6212	73	10	 	 	SPACE
ejpam-6212	73	11	applications	application	NOUN
ejpam-6212	73	12	,	,	PUNCT
ejpam-6212	73	13	including	include	VERB
ejpam-6212	73	14	pharmaceuticals	pharmaceutical	NOUN
ejpam-6212	73	15	and	and	CCONJ
ejpam-6212	73	16	materials	material	NOUN
ejpam-6212	73	17	science	science	NOUN
ejpam-6212	73	18	because	because	SCONJ
ejpam-6212	73	19	 	 	SPACE
ejpam-6212	73	20	it	it	PRON
ejpam-6212	73	21	can	can	AUX
ejpam-6212	73	22	 	 	SPACE
ejpam-6212	73	23	impart	impart	VERB
ejpam-6212	73	24	 	 	SPACE
ejpam-6212	73	25	specific	specific	ADJ
ejpam-6212	73	26	 	 	SPACE
ejpam-6212	73	27	stereochemistry	stereochemistry	NOUN
ejpam-6212	73	28	and	and	CCONJ
ejpam-6212	73	29	stability	stability	NOUN
ejpam-6212	73	30	to	to	ADP
ejpam-6212	73	31	the	the	DET
ejpam-6212	73	32	molecules	molecule	NOUN
ejpam-6212	73	33	it	it	PRON
ejpam-6212	73	34	 	 	SPACE
ejpam-6212	73	35	is	be	AUX
ejpam-6212	73	36	 	 	SPACE
ejpam-6212	73	37	incorporated	incorporate	VERB
ejpam-6212	73	38	into	into	ADP
ejpam-6212	73	39	 	 	SPACE
ejpam-6212	73	40	[	[	NOUN
ejpam-6212	73	41	27	27	NUM
ejpam-6212	73	42	]	]	PUNCT
ejpam-6212	73	43	.	.	PUNCT
ejpam-6212	74	1	bicyclic	bicyclic	NOUN
ejpam-6212	74	2	graphs	graph	NOUN
ejpam-6212	74	3	are	be	AUX
ejpam-6212	74	4	graphs	graph	NOUN
ejpam-6212	74	5	that	that	PRON
ejpam-6212	74	6	contain	contain	VERB
ejpam-6212	74	7	exactly	exactly	ADV
ejpam-6212	74	8	two	two	NUM
ejpam-6212	74	9	cycles	cycle	NOUN
ejpam-6212	74	10	.	.	PUNCT
ejpam-6212	75	1	simple	simple	ADJ
ejpam-6212	75	2	spirocyclic	spirocyclic	NOUN
ejpam-6212	75	3	graphs	graph	NOUN
ejpam-6212	75	4	are	be	AUX
ejpam-6212	75	5	bicyclic	bicyclic	NOUN
ejpam-6212	75	6	graphs	graph	NOUN
ejpam-6212	75	7	whose	whose	DET
ejpam-6212	75	8	cycles	cycle	NOUN
ejpam-6212	75	9	share	share	VERB
ejpam-6212	75	10	a	a	DET
ejpam-6212	75	11	common	common	ADJ
ejpam-6212	75	12	vertex	vertex	NOUN
ejpam-6212	75	13	called	call	VERB
ejpam-6212	75	14	the	the	DET
ejpam-6212	75	15	spiro	spiro	NOUN
ejpam-6212	75	16	vertex	vertex	NOUN
ejpam-6212	75	17	.	.	PUNCT
ejpam-6212	76	1	3	3	X
ejpam-6212	76	2	.	.	X
ejpam-6212	76	3	geodetic	geodetic	ADJ
ejpam-6212	76	4	-	-	PUNCT
ejpam-6212	76	5	wiener	wiener	NOUN
ejpam-6212	76	6	index	index	NOUN
ejpam-6212	76	7	formulation	formulation	NOUN
ejpam-6212	76	8	the	the	DET
ejpam-6212	76	9	study	study	NOUN
ejpam-6212	76	10	of	of	ADP
ejpam-6212	76	11	geodesics	geodesic	NOUN
ejpam-6212	76	12	is	be	AUX
ejpam-6212	76	13	a	a	DET
ejpam-6212	76	14	graph	graph	NOUN
ejpam-6212	76	15	is	be	AUX
ejpam-6212	76	16	an	an	DET
ejpam-6212	76	17	important	important	ADJ
ejpam-6212	76	18	graph	graph	NOUN
ejpam-6212	76	19	-	-	PUNCT
ejpam-6212	76	20	theoretic	theoretic	NOUN
ejpam-6212	76	21	property	property	NOUN
ejpam-6212	76	22	to	to	PART
ejpam-6212	76	23	be	be	AUX
ejpam-6212	76	24	considered	consider	VERB
ejpam-6212	76	25	in	in	ADP
ejpam-6212	76	26	topological	topological	ADJ
ejpam-6212	76	27	properties	property	NOUN
ejpam-6212	76	28	of	of	ADP
ejpam-6212	76	29	a	a	DET
ejpam-6212	76	30	graph	graph	NOUN
ejpam-6212	76	31	[	[	X
ejpam-6212	76	32	28	28	NUM
ejpam-6212	76	33	]	]	PUNCT
ejpam-6212	76	34	.	.	PUNCT
ejpam-6212	77	1	for	for	ADP
ejpam-6212	77	2	example	example	NOUN
ejpam-6212	77	3	,	,	PUNCT
ejpam-6212	77	4	in	in	ADP
ejpam-6212	77	5	a	a	DET
ejpam-6212	77	6	real	real	ADJ
ejpam-6212	77	7	-	-	PUNCT
ejpam-6212	77	8	world	world	NOUN
ejpam-6212	77	9	scenario	scenario	NOUN
ejpam-6212	77	10	,	,	PUNCT
ejpam-6212	77	11	the	the	DET
ejpam-6212	77	12	idea	idea	NOUN
ejpam-6212	77	13	of	of	ADP
ejpam-6212	77	14	considering	consider	VERB
ejpam-6212	77	15	different	different	ADJ
ejpam-6212	77	16	shortest	short	ADJ
ejpam-6212	77	17	routes	route	NOUN
ejpam-6212	77	18	from	from	ADP
ejpam-6212	77	19	station	station	NOUN
ejpam-6212	77	20	a	a	PRON
ejpam-6212	77	21	to	to	ADP
ejpam-6212	77	22	station	station	NOUN
ejpam-6212	77	23	b	b	NOUN
ejpam-6212	77	24	can	can	AUX
ejpam-6212	77	25	be	be	AUX
ejpam-6212	77	26	modeled	model	VERB
ejpam-6212	77	27	by	by	ADP
ejpam-6212	77	28	the	the	DET
ejpam-6212	77	29	number	number	NOUN
ejpam-6212	77	30	of	of	ADP
ejpam-6212	77	31	geodesics	geodesic	NOUN
ejpam-6212	77	32	between	between	ADP
ejpam-6212	77	33	these	these	DET
ejpam-6212	77	34	two	two	NUM
ejpam-6212	77	35	stations	station	NOUN
ejpam-6212	77	36	.	.	PUNCT
ejpam-6212	78	1	in	in	ADP
ejpam-6212	78	2	this	this	DET
ejpam-6212	78	3	particular	particular	ADJ
ejpam-6212	78	4	scenario	scenario	NOUN
ejpam-6212	78	5	,	,	PUNCT
ejpam-6212	78	6	transporting	transport	VERB
ejpam-6212	78	7	goods	good	NOUN
ejpam-6212	78	8	from	from	ADP
ejpam-6212	78	9	a	a	DET
ejpam-6212	78	10	to	to	PART
ejpam-6212	78	11	b	b	NOUN
ejpam-6212	78	12	could	could	AUX
ejpam-6212	78	13	take	take	VERB
ejpam-6212	78	14	less	less	ADJ
ejpam-6212	78	15	time	time	NOUN
ejpam-6212	78	16	by	by	ADP
ejpam-6212	78	17	utilizing	utilize	VERB
ejpam-6212	78	18	different	different	ADJ
ejpam-6212	78	19	transportation	transportation	NOUN
ejpam-6212	78	20	services	service	NOUN
ejpam-6212	78	21	on	on	ADP
ejpam-6212	78	22	different	different	ADJ
ejpam-6212	78	23	shortest	short	ADJ
ejpam-6212	78	24	routes	route	NOUN
ejpam-6212	78	25	.	.	PUNCT
ejpam-6212	79	1	the	the	DET
ejpam-6212	79	2	volume	volume	NOUN
ejpam-6212	79	3	of	of	ADP
ejpam-6212	79	4	goods	good	NOUN
ejpam-6212	79	5	that	that	PRON
ejpam-6212	79	6	can	can	AUX
ejpam-6212	79	7	be	be	AUX
ejpam-6212	79	8	transported	transport	VERB
ejpam-6212	79	9	at	at	ADP
ejpam-6212	79	10	the	the	DET
ejpam-6212	79	11	same	same	ADJ
ejpam-6212	79	12	time	time	NOUN
ejpam-6212	79	13	is	be	AUX
ejpam-6212	79	14	determined	determine	VERB
ejpam-6212	79	15	by	by	ADP
ejpam-6212	79	16	the	the	DET
ejpam-6212	79	17	number	number	NOUN
ejpam-6212	79	18	of	of	ADP
ejpam-6212	79	19	shortest	short	ADJ
ejpam-6212	79	20	routes	route	NOUN
ejpam-6212	79	21	from	from	ADP
ejpam-6212	79	22	the	the	DET
ejpam-6212	79	23	initial	initial	ADJ
ejpam-6212	79	24	station	station	NOUN
ejpam-6212	79	25	to	to	ADP
ejpam-6212	79	26	the	the	DET
ejpam-6212	79	27	terminal	terminal	ADJ
ejpam-6212	79	28	station	station	NOUN
ejpam-6212	79	29	.	.	PUNCT
ejpam-6212	80	1	in	in	ADP
ejpam-6212	80	2	general	general	ADJ
ejpam-6212	80	3	,	,	PUNCT
ejpam-6212	80	4	the	the	DET
ejpam-6212	80	5	transport	transport	NOUN
ejpam-6212	80	6	of	of	ADP
ejpam-6212	80	7	energy	energy	NOUN
ejpam-6212	80	8	from	from	ADP
ejpam-6212	80	9	one	one	NUM
ejpam-6212	80	10	point	point	NOUN
ejpam-6212	80	11	to	to	ADP
ejpam-6212	80	12	another	another	PRON
ejpam-6212	80	13	can	can	AUX
ejpam-6212	80	14	be	be	AUX
ejpam-6212	80	15	represented	represent	VERB
ejpam-6212	80	16	by	by	ADP
ejpam-6212	80	17	geodesics	geodesic	NOUN
ejpam-6212	80	18	in	in	ADP
ejpam-6212	80	19	a	a	DET
ejpam-6212	80	20	network	network	NOUN
ejpam-6212	80	21	.	.	PUNCT
ejpam-6212	81	1	these	these	DET
ejpam-6212	81	2	scenarios	scenario	NOUN
ejpam-6212	81	3	give	give	VERB
ejpam-6212	81	4	us	we	PRON
ejpam-6212	81	5	some	some	DET
ejpam-6212	81	6	motivations	motivation	NOUN
ejpam-6212	81	7	to	to	PART
ejpam-6212	81	8	study	study	VERB
ejpam-6212	81	9	the	the	DET
ejpam-6212	81	10	number	number	NOUN
ejpam-6212	81	11	of	of	ADP
ejpam-6212	81	12	geodesics	geodesic	NOUN
ejpam-6212	81	13	in	in	ADP
ejpam-6212	81	14	a	a	DET
ejpam-6212	81	15	graph	graph	NOUN
ejpam-6212	81	16	and	and	CCONJ
ejpam-6212	81	17	integrate	integrate	VERB
ejpam-6212	81	18	the	the	DET
ejpam-6212	81	19	concept	concept	NOUN
ejpam-6212	81	20	with	with	ADP
ejpam-6212	81	21	the	the	DET
ejpam-6212	81	22	wiener	wiener	NOUN
ejpam-6212	81	23	index	index	NOUN
ejpam-6212	81	24	.	.	PUNCT
ejpam-6212	82	1	the	the	DET
ejpam-6212	82	2	distance	distance	NOUN
ejpam-6212	82	3	d(u	d(u	PROPN
ejpam-6212	82	4	,	,	PUNCT
ejpam-6212	82	5	v	v	NOUN
ejpam-6212	82	6	)	)	PUNCT
ejpam-6212	82	7	between	between	ADP
ejpam-6212	82	8	two	two	NUM
ejpam-6212	82	9	vertices	vertex	NOUN
ejpam-6212	82	10	u	u	NOUN
ejpam-6212	82	11	and	and	CCONJ
ejpam-6212	82	12	v	v	NOUN
ejpam-6212	82	13	in	in	ADP
ejpam-6212	82	14	a	a	DET
ejpam-6212	82	15	connected	connected	ADJ
ejpam-6212	82	16	graph	graph	NOUN
ejpam-6212	82	17	g	g	PROPN
ejpam-6212	82	18	is	be	AUX
ejpam-6212	82	19	the	the	DET
ejpam-6212	82	20	length	length	NOUN
ejpam-6212	82	21	of	of	ADP
ejpam-6212	82	22	a	a	DET
ejpam-6212	82	23	u	u	NOUN
ejpam-6212	82	24	-	-	NOUN
ejpam-6212	82	25	v	v	ADJ
ejpam-6212	82	26	geodesic	geodesic	NOUN
ejpam-6212	82	27	in	in	ADP
ejpam-6212	82	28	g.	g.	PROPN
ejpam-6212	82	29	a	a	DET
ejpam-6212	82	30	u	u	NOUN
ejpam-6212	82	31	-	-	NOUN
ejpam-6212	82	32	v	v	ADJ
ejpam-6212	82	33	geodesic	geodesic	NOUN
ejpam-6212	82	34	in	in	ADP
ejpam-6212	82	35	g	g	PROPN
ejpam-6212	82	36	is	be	AUX
ejpam-6212	82	37	a	a	DET
ejpam-6212	82	38	shortest	short	ADJ
ejpam-6212	82	39	path	path	NOUN
ejpam-6212	82	40	joining	join	VERB
ejpam-6212	82	41	u	u	NOUN
ejpam-6212	82	42	and	and	CCONJ
ejpam-6212	82	43	v	v	NOUN
ejpam-6212	82	44	in	in	ADP
ejpam-6212	82	45	g	g	PROPN
ejpam-6212	82	46	[	[	X
ejpam-6212	82	47	29	29	NUM
ejpam-6212	82	48	]	]	PUNCT
ejpam-6212	82	49	.	.	PUNCT
ejpam-6212	83	1	r.	r.	PROPN
ejpam-6212	83	2	g.	g.	PROPN
ejpam-6212	83	3	artes	artes	PROPN
ejpam-6212	83	4	jr	jr	PROPN
ejpam-6212	83	5	.	.	PROPN
ejpam-6212	83	6	et	et	PROPN
ejpam-6212	83	7	al	al	PROPN
ejpam-6212	83	8	.	.	PUNCT
ejpam-6212	83	9	/	/	SYM
ejpam-6212	83	10	eur	eur	PROPN
ejpam-6212	83	11	.	.	PUNCT
ejpam-6212	84	1	j.	j.	PROPN
ejpam-6212	84	2	pure	pure	PROPN
ejpam-6212	84	3	appl	appl	PROPN
ejpam-6212	84	4	.	.	PROPN
ejpam-6212	84	5	math	math	PROPN
ejpam-6212	84	6	,	,	PUNCT
ejpam-6212	84	7	18	18	NUM
ejpam-6212	84	8	(	(	PUNCT
ejpam-6212	84	9	4	4	NUM
ejpam-6212	84	10	)	)	PUNCT
ejpam-6212	84	11	(	(	PUNCT
ejpam-6212	84	12	2025	2025	NUM
ejpam-6212	84	13	)	)	PUNCT
ejpam-6212	84	14	,	,	PUNCT
ejpam-6212	84	15	6212	6212	NUM
ejpam-6212	84	16	5	5	NUM
ejpam-6212	84	17	of	of	ADP
ejpam-6212	84	18	20	20	NUM
ejpam-6212	84	19	the	the	DET
ejpam-6212	84	20	degree	degree	NOUN
ejpam-6212	84	21	of	of	ADP
ejpam-6212	84	22	a	a	DET
ejpam-6212	84	23	vertex	vertex	NOUN
ejpam-6212	84	24	u	u	NOUN
ejpam-6212	84	25	in	in	ADP
ejpam-6212	84	26	g	g	PROPN
ejpam-6212	84	27	is	be	AUX
ejpam-6212	84	28	denoted	denote	VERB
ejpam-6212	84	29	by	by	ADP
ejpam-6212	84	30	du	du	PROPN
ejpam-6212	84	31	=	=	NOUN
ejpam-6212	84	32	dg(u	dg(u	X
ejpam-6212	84	33	)	)	PUNCT
ejpam-6212	85	1	[	[	X
ejpam-6212	85	2	30	30	NUM
ejpam-6212	85	3	]	]	PUNCT
ejpam-6212	85	4	.	.	PUNCT
ejpam-6212	86	1	the	the	DET
ejpam-6212	86	2	minimum	minimum	NOUN
ejpam-6212	86	3	degree	degree	NOUN
ejpam-6212	86	4	δ	δ	PROPN
ejpam-6212	86	5	and	and	CCONJ
ejpam-6212	86	6	the	the	DET
ejpam-6212	86	7	maximum	maximum	ADJ
ejpam-6212	86	8	degree	degree	NOUN
ejpam-6212	86	9	∆	∆	PROPN
ejpam-6212	86	10	are	be	AUX
ejpam-6212	86	11	,	,	PUNCT
ejpam-6212	86	12	respectively	respectively	ADV
ejpam-6212	86	13	,	,	PUNCT
ejpam-6212	86	14	defined	define	VERB
ejpam-6212	86	15	as	as	SCONJ
ejpam-6212	86	16	follows	follow	VERB
ejpam-6212	86	17	[	[	X
ejpam-6212	86	18	31	31	NUM
ejpam-6212	86	19	]	]	PUNCT
ejpam-6212	86	20	:	:	PUNCT
ejpam-6212	86	21	δ	δ	X
ejpam-6212	86	22	=	=	SYM
ejpam-6212	86	23	min	min	PROPN
ejpam-6212	86	24	v∈v	v∈v	NOUN
ejpam-6212	86	25	(	(	PUNCT
ejpam-6212	86	26	g	g	NOUN
ejpam-6212	86	27	)	)	PUNCT
ejpam-6212	86	28	{	{	PUNCT
ejpam-6212	86	29	dg(v	dg(v	NOUN
ejpam-6212	86	30	)	)	PUNCT
ejpam-6212	86	31	}	}	PUNCT
ejpam-6212	86	32	,	,	PUNCT
ejpam-6212	86	33	∆	∆	PROPN
ejpam-6212	86	34	=	=	SYM
ejpam-6212	86	35	max	max	PROPN
ejpam-6212	86	36	v∈v	v∈v	PROPN
ejpam-6212	86	37	(	(	PUNCT
ejpam-6212	86	38	g	g	NOUN
ejpam-6212	86	39	)	)	PUNCT
ejpam-6212	86	40	{	{	PUNCT
ejpam-6212	86	41	dg(v	dg(v	NOUN
ejpam-6212	86	42	)	)	PUNCT
ejpam-6212	86	43	}	}	PUNCT
ejpam-6212	86	44	.	.	PUNCT
ejpam-6212	87	1	the	the	DET
ejpam-6212	87	2	following	follow	VERB
ejpam-6212	87	3	formulation	formulation	NOUN
ejpam-6212	87	4	can	can	AUX
ejpam-6212	87	5	be	be	AUX
ejpam-6212	87	6	found	find	VERB
ejpam-6212	87	7	in	in	ADP
ejpam-6212	87	8	[	[	X
ejpam-6212	87	9	32	32	NUM
ejpam-6212	87	10	]	]	PUNCT
ejpam-6212	87	11	.	.	PUNCT
ejpam-6212	88	1	we	we	PRON
ejpam-6212	88	2	now	now	ADV
ejpam-6212	88	3	introduce	introduce	VERB
ejpam-6212	88	4	a	a	DET
ejpam-6212	88	5	wiener	wiener	NOUN
ejpam-6212	88	6	-	-	PUNCT
ejpam-6212	88	7	type	type	NOUN
ejpam-6212	88	8	topological	topological	ADJ
ejpam-6212	88	9	index	index	NOUN
ejpam-6212	88	10	.	.	PUNCT
ejpam-6212	89	1	consider	consider	VERB
ejpam-6212	89	2	the	the	DET
ejpam-6212	89	3	function	function	NOUN
ejpam-6212	89	4	α	α	NOUN
ejpam-6212	89	5	:	:	PUNCT
ejpam-6212	89	6	v	v	NOUN
ejpam-6212	89	7	(	(	PUNCT
ejpam-6212	89	8	g)×	g)×	NOUN
ejpam-6212	89	9	v	v	NOUN
ejpam-6212	89	10	(	(	PUNCT
ejpam-6212	89	11	g	g	NOUN
ejpam-6212	89	12	)	)	PUNCT
ejpam-6212	89	13	−→	−→	NOUN
ejpam-6212	89	14	n	n	CCONJ
ejpam-6212	89	15	,	,	PUNCT
ejpam-6212	89	16	where	where	SCONJ
ejpam-6212	89	17	α(u	α(u	NOUN
ejpam-6212	89	18	,	,	PUNCT
ejpam-6212	89	19	v	v	NOUN
ejpam-6212	89	20	)	)	PUNCT
ejpam-6212	89	21	is	be	AUX
ejpam-6212	89	22	counts	count	VERB
ejpam-6212	89	23	the	the	DET
ejpam-6212	89	24	number	number	NOUN
ejpam-6212	89	25	of	of	ADP
ejpam-6212	89	26	geodesics	geodesic	NOUN
ejpam-6212	89	27	between	between	ADP
ejpam-6212	89	28	vertices	vertex	NOUN
ejpam-6212	89	29	u	u	NOUN
ejpam-6212	89	30	and	and	CCONJ
ejpam-6212	89	31	v	v	NOUN
ejpam-6212	89	32	in	in	ADP
ejpam-6212	89	33	a	a	DET
ejpam-6212	89	34	graph	graph	NOUN
ejpam-6212	89	35	g	g	NOUN
ejpam-6212	89	36	as	as	SCONJ
ejpam-6212	89	37	defined	define	VERB
ejpam-6212	89	38	in	in	ADP
ejpam-6212	89	39	[	[	X
ejpam-6212	89	40	29	29	NUM
ejpam-6212	89	41	]	]	PUNCT
ejpam-6212	89	42	.	.	PUNCT
ejpam-6212	90	1	the	the	DET
ejpam-6212	90	2	geodetic	geodetic	ADJ
ejpam-6212	90	3	-	-	PUNCT
ejpam-6212	90	4	wiener	wiener	NOUN
ejpam-6212	90	5	index	index	NOUN
ejpam-6212	90	6	(	(	PUNCT
ejpam-6212	90	7	g	g	NOUN
ejpam-6212	90	8	-	-	PUNCT
ejpam-6212	90	9	wiener	wiener	NOUN
ejpam-6212	90	10	index	index	NOUN
ejpam-6212	90	11	)	)	PUNCT
ejpam-6212	90	12	of	of	ADP
ejpam-6212	90	13	g	g	PROPN
ejpam-6212	90	14	,	,	PUNCT
ejpam-6212	90	15	as	as	SCONJ
ejpam-6212	90	16	defined	define	VERB
ejpam-6212	90	17	in	in	ADP
ejpam-6212	90	18	[	[	X
ejpam-6212	90	19	32	32	NUM
ejpam-6212	90	20	]	]	PUNCT
ejpam-6212	90	21	,	,	PUNCT
ejpam-6212	90	22	is	be	AUX
ejpam-6212	90	23	given	give	VERB
ejpam-6212	90	24	by	by	ADP
ejpam-6212	90	25	wg(g	wg(g	NOUN
ejpam-6212	90	26	)	)	PUNCT
ejpam-6212	90	27	=	=	PUNCT
ejpam-6212	91	1	∑	∑	PUNCT
ejpam-6212	91	2	{	{	PUNCT
ejpam-6212	91	3	u	u	NOUN
ejpam-6212	91	4	,	,	PUNCT
ejpam-6212	91	5	v}⊆v	v}⊆v	PROPN
ejpam-6212	91	6	(	(	PUNCT
ejpam-6212	91	7	g	g	NOUN
ejpam-6212	91	8	)	)	PUNCT
ejpam-6212	91	9	α(u	α(u	NOUN
ejpam-6212	91	10	,	,	PUNCT
ejpam-6212	91	11	v)d(u	v)d(u	NOUN
ejpam-6212	91	12	,	,	PUNCT
ejpam-6212	91	13	v	v	NOUN
ejpam-6212	91	14	)	)	PUNCT
ejpam-6212	91	15	.	.	PUNCT
ejpam-6212	92	1	in	in	ADP
ejpam-6212	92	2	[	[	X
ejpam-6212	92	3	32	32	NUM
ejpam-6212	92	4	]	]	PUNCT
ejpam-6212	92	5	,	,	PUNCT
ejpam-6212	92	6	we	we	PRON
ejpam-6212	92	7	establish	establish	VERB
ejpam-6212	92	8	several	several	ADJ
ejpam-6212	92	9	bounds	bound	NOUN
ejpam-6212	92	10	for	for	ADP
ejpam-6212	92	11	geodetic	geodetic	ADJ
ejpam-6212	92	12	-	-	PUNCT
ejpam-6212	92	13	wiener	wiener	NOUN
ejpam-6212	92	14	index	index	NOUN
ejpam-6212	92	15	for	for	ADP
ejpam-6212	92	16	unicyclic	unicyclic	ADJ
ejpam-6212	92	17	graphs	graph	NOUN
ejpam-6212	92	18	in	in	ADP
ejpam-6212	92	19	terms	term	NOUN
ejpam-6212	92	20	of	of	ADP
ejpam-6212	92	21	other	other	ADJ
ejpam-6212	92	22	distance	distance	NOUN
ejpam-6212	92	23	-	-	PUNCT
ejpam-6212	92	24	based	base	VERB
ejpam-6212	92	25	topological	topological	ADJ
ejpam-6212	92	26	indices	index	NOUN
ejpam-6212	92	27	.	.	PUNCT
ejpam-6212	93	1	4	4	X
ejpam-6212	93	2	.	.	X
ejpam-6212	93	3	the	the	DET
ejpam-6212	93	4	partitioning	partitioning	ADJ
ejpam-6212	93	5	definition	definition	NOUN
ejpam-6212	93	6	1	1	NUM
ejpam-6212	93	7	.	.	PUNCT
ejpam-6212	94	1	let	let	VERB
ejpam-6212	94	2	g	g	PRON
ejpam-6212	94	3	be	be	AUX
ejpam-6212	94	4	a	a	DET
ejpam-6212	94	5	connected	connected	ADJ
ejpam-6212	94	6	graph	graph	NOUN
ejpam-6212	94	7	.	.	PUNCT
ejpam-6212	95	1	the	the	DET
ejpam-6212	95	2	projection	projection	NOUN
ejpam-6212	95	3	of	of	ADP
ejpam-6212	95	4	u	u	PROPN
ejpam-6212	95	5	∈	∈	PROPN
ejpam-6212	95	6	v	v	ADP
ejpam-6212	95	7	(	(	PUNCT
ejpam-6212	95	8	g	g	NOUN
ejpam-6212	95	9	)	)	PUNCT
ejpam-6212	95	10	onto	onto	ADP
ejpam-6212	95	11	a	a	DET
ejpam-6212	95	12	subgraph	subgraph	NOUN
ejpam-6212	95	13	h	h	NOUN
ejpam-6212	95	14	of	of	ADP
ejpam-6212	95	15	g	g	PROPN
ejpam-6212	95	16	as	as	ADP
ejpam-6212	95	17	the	the	DET
ejpam-6212	95	18	set	set	NOUN
ejpam-6212	95	19	ph(u	ph(u	PUNCT
ejpam-6212	95	20	)	)	PUNCT
ejpam-6212	95	21	=	=	PRON
ejpam-6212	95	22	{	{	PUNCT
ejpam-6212	95	23	w	w	PROPN
ejpam-6212	95	24	∈	∈	PROPN
ejpam-6212	95	25	v	v	ADP
ejpam-6212	95	26	(	(	PUNCT
ejpam-6212	95	27	h	h	NOUN
ejpam-6212	95	28	)	)	PUNCT
ejpam-6212	95	29	:	:	PUNCT
ejpam-6212	95	30	d(u	d(u	PROPN
ejpam-6212	95	31	,	,	PUNCT
ejpam-6212	95	32	w	w	NOUN
ejpam-6212	95	33	)	)	PUNCT
ejpam-6212	95	34	=	=	SYM
ejpam-6212	95	35	d(u	d(u	PROPN
ejpam-6212	95	36	,	,	PUNCT
ejpam-6212	95	37	v	v	X
ejpam-6212	95	38	(	(	PUNCT
ejpam-6212	95	39	h	h	NOUN
ejpam-6212	95	40	)	)	PUNCT
ejpam-6212	95	41	)	)	PUNCT
ejpam-6212	95	42	}	}	PUNCT
ejpam-6212	95	43	=	=	PRON
ejpam-6212	95	44	{	{	PUNCT
ejpam-6212	95	45	w	w	PROPN
ejpam-6212	95	46	∈	∈	PROPN
ejpam-6212	95	47	v	v	ADP
ejpam-6212	95	48	(	(	PUNCT
ejpam-6212	95	49	h	h	NOUN
ejpam-6212	95	50	)	)	PUNCT
ejpam-6212	95	51	:	:	PUNCT
ejpam-6212	95	52	d(u	d(u	PROPN
ejpam-6212	95	53	,	,	PUNCT
ejpam-6212	95	54	w	w	NOUN
ejpam-6212	95	55	)	)	PUNCT
ejpam-6212	95	56	≤	≤	PUNCT
ejpam-6212	95	57	d(u	d(u	PROPN
ejpam-6212	95	58	,	,	PUNCT
ejpam-6212	95	59	z	z	NOUN
ejpam-6212	95	60	)	)	PUNCT
ejpam-6212	95	61	for	for	ADP
ejpam-6212	95	62	any	any	DET
ejpam-6212	95	63	z	z	PROPN
ejpam-6212	95	64	∈	∈	PROPN
ejpam-6212	95	65	v	v	NOUN
ejpam-6212	95	66	(	(	PUNCT
ejpam-6212	95	67	h	h	NOUN
ejpam-6212	95	68	)	)	PUNCT
ejpam-6212	95	69	}	}	PUNCT
ejpam-6212	95	70	if	if	SCONJ
ejpam-6212	95	71	ph(u	ph(u	NUM
ejpam-6212	95	72	)	)	PUNCT
ejpam-6212	95	73	=	=	PRON
ejpam-6212	95	74	{	{	PUNCT
ejpam-6212	95	75	w	w	NOUN
ejpam-6212	95	76	}	}	PUNCT
ejpam-6212	95	77	,	,	PUNCT
ejpam-6212	95	78	we	we	PRON
ejpam-6212	95	79	simply	simply	ADV
ejpam-6212	95	80	write	write	VERB
ejpam-6212	95	81	ph(u	ph(u	PUNCT
ejpam-6212	95	82	)	)	PUNCT
ejpam-6212	96	1	=	=	SYM
ejpam-6212	96	2	w.	w.	NOUN
ejpam-6212	96	3	consider	consider	VERB
ejpam-6212	96	4	a	a	DET
ejpam-6212	96	5	simple	simple	ADJ
ejpam-6212	96	6	spirocyclic	spirocyclic	NOUN
ejpam-6212	96	7	graph	graph	NOUN
ejpam-6212	96	8	g	g	NOUN
ejpam-6212	96	9	with	with	ADP
ejpam-6212	96	10	even	even	ADV
ejpam-6212	96	11	cycles	cycle	NOUN
ejpam-6212	96	12	c2t1	c2t1	NOUN
ejpam-6212	97	1	=	=	SYM
ejpam-6212	98	1	[	[	X
ejpam-6212	98	2	u1	u1	NOUN
ejpam-6212	98	3	,	,	PUNCT
ejpam-6212	98	4	u2	u2	NOUN
ejpam-6212	98	5	,	,	PUNCT
ejpam-6212	98	6	.	.	PUNCT
ejpam-6212	98	7	.	.	PUNCT
ejpam-6212	98	8	.	.	PUNCT
ejpam-6212	99	1	,	,	PUNCT
ejpam-6212	99	2	u2t1	u2t1	VERB
ejpam-6212	99	3	]	]	PUNCT
ejpam-6212	99	4	and	and	CCONJ
ejpam-6212	99	5	c2t2	c2t2	NOUN
ejpam-6212	100	1	=	=	PUNCT
ejpam-6212	101	1	[	[	X
ejpam-6212	101	2	u1	u1	NOUN
ejpam-6212	101	3	=	=	SYM
ejpam-6212	101	4	v1	v1	NOUN
ejpam-6212	101	5	,	,	PUNCT
ejpam-6212	101	6	v2	v2	NOUN
ejpam-6212	101	7	,	,	PUNCT
ejpam-6212	101	8	.	.	PUNCT
ejpam-6212	101	9	.	.	PUNCT
ejpam-6212	101	10	.	.	PUNCT
ejpam-6212	102	1	,	,	PUNCT
ejpam-6212	102	2	v2t2	v2t2	X
ejpam-6212	102	3	]	]	X
ejpam-6212	102	4	,	,	PUNCT
ejpam-6212	102	5	for	for	ADP
ejpam-6212	102	6	some	some	DET
ejpam-6212	102	7	natural	natural	ADJ
ejpam-6212	102	8	numbers	number	NOUN
ejpam-6212	102	9	t1	t1	PROPN
ejpam-6212	102	10	,	,	PUNCT
ejpam-6212	102	11	t2	t2	NOUN
ejpam-6212	102	12	≥	≥	NUM
ejpam-6212	102	13	2	2	NUM
ejpam-6212	102	14	.	.	X
ejpam-6212	103	1	for	for	ADP
ejpam-6212	103	2	each	each	DET
ejpam-6212	103	3	i	i	PRON
ejpam-6212	103	4	∈	∈	PROPN
ejpam-6212	103	5	{	{	PUNCT
ejpam-6212	103	6	1	1	NUM
ejpam-6212	103	7	,	,	PUNCT
ejpam-6212	103	8	2	2	NUM
ejpam-6212	103	9	,	,	PUNCT
ejpam-6212	103	10	.	.	PUNCT
ejpam-6212	103	11	.	.	PUNCT
ejpam-6212	103	12	.	.	PUNCT
ejpam-6212	104	1	,	,	PUNCT
ejpam-6212	104	2	2t1	2t1	NUM
ejpam-6212	104	3	}	}	PUNCT
ejpam-6212	104	4	,	,	PUNCT
ejpam-6212	104	5	let	let	VERB
ejpam-6212	104	6	ui	ui	NOUN
ejpam-6212	104	7	=	=	PUNCT
ejpam-6212	104	8	{	{	PUNCT
ejpam-6212	104	9	u	u	NOUN
ejpam-6212	104	10	∈	∈	PROPN
ejpam-6212	104	11	v	v	NOUN
ejpam-6212	104	12	(	(	PUNCT
ejpam-6212	104	13	g	g	NOUN
ejpam-6212	104	14	)	)	PUNCT
ejpam-6212	104	15	:	:	PUNCT
ejpam-6212	104	16	pc2t1∪c2t2	pc2t1∪c2t2	ADV
ejpam-6212	104	17	(	(	PUNCT
ejpam-6212	104	18	u	u	NOUN
ejpam-6212	104	19	)	)	PUNCT
ejpam-6212	104	20	=	=	SYM
ejpam-6212	104	21	ui	ui	PROPN
ejpam-6212	104	22	}	}	PUNCT
ejpam-6212	104	23	.	.	PUNCT
ejpam-6212	105	1	similarly	similarly	ADV
ejpam-6212	105	2	,	,	PUNCT
ejpam-6212	105	3	for	for	ADP
ejpam-6212	105	4	each	each	DET
ejpam-6212	105	5	j	j	PROPN
ejpam-6212	105	6	∈	∈	PROPN
ejpam-6212	105	7	{	{	PUNCT
ejpam-6212	105	8	1	1	NUM
ejpam-6212	105	9	,	,	PUNCT
ejpam-6212	105	10	2	2	NUM
ejpam-6212	105	11	,	,	PUNCT
ejpam-6212	105	12	.	.	PUNCT
ejpam-6212	105	13	.	.	PUNCT
ejpam-6212	105	14	.	.	PUNCT
ejpam-6212	106	1	,	,	PUNCT
ejpam-6212	106	2	2t2	2t2	NUM
ejpam-6212	106	3	}	}	PUNCT
ejpam-6212	106	4	,	,	PUNCT
ejpam-6212	106	5	let	let	VERB
ejpam-6212	106	6	vj	vj	INTJ
ejpam-6212	106	7	=	=	PRON
ejpam-6212	106	8	{	{	PUNCT
ejpam-6212	106	9	v	v	NUM
ejpam-6212	106	10	∈	∈	NOUN
ejpam-6212	106	11	v	v	NOUN
ejpam-6212	106	12	(	(	PUNCT
ejpam-6212	106	13	g	g	NOUN
ejpam-6212	106	14	)	)	PUNCT
ejpam-6212	106	15	:	:	PUNCT
ejpam-6212	106	16	pc2t1∪c2t2	pc2t1∪c2t2	INTJ
ejpam-6212	106	17	(	(	PUNCT
ejpam-6212	106	18	v	v	NOUN
ejpam-6212	106	19	)	)	PUNCT
ejpam-6212	106	20	=	=	SYM
ejpam-6212	106	21	vj	vj	PROPN
ejpam-6212	106	22	}	}	PUNCT
ejpam-6212	106	23	.	.	PUNCT
ejpam-6212	107	1	then	then	ADV
ejpam-6212	107	2	the	the	DET
ejpam-6212	107	3	projection	projection	NOUN
ejpam-6212	107	4	operator	operator	NOUN
ejpam-6212	107	5	onto	onto	ADP
ejpam-6212	107	6	the	the	DET
ejpam-6212	107	7	union	union	NOUN
ejpam-6212	107	8	of	of	ADP
ejpam-6212	107	9	c2t1	c2t1	NOUN
ejpam-6212	107	10	and	and	CCONJ
ejpam-6212	107	11	c2t2	c2t2	PROPN
ejpam-6212	107	12	generates	generate	VERB
ejpam-6212	107	13	the	the	DET
ejpam-6212	107	14	tree	tree	NOUN
ejpam-6212	107	15	-	-	PUNCT
ejpam-6212	107	16	partition	partition	NOUN
ejpam-6212	107	17	{	{	PUNCT
ejpam-6212	107	18	u1	u1	NOUN
ejpam-6212	107	19	=	=	SYM
ejpam-6212	107	20	v1	v1	PROPN
ejpam-6212	107	21	,	,	PUNCT
ejpam-6212	107	22	u2	u2	NOUN
ejpam-6212	107	23	,	,	PUNCT
ejpam-6212	107	24	.	.	PUNCT
ejpam-6212	107	25	.	.	PUNCT
ejpam-6212	108	1	.	.	PUNCT
ejpam-6212	109	1	,	,	PUNCT
ejpam-6212	109	2	u2t1	u2t1	INTJ
ejpam-6212	109	3	,	,	PUNCT
ejpam-6212	109	4	v2	v2	PROPN
ejpam-6212	109	5	,	,	PUNCT
ejpam-6212	109	6	v3	v3	PROPN
ejpam-6212	109	7	,	,	PUNCT
ejpam-6212	109	8	.	.	PUNCT
ejpam-6212	109	9	.	.	PUNCT
ejpam-6212	110	1	.	.	PUNCT
ejpam-6212	111	1	,	,	PUNCT
ejpam-6212	111	2	v2t2	v2t2	NOUN
ejpam-6212	111	3	}	}	PUNCT
ejpam-6212	111	4	of	of	ADP
ejpam-6212	111	5	v	v	NOUN
ejpam-6212	111	6	(	(	PUNCT
ejpam-6212	111	7	g	g	NOUN
ejpam-6212	111	8	)	)	PUNCT
ejpam-6212	111	9	.	.	PUNCT
ejpam-6212	112	1	this	this	PRON
ejpam-6212	112	2	means	mean	VERB
ejpam-6212	112	3	that	that	SCONJ
ejpam-6212	112	4	〈	〈	PROPN
ejpam-6212	112	5	ui	ui	PROPN
ejpam-6212	112	6	〉	〉	PROPN
ejpam-6212	112	7	and	and	CCONJ
ejpam-6212	112	8	〈	〈	PROPN
ejpam-6212	112	9	vj	vj	PROPN
ejpam-6212	112	10	〉	〉	PROPN
ejpam-6212	112	11	are	be	AUX
ejpam-6212	112	12	trees	tree	NOUN
ejpam-6212	112	13	in	in	ADP
ejpam-6212	112	14	g	g	PROPN
ejpam-6212	112	15	for	for	ADP
ejpam-6212	112	16	each	each	DET
ejpam-6212	112	17	i	i	PRON
ejpam-6212	112	18	∈	∈	PROPN
ejpam-6212	112	19	{	{	PUNCT
ejpam-6212	112	20	1	1	NUM
ejpam-6212	112	21	,	,	PUNCT
ejpam-6212	112	22	2	2	NUM
ejpam-6212	112	23	,	,	PUNCT
ejpam-6212	112	24	.	.	PUNCT
ejpam-6212	112	25	.	.	PUNCT
ejpam-6212	113	1	.	.	PUNCT
ejpam-6212	114	1	,	,	PUNCT
ejpam-6212	114	2	2t1	2t1	NUM
ejpam-6212	114	3	}	}	PUNCT
ejpam-6212	114	4	and	and	CCONJ
ejpam-6212	114	5	j	j	PROPN
ejpam-6212	114	6	∈	∈	PROPN
ejpam-6212	114	7	{	{	PUNCT
ejpam-6212	114	8	1	1	NUM
ejpam-6212	114	9	,	,	PUNCT
ejpam-6212	114	10	2	2	NUM
ejpam-6212	114	11	,	,	PUNCT
ejpam-6212	114	12	.	.	PUNCT
ejpam-6212	114	13	.	.	PUNCT
ejpam-6212	115	1	.	.	PUNCT
ejpam-6212	116	1	,	,	PUNCT
ejpam-6212	116	2	2t2	2t2	NUM
ejpam-6212	116	3	}	}	PUNCT
ejpam-6212	116	4	.	.	PUNCT
ejpam-6212	117	1	we	we	PRON
ejpam-6212	117	2	call	call	VERB
ejpam-6212	117	3	the	the	DET
ejpam-6212	117	4	set	set	NOUN
ejpam-6212	117	5	{	{	PUNCT
ejpam-6212	117	6	u1	u1	NOUN
ejpam-6212	117	7	=	=	SYM
ejpam-6212	117	8	v1	v1	PROPN
ejpam-6212	117	9	,	,	PUNCT
ejpam-6212	117	10	u2	u2	NOUN
ejpam-6212	117	11	,	,	PUNCT
ejpam-6212	117	12	.	.	PUNCT
ejpam-6212	117	13	.	.	PUNCT
ejpam-6212	118	1	.	.	PUNCT
ejpam-6212	119	1	,	,	PUNCT
ejpam-6212	119	2	u2t1	u2t1	INTJ
ejpam-6212	119	3	,	,	PUNCT
ejpam-6212	119	4	v2	v2	PROPN
ejpam-6212	119	5	,	,	PUNCT
ejpam-6212	119	6	v3	v3	PROPN
ejpam-6212	119	7	,	,	PUNCT
ejpam-6212	119	8	.	.	PUNCT
ejpam-6212	119	9	.	.	PUNCT
ejpam-6212	120	1	.	.	PUNCT
ejpam-6212	121	1	,	,	PUNCT
ejpam-6212	121	2	v2t2	v2t2	X
ejpam-6212	121	3	}	}	PUNCT
ejpam-6212	121	4	the	the	DET
ejpam-6212	121	5	tree	tree	NOUN
ejpam-6212	121	6	-	-	PUNCT
ejpam-6212	121	7	partition	partition	NOUN
ejpam-6212	121	8	of	of	ADP
ejpam-6212	121	9	v	v	NOUN
ejpam-6212	121	10	(	(	PUNCT
ejpam-6212	121	11	g	g	NOUN
ejpam-6212	121	12	)	)	PUNCT
ejpam-6212	121	13	with	with	ADP
ejpam-6212	121	14	respect	respect	NOUN
ejpam-6212	121	15	to	to	ADP
ejpam-6212	121	16	its	its	PRON
ejpam-6212	121	17	projection	projection	NOUN
ejpam-6212	121	18	onto	onto	ADP
ejpam-6212	121	19	the	the	DET
ejpam-6212	121	20	union	union	NOUN
ejpam-6212	121	21	of	of	ADP
ejpam-6212	121	22	cycles	cycle	NOUN
ejpam-6212	121	23	c2t1	c2t1	NOUN
ejpam-6212	121	24	and	and	CCONJ
ejpam-6212	121	25	c2t2	c2t2	INTJ
ejpam-6212	121	26	.	.	PUNCT
ejpam-6212	122	1	in	in	ADP
ejpam-6212	122	2	the	the	DET
ejpam-6212	122	3	above	above	ADJ
ejpam-6212	122	4	illustration	illustration	NOUN
ejpam-6212	122	5	,	,	PUNCT
ejpam-6212	122	6	pc6∪c4(a	pc6∪c4(a	NOUN
ejpam-6212	122	7	)	)	PUNCT
ejpam-6212	122	8	=	=	SYM
ejpam-6212	122	9	pc6∪c4(b	pc6∪c4(b	NOUN
ejpam-6212	122	10	)	)	PUNCT
ejpam-6212	122	11	=	=	SYM
ejpam-6212	122	12	pc6∪c4(c	pc6∪c4(c	NOUN
ejpam-6212	122	13	)	)	PUNCT
ejpam-6212	122	14	=	=	SYM
ejpam-6212	123	1	pc6∪c4(d	pc6∪c4(d	X
ejpam-6212	123	2	)	)	PUNCT
ejpam-6212	123	3	=	=	SYM
ejpam-6212	123	4	pc6∪c4(u4	pc6∪c4(u4	NOUN
ejpam-6212	123	5	)	)	PUNCT
ejpam-6212	123	6	=	=	SYM
ejpam-6212	123	7	u4	u4	PROPN
ejpam-6212	123	8	.	.	PUNCT
ejpam-6212	124	1	this	this	PRON
ejpam-6212	124	2	gives	give	VERB
ejpam-6212	124	3	u4	u4	PROPN
ejpam-6212	124	4	=	=	PUNCT
ejpam-6212	124	5	{	{	PUNCT
ejpam-6212	124	6	a	a	PRON
ejpam-6212	124	7	,	,	PUNCT
ejpam-6212	124	8	b	b	NOUN
ejpam-6212	124	9	,	,	PUNCT
ejpam-6212	124	10	c	c	NOUN
ejpam-6212	124	11	,	,	PUNCT
ejpam-6212	124	12	d	d	PROPN
ejpam-6212	124	13	,	,	PUNCT
ejpam-6212	124	14	u4	u4	PROPN
ejpam-6212	124	15	}	}	PUNCT
ejpam-6212	124	16	.	.	PUNCT
ejpam-6212	125	1	also	also	ADV
ejpam-6212	125	2	,	,	PUNCT
ejpam-6212	125	3	u1	u1	NOUN
ejpam-6212	125	4	=	=	SYM
ejpam-6212	125	5	{	{	PUNCT
ejpam-6212	125	6	u1	u1	NOUN
ejpam-6212	125	7	}	}	PUNCT
ejpam-6212	125	8	and	and	CCONJ
ejpam-6212	125	9	u3	u3	NOUN
ejpam-6212	125	10	=	=	SYM
ejpam-6212	125	11	{	{	PUNCT
ejpam-6212	125	12	e	e	PROPN
ejpam-6212	125	13	,	,	PUNCT
ejpam-6212	125	14	u3	u3	PROPN
ejpam-6212	125	15	}	}	PUNCT
ejpam-6212	125	16	.	.	PUNCT
ejpam-6212	126	1	moveover	moveover	PROPN
ejpam-6212	126	2	,	,	PUNCT
ejpam-6212	126	3	the	the	DET
ejpam-6212	126	4	projection	projection	NOUN
ejpam-6212	126	5	of	of	ADP
ejpam-6212	126	6	f	f	PROPN
ejpam-6212	126	7	onto	onto	ADP
ejpam-6212	126	8	c6	c6	PROPN
ejpam-6212	126	9	∪	∪	PROPN
ejpam-6212	126	10	c4	c4	PROPN
ejpam-6212	126	11	is	be	AUX
ejpam-6212	126	12	v2	v2	PROPN
ejpam-6212	126	13	.	.	PUNCT
ejpam-6212	127	1	note	note	NOUN
ejpam-6212	127	2	also	also	ADV
ejpam-6212	127	3	that	that	SCONJ
ejpam-6212	127	4	α(u4	α(u4	NOUN
ejpam-6212	127	5	,	,	PUNCT
ejpam-6212	127	6	v3	v3	PROPN
ejpam-6212	127	7	)	)	PUNCT
ejpam-6212	127	8	=	=	PUNCT
ejpam-6212	128	1	4	4	X
ejpam-6212	128	2	.	.	PUNCT
ejpam-6212	128	3	r.	r.	PROPN
ejpam-6212	128	4	g.	g.	PROPN
ejpam-6212	128	5	artes	artes	PROPN
ejpam-6212	128	6	jr	jr	PROPN
ejpam-6212	128	7	.	.	PROPN
ejpam-6212	128	8	et	et	PROPN
ejpam-6212	128	9	al	al	PROPN
ejpam-6212	128	10	.	.	PUNCT
ejpam-6212	128	11	/	/	SYM
ejpam-6212	128	12	eur	eur	PROPN
ejpam-6212	128	13	.	.	PUNCT
ejpam-6212	129	1	j.	j.	PROPN
ejpam-6212	129	2	pure	pure	PROPN
ejpam-6212	129	3	appl	appl	PROPN
ejpam-6212	129	4	.	.	PROPN
ejpam-6212	129	5	math	math	PROPN
ejpam-6212	129	6	,	,	PUNCT
ejpam-6212	129	7	18	18	NUM
ejpam-6212	129	8	(	(	PUNCT
ejpam-6212	129	9	4	4	NUM
ejpam-6212	129	10	)	)	PUNCT
ejpam-6212	129	11	(	(	PUNCT
ejpam-6212	129	12	2025	2025	NUM
ejpam-6212	129	13	)	)	PUNCT
ejpam-6212	129	14	,	,	PUNCT
ejpam-6212	129	15	6212	6212	NUM
ejpam-6212	129	16	6	6	NUM
ejpam-6212	129	17	of	of	ADP
ejpam-6212	129	18	20	20	NUM
ejpam-6212	129	19	..........................................................................	..........................................................................	PUNCT
ejpam-6212	129	20	.....	.....	PUNCT
ejpam-6212	129	21	...	...	PUNCT
ejpam-6212	129	22	.	.	PUNCT
ejpam-6212	130	1	..	..	PUNCT
ejpam-6212	130	2	..	..	PUNCT
ejpam-6212	130	3	...	...	PUNCT
ejpam-6212	130	4	.	.	PUNCT
ejpam-6212	131	1	..	..	PUNCT
ejpam-6212	131	2	..	..	PUNCT
ejpam-6212	131	3	..	..	PUNCT
ejpam-6212	131	4	.	.	PUNCT
ejpam-6212	131	5	.	.	PUNCT
ejpam-6212	132	1	..	..	PUNCT
ejpam-6212	132	2	.	.	PUNCT
ejpam-6212	132	3	.	.	PUNCT
ejpam-6212	133	1	.........	.........	PUNCT
ejpam-6212	134	1	.........	.........	PUNCT
ejpam-6212	134	2	.........	.........	PUNCT
ejpam-6212	135	1	.........	.........	PUNCT
ejpam-6212	135	2	.........	.........	PUNCT
ejpam-6212	136	1	.........	.........	PUNCT
ejpam-6212	136	2	.........	.........	PUNCT
ejpam-6212	137	1	.........	.........	PUNCT
ejpam-6212	137	2	.........	.........	PUNCT
ejpam-6212	137	3	.........	.........	PUNCT
ejpam-6212	138	1	........	........	PUNCT
ejpam-6212	138	2	.......	.......	PUNCT
ejpam-6212	139	1	.....	.....	PUNCT
ejpam-6212	139	2	...	...	PUNCT
ejpam-6212	139	3	.	.	PUNCT
ejpam-6212	140	1	..	..	PUNCT
ejpam-6212	140	2	..	..	PUNCT
ejpam-6212	140	3	...	...	PUNCT
ejpam-6212	140	4	.	.	PUNCT
ejpam-6212	141	1	..	..	PUNCT
ejpam-6212	141	2	..	..	PUNCT
ejpam-6212	141	3	..	..	PUNCT
ejpam-6212	141	4	.	.	PUNCT
ejpam-6212	141	5	.	.	PUNCT
ejpam-6212	142	1	..	..	PUNCT
ejpam-6212	142	2	.	.	PUNCT
ejpam-6212	142	3	.	.	PUNCT
ejpam-6212	143	1	..................................................................................................	..................................................................................................	PUNCT
ejpam-6212	143	2	.......	.......	PUNCT
ejpam-6212	144	1	.....	.....	PUNCT
ejpam-6212	144	2	...	...	PUNCT
ejpam-6212	144	3	.	.	PUNCT
ejpam-6212	145	1	..	..	PUNCT
ejpam-6212	145	2	..	..	PUNCT
ejpam-6212	145	3	...	...	PUNCT
ejpam-6212	145	4	.	.	PUNCT
ejpam-6212	146	1	..	..	PUNCT
ejpam-6212	146	2	..	..	PUNCT
ejpam-6212	146	3	..	..	PUNCT
ejpam-6212	146	4	.	.	PUNCT
ejpam-6212	146	5	.	.	PUNCT
ejpam-6212	147	1	..	..	PUNCT
ejpam-6212	147	2	.	.	PUNCT
ejpam-6212	147	3	.	.	PUNCT
ejpam-6212	148	1	..........................................................................	..........................................................................	PUNCT
ejpam-6212	149	1	.....	.....	PUNCT
ejpam-6212	149	2	...	...	PUNCT
ejpam-6212	149	3	.	.	PUNCT
ejpam-6212	150	1	..	..	PUNCT
ejpam-6212	150	2	..	..	PUNCT
ejpam-6212	150	3	...	...	PUNCT
ejpam-6212	150	4	.	.	PUNCT
ejpam-6212	151	1	..	..	PUNCT
ejpam-6212	151	2	..	..	PUNCT
ejpam-6212	151	3	..	..	PUNCT
ejpam-6212	151	4	.	.	PUNCT
ejpam-6212	151	5	.	.	PUNCT
ejpam-6212	152	1	..	..	PUNCT
ejpam-6212	152	2	.	.	PUNCT
ejpam-6212	152	3	.	.	PUNCT
ejpam-6212	153	1	.........	.........	PUNCT
ejpam-6212	154	1	.........	.........	PUNCT
ejpam-6212	154	2	.........	.........	PUNCT
ejpam-6212	155	1	.........	.........	PUNCT
ejpam-6212	155	2	.........	.........	PUNCT
ejpam-6212	156	1	.........	.........	PUNCT
ejpam-6212	156	2	.........	.........	PUNCT
ejpam-6212	157	1	.........	.........	PUNCT
ejpam-6212	157	2	.........	.........	PUNCT
ejpam-6212	157	3	.........	.........	PUNCT
ejpam-6212	158	1	........	........	PUNCT
ejpam-6212	158	2	.......	.......	PUNCT
ejpam-6212	159	1	.....	.....	PUNCT
ejpam-6212	159	2	...	...	PUNCT
ejpam-6212	159	3	.	.	PUNCT
ejpam-6212	160	1	..	..	PUNCT
ejpam-6212	160	2	..	..	PUNCT
ejpam-6212	160	3	...	...	PUNCT
ejpam-6212	160	4	.	.	PUNCT
ejpam-6212	161	1	..	..	PUNCT
ejpam-6212	161	2	..	..	PUNCT
ejpam-6212	161	3	..	..	PUNCT
ejpam-6212	161	4	.	.	PUNCT
ejpam-6212	161	5	.	.	PUNCT
ejpam-6212	162	1	..	..	PUNCT
ejpam-6212	162	2	.	.	PUNCT
ejpam-6212	162	3	.	.	PUNCT
ejpam-6212	163	1	..................................................................................................	..................................................................................................	PUNCT
ejpam-6212	163	2	.......	.......	PUNCT
ejpam-6212	164	1	.....	.....	PUNCT
ejpam-6212	164	2	...	...	PUNCT
ejpam-6212	164	3	.	.	PUNCT
ejpam-6212	165	1	..	..	PUNCT
ejpam-6212	165	2	..	..	PUNCT
ejpam-6212	165	3	...	...	PUNCT
ejpam-6212	165	4	.	.	PUNCT
ejpam-6212	166	1	..	..	PUNCT
ejpam-6212	166	2	..	..	PUNCT
ejpam-6212	166	3	..	..	PUNCT
ejpam-6212	166	4	.	.	PUNCT
ejpam-6212	166	5	.	.	PUNCT
ejpam-6212	167	1	..	..	PUNCT
ejpam-6212	167	2	.	.	PUNCT
ejpam-6212	167	3	.	.	PUNCT
ejpam-6212	168	1	.........	.........	PUNCT
ejpam-6212	169	1	.........	.........	PUNCT
ejpam-6212	169	2	.........	.........	PUNCT
ejpam-6212	170	1	.........	.........	PUNCT
ejpam-6212	170	2	.........	.........	PUNCT
ejpam-6212	171	1	.........	.........	PUNCT
ejpam-6212	171	2	.........	.........	PUNCT
ejpam-6212	172	1	.........	.........	PUNCT
ejpam-6212	172	2	.........	.........	PUNCT
ejpam-6212	172	3	.........	.........	PUNCT
ejpam-6212	173	1	........	........	PUNCT
ejpam-6212	173	2	.......	.......	PUNCT
ejpam-6212	174	1	.....	.....	PUNCT
ejpam-6212	174	2	...	...	PUNCT
ejpam-6212	174	3	.	.	PUNCT
ejpam-6212	175	1	..	..	PUNCT
ejpam-6212	175	2	..	..	PUNCT
ejpam-6212	175	3	...	...	PUNCT
ejpam-6212	175	4	.	.	PUNCT
ejpam-6212	176	1	..	..	PUNCT
ejpam-6212	176	2	..	..	PUNCT
ejpam-6212	176	3	..	..	PUNCT
ejpam-6212	176	4	.	.	PUNCT
ejpam-6212	176	5	.	.	PUNCT
ejpam-6212	177	1	..	..	PUNCT
ejpam-6212	177	2	.	.	PUNCT
ejpam-6212	177	3	.	.	PUNCT
ejpam-6212	178	1	.......	.......	PUNCT
ejpam-6212	179	1	.....	.....	PUNCT
ejpam-6212	179	2	...	...	PUNCT
ejpam-6212	179	3	.	.	PUNCT
ejpam-6212	180	1	..	..	PUNCT
ejpam-6212	180	2	..	..	PUNCT
ejpam-6212	180	3	...	...	PUNCT
ejpam-6212	180	4	.	.	PUNCT
ejpam-6212	181	1	..	..	PUNCT
ejpam-6212	181	2	..	..	PUNCT
ejpam-6212	181	3	..	..	PUNCT
ejpam-6212	181	4	.	.	PUNCT
ejpam-6212	181	5	.	.	PUNCT
ejpam-6212	182	1	..	..	PUNCT
ejpam-6212	182	2	.	.	PUNCT
ejpam-6212	182	3	.	.	PUNCT
ejpam-6212	183	1	..........................................................................	..........................................................................	PUNCT
ejpam-6212	184	1	.....	.....	PUNCT
ejpam-6212	184	2	...	...	PUNCT
ejpam-6212	184	3	.	.	PUNCT
ejpam-6212	185	1	..	..	PUNCT
ejpam-6212	185	2	..	..	PUNCT
ejpam-6212	185	3	...	...	PUNCT
ejpam-6212	185	4	.	.	PUNCT
ejpam-6212	186	1	..	..	PUNCT
ejpam-6212	186	2	..	..	PUNCT
ejpam-6212	186	3	..	..	PUNCT
ejpam-6212	186	4	.	.	PUNCT
ejpam-6212	186	5	.	.	PUNCT
ejpam-6212	187	1	..	..	PUNCT
ejpam-6212	187	2	.	.	PUNCT
ejpam-6212	187	3	.	.	PUNCT
ejpam-6212	188	1	..................................................................................................	..................................................................................................	PUNCT
ejpam-6212	188	2	.......	.......	PUNCT
ejpam-6212	189	1	.....	.....	PUNCT
ejpam-6212	189	2	...	...	PUNCT
ejpam-6212	189	3	.	.	PUNCT
ejpam-6212	190	1	..	..	PUNCT
ejpam-6212	190	2	..	..	PUNCT
ejpam-6212	190	3	...	...	PUNCT
ejpam-6212	190	4	.	.	PUNCT
ejpam-6212	191	1	..	..	PUNCT
ejpam-6212	191	2	..	..	PUNCT
ejpam-6212	191	3	..	..	PUNCT
ejpam-6212	191	4	.	.	PUNCT
ejpam-6212	191	5	.	.	PUNCT
ejpam-6212	192	1	..	..	PUNCT
ejpam-6212	192	2	.	.	PUNCT
ejpam-6212	192	3	.	.	PUNCT
ejpam-6212	193	1	.........	.........	PUNCT
ejpam-6212	194	1	.........	.........	PUNCT
ejpam-6212	194	2	.........	.........	PUNCT
ejpam-6212	195	1	.........	.........	PUNCT
ejpam-6212	195	2	.........	.........	PUNCT
ejpam-6212	196	1	.........	.........	PUNCT
ejpam-6212	196	2	.........	.........	PUNCT
ejpam-6212	197	1	.........	.........	PUNCT
ejpam-6212	197	2	.........	.........	PUNCT
ejpam-6212	197	3	.........	.........	PUNCT
ejpam-6212	198	1	........	........	PUNCT
ejpam-6212	198	2	.......	.......	PUNCT
ejpam-6212	199	1	.....	.....	PUNCT
ejpam-6212	199	2	...	...	PUNCT
ejpam-6212	199	3	.	.	PUNCT
ejpam-6212	200	1	..	..	PUNCT
ejpam-6212	200	2	..	..	PUNCT
ejpam-6212	200	3	...	...	PUNCT
ejpam-6212	200	4	.	.	PUNCT
ejpam-6212	201	1	..	..	PUNCT
ejpam-6212	201	2	..	..	PUNCT
ejpam-6212	201	3	..	..	PUNCT
ejpam-6212	201	4	.	.	PUNCT
ejpam-6212	201	5	.	.	PUNCT
ejpam-6212	202	1	..	..	PUNCT
ejpam-6212	202	2	.	.	PUNCT
ejpam-6212	202	3	.	.	PUNCT
ejpam-6212	203	1	..........................................................................	..........................................................................	PUNCT
ejpam-6212	204	1	.....	.....	PUNCT
ejpam-6212	204	2	...	...	PUNCT
ejpam-6212	204	3	.	.	PUNCT
ejpam-6212	205	1	..	..	PUNCT
ejpam-6212	205	2	..	..	PUNCT
ejpam-6212	205	3	...	...	PUNCT
ejpam-6212	205	4	.	.	PUNCT
ejpam-6212	206	1	..	..	PUNCT
ejpam-6212	206	2	..	..	PUNCT
ejpam-6212	206	3	..	..	PUNCT
ejpam-6212	206	4	.	.	PUNCT
ejpam-6212	206	5	.	.	PUNCT
ejpam-6212	207	1	..	..	PUNCT
ejpam-6212	207	2	.	.	PUNCT
ejpam-6212	207	3	.	.	PUNCT
ejpam-6212	208	1	..................................................................................................	..................................................................................................	PUNCT
ejpam-6212	208	2	.......	.......	PUNCT
ejpam-6212	209	1	.....	.....	PUNCT
ejpam-6212	209	2	...	...	PUNCT
ejpam-6212	209	3	.	.	PUNCT
ejpam-6212	210	1	..	..	PUNCT
ejpam-6212	210	2	..	..	PUNCT
ejpam-6212	210	3	...	...	PUNCT
ejpam-6212	210	4	.	.	PUNCT
ejpam-6212	211	1	..	..	PUNCT
ejpam-6212	211	2	..	..	PUNCT
ejpam-6212	211	3	..	..	PUNCT
ejpam-6212	211	4	.	.	PUNCT
ejpam-6212	211	5	.	.	PUNCT
ejpam-6212	212	1	..	..	PUNCT
ejpam-6212	212	2	.	.	PUNCT
ejpam-6212	212	3	.	.	PUNCT
ejpam-6212	213	1	.........	.........	PUNCT
ejpam-6212	214	1	.........	.........	PUNCT
ejpam-6212	214	2	.........	.........	PUNCT
ejpam-6212	215	1	.........	.........	PUNCT
ejpam-6212	215	2	.........	.........	PUNCT
ejpam-6212	216	1	.........	.........	PUNCT
ejpam-6212	216	2	.........	.........	PUNCT
ejpam-6212	217	1	.........	.........	PUNCT
ejpam-6212	217	2	.........	.........	PUNCT
ejpam-6212	217	3	.........	.........	PUNCT
ejpam-6212	218	1	........	........	PUNCT
ejpam-6212	218	2	.......	.......	PUNCT
ejpam-6212	219	1	.....	.....	PUNCT
ejpam-6212	219	2	...	...	PUNCT
ejpam-6212	219	3	.	.	PUNCT
ejpam-6212	220	1	..	..	PUNCT
ejpam-6212	220	2	..	..	PUNCT
ejpam-6212	220	3	...	...	PUNCT
ejpam-6212	220	4	.	.	PUNCT
ejpam-6212	221	1	..	..	PUNCT
ejpam-6212	221	2	..	..	PUNCT
ejpam-6212	221	3	..	..	PUNCT
ejpam-6212	221	4	.	.	PUNCT
ejpam-6212	221	5	.	.	PUNCT
ejpam-6212	222	1	..	..	PUNCT
ejpam-6212	222	2	.	.	PUNCT
ejpam-6212	222	3	.	.	PUNCT
ejpam-6212	223	1	..................................................................................................	..................................................................................................	PUNCT
ejpam-6212	223	2	.......	.......	PUNCT
ejpam-6212	224	1	.....	.....	PUNCT
ejpam-6212	224	2	...	...	PUNCT
ejpam-6212	224	3	.	.	PUNCT
ejpam-6212	225	1	..	..	PUNCT
ejpam-6212	225	2	..	..	PUNCT
ejpam-6212	225	3	...	...	PUNCT
ejpam-6212	225	4	.	.	PUNCT
ejpam-6212	226	1	..	..	PUNCT
ejpam-6212	226	2	..	..	PUNCT
ejpam-6212	226	3	..	..	PUNCT
ejpam-6212	226	4	.	.	PUNCT
ejpam-6212	226	5	.	.	PUNCT
ejpam-6212	227	1	..	..	PUNCT
ejpam-6212	227	2	.	.	PUNCT
ejpam-6212	227	3	.	.	PUNCT
ejpam-6212	228	1	.......	.......	PUNCT
ejpam-6212	229	1	.....	.....	PUNCT
ejpam-6212	229	2	...	...	PUNCT
ejpam-6212	229	3	.	.	PUNCT
ejpam-6212	230	1	..	..	PUNCT
ejpam-6212	230	2	..	..	PUNCT
ejpam-6212	230	3	...	...	PUNCT
ejpam-6212	230	4	.	.	PUNCT
ejpam-6212	231	1	..	..	PUNCT
ejpam-6212	231	2	..	..	PUNCT
ejpam-6212	231	3	..	..	PUNCT
ejpam-6212	231	4	.	.	PUNCT
ejpam-6212	231	5	.	.	PUNCT
ejpam-6212	232	1	..	..	PUNCT
ejpam-6212	232	2	.	.	PUNCT
ejpam-6212	232	3	.	.	PUNCT
ejpam-6212	233	1	..........................................................................	..........................................................................	PUNCT
ejpam-6212	234	1	.....	.....	PUNCT
ejpam-6212	234	2	...	...	PUNCT
ejpam-6212	234	3	.	.	PUNCT
ejpam-6212	235	1	..	..	PUNCT
ejpam-6212	235	2	..	..	PUNCT
ejpam-6212	235	3	...	...	PUNCT
ejpam-6212	235	4	.	.	PUNCT
ejpam-6212	236	1	..	..	PUNCT
ejpam-6212	236	2	..	..	PUNCT
ejpam-6212	236	3	..	..	PUNCT
ejpam-6212	236	4	.	.	PUNCT
ejpam-6212	236	5	.	.	PUNCT
ejpam-6212	237	1	..	..	PUNCT
ejpam-6212	237	2	.	.	PUNCT
ejpam-6212	237	3	.	.	PUNCT
ejpam-6212	238	1	..........................................................................	..........................................................................	PUNCT
ejpam-6212	239	1	.....	.....	PUNCT
ejpam-6212	239	2	...	...	PUNCT
ejpam-6212	239	3	.	.	PUNCT
ejpam-6212	240	1	..	..	PUNCT
ejpam-6212	240	2	..	..	PUNCT
ejpam-6212	240	3	...	...	PUNCT
ejpam-6212	240	4	.	.	PUNCT
ejpam-6212	241	1	..	..	PUNCT
ejpam-6212	241	2	..	..	PUNCT
ejpam-6212	241	3	..	..	PUNCT
ejpam-6212	241	4	.	.	PUNCT
ejpam-6212	241	5	.	.	PUNCT
ejpam-6212	242	1	..	..	PUNCT
ejpam-6212	242	2	.	.	PUNCT
ejpam-6212	242	3	.	.	PUNCT
ejpam-6212	243	1	.......	.......	PUNCT
ejpam-6212	244	1	.....	.....	PUNCT
ejpam-6212	244	2	...	...	PUNCT
ejpam-6212	244	3	.	.	PUNCT
ejpam-6212	245	1	..	..	PUNCT
ejpam-6212	245	2	..	..	PUNCT
ejpam-6212	245	3	...	...	PUNCT
ejpam-6212	245	4	.	.	PUNCT
ejpam-6212	246	1	..	..	PUNCT
ejpam-6212	246	2	..	..	PUNCT
ejpam-6212	246	3	..	..	PUNCT
ejpam-6212	246	4	.	.	PUNCT
ejpam-6212	246	5	.	.	PUNCT
ejpam-6212	247	1	..	..	PUNCT
ejpam-6212	247	2	.	.	PUNCT
ejpam-6212	247	3	.	.	PUNCT
ejpam-6212	248	1	...................................................................	...................................................................	PUNCT
ejpam-6212	248	2	.......	.......	PUNCT
ejpam-6212	249	1	.....	.....	PUNCT
ejpam-6212	249	2	...	...	PUNCT
ejpam-6212	249	3	.	.	PUNCT
ejpam-6212	250	1	..	..	PUNCT
ejpam-6212	250	2	..	..	PUNCT
ejpam-6212	250	3	...	...	PUNCT
ejpam-6212	250	4	.	.	PUNCT
ejpam-6212	251	1	..	..	PUNCT
ejpam-6212	251	2	..	..	PUNCT
ejpam-6212	251	3	..	..	PUNCT
ejpam-6212	251	4	.	.	PUNCT
ejpam-6212	251	5	.	.	PUNCT
ejpam-6212	252	1	..	..	PUNCT
ejpam-6212	252	2	.	.	PUNCT
ejpam-6212	252	3	.	.	PUNCT
ejpam-6212	253	1	.......	.......	PUNCT
ejpam-6212	254	1	.....	.....	PUNCT
ejpam-6212	254	2	...	...	PUNCT
ejpam-6212	254	3	.	.	PUNCT
ejpam-6212	255	1	..	..	PUNCT
ejpam-6212	255	2	..	..	PUNCT
ejpam-6212	255	3	...	...	PUNCT
ejpam-6212	255	4	.	.	PUNCT
ejpam-6212	256	1	..	..	PUNCT
ejpam-6212	256	2	..	..	PUNCT
ejpam-6212	256	3	..	..	PUNCT
ejpam-6212	256	4	.	.	PUNCT
ejpam-6212	256	5	.	.	PUNCT
ejpam-6212	257	1	..	..	PUNCT
ejpam-6212	257	2	.	.	PUNCT
ejpam-6212	257	3	.	.	PUNCT
ejpam-6212	258	1	a	a	DET
ejpam-6212	258	2	c6	c6	PROPN
ejpam-6212	258	3	c4u4	c4u4	X
ejpam-6212	258	4	u1	u1	NOUN
ejpam-6212	258	5	v2	v2	PROPN
ejpam-6212	258	6	c	c	PROPN
ejpam-6212	258	7	b	b	PROPN
ejpam-6212	258	8	f	f	X
ejpam-6212	258	9	d	d	X
ejpam-6212	258	10	e	e	PROPN
ejpam-6212	258	11	u3	u3	PROPN
ejpam-6212	258	12	v3	v3	PROPN
ejpam-6212	258	13	figure	figure	NOUN
ejpam-6212	258	14	2	2	NUM
ejpam-6212	258	15	:	:	PUNCT
ejpam-6212	258	16	spirocyclic	spirocyclic	ADJ
ejpam-6212	258	17	graph	graph	NOUN
ejpam-6212	258	18	with	with	ADP
ejpam-6212	258	19	c6	c6	PROPN
ejpam-6212	258	20	and	and	CCONJ
ejpam-6212	258	21	c4	c4	VERB
ejpam-6212	258	22	the	the	DET
ejpam-6212	258	23	geodetic	geodetic	ADJ
ejpam-6212	258	24	-	-	PUNCT
ejpam-6212	258	25	wiener	wiener	NOUN
ejpam-6212	258	26	index	index	NOUN
ejpam-6212	258	27	and	and	CCONJ
ejpam-6212	258	28	wiener	wiener	NOUN
ejpam-6212	258	29	index	index	NOUN
ejpam-6212	258	30	differ	differ	VERB
ejpam-6212	258	31	only	only	ADV
ejpam-6212	258	32	on	on	ADP
ejpam-6212	258	33	the	the	DET
ejpam-6212	258	34	number	number	NOUN
ejpam-6212	258	35	of	of	ADP
ejpam-6212	258	36	geodesics	geodesic	NOUN
ejpam-6212	258	37	between	between	ADP
ejpam-6212	258	38	pairs	pair	NOUN
ejpam-6212	258	39	of	of	ADP
ejpam-6212	258	40	vertices	vertex	NOUN
ejpam-6212	258	41	.	.	PUNCT
ejpam-6212	259	1	hence	hence	ADV
ejpam-6212	259	2	,	,	PUNCT
ejpam-6212	259	3	we	we	PRON
ejpam-6212	259	4	will	will	AUX
ejpam-6212	259	5	consider	consider	VERB
ejpam-6212	259	6	those	those	DET
ejpam-6212	259	7	pairs	pair	NOUN
ejpam-6212	259	8	where	where	SCONJ
ejpam-6212	259	9	the	the	DET
ejpam-6212	259	10	number	number	NOUN
ejpam-6212	259	11	of	of	ADP
ejpam-6212	259	12	geodesics	geodesic	NOUN
ejpam-6212	259	13	is	be	AUX
ejpam-6212	259	14	at	at	ADV
ejpam-6212	259	15	least	least	ADJ
ejpam-6212	259	16	two	two	NUM
ejpam-6212	259	17	.	.	PUNCT
ejpam-6212	260	1	for	for	ADP
ejpam-6212	260	2	u	u	NOUN
ejpam-6212	260	3	,	,	PUNCT
ejpam-6212	260	4	v	v	PROPN
ejpam-6212	260	5	∈	∈	PROPN
ejpam-6212	260	6	v	v	NOUN
ejpam-6212	260	7	(	(	PUNCT
ejpam-6212	260	8	g	g	NOUN
ejpam-6212	260	9	)	)	PUNCT
ejpam-6212	260	10	,	,	PUNCT
ejpam-6212	260	11	the	the	DET
ejpam-6212	260	12	value	value	NOUN
ejpam-6212	260	13	of	of	ADP
ejpam-6212	260	14	α(u	α(u	PROPN
ejpam-6212	260	15	,	,	PUNCT
ejpam-6212	260	16	v	v	NOUN
ejpam-6212	260	17	)	)	PUNCT
ejpam-6212	260	18	is	be	AUX
ejpam-6212	260	19	determined	determine	VERB
ejpam-6212	260	20	by	by	ADP
ejpam-6212	260	21	the	the	DET
ejpam-6212	260	22	following	follow	VERB
ejpam-6212	260	23	classes	class	NOUN
ejpam-6212	260	24	of	of	ADP
ejpam-6212	260	25	subsets	subset	NOUN
ejpam-6212	260	26	of	of	ADP
ejpam-6212	260	27	v	v	NOUN
ejpam-6212	260	28	(	(	PUNCT
ejpam-6212	260	29	g	g	NOUN
ejpam-6212	260	30	)	)	PUNCT
ejpam-6212	260	31	.	.	PUNCT
ejpam-6212	261	1	lemma	lemma	PROPN
ejpam-6212	261	2	1	1	X
ejpam-6212	261	3	.	.	PUNCT
ejpam-6212	262	1	let	let	VERB
ejpam-6212	262	2	g	g	PRON
ejpam-6212	262	3	be	be	AUX
ejpam-6212	262	4	a	a	DET
ejpam-6212	262	5	simple	simple	ADJ
ejpam-6212	262	6	spirocyclic	spirocyclic	NOUN
ejpam-6212	262	7	graph	graph	NOUN
ejpam-6212	262	8	with	with	ADP
ejpam-6212	262	9	even	even	ADV
ejpam-6212	262	10	cycles	cycle	NOUN
ejpam-6212	262	11	c2t1	c2t1	NOUN
ejpam-6212	263	1	=	=	SYM
ejpam-6212	264	1	[	[	X
ejpam-6212	264	2	u1	u1	NOUN
ejpam-6212	264	3	,	,	PUNCT
ejpam-6212	264	4	u2	u2	NOUN
ejpam-6212	264	5	,	,	PUNCT
ejpam-6212	264	6	.	.	PUNCT
ejpam-6212	264	7	.	.	PUNCT
ejpam-6212	264	8	.	.	PUNCT
ejpam-6212	265	1	,	,	PUNCT
ejpam-6212	265	2	u2t1	u2t1	VERB
ejpam-6212	265	3	]	]	PUNCT
ejpam-6212	265	4	and	and	CCONJ
ejpam-6212	265	5	c2t2	c2t2	NOUN
ejpam-6212	266	1	=	=	PUNCT
ejpam-6212	267	1	[	[	X
ejpam-6212	267	2	u1	u1	NOUN
ejpam-6212	267	3	=	=	SYM
ejpam-6212	267	4	v1	v1	NOUN
ejpam-6212	267	5	,	,	PUNCT
ejpam-6212	267	6	v2	v2	NOUN
ejpam-6212	267	7	,	,	PUNCT
ejpam-6212	267	8	.	.	PUNCT
ejpam-6212	267	9	.	.	PUNCT
ejpam-6212	267	10	.	.	PUNCT
ejpam-6212	268	1	,	,	PUNCT
ejpam-6212	268	2	v2t2	v2t2	X
ejpam-6212	268	3	]	]	X
ejpam-6212	268	4	,	,	PUNCT
ejpam-6212	268	5	for	for	ADP
ejpam-6212	268	6	some	some	DET
ejpam-6212	268	7	natural	natural	ADJ
ejpam-6212	268	8	numbers	number	NOUN
ejpam-6212	268	9	t1	t1	PROPN
ejpam-6212	268	10	,	,	PUNCT
ejpam-6212	268	11	t2	t2	NOUN
ejpam-6212	268	12	≥	≥	NUM
ejpam-6212	268	13	2	2	NUM
ejpam-6212	268	14	,	,	PUNCT
ejpam-6212	268	15	and	and	CCONJ
ejpam-6212	268	16	{	{	PUNCT
ejpam-6212	268	17	u1	u1	NOUN
ejpam-6212	268	18	=	=	SYM
ejpam-6212	268	19	v1	v1	PROPN
ejpam-6212	268	20	,	,	PUNCT
ejpam-6212	268	21	u2	u2	NOUN
ejpam-6212	268	22	,	,	PUNCT
ejpam-6212	268	23	.	.	PUNCT
ejpam-6212	268	24	.	.	PUNCT
ejpam-6212	268	25	.	.	PUNCT
ejpam-6212	269	1	,	,	PUNCT
ejpam-6212	269	2	u2t1	u2t1	INTJ
ejpam-6212	269	3	,	,	PUNCT
ejpam-6212	269	4	v2	v2	PROPN
ejpam-6212	269	5	,	,	PUNCT
ejpam-6212	269	6	v3	v3	PROPN
ejpam-6212	269	7	,	,	PUNCT
ejpam-6212	269	8	.	.	PUNCT
ejpam-6212	269	9	.	.	PUNCT
ejpam-6212	270	1	.	.	PUNCT
ejpam-6212	271	1	,	,	PUNCT
ejpam-6212	271	2	v2t2	v2t2	NOUN
ejpam-6212	271	3	}	}	PUNCT
ejpam-6212	271	4	is	be	AUX
ejpam-6212	271	5	the	the	DET
ejpam-6212	271	6	tree	tree	NOUN
ejpam-6212	271	7	-	-	PUNCT
ejpam-6212	271	8	partition	partition	NOUN
ejpam-6212	271	9	of	of	ADP
ejpam-6212	271	10	v	v	NOUN
ejpam-6212	271	11	(	(	PUNCT
ejpam-6212	271	12	g	g	NOUN
ejpam-6212	271	13	)	)	PUNCT
ejpam-6212	271	14	with	with	ADP
ejpam-6212	271	15	respect	respect	NOUN
ejpam-6212	271	16	to	to	ADP
ejpam-6212	271	17	the	the	DET
ejpam-6212	271	18	projection	projection	NOUN
ejpam-6212	271	19	of	of	ADP
ejpam-6212	271	20	v	v	NOUN
ejpam-6212	271	21	(	(	PUNCT
ejpam-6212	271	22	g	g	NOUN
ejpam-6212	271	23	)	)	PUNCT
ejpam-6212	271	24	onto	onto	ADP
ejpam-6212	271	25	the	the	DET
ejpam-6212	271	26	union	union	NOUN
ejpam-6212	271	27	of	of	ADP
ejpam-6212	271	28	cycles	cycle	NOUN
ejpam-6212	271	29	c2t1	c2t1	NOUN
ejpam-6212	271	30	and	and	CCONJ
ejpam-6212	271	31	c2t2	c2t2	NOUN
ejpam-6212	271	32	.	.	PUNCT
ejpam-6212	272	1	then	then	ADV
ejpam-6212	272	2	(	(	PUNCT
ejpam-6212	272	3	i	i	NOUN
ejpam-6212	272	4	)	)	PUNCT
ejpam-6212	272	5	α(u	α(u	PROPN
ejpam-6212	272	6	,	,	PUNCT
ejpam-6212	272	7	v	v	NOUN
ejpam-6212	272	8	)	)	PUNCT
ejpam-6212	272	9	=	=	SYM
ejpam-6212	272	10	2	2	NUM
ejpam-6212	272	11	if	if	SCONJ
ejpam-6212	272	12	u	u	PROPN
ejpam-6212	272	13	∈	∈	PROPN
ejpam-6212	272	14	ui	ui	NOUN
ejpam-6212	272	15	and	and	CCONJ
ejpam-6212	272	16	v	v	ADP
ejpam-6212	272	17	∈	∈	NOUN
ejpam-6212	272	18	ui+t1	ui+t1	NOUN
ejpam-6212	272	19	,	,	PUNCT
ejpam-6212	272	20	for	for	ADP
ejpam-6212	272	21	i	i	PRON
ejpam-6212	272	22	∈	∈	PROPN
ejpam-6212	272	23	{	{	PUNCT
ejpam-6212	272	24	1	1	NUM
ejpam-6212	272	25	,	,	PUNCT
ejpam-6212	272	26	2	2	NUM
ejpam-6212	272	27	,	,	PUNCT
ejpam-6212	272	28	.	.	PUNCT
ejpam-6212	272	29	.	.	PUNCT
ejpam-6212	272	30	.	.	PUNCT
ejpam-6212	273	1	,	,	PUNCT
ejpam-6212	273	2	t1	t1	NOUN
ejpam-6212	273	3	}	}	PUNCT
ejpam-6212	273	4	.	.	PUNCT
ejpam-6212	274	1	(	(	PUNCT
ejpam-6212	274	2	ii	ii	NOUN
ejpam-6212	274	3	)	)	PUNCT
ejpam-6212	274	4	α(u	α(u	PROPN
ejpam-6212	274	5	,	,	PUNCT
ejpam-6212	274	6	v	v	NOUN
ejpam-6212	274	7	)	)	PUNCT
ejpam-6212	274	8	=	=	SYM
ejpam-6212	274	9	2	2	NUM
ejpam-6212	274	10	if	if	SCONJ
ejpam-6212	274	11	u	u	PROPN
ejpam-6212	274	12	∈	∈	PROPN
ejpam-6212	274	13	vj	vj	X
ejpam-6212	274	14	and	and	CCONJ
ejpam-6212	274	15	v	v	ADP
ejpam-6212	274	16	∈	∈	PROPN
ejpam-6212	274	17	vj+t2	vj+t2	NOUN
ejpam-6212	274	18	,	,	PUNCT
ejpam-6212	274	19	for	for	ADP
ejpam-6212	274	20	j	j	PROPN
ejpam-6212	274	21	∈	∈	PROPN
ejpam-6212	274	22	{	{	PUNCT
ejpam-6212	274	23	1	1	NUM
ejpam-6212	274	24	,	,	PUNCT
ejpam-6212	274	25	2	2	NUM
ejpam-6212	274	26	,	,	PUNCT
ejpam-6212	274	27	.	.	PUNCT
ejpam-6212	274	28	.	.	PUNCT
ejpam-6212	274	29	.	.	PUNCT
ejpam-6212	275	1	,	,	PUNCT
ejpam-6212	275	2	t2	t2	NOUN
ejpam-6212	275	3	}	}	PUNCT
ejpam-6212	275	4	.	.	PUNCT
ejpam-6212	276	1	(	(	PUNCT
ejpam-6212	276	2	iii	iii	X
ejpam-6212	276	3	)	)	PUNCT
ejpam-6212	276	4	α(u	α(u	NOUN
ejpam-6212	276	5	,	,	PUNCT
ejpam-6212	276	6	v	v	NOUN
ejpam-6212	276	7	)	)	PUNCT
ejpam-6212	276	8	=	=	SYM
ejpam-6212	276	9	2	2	NUM
ejpam-6212	276	10	if	if	SCONJ
ejpam-6212	276	11	u	u	PROPN
ejpam-6212	276	12	∈	∈	PROPN
ejpam-6212	276	13	vt2	vt2	VERB
ejpam-6212	276	14	+	+	PROPN
ejpam-6212	276	15	1	1	NUM
ejpam-6212	276	16	and	and	CCONJ
ejpam-6212	276	17	v	v	ADP
ejpam-6212	276	18	∈	∈	PROPN
ejpam-6212	276	19	ui	ui	NOUN
ejpam-6212	276	20	,	,	PUNCT
ejpam-6212	276	21	for	for	ADP
ejpam-6212	276	22	i	i	PRON
ejpam-6212	276	23	∈	∈	PROPN
ejpam-6212	276	24	{	{	PUNCT
ejpam-6212	276	25	2	2	NUM
ejpam-6212	276	26	,	,	PUNCT
ejpam-6212	276	27	.	.	PUNCT
ejpam-6212	276	28	.	.	PUNCT
ejpam-6212	276	29	.	.	PUNCT
ejpam-6212	277	1	,	,	PUNCT
ejpam-6212	277	2	t1	t1	NOUN
ejpam-6212	277	3	}	}	PUNCT
ejpam-6212	277	4	.	.	PUNCT
ejpam-6212	278	1	(	(	PUNCT
ejpam-6212	278	2	iv	iv	X
ejpam-6212	278	3	)	)	PUNCT
ejpam-6212	278	4	α(u	α(u	NOUN
ejpam-6212	278	5	,	,	PUNCT
ejpam-6212	278	6	v	v	NOUN
ejpam-6212	278	7	)	)	PUNCT
ejpam-6212	278	8	=	=	SYM
ejpam-6212	278	9	2	2	NUM
ejpam-6212	278	10	if	if	SCONJ
ejpam-6212	278	11	u	u	NOUN
ejpam-6212	278	12	∈	∈	NOUN
ejpam-6212	278	13	ut1	ut1	VERB
ejpam-6212	278	14	+	+	NOUN
ejpam-6212	278	15	1	1	NUM
ejpam-6212	278	16	and	and	CCONJ
ejpam-6212	278	17	v	v	ADP
ejpam-6212	278	18	∈	∈	PROPN
ejpam-6212	278	19	vj	vj	NOUN
ejpam-6212	278	20	,	,	PUNCT
ejpam-6212	278	21	for	for	ADP
ejpam-6212	278	22	j	j	PROPN
ejpam-6212	278	23	∈	∈	PROPN
ejpam-6212	278	24	{	{	PUNCT
ejpam-6212	278	25	2	2	NUM
ejpam-6212	278	26	,	,	PUNCT
ejpam-6212	278	27	.	.	PUNCT
ejpam-6212	278	28	.	.	PUNCT
ejpam-6212	278	29	.	.	PUNCT
ejpam-6212	279	1	,	,	PUNCT
ejpam-6212	279	2	t2	t2	NOUN
ejpam-6212	279	3	}	}	PUNCT
ejpam-6212	279	4	.	.	PUNCT
ejpam-6212	280	1	(	(	PUNCT
ejpam-6212	280	2	v	v	NOUN
ejpam-6212	280	3	)	)	PUNCT
ejpam-6212	280	4	α(u	α(u	NOUN
ejpam-6212	280	5	,	,	PUNCT
ejpam-6212	280	6	v	v	NOUN
ejpam-6212	280	7	)	)	PUNCT
ejpam-6212	280	8	=	=	SYM
ejpam-6212	280	9	4	4	NUM
ejpam-6212	280	10	if	if	SCONJ
ejpam-6212	280	11	u	u	NOUN
ejpam-6212	280	12	∈	∈	NOUN
ejpam-6212	280	13	ut1	ut1	VERB
ejpam-6212	280	14	+	+	NOUN
ejpam-6212	280	15	1	1	NUM
ejpam-6212	280	16	and	and	CCONJ
ejpam-6212	280	17	v	v	ADP
ejpam-6212	280	18	∈	∈	PROPN
ejpam-6212	280	19	vt2	vt2	PROPN
ejpam-6212	280	20	+	+	PROPN
ejpam-6212	280	21	1	1	NUM
ejpam-6212	280	22	.	.	PUNCT
ejpam-6212	281	1	moreover	moreover	ADV
ejpam-6212	281	2	,	,	PUNCT
ejpam-6212	281	3	if	if	SCONJ
ejpam-6212	281	4	(	(	PUNCT
ejpam-6212	281	5	u	u	NOUN
ejpam-6212	281	6	,	,	PUNCT
ejpam-6212	281	7	v	v	NOUN
ejpam-6212	281	8	)	)	PUNCT
ejpam-6212	281	9	is	be	AUX
ejpam-6212	281	10	not	not	PART
ejpam-6212	281	11	in	in	ADP
ejpam-6212	281	12	the	the	DET
ejpam-6212	281	13	above	above	ADJ
ejpam-6212	281	14	categories	category	NOUN
ejpam-6212	281	15	,	,	PUNCT
ejpam-6212	281	16	then	then	ADV
ejpam-6212	281	17	α(u	α(u	PROPN
ejpam-6212	281	18	,	,	PUNCT
ejpam-6212	281	19	v	v	NOUN
ejpam-6212	281	20	)	)	PUNCT
ejpam-6212	281	21	=	=	SYM
ejpam-6212	281	22	1	1	X
ejpam-6212	281	23	.	.	PUNCT
ejpam-6212	282	1	proof	proof	NOUN
ejpam-6212	282	2	.	.	PUNCT
ejpam-6212	283	1	let	let	VERB
ejpam-6212	283	2	c2t1	c2t1	NOUN
ejpam-6212	283	3	=	=	PUNCT
ejpam-6212	284	1	[	[	X
ejpam-6212	284	2	u1	u1	NOUN
ejpam-6212	284	3	,	,	PUNCT
ejpam-6212	284	4	u2	u2	NOUN
ejpam-6212	284	5	,	,	PUNCT
ejpam-6212	284	6	.	.	PUNCT
ejpam-6212	284	7	.	.	PUNCT
ejpam-6212	284	8	.	.	PUNCT
ejpam-6212	285	1	,	,	PUNCT
ejpam-6212	285	2	u2t1	u2t1	VERB
ejpam-6212	285	3	]	]	PUNCT
ejpam-6212	285	4	and	and	CCONJ
ejpam-6212	285	5	c2t2	c2t2	NOUN
ejpam-6212	286	1	=	=	PUNCT
ejpam-6212	287	1	[	[	X
ejpam-6212	287	2	u1	u1	NOUN
ejpam-6212	287	3	=	=	SYM
ejpam-6212	287	4	v1	v1	NOUN
ejpam-6212	287	5	,	,	PUNCT
ejpam-6212	287	6	v2	v2	NOUN
ejpam-6212	287	7	,	,	PUNCT
ejpam-6212	287	8	.	.	PUNCT
ejpam-6212	287	9	.	.	PUNCT
ejpam-6212	287	10	.	.	PUNCT
ejpam-6212	288	1	,	,	PUNCT
ejpam-6212	288	2	v2t2	v2t2	X
ejpam-6212	288	3	]	]	PUNCT
ejpam-6212	288	4	be	be	AUX
ejpam-6212	288	5	the	the	DET
ejpam-6212	288	6	cycles	cycle	NOUN
ejpam-6212	288	7	in	in	ADP
ejpam-6212	288	8	g	g	NOUN
ejpam-6212	288	9	,	,	PUNCT
ejpam-6212	288	10	for	for	ADP
ejpam-6212	288	11	some	some	DET
ejpam-6212	288	12	natural	natural	ADJ
ejpam-6212	288	13	numbers	number	NOUN
ejpam-6212	288	14	t1	t1	PROPN
ejpam-6212	288	15	,	,	PUNCT
ejpam-6212	288	16	t2	t2	NOUN
ejpam-6212	288	17	≥	≥	NUM
ejpam-6212	288	18	2	2	NUM
ejpam-6212	288	19	,	,	PUNCT
ejpam-6212	288	20	and	and	CCONJ
ejpam-6212	288	21	{	{	PUNCT
ejpam-6212	288	22	u1	u1	NOUN
ejpam-6212	288	23	=	=	SYM
ejpam-6212	288	24	v1	v1	PROPN
ejpam-6212	288	25	,	,	PUNCT
ejpam-6212	288	26	u2	u2	NOUN
ejpam-6212	288	27	,	,	PUNCT
ejpam-6212	288	28	.	.	PUNCT
ejpam-6212	288	29	.	.	PUNCT
ejpam-6212	289	1	.	.	PUNCT
ejpam-6212	290	1	,	,	PUNCT
ejpam-6212	290	2	u2t1	u2t1	INTJ
ejpam-6212	290	3	,	,	PUNCT
ejpam-6212	290	4	v2	v2	PROPN
ejpam-6212	290	5	,	,	PUNCT
ejpam-6212	290	6	v3	v3	PROPN
ejpam-6212	290	7	,	,	PUNCT
ejpam-6212	290	8	.	.	PUNCT
ejpam-6212	290	9	.	.	PUNCT
ejpam-6212	291	1	.	.	PUNCT
ejpam-6212	292	1	,	,	PUNCT
ejpam-6212	292	2	v2t2	v2t2	NOUN
ejpam-6212	292	3	}	}	PUNCT
ejpam-6212	292	4	is	be	AUX
ejpam-6212	292	5	the	the	DET
ejpam-6212	292	6	tree	tree	NOUN
ejpam-6212	292	7	-	-	PUNCT
ejpam-6212	292	8	partition	partition	NOUN
ejpam-6212	292	9	of	of	ADP
ejpam-6212	292	10	v	v	NOUN
ejpam-6212	292	11	(	(	PUNCT
ejpam-6212	292	12	g	g	NOUN
ejpam-6212	292	13	)	)	PUNCT
ejpam-6212	292	14	with	with	ADP
ejpam-6212	292	15	respect	respect	NOUN
ejpam-6212	292	16	to	to	ADP
ejpam-6212	292	17	the	the	DET
ejpam-6212	292	18	projection	projection	NOUN
ejpam-6212	292	19	of	of	ADP
ejpam-6212	292	20	v	v	NOUN
ejpam-6212	292	21	(	(	PUNCT
ejpam-6212	292	22	g	g	NOUN
ejpam-6212	292	23	)	)	PUNCT
ejpam-6212	292	24	onto	onto	ADP
ejpam-6212	292	25	the	the	DET
ejpam-6212	292	26	union	union	NOUN
ejpam-6212	292	27	of	of	ADP
ejpam-6212	292	28	cycles	cycle	NOUN
ejpam-6212	292	29	c2t1	c2t1	NOUN
ejpam-6212	292	30	and	and	CCONJ
ejpam-6212	292	31	c2t2	c2t2	NOUN
ejpam-6212	292	32	.	.	PUNCT
ejpam-6212	293	1	(	(	PUNCT
ejpam-6212	293	2	i	i	NOUN
ejpam-6212	293	3	)	)	PUNCT
ejpam-6212	293	4	fix	fix	VERB
ejpam-6212	293	5	i	i	PRON
ejpam-6212	293	6	∈	∈	PROPN
ejpam-6212	293	7	{	{	PUNCT
ejpam-6212	293	8	1	1	NUM
ejpam-6212	293	9	,	,	PUNCT
ejpam-6212	293	10	2	2	NUM
ejpam-6212	293	11	,	,	PUNCT
ejpam-6212	293	12	.	.	PUNCT
ejpam-6212	293	13	.	.	PUNCT
ejpam-6212	294	1	.	.	PUNCT
ejpam-6212	295	1	,	,	PUNCT
ejpam-6212	295	2	t1	t1	NOUN
ejpam-6212	295	3	}	}	PUNCT
ejpam-6212	295	4	.	.	PUNCT
ejpam-6212	296	1	let	let	VERB
ejpam-6212	296	2	u	u	PRON
ejpam-6212	296	3	∈	∈	PROPN
ejpam-6212	296	4	ui	ui	NOUN
ejpam-6212	296	5	and	and	CCONJ
ejpam-6212	296	6	v	v	ADP
ejpam-6212	296	7	∈	∈	NOUN
ejpam-6212	296	8	ui+t1	ui+t1	NOUN
ejpam-6212	296	9	.	.	PUNCT
ejpam-6212	297	1	α(u	α(u	NOUN
ejpam-6212	297	2	,	,	PUNCT
ejpam-6212	297	3	v	v	NOUN
ejpam-6212	297	4	)	)	PUNCT
ejpam-6212	297	5	=	=	SYM
ejpam-6212	297	6	2	2	NUM
ejpam-6212	297	7	if	if	SCONJ
ejpam-6212	297	8	u	u	PROPN
ejpam-6212	297	9	∈	∈	PROPN
ejpam-6212	297	10	ui	ui	NOUN
ejpam-6212	297	11	and	and	CCONJ
ejpam-6212	297	12	v	v	ADP
ejpam-6212	297	13	∈	∈	NOUN
ejpam-6212	297	14	ui+t1	ui+t1	NOUN
ejpam-6212	297	15	.	.	PUNCT
ejpam-6212	298	1	then	then	ADV
ejpam-6212	298	2	there	there	PRON
ejpam-6212	298	3	exist	exist	VERB
ejpam-6212	298	4	ui	ui	NOUN
ejpam-6212	298	5	,	,	PUNCT
ejpam-6212	298	6	ui+t1	ui+t1	NOUN
ejpam-6212	298	7	in	in	ADP
ejpam-6212	298	8	c2t1	c2t1	NOUN
ejpam-6212	298	9	such	such	ADJ
ejpam-6212	298	10	that	that	DET
ejpam-6212	298	11	pc2t1∪c2t2	pc2t1∪c2t2	ADJ
ejpam-6212	298	12	(	(	PUNCT
ejpam-6212	298	13	u	u	NOUN
ejpam-6212	298	14	)	)	PUNCT
ejpam-6212	298	15	=	=	SYM
ejpam-6212	298	16	ui	ui	NOUN
ejpam-6212	298	17	and	and	CCONJ
ejpam-6212	298	18	pc2t1∪c2t2	pc2t1∪c2t2	ADJ
ejpam-6212	298	19	(	(	PUNCT
ejpam-6212	298	20	v	v	NOUN
ejpam-6212	298	21	)	)	PUNCT
ejpam-6212	298	22	=	=	NOUN
ejpam-6212	298	23	ui+t1	ui+t1	NOUN
ejpam-6212	298	24	.	.	PUNCT
ejpam-6212	299	1	note	note	VERB
ejpam-6212	299	2	that	that	SCONJ
ejpam-6212	299	3	there	there	PRON
ejpam-6212	299	4	are	be	VERB
ejpam-6212	299	5	exactly	exactly	ADV
ejpam-6212	299	6	2	2	NUM
ejpam-6212	299	7	geodesics	geodesic	NOUN
ejpam-6212	299	8	from	from	ADP
ejpam-6212	299	9	ui	ui	PROPN
ejpam-6212	299	10	to	to	ADP
ejpam-6212	299	11	ui+t1	ui+t1	NOUN
ejpam-6212	299	12	.	.	PUNCT
ejpam-6212	300	1	consequently	consequently	ADV
ejpam-6212	300	2	,	,	PUNCT
ejpam-6212	300	3	there	there	PRON
ejpam-6212	300	4	are	be	VERB
ejpam-6212	300	5	exactly	exactly	ADV
ejpam-6212	300	6	2	2	NUM
ejpam-6212	300	7	geodesics	geodesic	NOUN
ejpam-6212	300	8	from	from	ADP
ejpam-6212	300	9	u	u	PRON
ejpam-6212	300	10	to	to	ADP
ejpam-6212	300	11	v.	v.	NOUN
ejpam-6212	300	12	accordingly	accordingly	ADV
ejpam-6212	300	13	,	,	PUNCT
ejpam-6212	300	14	α(u	α(u	PROPN
ejpam-6212	300	15	,	,	PUNCT
ejpam-6212	300	16	v	v	NOUN
ejpam-6212	300	17	)	)	PUNCT
ejpam-6212	300	18	=	=	SYM
ejpam-6212	300	19	2	2	X
ejpam-6212	300	20	.	.	PUNCT
ejpam-6212	300	21	(	(	PUNCT
ejpam-6212	300	22	ii	ii	NOUN
ejpam-6212	300	23	)	)	PUNCT
ejpam-6212	300	24	the	the	DET
ejpam-6212	300	25	proof	proof	NOUN
ejpam-6212	300	26	is	be	AUX
ejpam-6212	300	27	similar	similar	ADJ
ejpam-6212	300	28	to	to	ADP
ejpam-6212	300	29	(	(	PUNCT
ejpam-6212	300	30	i	i	NOUN
ejpam-6212	300	31	)	)	PUNCT
ejpam-6212	300	32	.	.	PUNCT
ejpam-6212	301	1	(	(	PUNCT
ejpam-6212	301	2	iii	iii	X
ejpam-6212	301	3	)	)	PUNCT
ejpam-6212	301	4	note	note	NOUN
ejpam-6212	301	5	that	that	SCONJ
ejpam-6212	301	6	any	any	DET
ejpam-6212	301	7	geodesic	geodesic	NOUN
ejpam-6212	301	8	from	from	ADP
ejpam-6212	301	9	c2t2	c2t2	PROPN
ejpam-6212	301	10	to	to	ADP
ejpam-6212	301	11	c2t1	c2t1	NOUN
ejpam-6212	301	12	passes	pass	NOUN
ejpam-6212	301	13	through	through	ADP
ejpam-6212	301	14	v1	v1	NOUN
ejpam-6212	301	15	=	=	SYM
ejpam-6212	301	16	u1	u1	NOUN
ejpam-6212	301	17	.	.	PUNCT
ejpam-6212	302	1	here	here	ADV
ejpam-6212	302	2	,	,	PUNCT
ejpam-6212	302	3	there	there	PRON
ejpam-6212	302	4	are	be	VERB
ejpam-6212	302	5	exactly	exactly	ADV
ejpam-6212	302	6	2	2	NUM
ejpam-6212	302	7	geodesics	geodesic	NOUN
ejpam-6212	302	8	from	from	ADP
ejpam-6212	302	9	a	a	DET
ejpam-6212	302	10	vertex	vertex	NOUN
ejpam-6212	302	11	in	in	ADP
ejpam-6212	302	12	vt2	vt2	PROPN
ejpam-6212	302	13	+	+	PROPN
ejpam-6212	302	14	1	1	NUM
ejpam-6212	302	15	to	to	ADP
ejpam-6212	302	16	any	any	DET
ejpam-6212	302	17	vertex	vertex	NOUN
ejpam-6212	302	18	in	in	ADP
ejpam-6212	302	19	v1	v1	NOUN
ejpam-6212	302	20	=	=	SYM
ejpam-6212	302	21	u1	u1	NOUN
ejpam-6212	302	22	.	.	PUNCT
ejpam-6212	303	1	moreover	moreover	ADV
ejpam-6212	303	2	,	,	PUNCT
ejpam-6212	303	3	for	for	ADP
ejpam-6212	303	4	each	each	DET
ejpam-6212	303	5	i	i	PRON
ejpam-6212	303	6	∈	∈	PROPN
ejpam-6212	303	7	{	{	PUNCT
ejpam-6212	303	8	2	2	NUM
ejpam-6212	303	9	,	,	PUNCT
ejpam-6212	303	10	.	.	PUNCT
ejpam-6212	303	11	.	.	PUNCT
ejpam-6212	303	12	.	.	PUNCT
ejpam-6212	304	1	,	,	PUNCT
ejpam-6212	304	2	t1	t1	NOUN
ejpam-6212	304	3	}	}	PUNCT
ejpam-6212	304	4	,	,	PUNCT
ejpam-6212	304	5	there	there	PRON
ejpam-6212	304	6	is	be	VERB
ejpam-6212	304	7	only	only	ADV
ejpam-6212	304	8	one	one	NUM
ejpam-6212	304	9	shortest	short	ADJ
ejpam-6212	304	10	path	path	NOUN
ejpam-6212	304	11	from	from	ADP
ejpam-6212	304	12	a	a	DET
ejpam-6212	304	13	vertex	vertex	NOUN
ejpam-6212	304	14	in	in	ADP
ejpam-6212	304	15	u1	u1	NOUN
ejpam-6212	304	16	to	to	ADP
ejpam-6212	304	17	a	a	DET
ejpam-6212	304	18	vertex	vertex	NOUN
ejpam-6212	304	19	in	in	ADP
ejpam-6212	304	20	ui	ui	PROPN
ejpam-6212	304	21	.	.	PUNCT
ejpam-6212	305	1	consequently	consequently	ADV
ejpam-6212	305	2	,	,	PUNCT
ejpam-6212	305	3	if	if	SCONJ
ejpam-6212	305	4	u	u	PROPN
ejpam-6212	305	5	∈	∈	PROPN
ejpam-6212	305	6	vt2	vt2	VERB
ejpam-6212	305	7	+	+	PROPN
ejpam-6212	305	8	1	1	NUM
ejpam-6212	305	9	and	and	CCONJ
ejpam-6212	305	10	v	v	ADP
ejpam-6212	305	11	∈	∈	PROPN
ejpam-6212	305	12	ui	ui	NOUN
ejpam-6212	305	13	,	,	PUNCT
ejpam-6212	305	14	for	for	ADP
ejpam-6212	305	15	i	i	PRON
ejpam-6212	305	16	∈	∈	PROPN
ejpam-6212	305	17	{	{	PUNCT
ejpam-6212	305	18	2	2	NUM
ejpam-6212	305	19	,	,	PUNCT
ejpam-6212	305	20	.	.	PUNCT
ejpam-6212	305	21	.	.	PUNCT
ejpam-6212	305	22	.	.	PUNCT
ejpam-6212	306	1	,	,	PUNCT
ejpam-6212	306	2	t1	t1	NOUN
ejpam-6212	306	3	}	}	PUNCT
ejpam-6212	306	4	,	,	PUNCT
ejpam-6212	306	5	then	then	ADV
ejpam-6212	306	6	α(u	α(u	PROPN
ejpam-6212	306	7	,	,	PUNCT
ejpam-6212	306	8	v	v	NOUN
ejpam-6212	306	9	)	)	PUNCT
ejpam-6212	307	1	=	=	SYM
ejpam-6212	307	2	2	2	X
ejpam-6212	307	3	.	.	PUNCT
ejpam-6212	307	4	r.	r.	PROPN
ejpam-6212	307	5	g.	g.	PROPN
ejpam-6212	307	6	artes	artes	PROPN
ejpam-6212	307	7	jr	jr	PROPN
ejpam-6212	307	8	.	.	PROPN
ejpam-6212	307	9	et	et	PROPN
ejpam-6212	307	10	al	al	PROPN
ejpam-6212	307	11	.	.	PUNCT
ejpam-6212	307	12	/	/	SYM
ejpam-6212	307	13	eur	eur	PROPN
ejpam-6212	307	14	.	.	PUNCT
ejpam-6212	308	1	j.	j.	PROPN
ejpam-6212	308	2	pure	pure	PROPN
ejpam-6212	308	3	appl	appl	PROPN
ejpam-6212	308	4	.	.	PROPN
ejpam-6212	308	5	math	math	PROPN
ejpam-6212	308	6	,	,	PUNCT
ejpam-6212	308	7	18	18	NUM
ejpam-6212	308	8	(	(	PUNCT
ejpam-6212	308	9	4	4	NUM
ejpam-6212	308	10	)	)	PUNCT
ejpam-6212	308	11	(	(	PUNCT
ejpam-6212	308	12	2025	2025	NUM
ejpam-6212	308	13	)	)	PUNCT
ejpam-6212	308	14	,	,	PUNCT
ejpam-6212	308	15	6212	6212	NUM
ejpam-6212	308	16	7	7	NUM
ejpam-6212	308	17	of	of	ADP
ejpam-6212	308	18	20	20	NUM
ejpam-6212	308	19	(	(	PUNCT
ejpam-6212	308	20	iv	iv	NOUN
ejpam-6212	308	21	)	)	PUNCT
ejpam-6212	308	22	similar	similar	ADJ
ejpam-6212	308	23	arguments	argument	NOUN
ejpam-6212	308	24	with	with	ADP
ejpam-6212	308	25	(	(	PUNCT
ejpam-6212	308	26	iii	iii	NOUN
ejpam-6212	308	27	)	)	PUNCT
ejpam-6212	308	28	gives	give	VERB
ejpam-6212	308	29	the	the	DET
ejpam-6212	308	30	desired	desire	VERB
ejpam-6212	308	31	result	result	NOUN
ejpam-6212	308	32	.	.	PUNCT
ejpam-6212	309	1	(	(	PUNCT
ejpam-6212	309	2	v	v	NOUN
ejpam-6212	309	3	)	)	PUNCT
ejpam-6212	309	4	let	let	VERB
ejpam-6212	309	5	u	u	PRON
ejpam-6212	309	6	∈	∈	NOUN
ejpam-6212	309	7	ut1	ut1	VERB
ejpam-6212	309	8	+	+	NOUN
ejpam-6212	309	9	1	1	NUM
ejpam-6212	309	10	and	and	CCONJ
ejpam-6212	309	11	v	v	ADP
ejpam-6212	309	12	∈	∈	PROPN
ejpam-6212	309	13	vt2	vt2	PROPN
ejpam-6212	310	1	+	+	PROPN
ejpam-6212	310	2	1	1	NUM
ejpam-6212	310	3	.	.	PUNCT
ejpam-6212	311	1	then	then	ADV
ejpam-6212	311	2	any	any	DET
ejpam-6212	311	3	geodesic	geodesic	NOUN
ejpam-6212	311	4	from	from	ADP
ejpam-6212	311	5	u	u	PRON
ejpam-6212	311	6	to	to	ADP
ejpam-6212	311	7	v	v	NOUN
ejpam-6212	311	8	passes	pass	NOUN
ejpam-6212	311	9	through	through	ADP
ejpam-6212	311	10	u1	u1	NOUN
ejpam-6212	311	11	=	=	SYM
ejpam-6212	311	12	v1	v1	PROPN
ejpam-6212	311	13	.	.	PUNCT
ejpam-6212	312	1	from	from	ADP
ejpam-6212	312	2	(	(	PUNCT
ejpam-6212	312	3	i	i	NOUN
ejpam-6212	312	4	)	)	PUNCT
ejpam-6212	312	5	,	,	PUNCT
ejpam-6212	312	6	there	there	PRON
ejpam-6212	312	7	are	be	VERB
ejpam-6212	312	8	exactly	exactly	ADV
ejpam-6212	312	9	2	2	NUM
ejpam-6212	312	10	geodesics	geodesic	NOUN
ejpam-6212	312	11	from	from	ADP
ejpam-6212	312	12	u	u	PRON
ejpam-6212	312	13	to	to	PART
ejpam-6212	312	14	u1	u1	VERB
ejpam-6212	312	15	.	.	PUNCT
ejpam-6212	313	1	similarly	similarly	ADV
ejpam-6212	313	2	,	,	PUNCT
ejpam-6212	313	3	from	from	ADP
ejpam-6212	313	4	(	(	PUNCT
ejpam-6212	313	5	ii	ii	NOUN
ejpam-6212	313	6	)	)	PUNCT
ejpam-6212	313	7	,	,	PUNCT
ejpam-6212	313	8	there	there	PRON
ejpam-6212	313	9	are	be	VERB
ejpam-6212	313	10	exactly	exactly	ADV
ejpam-6212	313	11	2	2	NUM
ejpam-6212	313	12	geodesics	geodesic	NOUN
ejpam-6212	313	13	from	from	ADP
ejpam-6212	313	14	v	v	NUM
ejpam-6212	313	15	to	to	AUX
ejpam-6212	313	16	v1	v1	VERB
ejpam-6212	313	17	.	.	PUNCT
ejpam-6212	314	1	accordingly	accordingly	ADV
ejpam-6212	314	2	,	,	PUNCT
ejpam-6212	314	3	α(u	α(u	PROPN
ejpam-6212	314	4	,	,	PUNCT
ejpam-6212	314	5	v	v	NOUN
ejpam-6212	314	6	)	)	PUNCT
ejpam-6212	314	7	=	=	SYM
ejpam-6212	314	8	4	4	X
ejpam-6212	314	9	.	.	PUNCT
ejpam-6212	314	10	the	the	DET
ejpam-6212	314	11	following	following	NOUN
ejpam-6212	314	12	gives	give	VERB
ejpam-6212	314	13	the	the	DET
ejpam-6212	314	14	exact	exact	ADJ
ejpam-6212	314	15	relation	relation	NOUN
ejpam-6212	314	16	between	between	ADP
ejpam-6212	314	17	g	g	NOUN
ejpam-6212	314	18	-	-	PUNCT
ejpam-6212	314	19	wiener	wiener	NOUN
ejpam-6212	314	20	and	and	CCONJ
ejpam-6212	314	21	wiener	wiener	NOUN
ejpam-6212	314	22	indices	index	NOUN
ejpam-6212	314	23	.	.	PUNCT
ejpam-6212	315	1	lemma	lemma	PROPN
ejpam-6212	315	2	2	2	X
ejpam-6212	315	3	.	.	PUNCT
ejpam-6212	316	1	let	let	VERB
ejpam-6212	316	2	g	g	PRON
ejpam-6212	316	3	be	be	AUX
ejpam-6212	316	4	a	a	DET
ejpam-6212	316	5	simple	simple	ADJ
ejpam-6212	316	6	spirocyclic	spirocyclic	NOUN
ejpam-6212	316	7	graph	graph	NOUN
ejpam-6212	316	8	with	with	ADP
ejpam-6212	316	9	even	even	ADV
ejpam-6212	316	10	cycles	cycle	NOUN
ejpam-6212	316	11	c2t1	c2t1	NOUN
ejpam-6212	317	1	=	=	SYM
ejpam-6212	318	1	[	[	X
ejpam-6212	318	2	u1	u1	NOUN
ejpam-6212	318	3	,	,	PUNCT
ejpam-6212	318	4	u2	u2	NOUN
ejpam-6212	318	5	,	,	PUNCT
ejpam-6212	318	6	.	.	PUNCT
ejpam-6212	318	7	.	.	PUNCT
ejpam-6212	318	8	.	.	PUNCT
ejpam-6212	319	1	,	,	PUNCT
ejpam-6212	319	2	u2t1	u2t1	VERB
ejpam-6212	319	3	]	]	PUNCT
ejpam-6212	319	4	and	and	CCONJ
ejpam-6212	319	5	c2t2	c2t2	NOUN
ejpam-6212	320	1	=	=	PUNCT
ejpam-6212	321	1	[	[	X
ejpam-6212	321	2	u1	u1	NOUN
ejpam-6212	321	3	=	=	SYM
ejpam-6212	321	4	v1	v1	NOUN
ejpam-6212	321	5	,	,	PUNCT
ejpam-6212	321	6	v2	v2	NOUN
ejpam-6212	321	7	,	,	PUNCT
ejpam-6212	321	8	.	.	PUNCT
ejpam-6212	321	9	.	.	PUNCT
ejpam-6212	321	10	.	.	PUNCT
ejpam-6212	322	1	,	,	PUNCT
ejpam-6212	322	2	v2t2	v2t2	X
ejpam-6212	322	3	]	]	X
ejpam-6212	322	4	,	,	PUNCT
ejpam-6212	322	5	for	for	ADP
ejpam-6212	322	6	some	some	DET
ejpam-6212	322	7	natural	natural	ADJ
ejpam-6212	322	8	numbers	number	NOUN
ejpam-6212	322	9	t1	t1	PROPN
ejpam-6212	322	10	,	,	PUNCT
ejpam-6212	322	11	t2	t2	NOUN
ejpam-6212	322	12	≥	≥	NUM
ejpam-6212	322	13	2	2	NUM
ejpam-6212	322	14	.	.	PUNCT
ejpam-6212	322	15	then	then	ADV
ejpam-6212	322	16	wg(g	wg(g	NUM
ejpam-6212	322	17	)	)	PUNCT
ejpam-6212	323	1	=	=	SYM
ejpam-6212	323	2	w	w	PROPN
ejpam-6212	323	3	(	(	PUNCT
ejpam-6212	323	4	g	g	NOUN
ejpam-6212	323	5	)	)	PUNCT
ejpam-6212	324	1	+	+	CCONJ
ejpam-6212	324	2	t1∑	t1∑	PROPN
ejpam-6212	324	3	i=1	i=1	PROPN
ejpam-6212	324	4	w	w	PROPN
ejpam-6212	324	5	(	(	PUNCT
ejpam-6212	324	6	ui	ui	PROPN
ejpam-6212	324	7	,	,	PUNCT
ejpam-6212	324	8	ui+t1	ui+t1	ADV
ejpam-6212	324	9	;	;	PUNCT
ejpam-6212	324	10	g	g	NOUN
ejpam-6212	324	11	)	)	PUNCT
ejpam-6212	325	1	+	+	PUNCT
ejpam-6212	325	2	t2∑	t2∑	PROPN
ejpam-6212	325	3	j=1	j=1	NOUN
ejpam-6212	325	4	w	w	PROPN
ejpam-6212	325	5	(	(	PUNCT
ejpam-6212	325	6	vj	vj	INTJ
ejpam-6212	325	7	,	,	PUNCT
ejpam-6212	325	8	vj+t2	vj+t2	NOUN
ejpam-6212	325	9	;	;	PUNCT
ejpam-6212	325	10	g	g	X
ejpam-6212	325	11	)	)	PUNCT
ejpam-6212	326	1	+	+	NUM
ejpam-6212	326	2	2t1∑	2t1∑	NUM
ejpam-6212	326	3	i=2	i=2	PROPN
ejpam-6212	326	4	w	w	PROPN
ejpam-6212	326	5	(	(	PUNCT
ejpam-6212	326	6	vt2	vt2	PROPN
ejpam-6212	326	7	+	+	PROPN
ejpam-6212	326	8	1	1	NUM
ejpam-6212	326	9	,	,	PUNCT
ejpam-6212	326	10	ui;g	ui;g	ADJ
ejpam-6212	326	11	)	)	PUNCT
ejpam-6212	327	1	+	+	NUM
ejpam-6212	327	2	2t2∑	2t2∑	NUM
ejpam-6212	327	3	j=2	j=2	PROPN
ejpam-6212	327	4	w	w	NOUN
ejpam-6212	327	5	(	(	PUNCT
ejpam-6212	327	6	ut1	ut1	PROPN
ejpam-6212	327	7	+	+	ADJ
ejpam-6212	327	8	1	1	NUM
ejpam-6212	327	9	,	,	PUNCT
ejpam-6212	327	10	vj	vj	INTJ
ejpam-6212	327	11	;	;	PUNCT
ejpam-6212	327	12	g	g	X
ejpam-6212	327	13	)	)	PUNCT
ejpam-6212	328	1	+	+	NOUN
ejpam-6212	328	2	w	w	NOUN
ejpam-6212	328	3	(	(	PUNCT
ejpam-6212	328	4	ut1	ut1	PROPN
ejpam-6212	328	5	+	+	NOUN
ejpam-6212	328	6	1	1	NUM
ejpam-6212	328	7	,	,	PUNCT
ejpam-6212	328	8	vt2	vt2	VERB
ejpam-6212	328	9	+	+	NOUN
ejpam-6212	328	10	1;g	1;g	NUM
ejpam-6212	328	11	)	)	PUNCT
ejpam-6212	328	12	.	.	PUNCT
ejpam-6212	329	1	where	where	SCONJ
ejpam-6212	329	2	{	{	PUNCT
ejpam-6212	329	3	u1	u1	NOUN
ejpam-6212	329	4	=	=	SYM
ejpam-6212	329	5	v1	v1	PROPN
ejpam-6212	329	6	,	,	PUNCT
ejpam-6212	329	7	u2	u2	NOUN
ejpam-6212	329	8	,	,	PUNCT
ejpam-6212	329	9	.	.	PUNCT
ejpam-6212	329	10	.	.	PUNCT
ejpam-6212	329	11	.	.	PUNCT
ejpam-6212	330	1	,	,	PUNCT
ejpam-6212	330	2	u2t1	u2t1	INTJ
ejpam-6212	330	3	,	,	PUNCT
ejpam-6212	330	4	v2	v2	PROPN
ejpam-6212	330	5	,	,	PUNCT
ejpam-6212	330	6	.	.	PUNCT
ejpam-6212	330	7	.	.	PUNCT
ejpam-6212	331	1	.	.	PUNCT
ejpam-6212	332	1	,	,	PUNCT
ejpam-6212	332	2	v2t2	v2t2	NOUN
ejpam-6212	332	3	}	}	PUNCT
ejpam-6212	332	4	is	be	AUX
ejpam-6212	332	5	the	the	DET
ejpam-6212	332	6	tree	tree	NOUN
ejpam-6212	332	7	-	-	PUNCT
ejpam-6212	332	8	partition	partition	NOUN
ejpam-6212	332	9	of	of	ADP
ejpam-6212	332	10	v	v	NOUN
ejpam-6212	332	11	(	(	PUNCT
ejpam-6212	332	12	g	g	NOUN
ejpam-6212	332	13	)	)	PUNCT
ejpam-6212	332	14	with	with	ADP
ejpam-6212	332	15	respect	respect	NOUN
ejpam-6212	332	16	to	to	ADP
ejpam-6212	332	17	the	the	DET
ejpam-6212	332	18	projection	projection	NOUN
ejpam-6212	332	19	of	of	ADP
ejpam-6212	332	20	v	v	NOUN
ejpam-6212	332	21	(	(	PUNCT
ejpam-6212	332	22	g	g	NOUN
ejpam-6212	332	23	)	)	PUNCT
ejpam-6212	332	24	onto	onto	ADP
ejpam-6212	332	25	the	the	DET
ejpam-6212	332	26	union	union	NOUN
ejpam-6212	332	27	of	of	ADP
ejpam-6212	332	28	the	the	DET
ejpam-6212	332	29	cycles	cycle	NOUN
ejpam-6212	332	30	c2t1	c2t1	NOUN
ejpam-6212	332	31	and	and	CCONJ
ejpam-6212	332	32	c2t2	c2t2	NOUN
ejpam-6212	332	33	.	.	PUNCT
ejpam-6212	333	1	proof	proof	NOUN
ejpam-6212	333	2	.	.	PUNCT
ejpam-6212	334	1	the	the	DET
ejpam-6212	334	2	geodesics	geodesic	NOUN
ejpam-6212	334	3	in	in	ADP
ejpam-6212	334	4	lemma	lemma	PROPN
ejpam-6212	334	5	1(i	1(i	NUM
ejpam-6212	334	6	)	)	PUNCT
ejpam-6212	334	7	are	be	AUX
ejpam-6212	334	8	covered	cover	VERB
ejpam-6212	334	9	in	in	ADP
ejpam-6212	334	10	the	the	DET
ejpam-6212	334	11	first	first	ADJ
ejpam-6212	334	12	and	and	CCONJ
ejpam-6212	334	13	the	the	DET
ejpam-6212	334	14	second	second	ADJ
ejpam-6212	334	15	quantities	quantity	NOUN
ejpam-6212	334	16	.	.	PUNCT
ejpam-6212	335	1	similarly	similarly	ADV
ejpam-6212	335	2	,	,	PUNCT
ejpam-6212	335	3	the	the	DET
ejpam-6212	335	4	geodesics	geodesic	NOUN
ejpam-6212	335	5	in	in	ADP
ejpam-6212	335	6	lemma	lemma	PROPN
ejpam-6212	335	7	1(ii	1(ii	NUM
ejpam-6212	335	8	)	)	PUNCT
ejpam-6212	335	9	are	be	AUX
ejpam-6212	335	10	covered	cover	VERB
ejpam-6212	335	11	in	in	ADP
ejpam-6212	335	12	the	the	DET
ejpam-6212	335	13	first	first	ADJ
ejpam-6212	335	14	and	and	CCONJ
ejpam-6212	335	15	the	the	DET
ejpam-6212	335	16	third	third	ADJ
ejpam-6212	335	17	quantities	quantity	NOUN
ejpam-6212	335	18	.	.	PUNCT
ejpam-6212	336	1	lemma	lemma	PROPN
ejpam-6212	336	2	1(iii	1(iii	NUM
ejpam-6212	336	3	)	)	PUNCT
ejpam-6212	336	4	gives	give	VERB
ejpam-6212	336	5	the	the	DET
ejpam-6212	336	6	fourth	fourth	ADJ
ejpam-6212	336	7	and	and	CCONJ
ejpam-6212	336	8	first	first	ADJ
ejpam-6212	336	9	quantities	quantity	NOUN
ejpam-6212	336	10	.	.	PUNCT
ejpam-6212	337	1	similarly	similarly	ADV
ejpam-6212	337	2	,	,	PUNCT
ejpam-6212	337	3	lemma	lemma	PROPN
ejpam-6212	337	4	1(iv	1(iv	NUM
ejpam-6212	337	5	)	)	PUNCT
ejpam-6212	337	6	are	be	AUX
ejpam-6212	337	7	covered	cover	VERB
ejpam-6212	337	8	in	in	ADP
ejpam-6212	337	9	the	the	DET
ejpam-6212	337	10	fifth	fifth	ADJ
ejpam-6212	337	11	and	and	CCONJ
ejpam-6212	337	12	the	the	DET
ejpam-6212	337	13	first	first	ADJ
ejpam-6212	337	14	quantities	quantity	NOUN
ejpam-6212	337	15	.	.	PUNCT
ejpam-6212	338	1	the	the	DET
ejpam-6212	338	2	4	4	NUM
ejpam-6212	338	3	geodesics	geodesic	NOUN
ejpam-6212	338	4	in	in	ADP
ejpam-6212	338	5	lemma	lemma	PROPN
ejpam-6212	338	6	1(v	1(v	NUM
ejpam-6212	338	7	)	)	PUNCT
ejpam-6212	338	8	are	be	AUX
ejpam-6212	338	9	covered	cover	VERB
ejpam-6212	338	10	in	in	ADP
ejpam-6212	338	11	the	the	DET
ejpam-6212	338	12	sixth	sixth	ADJ
ejpam-6212	338	13	,	,	PUNCT
ejpam-6212	338	14	first	first	ADJ
ejpam-6212	338	15	,	,	PUNCT
ejpam-6212	338	16	fourth	fourth	ADJ
ejpam-6212	338	17	,	,	PUNCT
ejpam-6212	338	18	and	and	CCONJ
ejpam-6212	338	19	fifth	fifth	ADJ
ejpam-6212	338	20	quantities	quantity	NOUN
ejpam-6212	338	21	.	.	PUNCT
ejpam-6212	339	1	the	the	DET
ejpam-6212	339	2	result	result	NOUN
ejpam-6212	339	3	follows	follow	VERB
ejpam-6212	339	4	.	.	PUNCT
ejpam-6212	340	1	5	5	X
ejpam-6212	340	2	.	.	NUM
ejpam-6212	340	3	bounds	bound	NOUN
ejpam-6212	340	4	of	of	ADP
ejpam-6212	340	5	g	g	NOUN
ejpam-6212	340	6	-	-	PUNCT
ejpam-6212	340	7	wiener	wiener	NOUN
ejpam-6212	340	8	index	index	NOUN
ejpam-6212	340	9	with	with	ADP
ejpam-6212	340	10	wiener	wiener	NOUN
ejpam-6212	340	11	index	index	NOUN
ejpam-6212	340	12	the	the	DET
ejpam-6212	340	13	following	follow	VERB
ejpam-6212	340	14	result	result	NOUN
ejpam-6212	340	15	establishes	establish	VERB
ejpam-6212	340	16	relation	relation	NOUN
ejpam-6212	340	17	between	between	ADP
ejpam-6212	340	18	g	g	NOUN
ejpam-6212	340	19	-	-	PUNCT
ejpam-6212	340	20	wiener	wiener	NOUN
ejpam-6212	340	21	index	index	NOUN
ejpam-6212	340	22	and	and	CCONJ
ejpam-6212	340	23	wiener	wiener	NOUN
ejpam-6212	340	24	index	index	NOUN
ejpam-6212	340	25	as	as	SCONJ
ejpam-6212	340	26	defined	define	VERB
ejpam-6212	340	27	in	in	ADP
ejpam-6212	340	28	[	[	X
ejpam-6212	340	29	2	2	NUM
ejpam-6212	340	30	]	]	PUNCT
ejpam-6212	340	31	for	for	ADP
ejpam-6212	340	32	simple	simple	ADJ
ejpam-6212	340	33	spirocyclic	spirocyclic	NOUN
ejpam-6212	340	34	graphs	graph	NOUN
ejpam-6212	340	35	.	.	PUNCT
ejpam-6212	341	1	theorem	theorem	NOUN
ejpam-6212	341	2	1	1	NUM
ejpam-6212	341	3	.	.	PUNCT
ejpam-6212	342	1	let	let	VERB
ejpam-6212	342	2	g	g	PRON
ejpam-6212	342	3	be	be	AUX
ejpam-6212	342	4	a	a	DET
ejpam-6212	342	5	simple	simple	ADJ
ejpam-6212	342	6	spirocyclic	spirocyclic	NOUN
ejpam-6212	342	7	graph	graph	NOUN
ejpam-6212	342	8	with	with	ADP
ejpam-6212	342	9	even	even	ADV
ejpam-6212	342	10	cycles	cycle	NOUN
ejpam-6212	342	11	c2t1	c2t1	NOUN
ejpam-6212	343	1	=	=	SYM
ejpam-6212	344	1	[	[	X
ejpam-6212	344	2	u1	u1	NOUN
ejpam-6212	344	3	,	,	PUNCT
ejpam-6212	344	4	u2	u2	NOUN
ejpam-6212	344	5	,	,	PUNCT
ejpam-6212	344	6	.	.	PUNCT
ejpam-6212	344	7	.	.	PUNCT
ejpam-6212	344	8	.	.	PUNCT
ejpam-6212	345	1	,	,	PUNCT
ejpam-6212	345	2	u2t1	u2t1	VERB
ejpam-6212	345	3	]	]	PUNCT
ejpam-6212	345	4	and	and	CCONJ
ejpam-6212	345	5	c2t2	c2t2	NOUN
ejpam-6212	346	1	=	=	PUNCT
ejpam-6212	347	1	[	[	X
ejpam-6212	347	2	u1	u1	NOUN
ejpam-6212	347	3	=	=	SYM
ejpam-6212	347	4	v1	v1	NOUN
ejpam-6212	347	5	,	,	PUNCT
ejpam-6212	347	6	v2	v2	NOUN
ejpam-6212	347	7	,	,	PUNCT
ejpam-6212	347	8	.	.	PUNCT
ejpam-6212	347	9	.	.	PUNCT
ejpam-6212	347	10	.	.	PUNCT
ejpam-6212	348	1	,	,	PUNCT
ejpam-6212	348	2	v2t2	v2t2	X
ejpam-6212	348	3	]	]	X
ejpam-6212	348	4	,	,	PUNCT
ejpam-6212	348	5	for	for	ADP
ejpam-6212	348	6	some	some	DET
ejpam-6212	348	7	natural	natural	ADJ
ejpam-6212	348	8	numbers	number	NOUN
ejpam-6212	348	9	t1	t1	PROPN
ejpam-6212	348	10	,	,	PUNCT
ejpam-6212	348	11	t2	t2	NOUN
ejpam-6212	348	12	≥	≥	NUM
ejpam-6212	348	13	2	2	NUM
ejpam-6212	348	14	.	.	PUNCT
ejpam-6212	349	1	then	then	ADV
ejpam-6212	349	2	w	w	PROPN
ejpam-6212	349	3	(	(	PUNCT
ejpam-6212	349	4	g	g	NOUN
ejpam-6212	349	5	)	)	PUNCT
ejpam-6212	350	1	+	+	NOUN
ejpam-6212	350	2	at1	at1	PROPN
ejpam-6212	350	3	+	+	PROPN
ejpam-6212	350	4	bt2	bt2	PROPN
ejpam-6212	350	5	≤	≤	NOUN
ejpam-6212	350	6	wg(g	wg(g	NOUN
ejpam-6212	350	7	)	)	PUNCT
ejpam-6212	350	8	≤	≤	NUM
ejpam-6212	350	9	w	w	ADP
ejpam-6212	350	10	(	(	PUNCT
ejpam-6212	350	11	g	g	NOUN
ejpam-6212	350	12	)	)	PUNCT
ejpam-6212	350	13	+	+	CCONJ
ejpam-6212	350	14	cdiam(g	cdiam(g	X
ejpam-6212	350	15	)	)	PUNCT
ejpam-6212	350	16	,	,	PUNCT
ejpam-6212	350	17	where	where	SCONJ
ejpam-6212	350	18	{	{	PUNCT
ejpam-6212	350	19	u1	u1	NOUN
ejpam-6212	350	20	=	=	SYM
ejpam-6212	350	21	v1	v1	PROPN
ejpam-6212	350	22	,	,	PUNCT
ejpam-6212	350	23	u2	u2	NOUN
ejpam-6212	350	24	,	,	PUNCT
ejpam-6212	350	25	.	.	PUNCT
ejpam-6212	350	26	.	.	PUNCT
ejpam-6212	350	27	.	.	PUNCT
ejpam-6212	351	1	,	,	PUNCT
ejpam-6212	351	2	u2t1	u2t1	INTJ
ejpam-6212	351	3	,	,	PUNCT
ejpam-6212	351	4	v2	v2	PROPN
ejpam-6212	351	5	,	,	PUNCT
ejpam-6212	351	6	.	.	PUNCT
ejpam-6212	351	7	.	.	PUNCT
ejpam-6212	352	1	.	.	PUNCT
ejpam-6212	353	1	,	,	PUNCT
ejpam-6212	353	2	v2t2	v2t2	NOUN
ejpam-6212	353	3	}	}	PUNCT
ejpam-6212	353	4	is	be	AUX
ejpam-6212	353	5	the	the	DET
ejpam-6212	353	6	tree	tree	NOUN
ejpam-6212	353	7	-	-	PUNCT
ejpam-6212	353	8	partition	partition	NOUN
ejpam-6212	353	9	of	of	ADP
ejpam-6212	353	10	v	v	NOUN
ejpam-6212	353	11	(	(	PUNCT
ejpam-6212	353	12	g	g	NOUN
ejpam-6212	353	13	)	)	PUNCT
ejpam-6212	353	14	with	with	ADP
ejpam-6212	353	15	respect	respect	NOUN
ejpam-6212	353	16	to	to	ADP
ejpam-6212	353	17	the	the	DET
ejpam-6212	353	18	projection	projection	NOUN
ejpam-6212	353	19	of	of	ADP
ejpam-6212	353	20	v	v	NOUN
ejpam-6212	353	21	(	(	PUNCT
ejpam-6212	353	22	g	g	NOUN
ejpam-6212	353	23	)	)	PUNCT
ejpam-6212	353	24	onto	onto	ADP
ejpam-6212	353	25	the	the	DET
ejpam-6212	353	26	union	union	NOUN
ejpam-6212	353	27	of	of	ADP
ejpam-6212	353	28	the	the	DET
ejpam-6212	353	29	cycles	cycle	NOUN
ejpam-6212	353	30	c2t1	c2t1	NOUN
ejpam-6212	353	31	and	and	CCONJ
ejpam-6212	353	32	c2t2	c2t2	NOUN
ejpam-6212	353	33	,	,	PUNCT
ejpam-6212	353	34	and	and	CCONJ
ejpam-6212	354	1	a	a	DET
ejpam-6212	354	2	=	=	X
ejpam-6212	354	3	t1∑	t1∑	PROPN
ejpam-6212	354	4	i=1	i=1	PROPN
ejpam-6212	354	5	|ui||ui+t1	|ui||ui+t1	ADP
ejpam-6212	354	6	|+	|+	NOUN
ejpam-6212	354	7	2t2∑	2t2∑	NUM
ejpam-6212	354	8	j=2	j=2	NOUN
ejpam-6212	354	9	|ut1	|ut1	PUNCT
ejpam-6212	354	10	+	+	NOUN
ejpam-6212	354	11	1||vj	1||vj	NOUN
ejpam-6212	354	12	|+	|+	X
ejpam-6212	354	13	|ut1	|ut1	PUNCT
ejpam-6212	354	14	+	+	NOUN
ejpam-6212	354	15	1||vt2	1||vt2	NUM
ejpam-6212	354	16	+	+	NOUN
ejpam-6212	354	17	1|	1|	NUM
ejpam-6212	354	18	,	,	PUNCT
ejpam-6212	354	19	r.	r.	PROPN
ejpam-6212	354	20	g.	g.	PROPN
ejpam-6212	354	21	artes	artes	PROPN
ejpam-6212	354	22	jr	jr	PROPN
ejpam-6212	354	23	.	.	PROPN
ejpam-6212	354	24	et	et	PROPN
ejpam-6212	354	25	al	al	PROPN
ejpam-6212	354	26	.	.	PUNCT
ejpam-6212	354	27	/	/	SYM
ejpam-6212	354	28	eur	eur	PROPN
ejpam-6212	354	29	.	.	PUNCT
ejpam-6212	355	1	j.	j.	PROPN
ejpam-6212	355	2	pure	pure	PROPN
ejpam-6212	355	3	appl	appl	PROPN
ejpam-6212	355	4	.	.	PROPN
ejpam-6212	355	5	math	math	PROPN
ejpam-6212	355	6	,	,	PUNCT
ejpam-6212	355	7	18	18	NUM
ejpam-6212	355	8	(	(	PUNCT
ejpam-6212	355	9	4	4	NUM
ejpam-6212	355	10	)	)	PUNCT
ejpam-6212	355	11	(	(	PUNCT
ejpam-6212	355	12	2025	2025	NUM
ejpam-6212	355	13	)	)	PUNCT
ejpam-6212	355	14	,	,	PUNCT
ejpam-6212	355	15	6212	6212	NUM
ejpam-6212	355	16	8	8	NUM
ejpam-6212	355	17	of	of	ADP
ejpam-6212	355	18	20	20	NUM
ejpam-6212	355	19	b	b	NOUN
ejpam-6212	355	20	=	=	SYM
ejpam-6212	355	21	t2∑	t2∑	PROPN
ejpam-6212	355	22	j=1	j=1	NOUN
ejpam-6212	356	1	|vj	|vj	X
ejpam-6212	356	2	||vj+t2	||vj+t2	PROPN
ejpam-6212	356	3	|+	|+	NOUN
ejpam-6212	356	4	2t1∑	2t1∑	NUM
ejpam-6212	356	5	i=2	i=2	PROPN
ejpam-6212	357	1	|vt2	|vt2	PROPN
ejpam-6212	358	1	+	+	NOUN
ejpam-6212	358	2	1||ui|+	1||ui|+	NOUN
ejpam-6212	358	3	|ut1	|ut1	NOUN
ejpam-6212	358	4	+	+	NOUN
ejpam-6212	358	5	1||vt2	1||vt2	NUM
ejpam-6212	358	6	+	+	NOUN
ejpam-6212	358	7	1|	1|	NUM
ejpam-6212	358	8	,	,	PUNCT
ejpam-6212	358	9	and	and	CCONJ
ejpam-6212	358	10	c	c	X
ejpam-6212	359	1	=	=	SYM
ejpam-6212	359	2	t1∑	t1∑	PROPN
ejpam-6212	359	3	i=1	i=1	PROPN
ejpam-6212	359	4	|ui||ui+t1	|ui||ui+t1	ADV
ejpam-6212	359	5	|+	|+	NOUN
ejpam-6212	359	6	t2∑	t2∑	PROPN
ejpam-6212	359	7	j=1	j=1	NOUN
ejpam-6212	360	1	|vj	|vj	X
ejpam-6212	360	2	||vj+t2	||vj+t2	PROPN
ejpam-6212	360	3	|+	|+	NOUN
ejpam-6212	360	4	2t2∑	2t2∑	NUM
ejpam-6212	360	5	j=2	j=2	NOUN
ejpam-6212	360	6	|ut1	|ut1	PUNCT
ejpam-6212	360	7	+	+	NOUN
ejpam-6212	360	8	1||vj	1||vj	PROPN
ejpam-6212	360	9	|+	|+	NOUN
ejpam-6212	360	10	2t1∑	2t1∑	NUM
ejpam-6212	360	11	i=2	i=2	PROPN
ejpam-6212	360	12	|vt2	|vt2	PROPN
ejpam-6212	361	1	+	+	NOUN
ejpam-6212	361	2	1||ui|+	1||ui|+	NOUN
ejpam-6212	361	3	|ut1	|ut1	NOUN
ejpam-6212	361	4	+	+	NOUN
ejpam-6212	361	5	1||vt2	1||vt2	NUM
ejpam-6212	361	6	+	+	NOUN
ejpam-6212	361	7	1|	1|	NUM
ejpam-6212	361	8	.	.	PUNCT
ejpam-6212	362	1	proof	proof	NOUN
ejpam-6212	362	2	.	.	PUNCT
ejpam-6212	363	1	let	let	VERB
ejpam-6212	363	2	t1	t1	NOUN
ejpam-6212	363	3	,	,	PUNCT
ejpam-6212	363	4	t2	t2	PROPN
ejpam-6212	363	5	≥	≥	NUM
ejpam-6212	363	6	2	2	NUM
ejpam-6212	363	7	be	be	AUX
ejpam-6212	363	8	a	a	DET
ejpam-6212	363	9	natural	natural	ADJ
ejpam-6212	363	10	numbers	number	NOUN
ejpam-6212	363	11	.	.	PUNCT
ejpam-6212	364	1	consider	consider	VERB
ejpam-6212	364	2	the	the	DET
ejpam-6212	364	3	even	even	ADV
ejpam-6212	364	4	cycles	cycle	NOUN
ejpam-6212	364	5	c2t1	c2t1	NOUN
ejpam-6212	364	6	=	=	SYM
ejpam-6212	365	1	[	[	X
ejpam-6212	365	2	u1	u1	NOUN
ejpam-6212	365	3	,	,	PUNCT
ejpam-6212	365	4	u2	u2	NOUN
ejpam-6212	365	5	,	,	PUNCT
ejpam-6212	365	6	.	.	PUNCT
ejpam-6212	365	7	.	.	PUNCT
ejpam-6212	365	8	.	.	PUNCT
ejpam-6212	366	1	,	,	PUNCT
ejpam-6212	366	2	u2t1	u2t1	VERB
ejpam-6212	366	3	]	]	PUNCT
ejpam-6212	366	4	and	and	CCONJ
ejpam-6212	366	5	c2t2	c2t2	NOUN
ejpam-6212	367	1	=	=	PUNCT
ejpam-6212	368	1	[	[	X
ejpam-6212	368	2	v1	v1	NOUN
ejpam-6212	368	3	,	,	PUNCT
ejpam-6212	368	4	v2	v2	NOUN
ejpam-6212	368	5	,	,	PUNCT
ejpam-6212	368	6	.	.	PUNCT
ejpam-6212	368	7	.	.	PUNCT
ejpam-6212	368	8	.	.	PUNCT
ejpam-6212	369	1	,	,	PUNCT
ejpam-6212	369	2	v2t2	v2t2	X
ejpam-6212	369	3	]	]	PUNCT
ejpam-6212	369	4	in	in	ADP
ejpam-6212	369	5	g.	g.	PROPN
ejpam-6212	369	6	note	note	VERB
ejpam-6212	369	7	that	that	SCONJ
ejpam-6212	369	8	{	{	PUNCT
ejpam-6212	369	9	u	u	NOUN
ejpam-6212	369	10	,	,	PUNCT
ejpam-6212	369	11	v	v	NOUN
ejpam-6212	369	12	}	}	PUNCT
ejpam-6212	369	13	⊆	⊆	NUM
ejpam-6212	369	14	v	v	NOUN
ejpam-6212	369	15	(	(	PUNCT
ejpam-6212	369	16	g	g	NOUN
ejpam-6212	369	17	)	)	PUNCT
ejpam-6212	369	18	,	,	PUNCT
ejpam-6212	369	19	d(u	d(u	PROPN
ejpam-6212	369	20	,	,	PUNCT
ejpam-6212	369	21	v	v	NOUN
ejpam-6212	369	22	)	)	PUNCT
ejpam-6212	369	23	≤	≤	NUM
ejpam-6212	369	24	diam(g	diam(g	NOUN
ejpam-6212	369	25	)	)	PUNCT
ejpam-6212	369	26	.	.	PUNCT
ejpam-6212	370	1	using	use	VERB
ejpam-6212	370	2	lemma	lemma	PROPN
ejpam-6212	370	3	2	2	NUM
ejpam-6212	370	4	,	,	PUNCT
ejpam-6212	370	5	wg(g	wg(g	NUM
ejpam-6212	370	6	)	)	PUNCT
ejpam-6212	371	1	=	=	PUNCT
ejpam-6212	371	2	∑	∑	PUNCT
ejpam-6212	371	3	{	{	PUNCT
ejpam-6212	371	4	u	u	NOUN
ejpam-6212	371	5	,	,	PUNCT
ejpam-6212	371	6	v}⊆v	v}⊆v	PROPN
ejpam-6212	371	7	(	(	PUNCT
ejpam-6212	371	8	g	g	NOUN
ejpam-6212	371	9	)	)	PUNCT
ejpam-6212	371	10	α(u	α(u	NOUN
ejpam-6212	371	11	,	,	PUNCT
ejpam-6212	371	12	v)d(u	v)d(u	NOUN
ejpam-6212	371	13	,	,	PUNCT
ejpam-6212	371	14	v	v	NOUN
ejpam-6212	371	15	)	)	PUNCT
ejpam-6212	371	16	=	=	SYM
ejpam-6212	371	17	w	w	PROPN
ejpam-6212	371	18	(	(	PUNCT
ejpam-6212	371	19	g	g	NOUN
ejpam-6212	371	20	)	)	PUNCT
ejpam-6212	372	1	+	+	CCONJ
ejpam-6212	372	2	t1∑	t1∑	PROPN
ejpam-6212	372	3	i=1	i=1	PROPN
ejpam-6212	372	4	w	w	PROPN
ejpam-6212	372	5	(	(	PUNCT
ejpam-6212	372	6	ui	ui	PROPN
ejpam-6212	372	7	,	,	PUNCT
ejpam-6212	372	8	ui+t1	ui+t1	ADV
ejpam-6212	372	9	;	;	PUNCT
ejpam-6212	372	10	g	g	NOUN
ejpam-6212	372	11	)	)	PUNCT
ejpam-6212	373	1	+	+	PUNCT
ejpam-6212	373	2	t2∑	t2∑	PROPN
ejpam-6212	373	3	j=1	j=1	NOUN
ejpam-6212	373	4	w	w	PROPN
ejpam-6212	373	5	(	(	PUNCT
ejpam-6212	373	6	vj	vj	INTJ
ejpam-6212	373	7	,	,	PUNCT
ejpam-6212	373	8	vj+t2	vj+t2	NOUN
ejpam-6212	373	9	;	;	PUNCT
ejpam-6212	373	10	g	g	X
ejpam-6212	373	11	)	)	PUNCT
ejpam-6212	374	1	+	+	NUM
ejpam-6212	374	2	2t1∑	2t1∑	NUM
ejpam-6212	374	3	i=2	i=2	PROPN
ejpam-6212	374	4	w	w	PROPN
ejpam-6212	374	5	(	(	PUNCT
ejpam-6212	374	6	vt2	vt2	PROPN
ejpam-6212	374	7	+	+	PROPN
ejpam-6212	374	8	1	1	NUM
ejpam-6212	374	9	,	,	PUNCT
ejpam-6212	374	10	ui;g	ui;g	ADJ
ejpam-6212	374	11	)	)	PUNCT
ejpam-6212	375	1	+	+	NUM
ejpam-6212	375	2	2t2∑	2t2∑	NUM
ejpam-6212	375	3	j=2	j=2	PROPN
ejpam-6212	375	4	w	w	NOUN
ejpam-6212	375	5	(	(	PUNCT
ejpam-6212	375	6	ut1	ut1	PROPN
ejpam-6212	375	7	+	+	ADJ
ejpam-6212	375	8	1	1	NUM
ejpam-6212	375	9	,	,	PUNCT
ejpam-6212	375	10	vj	vj	INTJ
ejpam-6212	375	11	;	;	PUNCT
ejpam-6212	375	12	g	g	X
ejpam-6212	375	13	)	)	PUNCT
ejpam-6212	376	1	+	+	NOUN
ejpam-6212	376	2	w	w	NOUN
ejpam-6212	376	3	(	(	PUNCT
ejpam-6212	376	4	ut1	ut1	PROPN
ejpam-6212	376	5	+	+	NOUN
ejpam-6212	376	6	1	1	NUM
ejpam-6212	376	7	,	,	PUNCT
ejpam-6212	376	8	vt2	vt2	VERB
ejpam-6212	376	9	+	+	NOUN
ejpam-6212	376	10	1;g	1;g	NOUN
ejpam-6212	376	11	)	)	PUNCT
ejpam-6212	376	12	=	=	SYM
ejpam-6212	376	13	w	w	PROPN
ejpam-6212	376	14	(	(	PUNCT
ejpam-6212	376	15	g	g	NOUN
ejpam-6212	376	16	)	)	PUNCT
ejpam-6212	377	1	+	+	CCONJ
ejpam-6212	377	2	t1∑	t1∑	PROPN
ejpam-6212	377	3	i=1	i=1	ADV
ejpam-6212	377	4	∑	∑	PROPN
ejpam-6212	377	5	(	(	PUNCT
ejpam-6212	377	6	u	u	NOUN
ejpam-6212	377	7	,	,	PUNCT
ejpam-6212	377	8	v)∈ui×ui+t1	v)∈ui×ui+t1	ADP
ejpam-6212	377	9	d(u	d(u	PROPN
ejpam-6212	377	10	,	,	PUNCT
ejpam-6212	377	11	v	v	NOUN
ejpam-6212	377	12	)	)	PUNCT
ejpam-6212	377	13	+	+	PUNCT
ejpam-6212	377	14	t2∑	t2∑	PROPN
ejpam-6212	377	15	j=1	j=1	NOUN
ejpam-6212	377	16	∑	∑	PUNCT
ejpam-6212	377	17	(	(	PUNCT
ejpam-6212	377	18	u	u	NOUN
ejpam-6212	377	19	,	,	PUNCT
ejpam-6212	377	20	v)∈vj×vj+t2	v)∈vj×vj+t2	PROPN
ejpam-6212	377	21	d(u	d(u	PROPN
ejpam-6212	377	22	,	,	PUNCT
ejpam-6212	377	23	v	v	NOUN
ejpam-6212	377	24	)	)	PUNCT
ejpam-6212	377	25	+	+	NUM
ejpam-6212	377	26	2t1∑	2t1∑	NUM
ejpam-6212	377	27	i=2	i=2	PROPN
ejpam-6212	377	28	∑	∑	PROPN
ejpam-6212	377	29	(	(	PUNCT
ejpam-6212	377	30	u	u	NOUN
ejpam-6212	377	31	,	,	PUNCT
ejpam-6212	377	32	v)∈vt2	v)∈vt2	PROPN
ejpam-6212	377	33	+	+	NOUN
ejpam-6212	377	34	1×ui	1×ui	NUM
ejpam-6212	377	35	d(u	d(u	PROPN
ejpam-6212	377	36	,	,	PUNCT
ejpam-6212	377	37	v	v	NOUN
ejpam-6212	377	38	)	)	PUNCT
ejpam-6212	377	39	+	+	SYM
ejpam-6212	377	40	2t2∑	2t2∑	NUM
ejpam-6212	377	41	j=2	j=2	NOUN
ejpam-6212	377	42	∑	∑	PROPN
ejpam-6212	377	43	(	(	PUNCT
ejpam-6212	377	44	u	u	NOUN
ejpam-6212	377	45	,	,	PUNCT
ejpam-6212	377	46	v)∈ut1	v)∈ut1	VERB
ejpam-6212	377	47	+	+	PRON
ejpam-6212	377	48	1×vj	1×vj	NUM
ejpam-6212	377	49	d(u	d(u	NOUN
ejpam-6212	377	50	,	,	PUNCT
ejpam-6212	377	51	v	v	NOUN
ejpam-6212	377	52	)	)	PUNCT
ejpam-6212	377	53	+	+	CCONJ
ejpam-6212	377	54	∑	∑	PROPN
ejpam-6212	377	55	(	(	PUNCT
ejpam-6212	377	56	u	u	NOUN
ejpam-6212	377	57	,	,	PUNCT
ejpam-6212	377	58	v)∈ut1	v)∈ut1	VERB
ejpam-6212	377	59	+	+	NOUN
ejpam-6212	377	60	1×vt2	1×vt2	NOUN
ejpam-6212	377	61	+	+	ADJ
ejpam-6212	377	62	1	1	NUM
ejpam-6212	377	63	d(u	d(u	PROPN
ejpam-6212	377	64	,	,	PUNCT
ejpam-6212	377	65	v	v	NOUN
ejpam-6212	377	66	)	)	PUNCT
ejpam-6212	377	67	≤	≤	NOUN
ejpam-6212	377	68	w	w	ADP
ejpam-6212	377	69	(	(	PUNCT
ejpam-6212	377	70	g	g	NOUN
ejpam-6212	377	71	)	)	PUNCT
ejpam-6212	377	72	+	+	NUM
ejpam-6212	377	73	diam(g	diam(g	NOUN
ejpam-6212	377	74	)	)	PUNCT
ejpam-6212	377	75	t1∑	t1∑	PROPN
ejpam-6212	378	1	i=1	i=1	PROPN
ejpam-6212	378	2	|ui||ui+t1	|ui||ui+t1	ADP
ejpam-6212	378	3	|+	|+	NOUN
ejpam-6212	378	4	diam(g	diam(g	NOUN
ejpam-6212	378	5	)	)	PUNCT
ejpam-6212	378	6	t2∑	t2∑	NOUN
ejpam-6212	378	7	j=1	j=1	NOUN
ejpam-6212	379	1	|vj	|vj	X
ejpam-6212	379	2	||vj+t2	||vj+t2	PROPN
ejpam-6212	379	3	|	|	ADV
ejpam-6212	379	4	+	+	NOUN
ejpam-6212	379	5	diam(g	diam(g	NOUN
ejpam-6212	379	6	)	)	PUNCT
ejpam-6212	379	7	2t1∑	2t1∑	NUM
ejpam-6212	380	1	i=2	i=2	PROPN
ejpam-6212	380	2	|vt2	|vt2	PROPN
ejpam-6212	381	1	+	+	NOUN
ejpam-6212	381	2	1||ui|+	1||ui|+	PROPN
ejpam-6212	381	3	diam(g	diam(g	NOUN
ejpam-6212	381	4	)	)	PUNCT
ejpam-6212	381	5	2t2∑	2t2∑	NUM
ejpam-6212	381	6	j=2	j=2	NOUN
ejpam-6212	381	7	|ut1	|ut1	PUNCT
ejpam-6212	382	1	+	+	NOUN
ejpam-6212	382	2	1||vj	1||vj	PROPN
ejpam-6212	382	3	|+	|+	NOUN
ejpam-6212	382	4	diam(g)|ut1	diam(g)|ut1	NOUN
ejpam-6212	382	5	+	+	PROPN
ejpam-6212	382	6	1||vt2	1||vt2	PROPN
ejpam-6212	382	7	+	+	ADJ
ejpam-6212	382	8	1|	1|	NUM
ejpam-6212	382	9	=	=	SYM
ejpam-6212	382	10	w	w	PROPN
ejpam-6212	382	11	(	(	PUNCT
ejpam-6212	382	12	g	g	NOUN
ejpam-6212	382	13	)	)	PUNCT
ejpam-6212	382	14	+	+	CCONJ
ejpam-6212	382	15	cdiam(g	cdiam(g	X
ejpam-6212	382	16	)	)	PUNCT
ejpam-6212	383	1	where	where	SCONJ
ejpam-6212	383	2	c	c	NOUN
ejpam-6212	383	3	=	=	SYM
ejpam-6212	383	4	t1∑	t1∑	PROPN
ejpam-6212	383	5	i=1	i=1	PROPN
ejpam-6212	383	6	|ui||ui+t1	|ui||ui+t1	ADV
ejpam-6212	383	7	|+	|+	NOUN
ejpam-6212	383	8	t2∑	t2∑	PROPN
ejpam-6212	383	9	j=1	j=1	NOUN
ejpam-6212	383	10	|vj	|vj	X
ejpam-6212	383	11	||vj+t2	||vj+t2	PROPN
ejpam-6212	383	12	|+	|+	NOUN
ejpam-6212	383	13	2t2∑	2t2∑	NUM
ejpam-6212	383	14	j=2	j=2	NOUN
ejpam-6212	383	15	|ut1	|ut1	PUNCT
ejpam-6212	384	1	+	+	NOUN
ejpam-6212	384	2	1||vj	1||vj	PROPN
ejpam-6212	384	3	|+	|+	NOUN
ejpam-6212	384	4	2t1∑	2t1∑	NUM
ejpam-6212	384	5	i=2	i=2	PROPN
ejpam-6212	384	6	|vt2	|vt2	PROPN
ejpam-6212	385	1	+	+	NOUN
ejpam-6212	385	2	1||ui|+	1||ui|+	NOUN
ejpam-6212	385	3	|ut1	|ut1	NOUN
ejpam-6212	385	4	+	+	NOUN
ejpam-6212	385	5	1||vt2	1||vt2	NUM
ejpam-6212	385	6	+	+	NOUN
ejpam-6212	385	7	1|	1|	NUM
ejpam-6212	385	8	.	.	PUNCT
ejpam-6212	386	1	now	now	ADV
ejpam-6212	386	2	,	,	PUNCT
ejpam-6212	386	3	for	for	ADP
ejpam-6212	386	4	(	(	PUNCT
ejpam-6212	386	5	u	u	NOUN
ejpam-6212	386	6	,	,	PUNCT
ejpam-6212	386	7	v	v	NOUN
ejpam-6212	386	8	)	)	PUNCT
ejpam-6212	386	9	∈	∈	PROPN
ejpam-6212	387	1	ui	ui	NOUN
ejpam-6212	388	1	×	×	NOUN
ejpam-6212	389	1	ui+t1	ui+t1	NOUN
ejpam-6212	389	2	,	,	PUNCT
ejpam-6212	389	3	d(u	d(u	PROPN
ejpam-6212	389	4	,	,	PUNCT
ejpam-6212	389	5	v	v	NOUN
ejpam-6212	389	6	)	)	PUNCT
ejpam-6212	389	7	≥	≥	NOUN
ejpam-6212	389	8	t1	t1	NOUN
ejpam-6212	389	9	.	.	PUNCT
ejpam-6212	390	1	also	also	ADV
ejpam-6212	390	2	,	,	PUNCT
ejpam-6212	390	3	for	for	ADP
ejpam-6212	390	4	(	(	PUNCT
ejpam-6212	390	5	u	u	NOUN
ejpam-6212	390	6	,	,	PUNCT
ejpam-6212	390	7	v	v	NOUN
ejpam-6212	390	8	)	)	PUNCT
ejpam-6212	390	9	∈	∈	PROPN
ejpam-6212	390	10	vj	vj	INTJ
ejpam-6212	390	11	×	×	PROPN
ejpam-6212	390	12	vj+t2	vj+t2	PROPN
ejpam-6212	390	13	,	,	PUNCT
ejpam-6212	390	14	d(u	d(u	PROPN
ejpam-6212	390	15	,	,	PUNCT
ejpam-6212	390	16	v	v	NOUN
ejpam-6212	390	17	)	)	PUNCT
ejpam-6212	390	18	≥	≥	NOUN
ejpam-6212	390	19	t2	t2	NOUN
ejpam-6212	390	20	.	.	PUNCT
ejpam-6212	391	1	moreover	moreover	ADV
ejpam-6212	391	2	,	,	PUNCT
ejpam-6212	391	3	if	if	SCONJ
ejpam-6212	391	4	(	(	PUNCT
ejpam-6212	391	5	u	u	NOUN
ejpam-6212	391	6	,	,	PUNCT
ejpam-6212	391	7	v	v	NOUN
ejpam-6212	391	8	)	)	PUNCT
ejpam-6212	391	9	∈	∈	NOUN
ejpam-6212	391	10	vt2	vt2	PROPN
ejpam-6212	391	11	+	+	PROPN
ejpam-6212	391	12	1	1	NUM
ejpam-6212	391	13	×	×	NOUN
ejpam-6212	391	14	ui	ui	NOUN
ejpam-6212	391	15	for	for	ADP
ejpam-6212	391	16	i	i	PRON
ejpam-6212	391	17	∈	∈	PROPN
ejpam-6212	391	18	{	{	PUNCT
ejpam-6212	391	19	2	2	NUM
ejpam-6212	391	20	,	,	PUNCT
ejpam-6212	391	21	3	3	NUM
ejpam-6212	391	22	,	,	PUNCT
ejpam-6212	391	23	.	.	PUNCT
ejpam-6212	391	24	.	.	PUNCT
ejpam-6212	392	1	.	.	PUNCT
ejpam-6212	393	1	,	,	PUNCT
ejpam-6212	393	2	2t1	2t1	NUM
ejpam-6212	393	3	}	}	PUNCT
ejpam-6212	393	4	,	,	PUNCT
ejpam-6212	393	5	d(u	d(u	PROPN
ejpam-6212	393	6	,	,	PUNCT
ejpam-6212	393	7	v	v	NOUN
ejpam-6212	393	8	)	)	PUNCT
ejpam-6212	393	9	≥	≥	NOUN
ejpam-6212	393	10	t2	t2	NOUN
ejpam-6212	393	11	since	since	SCONJ
ejpam-6212	393	12	a	a	DET
ejpam-6212	393	13	u	u	NOUN
ejpam-6212	393	14	−	−	PROPN
ejpam-6212	393	15	v	v	PRON
ejpam-6212	393	16	geodesic	geodesic	NOUN
ejpam-6212	393	17	passes	pass	VERB
ejpam-6212	393	18	through	through	ADP
ejpam-6212	393	19	v1	v1	NOUN
ejpam-6212	393	20	and	and	CCONJ
ejpam-6212	393	21	the	the	DET
ejpam-6212	393	22	distance	distance	NOUN
ejpam-6212	393	23	between	between	ADP
ejpam-6212	393	24	v1	v1	NOUN
ejpam-6212	393	25	and	and	CCONJ
ejpam-6212	393	26	vt2	vt2	VERB
ejpam-6212	393	27	+	+	PROPN
ejpam-6212	393	28	1	1	NUM
ejpam-6212	393	29	is	be	AUX
ejpam-6212	393	30	t2	t2	NOUN
ejpam-6212	393	31	.	.	PUNCT
ejpam-6212	394	1	similarly	similarly	ADV
ejpam-6212	394	2	,	,	PUNCT
ejpam-6212	394	3	if	if	SCONJ
ejpam-6212	394	4	r.	r.	PROPN
ejpam-6212	394	5	g.	g.	PROPN
ejpam-6212	394	6	artes	artes	PROPN
ejpam-6212	394	7	jr	jr	PROPN
ejpam-6212	394	8	.	.	PROPN
ejpam-6212	394	9	et	et	PROPN
ejpam-6212	394	10	al	al	PROPN
ejpam-6212	394	11	.	.	PUNCT
ejpam-6212	394	12	/	/	SYM
ejpam-6212	394	13	eur	eur	PROPN
ejpam-6212	394	14	.	.	PUNCT
ejpam-6212	395	1	j.	j.	PROPN
ejpam-6212	395	2	pure	pure	PROPN
ejpam-6212	395	3	appl	appl	PROPN
ejpam-6212	395	4	.	.	PROPN
ejpam-6212	395	5	math	math	PROPN
ejpam-6212	395	6	,	,	PUNCT
ejpam-6212	395	7	18	18	NUM
ejpam-6212	395	8	(	(	PUNCT
ejpam-6212	395	9	4	4	NUM
ejpam-6212	395	10	)	)	PUNCT
ejpam-6212	395	11	(	(	PUNCT
ejpam-6212	395	12	2025	2025	NUM
ejpam-6212	395	13	)	)	PUNCT
ejpam-6212	395	14	,	,	PUNCT
ejpam-6212	395	15	6212	6212	NUM
ejpam-6212	395	16	9	9	NUM
ejpam-6212	395	17	of	of	ADP
ejpam-6212	395	18	20	20	NUM
ejpam-6212	395	19	(	(	PUNCT
ejpam-6212	395	20	u	u	NOUN
ejpam-6212	395	21	,	,	PUNCT
ejpam-6212	395	22	v	v	NOUN
ejpam-6212	395	23	)	)	PUNCT
ejpam-6212	395	24	∈	∈	NOUN
ejpam-6212	395	25	ut1	ut1	NOUN
ejpam-6212	395	26	+	+	NOUN
ejpam-6212	395	27	1×vj	1×vj	NUM
ejpam-6212	395	28	for	for	ADP
ejpam-6212	395	29	j	j	PROPN
ejpam-6212	395	30	∈	∈	PROPN
ejpam-6212	395	31	{	{	PUNCT
ejpam-6212	395	32	2	2	NUM
ejpam-6212	395	33	,	,	PUNCT
ejpam-6212	395	34	3	3	NUM
ejpam-6212	395	35	,	,	PUNCT
ejpam-6212	395	36	.	.	PUNCT
ejpam-6212	395	37	.	.	PUNCT
ejpam-6212	396	1	.	.	PUNCT
ejpam-6212	397	1	,	,	PUNCT
ejpam-6212	397	2	2t2	2t2	NUM
ejpam-6212	397	3	}	}	PUNCT
ejpam-6212	397	4	,	,	PUNCT
ejpam-6212	397	5	d(u	d(u	PROPN
ejpam-6212	397	6	,	,	PUNCT
ejpam-6212	397	7	v	v	NOUN
ejpam-6212	397	8	)	)	PUNCT
ejpam-6212	397	9	≥	≥	NOUN
ejpam-6212	397	10	t1	t1	NOUN
ejpam-6212	397	11	since	since	SCONJ
ejpam-6212	397	12	a	a	DET
ejpam-6212	397	13	u−v	u−v	X
ejpam-6212	397	14	geodesic	geodesic	NOUN
ejpam-6212	397	15	passes	pass	VERB
ejpam-6212	397	16	through	through	ADP
ejpam-6212	397	17	u1	u1	NOUN
ejpam-6212	397	18	and	and	CCONJ
ejpam-6212	397	19	the	the	DET
ejpam-6212	397	20	distance	distance	NOUN
ejpam-6212	397	21	between	between	ADP
ejpam-6212	397	22	u1	u1	NOUN
ejpam-6212	397	23	and	and	CCONJ
ejpam-6212	397	24	ut1	ut1	NOUN
ejpam-6212	397	25	+	+	NOUN
ejpam-6212	397	26	1	1	NUM
ejpam-6212	397	27	is	be	AUX
ejpam-6212	397	28	t1	t1	NOUN
ejpam-6212	397	29	.	.	PUNCT
ejpam-6212	398	1	moreover	moreover	ADV
ejpam-6212	398	2	,	,	PUNCT
ejpam-6212	398	3	for	for	ADP
ejpam-6212	398	4	(	(	PUNCT
ejpam-6212	398	5	u	u	NOUN
ejpam-6212	398	6	,	,	PUNCT
ejpam-6212	398	7	v	v	NOUN
ejpam-6212	398	8	)	)	PUNCT
ejpam-6212	398	9	∈	∈	NOUN
ejpam-6212	398	10	ut1	ut1	NOUN
ejpam-6212	398	11	+	+	NOUN
ejpam-6212	398	12	1	1	NUM
ejpam-6212	398	13	×	×	NOUN
ejpam-6212	398	14	vt2	vt2	NOUN
ejpam-6212	398	15	+	+	PROPN
ejpam-6212	398	16	1	1	NUM
ejpam-6212	398	17	,	,	PUNCT
ejpam-6212	398	18	d(u	d(u	PROPN
ejpam-6212	398	19	,	,	PUNCT
ejpam-6212	398	20	v	v	NOUN
ejpam-6212	398	21	)	)	PUNCT
ejpam-6212	398	22	≥	≥	NOUN
ejpam-6212	398	23	t1	t1	NOUN
ejpam-6212	398	24	+	+	CCONJ
ejpam-6212	398	25	t2	t2	NOUN
ejpam-6212	398	26	.	.	PUNCT
ejpam-6212	398	27	applying	apply	VERB
ejpam-6212	398	28	lemma	lemma	PROPN
ejpam-6212	398	29	2	2	NUM
ejpam-6212	398	30	gives	give	VERB
ejpam-6212	398	31	wg(g	wg(g	NOUN
ejpam-6212	398	32	)	)	PUNCT
ejpam-6212	399	1	=	=	PUNCT
ejpam-6212	399	2	∑	∑	PUNCT
ejpam-6212	399	3	{	{	PUNCT
ejpam-6212	399	4	u	u	NOUN
ejpam-6212	399	5	,	,	PUNCT
ejpam-6212	399	6	v}⊆v	v}⊆v	PROPN
ejpam-6212	399	7	(	(	PUNCT
ejpam-6212	399	8	g	g	NOUN
ejpam-6212	399	9	)	)	PUNCT
ejpam-6212	399	10	α(u	α(u	NOUN
ejpam-6212	399	11	,	,	PUNCT
ejpam-6212	399	12	v)d(u	v)d(u	NOUN
ejpam-6212	399	13	,	,	PUNCT
ejpam-6212	399	14	v	v	NOUN
ejpam-6212	399	15	)	)	PUNCT
ejpam-6212	399	16	=	=	SYM
ejpam-6212	399	17	w	w	PROPN
ejpam-6212	399	18	(	(	PUNCT
ejpam-6212	399	19	g	g	NOUN
ejpam-6212	399	20	)	)	PUNCT
ejpam-6212	400	1	+	+	CCONJ
ejpam-6212	400	2	t1∑	t1∑	PROPN
ejpam-6212	400	3	i=1	i=1	PROPN
ejpam-6212	400	4	w	w	PROPN
ejpam-6212	400	5	(	(	PUNCT
ejpam-6212	400	6	ui	ui	PROPN
ejpam-6212	400	7	,	,	PUNCT
ejpam-6212	400	8	ui+t1	ui+t1	ADV
ejpam-6212	400	9	;	;	PUNCT
ejpam-6212	400	10	g	g	NOUN
ejpam-6212	400	11	)	)	PUNCT
ejpam-6212	401	1	+	+	PUNCT
ejpam-6212	401	2	t2∑	t2∑	PROPN
ejpam-6212	401	3	j=1	j=1	NOUN
ejpam-6212	401	4	w	w	PROPN
ejpam-6212	401	5	(	(	PUNCT
ejpam-6212	401	6	vj	vj	INTJ
ejpam-6212	401	7	,	,	PUNCT
ejpam-6212	401	8	vj+t2	vj+t2	NOUN
ejpam-6212	401	9	;	;	PUNCT
ejpam-6212	401	10	g	g	X
ejpam-6212	401	11	)	)	PUNCT
ejpam-6212	402	1	+	+	NUM
ejpam-6212	402	2	2t1∑	2t1∑	NUM
ejpam-6212	402	3	i=2	i=2	PROPN
ejpam-6212	402	4	w	w	PROPN
ejpam-6212	402	5	(	(	PUNCT
ejpam-6212	402	6	vt2	vt2	PROPN
ejpam-6212	402	7	+	+	PROPN
ejpam-6212	402	8	1	1	NUM
ejpam-6212	402	9	,	,	PUNCT
ejpam-6212	402	10	ui;g	ui;g	ADJ
ejpam-6212	402	11	)	)	PUNCT
ejpam-6212	403	1	+	+	NUM
ejpam-6212	403	2	2t2∑	2t2∑	NUM
ejpam-6212	403	3	j=2	j=2	PROPN
ejpam-6212	403	4	w	w	NOUN
ejpam-6212	403	5	(	(	PUNCT
ejpam-6212	403	6	ut1	ut1	PROPN
ejpam-6212	403	7	+	+	ADJ
ejpam-6212	403	8	1	1	NUM
ejpam-6212	403	9	,	,	PUNCT
ejpam-6212	403	10	vj	vj	INTJ
ejpam-6212	403	11	;	;	PUNCT
ejpam-6212	403	12	g	g	X
ejpam-6212	403	13	)	)	PUNCT
ejpam-6212	404	1	+	+	NOUN
ejpam-6212	404	2	w	w	NOUN
ejpam-6212	404	3	(	(	PUNCT
ejpam-6212	404	4	ut1	ut1	PROPN
ejpam-6212	404	5	+	+	NOUN
ejpam-6212	404	6	1	1	NUM
ejpam-6212	404	7	,	,	PUNCT
ejpam-6212	404	8	vt2	vt2	VERB
ejpam-6212	404	9	+	+	NOUN
ejpam-6212	404	10	1;g	1;g	NOUN
ejpam-6212	404	11	)	)	PUNCT
ejpam-6212	404	12	=	=	SYM
ejpam-6212	404	13	w	w	PROPN
ejpam-6212	404	14	(	(	PUNCT
ejpam-6212	404	15	g	g	NOUN
ejpam-6212	404	16	)	)	PUNCT
ejpam-6212	405	1	+	+	CCONJ
ejpam-6212	405	2	t1∑	t1∑	PROPN
ejpam-6212	405	3	i=1	i=1	ADV
ejpam-6212	405	4	∑	∑	PROPN
ejpam-6212	405	5	(	(	PUNCT
ejpam-6212	405	6	u	u	NOUN
ejpam-6212	405	7	,	,	PUNCT
ejpam-6212	405	8	v)∈ui×ui+t1	v)∈ui×ui+t1	ADP
ejpam-6212	405	9	d(u	d(u	PROPN
ejpam-6212	405	10	,	,	PUNCT
ejpam-6212	405	11	v	v	NOUN
ejpam-6212	405	12	)	)	PUNCT
ejpam-6212	405	13	+	+	PUNCT
ejpam-6212	405	14	t2∑	t2∑	PROPN
ejpam-6212	405	15	j=1	j=1	NOUN
ejpam-6212	405	16	∑	∑	PUNCT
ejpam-6212	405	17	(	(	PUNCT
ejpam-6212	405	18	u	u	NOUN
ejpam-6212	405	19	,	,	PUNCT
ejpam-6212	405	20	v)∈vj×vj+t2	v)∈vj×vj+t2	PROPN
ejpam-6212	405	21	d(u	d(u	PROPN
ejpam-6212	405	22	,	,	PUNCT
ejpam-6212	405	23	v	v	NOUN
ejpam-6212	405	24	)	)	PUNCT
ejpam-6212	405	25	+	+	NUM
ejpam-6212	405	26	2t1∑	2t1∑	NUM
ejpam-6212	405	27	i=2	i=2	PROPN
ejpam-6212	405	28	∑	∑	PROPN
ejpam-6212	405	29	(	(	PUNCT
ejpam-6212	405	30	u	u	NOUN
ejpam-6212	405	31	,	,	PUNCT
ejpam-6212	405	32	v)∈vt2	v)∈vt2	PROPN
ejpam-6212	405	33	+	+	NOUN
ejpam-6212	405	34	1×ui	1×ui	NUM
ejpam-6212	405	35	d(u	d(u	PROPN
ejpam-6212	405	36	,	,	PUNCT
ejpam-6212	405	37	v	v	NOUN
ejpam-6212	405	38	)	)	PUNCT
ejpam-6212	405	39	+	+	SYM
ejpam-6212	405	40	2t2∑	2t2∑	NUM
ejpam-6212	405	41	j=2	j=2	NOUN
ejpam-6212	405	42	∑	∑	PROPN
ejpam-6212	405	43	(	(	PUNCT
ejpam-6212	405	44	u	u	NOUN
ejpam-6212	405	45	,	,	PUNCT
ejpam-6212	405	46	v)∈ut1	v)∈ut1	VERB
ejpam-6212	405	47	+	+	PRON
ejpam-6212	405	48	1×vj	1×vj	NUM
ejpam-6212	405	49	d(u	d(u	NOUN
ejpam-6212	405	50	,	,	PUNCT
ejpam-6212	405	51	v	v	NOUN
ejpam-6212	405	52	)	)	PUNCT
ejpam-6212	405	53	+	+	CCONJ
ejpam-6212	405	54	∑	∑	PROPN
ejpam-6212	405	55	(	(	PUNCT
ejpam-6212	405	56	u	u	NOUN
ejpam-6212	405	57	,	,	PUNCT
ejpam-6212	405	58	v)∈ut1	v)∈ut1	VERB
ejpam-6212	405	59	+	+	NOUN
ejpam-6212	405	60	1×vt2	1×vt2	NOUN
ejpam-6212	405	61	+	+	ADJ
ejpam-6212	405	62	1	1	NUM
ejpam-6212	405	63	d(u	d(u	PROPN
ejpam-6212	405	64	,	,	PUNCT
ejpam-6212	405	65	v	v	NOUN
ejpam-6212	405	66	)	)	PUNCT
ejpam-6212	405	67	≥	≥	PROPN
ejpam-6212	405	68	w	w	NOUN
ejpam-6212	405	69	(	(	PUNCT
ejpam-6212	405	70	g	g	NOUN
ejpam-6212	405	71	)	)	PUNCT
ejpam-6212	405	72	+	+	CCONJ
ejpam-6212	405	73	t1	t1	NOUN
ejpam-6212	405	74	t1∑	t1∑	PROPN
ejpam-6212	405	75	i=1	i=1	PROPN
ejpam-6212	405	76	|ui||ui+t1	|ui||ui+t1	ADP
ejpam-6212	405	77	|+	|+	NOUN
ejpam-6212	405	78	t2	t2	PROPN
ejpam-6212	405	79	t2∑	t2∑	PROPN
ejpam-6212	405	80	j=1	j=1	NOUN
ejpam-6212	405	81	|vj	|vj	X
ejpam-6212	405	82	||vj+t2	||vj+t2	PROPN
ejpam-6212	405	83	|	|	ADV
ejpam-6212	405	84	+	+	PROPN
ejpam-6212	405	85	t2	t2	NOUN
ejpam-6212	405	86	2t1∑	2t1∑	NUM
ejpam-6212	405	87	i=2	i=2	PROPN
ejpam-6212	405	88	|vt2	|vt2	PROPN
ejpam-6212	406	1	+	+	NOUN
ejpam-6212	406	2	1||ui|+	1||ui|+	NOUN
ejpam-6212	406	3	t1	t1	NOUN
ejpam-6212	406	4	2t2∑	2t2∑	NUM
ejpam-6212	406	5	j=2	j=2	NOUN
ejpam-6212	406	6	|ut1	|ut1	PUNCT
ejpam-6212	407	1	+	+	NOUN
ejpam-6212	407	2	1||vj	1||vj	PROPN
ejpam-6212	407	3	|+	|+	NOUN
ejpam-6212	407	4	(	(	PUNCT
ejpam-6212	407	5	t1	t1	NOUN
ejpam-6212	407	6	+	+	X
ejpam-6212	407	7	t2)|ut1	t2)|ut1	ADJ
ejpam-6212	407	8	+	+	PROPN
ejpam-6212	407	9	1||vt2	1||vt2	NUM
ejpam-6212	407	10	+	+	ADJ
ejpam-6212	407	11	1|	1|	NUM
ejpam-6212	408	1	=	=	SYM
ejpam-6212	408	2	w	w	PROPN
ejpam-6212	408	3	(	(	PUNCT
ejpam-6212	408	4	g	g	NOUN
ejpam-6212	408	5	)	)	PUNCT
ejpam-6212	408	6	+	+	NOUN
ejpam-6212	408	7	at1	at1	PROPN
ejpam-6212	408	8	+	+	PROPN
ejpam-6212	408	9	bt2	bt2	PROPN
ejpam-6212	408	10	,	,	PUNCT
ejpam-6212	408	11	where	where	SCONJ
ejpam-6212	408	12	a	a	DET
ejpam-6212	408	13	=	=	X
ejpam-6212	408	14	t1∑	t1∑	PROPN
ejpam-6212	408	15	i=1	i=1	PROPN
ejpam-6212	408	16	|ui||ui+t1	|ui||ui+t1	ADP
ejpam-6212	408	17	|+	|+	NOUN
ejpam-6212	408	18	2t2∑	2t2∑	NUM
ejpam-6212	408	19	j=2	j=2	NOUN
ejpam-6212	408	20	|ut1	|ut1	PUNCT
ejpam-6212	408	21	+	+	NOUN
ejpam-6212	408	22	1||vj	1||vj	NOUN
ejpam-6212	408	23	|+	|+	X
ejpam-6212	408	24	|ut1	|ut1	PUNCT
ejpam-6212	408	25	+	+	NOUN
ejpam-6212	408	26	1||vt2	1||vt2	NUM
ejpam-6212	408	27	+	+	NOUN
ejpam-6212	408	28	1|	1|	NUM
ejpam-6212	408	29	and	and	CCONJ
ejpam-6212	408	30	b	b	NOUN
ejpam-6212	408	31	=	=	SYM
ejpam-6212	408	32	t2∑	t2∑	PROPN
ejpam-6212	408	33	j=1	j=1	NOUN
ejpam-6212	408	34	|vj	|vj	X
ejpam-6212	408	35	||vj+t2	||vj+t2	PROPN
ejpam-6212	408	36	|+	|+	NOUN
ejpam-6212	408	37	2t1∑	2t1∑	NUM
ejpam-6212	408	38	i=2	i=2	PROPN
ejpam-6212	408	39	|vt2	|vt2	PROPN
ejpam-6212	408	40	+	+	NOUN
ejpam-6212	408	41	1||ui|+	1||ui|+	NOUN
ejpam-6212	408	42	|ut1	|ut1	NOUN
ejpam-6212	408	43	+	+	NOUN
ejpam-6212	408	44	1||vt2	1||vt2	NUM
ejpam-6212	408	45	+	+	NOUN
ejpam-6212	408	46	1|	1|	NUM
ejpam-6212	408	47	.	.	PUNCT
ejpam-6212	409	1	the	the	DET
ejpam-6212	409	2	proof	proof	NOUN
ejpam-6212	409	3	is	be	AUX
ejpam-6212	409	4	complete	complete	ADJ
ejpam-6212	409	5	.	.	PUNCT
ejpam-6212	410	1	theorem	theorem	NOUN
ejpam-6212	410	2	2	2	NUM
ejpam-6212	410	3	.	.	PUNCT
ejpam-6212	411	1	let	let	VERB
ejpam-6212	411	2	g	g	PRON
ejpam-6212	411	3	be	be	AUX
ejpam-6212	411	4	a	a	DET
ejpam-6212	411	5	simple	simple	ADJ
ejpam-6212	411	6	spirocyclic	spirocyclic	NOUN
ejpam-6212	411	7	graph	graph	NOUN
ejpam-6212	411	8	with	with	ADP
ejpam-6212	411	9	minimum	minimum	NOUN
ejpam-6212	411	10	degree	degree	NOUN
ejpam-6212	411	11	δ	δ	NOUN
ejpam-6212	411	12	=	=	SYM
ejpam-6212	411	13	2	2	NUM
ejpam-6212	411	14	and	and	CCONJ
ejpam-6212	411	15	with	with	ADP
ejpam-6212	411	16	even	even	ADV
ejpam-6212	411	17	cycles	cycle	NOUN
ejpam-6212	411	18	c2t1	c2t1	NOUN
ejpam-6212	411	19	and	and	CCONJ
ejpam-6212	411	20	c2t2	c2t2	PROPN
ejpam-6212	411	21	,	,	PUNCT
ejpam-6212	411	22	for	for	SCONJ
ejpam-6212	411	23	some	some	DET
ejpam-6212	411	24	natural	natural	ADJ
ejpam-6212	411	25	numbers	number	NOUN
ejpam-6212	411	26	t1	t1	PROPN
ejpam-6212	411	27	,	,	PUNCT
ejpam-6212	411	28	t2	t2	NOUN
ejpam-6212	411	29	≥	≥	NUM
ejpam-6212	411	30	2	2	NUM
ejpam-6212	411	31	.	.	PUNCT
ejpam-6212	411	32	then	then	ADV
ejpam-6212	411	33	wg(g	wg(g	NUM
ejpam-6212	411	34	)	)	PUNCT
ejpam-6212	412	1	=	=	SYM
ejpam-6212	412	2	w	w	PROPN
ejpam-6212	412	3	(	(	PUNCT
ejpam-6212	412	4	g	g	NOUN
ejpam-6212	412	5	)	)	PUNCT
ejpam-6212	412	6	+	+	NOUN
ejpam-6212	413	1	2(t1	2(t1	NUM
ejpam-6212	414	1	+	+	NUM
ejpam-6212	414	2	t2	t2	NOUN
ejpam-6212	414	3	)	)	PUNCT
ejpam-6212	414	4	2	2	NUM
ejpam-6212	414	5	.	.	X
ejpam-6212	415	1	proof	proof	NOUN
ejpam-6212	415	2	.	.	PUNCT
ejpam-6212	416	1	let	let	VERB
ejpam-6212	416	2	c2t1	c2t1	NOUN
ejpam-6212	416	3	=	=	PUNCT
ejpam-6212	417	1	[	[	X
ejpam-6212	417	2	u1	u1	NOUN
ejpam-6212	417	3	,	,	PUNCT
ejpam-6212	417	4	u2	u2	NOUN
ejpam-6212	417	5	,	,	PUNCT
ejpam-6212	417	6	.	.	PUNCT
ejpam-6212	417	7	.	.	PUNCT
ejpam-6212	417	8	.	.	PUNCT
ejpam-6212	418	1	,	,	PUNCT
ejpam-6212	418	2	u2t1	u2t1	VERB
ejpam-6212	418	3	]	]	PUNCT
ejpam-6212	418	4	and	and	CCONJ
ejpam-6212	418	5	c2t2	c2t2	NOUN
ejpam-6212	419	1	=	=	PUNCT
ejpam-6212	420	1	[	[	X
ejpam-6212	420	2	v1	v1	NOUN
ejpam-6212	420	3	,	,	PUNCT
ejpam-6212	420	4	v2	v2	NOUN
ejpam-6212	420	5	,	,	PUNCT
ejpam-6212	420	6	.	.	PUNCT
ejpam-6212	420	7	.	.	PUNCT
ejpam-6212	420	8	.	.	PUNCT
ejpam-6212	421	1	,	,	PUNCT
ejpam-6212	421	2	v2t2	v2t2	X
ejpam-6212	421	3	]	]	PUNCT
ejpam-6212	421	4	be	be	AUX
ejpam-6212	421	5	the	the	DET
ejpam-6212	421	6	cycles	cycle	NOUN
ejpam-6212	421	7	in	in	ADP
ejpam-6212	421	8	g.	g.	PROPN
ejpam-6212	421	9	since	since	SCONJ
ejpam-6212	421	10	δ	δ	PROPN
ejpam-6212	421	11	=	=	SYM
ejpam-6212	421	12	2	2	NUM
ejpam-6212	421	13	,	,	PUNCT
ejpam-6212	421	14	g	g	PROPN
ejpam-6212	421	15	has	have	VERB
ejpam-6212	421	16	no	no	DET
ejpam-6212	421	17	pendant	pendant	ADJ
ejpam-6212	421	18	vertices	vertex	NOUN
ejpam-6212	421	19	.	.	PUNCT
ejpam-6212	422	1	consequently	consequently	ADV
ejpam-6212	422	2	,	,	PUNCT
ejpam-6212	422	3	g	g	PROPN
ejpam-6212	422	4	is	be	AUX
ejpam-6212	422	5	a	a	DET
ejpam-6212	422	6	vertex	vertex	NOUN
ejpam-6212	422	7	-	-	PUNCT
ejpam-6212	422	8	gluing	gluing	NOUN
ejpam-6212	422	9	of	of	ADP
ejpam-6212	422	10	c2t1	c2t1	NOUN
ejpam-6212	422	11	r.	r.	PROPN
ejpam-6212	422	12	g.	g.	PROPN
ejpam-6212	422	13	artes	artes	PROPN
ejpam-6212	422	14	jr	jr	PROPN
ejpam-6212	422	15	.	.	PROPN
ejpam-6212	422	16	et	et	PROPN
ejpam-6212	422	17	al	al	PROPN
ejpam-6212	422	18	.	.	PUNCT
ejpam-6212	422	19	/	/	SYM
ejpam-6212	422	20	eur	eur	PROPN
ejpam-6212	422	21	.	.	PUNCT
ejpam-6212	423	1	j.	j.	PROPN
ejpam-6212	423	2	pure	pure	PROPN
ejpam-6212	423	3	appl	appl	PROPN
ejpam-6212	423	4	.	.	PROPN
ejpam-6212	423	5	math	math	PROPN
ejpam-6212	423	6	,	,	PUNCT
ejpam-6212	423	7	18	18	NUM
ejpam-6212	423	8	(	(	PUNCT
ejpam-6212	423	9	4	4	NUM
ejpam-6212	423	10	)	)	PUNCT
ejpam-6212	423	11	(	(	PUNCT
ejpam-6212	423	12	2025	2025	NUM
ejpam-6212	423	13	)	)	PUNCT
ejpam-6212	423	14	,	,	PUNCT
ejpam-6212	423	15	6212	6212	NUM
ejpam-6212	423	16	10	10	NUM
ejpam-6212	423	17	of	of	ADP
ejpam-6212	423	18	20	20	NUM
ejpam-6212	423	19	and	and	CCONJ
ejpam-6212	423	20	c2t2	c2t2	INTJ
ejpam-6212	423	21	.	.	PUNCT
ejpam-6212	423	22	assume	assume	VERB
ejpam-6212	423	23	that	that	SCONJ
ejpam-6212	423	24	u1	u1	NOUN
ejpam-6212	423	25	=	=	SYM
ejpam-6212	423	26	v1	v1	PROPN
ejpam-6212	423	27	,	,	PUNCT
ejpam-6212	423	28	the	the	DET
ejpam-6212	423	29	spiro	spiro	NOUN
ejpam-6212	423	30	vertex	vertex	NOUN
ejpam-6212	423	31	.	.	PUNCT
ejpam-6212	424	1	consider	consider	VERB
ejpam-6212	424	2	the	the	DET
ejpam-6212	424	3	tree	tree	NOUN
ejpam-6212	424	4	-	-	PUNCT
ejpam-6212	424	5	partition	partition	NOUN
ejpam-6212	424	6	{	{	PUNCT
ejpam-6212	424	7	v1	v1	NOUN
ejpam-6212	424	8	=	=	SYM
ejpam-6212	424	9	u1	u1	NOUN
ejpam-6212	424	10	,	,	PUNCT
ejpam-6212	424	11	u2	u2	NOUN
ejpam-6212	424	12	,	,	PUNCT
ejpam-6212	424	13	.	.	PUNCT
ejpam-6212	424	14	.	.	PUNCT
ejpam-6212	425	1	.	.	PUNCT
ejpam-6212	426	1	,	,	PUNCT
ejpam-6212	426	2	u2t1	u2t1	INTJ
ejpam-6212	426	3	,	,	PUNCT
ejpam-6212	426	4	v2	v2	PROPN
ejpam-6212	426	5	,	,	PUNCT
ejpam-6212	426	6	v3	v3	PROPN
ejpam-6212	426	7	,	,	PUNCT
ejpam-6212	426	8	.	.	PUNCT
ejpam-6212	426	9	.	.	PUNCT
ejpam-6212	427	1	.	.	PUNCT
ejpam-6212	428	1	,	,	PUNCT
ejpam-6212	428	2	v2t2	v2t2	NOUN
ejpam-6212	428	3	}	}	PUNCT
ejpam-6212	428	4	of	of	ADP
ejpam-6212	428	5	v	v	NOUN
ejpam-6212	428	6	(	(	PUNCT
ejpam-6212	428	7	g	g	NOUN
ejpam-6212	428	8	)	)	PUNCT
ejpam-6212	428	9	using	use	VERB
ejpam-6212	428	10	its	its	PRON
ejpam-6212	428	11	projection	projection	NOUN
ejpam-6212	428	12	onto	onto	ADP
ejpam-6212	428	13	c2t1	c2t1	NOUN
ejpam-6212	428	14	∪	∪	NOUN
ejpam-6212	428	15	c2t2	c2t2	NOUN
ejpam-6212	428	16	.	.	PUNCT
ejpam-6212	429	1	that	that	PRON
ejpam-6212	429	2	is	be	AUX
ejpam-6212	429	3	,	,	PUNCT
ejpam-6212	429	4	ui	ui	PROPN
ejpam-6212	429	5	=	=	PUNCT
ejpam-6212	429	6	{	{	PUNCT
ejpam-6212	429	7	u	u	NOUN
ejpam-6212	429	8	∈	∈	PROPN
ejpam-6212	429	9	v	v	NOUN
ejpam-6212	429	10	(	(	PUNCT
ejpam-6212	429	11	g	g	NOUN
ejpam-6212	429	12	)	)	PUNCT
ejpam-6212	429	13	:	:	PUNCT
ejpam-6212	429	14	pc2t1∪c2t2	pc2t1∪c2t2	ADV
ejpam-6212	429	15	(	(	PUNCT
ejpam-6212	429	16	u	u	NOUN
ejpam-6212	429	17	)	)	PUNCT
ejpam-6212	429	18	=	=	SYM
ejpam-6212	430	1	ui	ui	PROPN
ejpam-6212	430	2	}	}	PUNCT
ejpam-6212	430	3	for	for	ADP
ejpam-6212	430	4	i	i	PROPN
ejpam-6212	430	5	∈	∈	PROPN
ejpam-6212	430	6	{	{	PUNCT
ejpam-6212	430	7	1	1	NUM
ejpam-6212	430	8	,	,	PUNCT
ejpam-6212	430	9	2	2	NUM
ejpam-6212	430	10	,	,	PUNCT
ejpam-6212	430	11	.	.	PUNCT
ejpam-6212	430	12	.	.	PUNCT
ejpam-6212	430	13	.	.	PUNCT
ejpam-6212	431	1	,	,	PUNCT
ejpam-6212	431	2	2t1	2t1	NUM
ejpam-6212	431	3	}	}	PUNCT
ejpam-6212	431	4	and	and	CCONJ
ejpam-6212	431	5	vj	vj	X
ejpam-6212	431	6	=	=	SYM
ejpam-6212	431	7	{	{	PUNCT
ejpam-6212	431	8	v	v	NUM
ejpam-6212	431	9	∈	∈	NOUN
ejpam-6212	431	10	v	v	NOUN
ejpam-6212	431	11	(	(	PUNCT
ejpam-6212	431	12	g	g	NOUN
ejpam-6212	431	13	)	)	PUNCT
ejpam-6212	431	14	:	:	PUNCT
ejpam-6212	431	15	pc2t1∪c2t2	pc2t1∪c2t2	INTJ
ejpam-6212	431	16	(	(	PUNCT
ejpam-6212	431	17	v	v	NOUN
ejpam-6212	431	18	)	)	PUNCT
ejpam-6212	431	19	=	=	SYM
ejpam-6212	431	20	vj	vj	PROPN
ejpam-6212	431	21	}	}	PUNCT
ejpam-6212	431	22	for	for	ADP
ejpam-6212	431	23	j	j	PROPN
ejpam-6212	431	24	∈	∈	PROPN
ejpam-6212	431	25	{	{	PUNCT
ejpam-6212	431	26	1	1	NUM
ejpam-6212	431	27	,	,	PUNCT
ejpam-6212	431	28	2	2	NUM
ejpam-6212	431	29	,	,	PUNCT
ejpam-6212	431	30	.	.	PUNCT
ejpam-6212	431	31	.	.	PUNCT
ejpam-6212	431	32	.	.	PUNCT
ejpam-6212	432	1	,	,	PUNCT
ejpam-6212	432	2	2t2	2t2	NUM
ejpam-6212	432	3	}	}	PUNCT
ejpam-6212	432	4	.	.	PUNCT
ejpam-6212	433	1	then	then	ADV
ejpam-6212	433	2	u1	u1	NOUN
ejpam-6212	433	3	=	=	SYM
ejpam-6212	433	4	v1	v1	PROPN
ejpam-6212	433	5	=	=	SYM
ejpam-6212	433	6	{	{	PUNCT
ejpam-6212	433	7	u1	u1	NOUN
ejpam-6212	433	8	=	=	SYM
ejpam-6212	433	9	v1	v1	PROPN
ejpam-6212	433	10	}	}	PUNCT
ejpam-6212	433	11	,	,	PUNCT
ejpam-6212	433	12	u2	u2	NOUN
ejpam-6212	433	13	=	=	PUNCT
ejpam-6212	433	14	{	{	PUNCT
ejpam-6212	433	15	u2	u2	PROPN
ejpam-6212	433	16	}	}	PUNCT
ejpam-6212	433	17	,	,	PUNCT
ejpam-6212	433	18	u3	u3	NOUN
ejpam-6212	433	19	=	=	SYM
ejpam-6212	433	20	{	{	PUNCT
ejpam-6212	433	21	u3	u3	PROPN
ejpam-6212	433	22	}	}	PUNCT
ejpam-6212	433	23	,	,	PUNCT
ejpam-6212	433	24	.	.	PUNCT
ejpam-6212	433	25	.	.	PUNCT
ejpam-6212	433	26	.	.	PUNCT
ejpam-6212	434	1	,	,	PUNCT
ejpam-6212	434	2	u2t1	u2t1	PUNCT
ejpam-6212	434	3	=	=	PRON
ejpam-6212	434	4	{	{	PUNCT
ejpam-6212	434	5	u2t1	u2t1	NOUN
ejpam-6212	434	6	}	}	PUNCT
ejpam-6212	434	7	,	,	PUNCT
ejpam-6212	434	8	v2	v2	PROPN
ejpam-6212	434	9	=	=	SYM
ejpam-6212	434	10	{	{	PUNCT
ejpam-6212	434	11	v2	v2	NOUN
ejpam-6212	434	12	}	}	PUNCT
ejpam-6212	434	13	,	,	PUNCT
ejpam-6212	434	14	v3	v3	PROPN
ejpam-6212	434	15	=	=	SYM
ejpam-6212	434	16	{	{	PUNCT
ejpam-6212	434	17	v3	v3	PROPN
ejpam-6212	434	18	}	}	PUNCT
ejpam-6212	434	19	,	,	PUNCT
ejpam-6212	434	20	.	.	PUNCT
ejpam-6212	434	21	.	.	PUNCT
ejpam-6212	434	22	.	.	PUNCT
ejpam-6212	435	1	,	,	PUNCT
ejpam-6212	435	2	v2t2	v2t2	X
ejpam-6212	435	3	=	=	X
ejpam-6212	435	4	{	{	PUNCT
ejpam-6212	435	5	v2t2	v2t2	NOUN
ejpam-6212	435	6	}	}	PUNCT
ejpam-6212	435	7	.	.	PUNCT
ejpam-6212	436	1	hence	hence	ADV
ejpam-6212	436	2	,	,	PUNCT
ejpam-6212	436	3	for	for	ADP
ejpam-6212	436	4	each	each	DET
ejpam-6212	436	5	i	i	PRON
ejpam-6212	436	6	∈	∈	PROPN
ejpam-6212	436	7	{	{	PUNCT
ejpam-6212	436	8	1	1	NUM
ejpam-6212	436	9	,	,	PUNCT
ejpam-6212	436	10	2	2	NUM
ejpam-6212	436	11	,	,	PUNCT
ejpam-6212	436	12	.	.	PUNCT
ejpam-6212	436	13	.	.	PUNCT
ejpam-6212	436	14	.	.	PUNCT
ejpam-6212	437	1	,	,	PUNCT
ejpam-6212	438	1	2t1	2t1	NUM
ejpam-6212	438	2	}	}	PUNCT
ejpam-6212	438	3	,	,	PUNCT
ejpam-6212	438	4	|ui|	|ui|	PROPN
ejpam-6212	438	5	=	=	SYM
ejpam-6212	438	6	1	1	X
ejpam-6212	438	7	.	.	PUNCT
ejpam-6212	438	8	similarly	similarly	ADV
ejpam-6212	438	9	,	,	PUNCT
ejpam-6212	438	10	for	for	ADP
ejpam-6212	438	11	each	each	DET
ejpam-6212	438	12	j	j	PROPN
ejpam-6212	438	13	∈	∈	PROPN
ejpam-6212	438	14	{	{	PUNCT
ejpam-6212	438	15	1	1	NUM
ejpam-6212	438	16	,	,	PUNCT
ejpam-6212	438	17	2	2	NUM
ejpam-6212	438	18	,	,	PUNCT
ejpam-6212	438	19	.	.	PUNCT
ejpam-6212	438	20	.	.	PUNCT
ejpam-6212	438	21	.	.	PUNCT
ejpam-6212	439	1	,	,	PUNCT
ejpam-6212	439	2	2t2	2t2	NUM
ejpam-6212	439	3	}	}	PUNCT
ejpam-6212	439	4	,	,	PUNCT
ejpam-6212	439	5	|vj	|vj	CCONJ
ejpam-6212	439	6	|	|	ADV
ejpam-6212	439	7	=	=	SYM
ejpam-6212	439	8	1	1	X
ejpam-6212	439	9	.	.	X
ejpam-6212	439	10	for	for	ADP
ejpam-6212	439	11	each	each	DET
ejpam-6212	439	12	i	i	PRON
ejpam-6212	439	13	∈	∈	PROPN
ejpam-6212	439	14	{	{	PUNCT
ejpam-6212	439	15	2	2	NUM
ejpam-6212	439	16	,	,	PUNCT
ejpam-6212	439	17	3	3	NUM
ejpam-6212	439	18	,	,	PUNCT
ejpam-6212	439	19	.	.	PUNCT
ejpam-6212	439	20	.	.	PUNCT
ejpam-6212	439	21	.	.	PUNCT
ejpam-6212	440	1	,	,	PUNCT
ejpam-6212	440	2	t1	t1	NOUN
ejpam-6212	440	3	}	}	PUNCT
ejpam-6212	440	4	,	,	PUNCT
ejpam-6212	440	5	d(u1	d(u1	NOUN
ejpam-6212	440	6	,	,	PUNCT
ejpam-6212	440	7	ui	ui	NOUN
ejpam-6212	440	8	)	)	PUNCT
ejpam-6212	440	9	=	=	SYM
ejpam-6212	440	10	d(u1	d(u1	NOUN
ejpam-6212	440	11	,	,	PUNCT
ejpam-6212	440	12	u2t1−i+2	u2t1−i+2	PROPN
ejpam-6212	440	13	)	)	PUNCT
ejpam-6212	441	1	=	=	SYM
ejpam-6212	441	2	i−	i−	PROPN
ejpam-6212	441	3	1	1	NUM
ejpam-6212	441	4	.	.	PUNCT
ejpam-6212	442	1	hence	hence	ADV
ejpam-6212	442	2	,	,	PUNCT
ejpam-6212	442	3	2t1∑	2t1∑	NUM
ejpam-6212	442	4	i=2	i=2	PROPN
ejpam-6212	442	5	∑	∑	PROPN
ejpam-6212	442	6	(	(	PUNCT
ejpam-6212	442	7	u	u	NOUN
ejpam-6212	442	8	,	,	PUNCT
ejpam-6212	442	9	v)∈vt2	v)∈vt2	PROPN
ejpam-6212	442	10	+	+	NOUN
ejpam-6212	442	11	1×ui	1×ui	NUM
ejpam-6212	442	12	d(u	d(u	PROPN
ejpam-6212	442	13	,	,	PUNCT
ejpam-6212	442	14	v	v	NOUN
ejpam-6212	442	15	)	)	PUNCT
ejpam-6212	442	16	=	=	SYM
ejpam-6212	442	17	(	(	PUNCT
ejpam-6212	442	18	t2	t2	PROPN
ejpam-6212	442	19	+	+	CCONJ
ejpam-6212	442	20	t1	t1	NOUN
ejpam-6212	442	21	)	)	PUNCT
ejpam-6212	442	22	+	+	CCONJ
ejpam-6212	442	23	2	2	NUM
ejpam-6212	442	24	t1∑	t1∑	NOUN
ejpam-6212	442	25	i=2	i=2	PROPN
ejpam-6212	442	26	(	(	PUNCT
ejpam-6212	442	27	t2	t2	PROPN
ejpam-6212	442	28	+	+	CCONJ
ejpam-6212	442	29	i−	i−	PROPN
ejpam-6212	442	30	1	1	NUM
ejpam-6212	442	31	)	)	PUNCT
ejpam-6212	442	32	=	=	SYM
ejpam-6212	442	33	2t1t2	2t1t2	PROPN
ejpam-6212	442	34	+	+	CCONJ
ejpam-6212	442	35	t21	t21	PROPN
ejpam-6212	442	36	−	−	PROPN
ejpam-6212	442	37	t2	t2	PROPN
ejpam-6212	442	38	.	.	PUNCT
ejpam-6212	443	1	similarly	similarly	ADV
ejpam-6212	443	2	,	,	PUNCT
ejpam-6212	443	3	for	for	ADP
ejpam-6212	443	4	each	each	DET
ejpam-6212	443	5	j	j	PROPN
ejpam-6212	443	6	∈	∈	PROPN
ejpam-6212	443	7	{	{	PUNCT
ejpam-6212	443	8	2	2	NUM
ejpam-6212	443	9	,	,	PUNCT
ejpam-6212	443	10	3	3	NUM
ejpam-6212	443	11	,	,	PUNCT
ejpam-6212	443	12	.	.	PUNCT
ejpam-6212	443	13	.	.	PUNCT
ejpam-6212	443	14	.	.	PUNCT
ejpam-6212	444	1	,	,	PUNCT
ejpam-6212	444	2	t2	t2	NOUN
ejpam-6212	444	3	}	}	PUNCT
ejpam-6212	444	4	,	,	PUNCT
ejpam-6212	444	5	d(v1	d(v1	NOUN
ejpam-6212	444	6	,	,	PUNCT
ejpam-6212	444	7	vj	vj	PROPN
ejpam-6212	444	8	)	)	PUNCT
ejpam-6212	445	1	=	=	SYM
ejpam-6212	445	2	d(v1	d(v1	NOUN
ejpam-6212	445	3	,	,	PUNCT
ejpam-6212	445	4	v2t2−j+2	v2t2−j+2	NOUN
ejpam-6212	445	5	)	)	PUNCT
ejpam-6212	445	6	=	=	SYM
ejpam-6212	446	1	j	j	PROPN
ejpam-6212	446	2	−	−	NOUN
ejpam-6212	447	1	1	1	NUM
ejpam-6212	447	2	.	.	PUNCT
ejpam-6212	448	1	thus	thus	ADV
ejpam-6212	448	2	,	,	PUNCT
ejpam-6212	448	3	2t2∑	2t2∑	PROPN
ejpam-6212	448	4	j=2	j=2	NOUN
ejpam-6212	448	5	∑	∑	PROPN
ejpam-6212	448	6	(	(	PUNCT
ejpam-6212	448	7	u	u	NOUN
ejpam-6212	448	8	,	,	PUNCT
ejpam-6212	448	9	v)∈ut1	v)∈ut1	VERB
ejpam-6212	448	10	+	+	PRON
ejpam-6212	448	11	1×vj	1×vj	NUM
ejpam-6212	448	12	d(u	d(u	NOUN
ejpam-6212	448	13	,	,	PUNCT
ejpam-6212	448	14	v	v	NOUN
ejpam-6212	448	15	)	)	PUNCT
ejpam-6212	448	16	=	=	SYM
ejpam-6212	448	17	(	(	PUNCT
ejpam-6212	448	18	t1	t1	NOUN
ejpam-6212	448	19	+	+	NUM
ejpam-6212	448	20	t2	t2	NOUN
ejpam-6212	448	21	)	)	PUNCT
ejpam-6212	449	1	+	+	CCONJ
ejpam-6212	449	2	2	2	NUM
ejpam-6212	449	3	t2∑	t2∑	PROPN
ejpam-6212	449	4	j=2	j=2	PROPN
ejpam-6212	449	5	(	(	PUNCT
ejpam-6212	449	6	t1	t1	NOUN
ejpam-6212	449	7	+	+	PROPN
ejpam-6212	449	8	j	j	PROPN
ejpam-6212	449	9	−	−	PROPN
ejpam-6212	449	10	1	1	NUM
ejpam-6212	449	11	)	)	PUNCT
ejpam-6212	449	12	=	=	SYM
ejpam-6212	449	13	2t2t1	2t2t1	NUM
ejpam-6212	449	14	+	+	CCONJ
ejpam-6212	449	15	t22	t22	PROPN
ejpam-6212	449	16	−	−	PROPN
ejpam-6212	449	17	t1	t1	PROPN
ejpam-6212	449	18	.	.	PUNCT
ejpam-6212	450	1	by	by	ADP
ejpam-6212	450	2	lemma	lemma	PROPN
ejpam-6212	450	3	2	2	NUM
ejpam-6212	450	4	,	,	PUNCT
ejpam-6212	450	5	we	we	PRON
ejpam-6212	450	6	have	have	VERB
ejpam-6212	450	7	wg(g	wg(g	NOUN
ejpam-6212	450	8	)	)	PUNCT
ejpam-6212	451	1	=	=	PUNCT
ejpam-6212	451	2	∑	∑	PUNCT
ejpam-6212	451	3	{	{	PUNCT
ejpam-6212	451	4	u	u	NOUN
ejpam-6212	451	5	,	,	PUNCT
ejpam-6212	451	6	v}⊆v	v}⊆v	PROPN
ejpam-6212	451	7	(	(	PUNCT
ejpam-6212	451	8	g	g	NOUN
ejpam-6212	451	9	)	)	PUNCT
ejpam-6212	451	10	α(u	α(u	NOUN
ejpam-6212	451	11	,	,	PUNCT
ejpam-6212	451	12	v)d(u	v)d(u	NOUN
ejpam-6212	451	13	,	,	PUNCT
ejpam-6212	451	14	v	v	NOUN
ejpam-6212	451	15	)	)	PUNCT
ejpam-6212	451	16	=	=	SYM
ejpam-6212	451	17	w	w	PROPN
ejpam-6212	451	18	(	(	PUNCT
ejpam-6212	451	19	g	g	NOUN
ejpam-6212	451	20	)	)	PUNCT
ejpam-6212	452	1	+	+	CCONJ
ejpam-6212	452	2	t1∑	t1∑	PROPN
ejpam-6212	452	3	i=1	i=1	PROPN
ejpam-6212	452	4	w	w	PROPN
ejpam-6212	452	5	(	(	PUNCT
ejpam-6212	452	6	ui	ui	PROPN
ejpam-6212	452	7	,	,	PUNCT
ejpam-6212	452	8	ui+t1	ui+t1	ADV
ejpam-6212	452	9	;	;	PUNCT
ejpam-6212	452	10	g	g	NOUN
ejpam-6212	452	11	)	)	PUNCT
ejpam-6212	453	1	+	+	PUNCT
ejpam-6212	453	2	t2∑	t2∑	PROPN
ejpam-6212	453	3	j=1	j=1	NOUN
ejpam-6212	453	4	w	w	PROPN
ejpam-6212	453	5	(	(	PUNCT
ejpam-6212	453	6	vj	vj	INTJ
ejpam-6212	453	7	,	,	PUNCT
ejpam-6212	453	8	vj+t2	vj+t2	NOUN
ejpam-6212	453	9	;	;	PUNCT
ejpam-6212	453	10	g	g	X
ejpam-6212	453	11	)	)	PUNCT
ejpam-6212	454	1	+	+	NUM
ejpam-6212	454	2	2t1∑	2t1∑	NUM
ejpam-6212	454	3	i=2	i=2	PROPN
ejpam-6212	454	4	w	w	PROPN
ejpam-6212	454	5	(	(	PUNCT
ejpam-6212	454	6	vt2	vt2	PROPN
ejpam-6212	454	7	+	+	PROPN
ejpam-6212	454	8	1	1	NUM
ejpam-6212	454	9	,	,	PUNCT
ejpam-6212	454	10	ui;g	ui;g	ADJ
ejpam-6212	454	11	)	)	PUNCT
ejpam-6212	455	1	+	+	NUM
ejpam-6212	455	2	2t2∑	2t2∑	NUM
ejpam-6212	455	3	j=2	j=2	PROPN
ejpam-6212	455	4	w	w	NOUN
ejpam-6212	455	5	(	(	PUNCT
ejpam-6212	455	6	ut1	ut1	PROPN
ejpam-6212	455	7	+	+	ADJ
ejpam-6212	455	8	1	1	NUM
ejpam-6212	455	9	,	,	PUNCT
ejpam-6212	455	10	vj	vj	INTJ
ejpam-6212	455	11	;	;	PUNCT
ejpam-6212	455	12	g	g	X
ejpam-6212	455	13	)	)	PUNCT
ejpam-6212	456	1	+	+	NOUN
ejpam-6212	456	2	w	w	NOUN
ejpam-6212	456	3	(	(	PUNCT
ejpam-6212	456	4	ut1	ut1	PROPN
ejpam-6212	456	5	+	+	NOUN
ejpam-6212	456	6	1	1	NUM
ejpam-6212	456	7	,	,	PUNCT
ejpam-6212	456	8	vt2	vt2	VERB
ejpam-6212	456	9	+	+	NOUN
ejpam-6212	456	10	1;g	1;g	NOUN
ejpam-6212	456	11	)	)	PUNCT
ejpam-6212	456	12	=	=	SYM
ejpam-6212	456	13	w	w	PROPN
ejpam-6212	456	14	(	(	PUNCT
ejpam-6212	456	15	g	g	NOUN
ejpam-6212	456	16	)	)	PUNCT
ejpam-6212	457	1	+	+	CCONJ
ejpam-6212	457	2	t1∑	t1∑	PROPN
ejpam-6212	457	3	i=1	i=1	ADV
ejpam-6212	457	4	∑	∑	PROPN
ejpam-6212	457	5	(	(	PUNCT
ejpam-6212	457	6	u	u	NOUN
ejpam-6212	457	7	,	,	PUNCT
ejpam-6212	457	8	v)∈ui×ui+t1	v)∈ui×ui+t1	ADP
ejpam-6212	457	9	d(u	d(u	PROPN
ejpam-6212	457	10	,	,	PUNCT
ejpam-6212	457	11	v	v	NOUN
ejpam-6212	457	12	)	)	PUNCT
ejpam-6212	457	13	+	+	PUNCT
ejpam-6212	457	14	t2∑	t2∑	PROPN
ejpam-6212	457	15	j=1	j=1	NOUN
ejpam-6212	457	16	∑	∑	PUNCT
ejpam-6212	457	17	(	(	PUNCT
ejpam-6212	457	18	u	u	NOUN
ejpam-6212	457	19	,	,	PUNCT
ejpam-6212	457	20	v)∈vj×vj+t2	v)∈vj×vj+t2	PROPN
ejpam-6212	457	21	d(u	d(u	PROPN
ejpam-6212	457	22	,	,	PUNCT
ejpam-6212	457	23	v	v	NOUN
ejpam-6212	457	24	)	)	PUNCT
ejpam-6212	457	25	+	+	NUM
ejpam-6212	457	26	2t1∑	2t1∑	NUM
ejpam-6212	457	27	i=2	i=2	PROPN
ejpam-6212	457	28	∑	∑	PROPN
ejpam-6212	457	29	(	(	PUNCT
ejpam-6212	457	30	u	u	NOUN
ejpam-6212	457	31	,	,	PUNCT
ejpam-6212	457	32	v)∈vt2	v)∈vt2	PROPN
ejpam-6212	457	33	+	+	NOUN
ejpam-6212	457	34	1×ui	1×ui	NUM
ejpam-6212	457	35	d(u	d(u	PROPN
ejpam-6212	457	36	,	,	PUNCT
ejpam-6212	457	37	v	v	NOUN
ejpam-6212	457	38	)	)	PUNCT
ejpam-6212	457	39	+	+	SYM
ejpam-6212	457	40	2t2∑	2t2∑	NUM
ejpam-6212	457	41	j=2	j=2	NOUN
ejpam-6212	457	42	∑	∑	PROPN
ejpam-6212	457	43	(	(	PUNCT
ejpam-6212	457	44	u	u	NOUN
ejpam-6212	457	45	,	,	PUNCT
ejpam-6212	457	46	v)∈ut1	v)∈ut1	VERB
ejpam-6212	457	47	+	+	PRON
ejpam-6212	457	48	1×vj	1×vj	NUM
ejpam-6212	457	49	d(u	d(u	NOUN
ejpam-6212	457	50	,	,	PUNCT
ejpam-6212	457	51	v	v	NOUN
ejpam-6212	457	52	)	)	PUNCT
ejpam-6212	457	53	+	+	CCONJ
ejpam-6212	457	54	∑	∑	PROPN
ejpam-6212	457	55	(	(	PUNCT
ejpam-6212	457	56	u	u	NOUN
ejpam-6212	457	57	,	,	PUNCT
ejpam-6212	457	58	v)∈ut1	v)∈ut1	VERB
ejpam-6212	457	59	+	+	NOUN
ejpam-6212	457	60	1×vt2	1×vt2	NOUN
ejpam-6212	457	61	+	+	ADJ
ejpam-6212	457	62	1	1	NUM
ejpam-6212	457	63	d(u	d(u	PROPN
ejpam-6212	457	64	,	,	PUNCT
ejpam-6212	457	65	v	v	NOUN
ejpam-6212	457	66	)	)	PUNCT
ejpam-6212	457	67	=	=	SYM
ejpam-6212	457	68	w	w	PROPN
ejpam-6212	457	69	(	(	PUNCT
ejpam-6212	457	70	g	g	NOUN
ejpam-6212	457	71	)	)	PUNCT
ejpam-6212	457	72	+	+	CCONJ
ejpam-6212	457	73	t21	t21	NOUN
ejpam-6212	457	74	+	+	CCONJ
ejpam-6212	457	75	t22	t22	NOUN
ejpam-6212	457	76	+	+	PROPN
ejpam-6212	458	1	[	[	X
ejpam-6212	458	2	2t1t2	2t1t2	ADJ
ejpam-6212	458	3	+	+	CCONJ
ejpam-6212	458	4	t21	t21	PROPN
ejpam-6212	458	5	−	−	PROPN
ejpam-6212	458	6	t2	t2	PROPN
ejpam-6212	458	7	]	]	PUNCT
ejpam-6212	459	1	+	+	CCONJ
ejpam-6212	459	2	[	[	X
ejpam-6212	459	3	2t2t1	2t2t1	NUM
ejpam-6212	459	4	+	+	CCONJ
ejpam-6212	459	5	t22	t22	PROPN
ejpam-6212	459	6	−	−	PROPN
ejpam-6212	459	7	t1	t1	PROPN
ejpam-6212	459	8	]	]	X
ejpam-6212	460	1	+	+	CCONJ
ejpam-6212	460	2	(	(	PUNCT
ejpam-6212	460	3	t1	t1	NOUN
ejpam-6212	460	4	+	+	NUM
ejpam-6212	460	5	t2	t2	NOUN
ejpam-6212	460	6	)	)	PUNCT
ejpam-6212	461	1	=	=	SYM
ejpam-6212	461	2	w	w	PROPN
ejpam-6212	461	3	(	(	PUNCT
ejpam-6212	461	4	g	g	NOUN
ejpam-6212	461	5	)	)	PUNCT
ejpam-6212	461	6	+	+	NOUN
ejpam-6212	462	1	2(t1	2(t1	NUM
ejpam-6212	462	2	+	+	NUM
ejpam-6212	462	3	t2	t2	NOUN
ejpam-6212	462	4	)	)	PUNCT
ejpam-6212	462	5	2	2	NUM
ejpam-6212	462	6	.	.	PUNCT
ejpam-6212	462	7	r.	r.	PROPN
ejpam-6212	462	8	g.	g.	PROPN
ejpam-6212	462	9	artes	artes	PROPN
ejpam-6212	462	10	jr	jr	PROPN
ejpam-6212	462	11	.	.	PROPN
ejpam-6212	462	12	et	et	PROPN
ejpam-6212	463	1	al	al	PROPN
ejpam-6212	463	2	.	.	PUNCT
ejpam-6212	463	3	/	/	SYM
ejpam-6212	463	4	eur	eur	PROPN
ejpam-6212	463	5	.	.	PUNCT
ejpam-6212	464	1	j.	j.	PROPN
ejpam-6212	464	2	pure	pure	PROPN
ejpam-6212	464	3	appl	appl	PROPN
ejpam-6212	464	4	.	.	PROPN
ejpam-6212	464	5	math	math	PROPN
ejpam-6212	464	6	,	,	PUNCT
ejpam-6212	464	7	18	18	NUM
ejpam-6212	464	8	(	(	PUNCT
ejpam-6212	464	9	4	4	NUM
ejpam-6212	464	10	)	)	PUNCT
ejpam-6212	464	11	(	(	PUNCT
ejpam-6212	464	12	2025	2025	NUM
ejpam-6212	464	13	)	)	PUNCT
ejpam-6212	464	14	,	,	PUNCT
ejpam-6212	464	15	6212	6212	NUM
ejpam-6212	464	16	11	11	NUM
ejpam-6212	464	17	of	of	ADP
ejpam-6212	464	18	20	20	NUM
ejpam-6212	464	19	6	6	NUM
ejpam-6212	464	20	.	.	PUNCT
ejpam-6212	465	1	bounds	bound	NOUN
ejpam-6212	465	2	of	of	ADP
ejpam-6212	465	3	g	g	NOUN
ejpam-6212	465	4	-	-	PUNCT
ejpam-6212	465	5	wiener	wiener	NOUN
ejpam-6212	465	6	index	index	NOUN
ejpam-6212	465	7	with	with	ADP
ejpam-6212	465	8	gutman	gutman	NOUN
ejpam-6212	465	9	index	index	NOUN
ejpam-6212	465	10	the	the	DET
ejpam-6212	465	11	following	following	ADJ
ejpam-6212	465	12	result	result	NOUN
ejpam-6212	465	13	establishes	establish	VERB
ejpam-6212	465	14	the	the	DET
ejpam-6212	465	15	extremal	extremal	ADJ
ejpam-6212	465	16	bounds	bound	NOUN
ejpam-6212	465	17	for	for	ADP
ejpam-6212	465	18	the	the	DET
ejpam-6212	465	19	geodetic	geodetic	ADJ
ejpam-6212	465	20	-	-	PUNCT
ejpam-6212	465	21	wiener	wiener	NOUN
ejpam-6212	465	22	index	index	NOUN
ejpam-6212	465	23	of	of	ADP
ejpam-6212	465	24	a	a	DET
ejpam-6212	465	25	simple	simple	ADJ
ejpam-6212	465	26	spirocyclic	spirocyclic	NOUN
ejpam-6212	465	27	graph	graph	NOUN
ejpam-6212	465	28	g	g	NOUN
ejpam-6212	465	29	containing	contain	VERB
ejpam-6212	465	30	even	even	ADV
ejpam-6212	465	31	cycles	cycle	NOUN
ejpam-6212	465	32	in	in	ADP
ejpam-6212	465	33	terms	term	NOUN
ejpam-6212	465	34	of	of	ADP
ejpam-6212	465	35	the	the	DET
ejpam-6212	465	36	gutman	gutman	NOUN
ejpam-6212	465	37	index	index	NOUN
ejpam-6212	465	38	of	of	ADP
ejpam-6212	465	39	g	g	PROPN
ejpam-6212	465	40	as	as	SCONJ
ejpam-6212	465	41	defined	define	VERB
ejpam-6212	465	42	in	in	ADP
ejpam-6212	465	43	[	[	X
ejpam-6212	465	44	17	17	NUM
ejpam-6212	465	45	]	]	PUNCT
ejpam-6212	465	46	.	.	PUNCT
ejpam-6212	466	1	theorem	theorem	NOUN
ejpam-6212	466	2	3	3	X
ejpam-6212	466	3	.	.	PUNCT
ejpam-6212	467	1	let	let	VERB
ejpam-6212	467	2	g	g	PRON
ejpam-6212	467	3	be	be	AUX
ejpam-6212	467	4	a	a	DET
ejpam-6212	467	5	simple	simple	ADJ
ejpam-6212	467	6	spirocyclic	spirocyclic	NOUN
ejpam-6212	467	7	graph	graph	NOUN
ejpam-6212	467	8	with	with	ADP
ejpam-6212	467	9	even	even	ADV
ejpam-6212	467	10	cycles	cycle	NOUN
ejpam-6212	467	11	c2t1	c2t1	NOUN
ejpam-6212	468	1	=	=	SYM
ejpam-6212	469	1	[	[	X
ejpam-6212	469	2	u1	u1	NOUN
ejpam-6212	469	3	,	,	PUNCT
ejpam-6212	469	4	u2	u2	NOUN
ejpam-6212	469	5	,	,	PUNCT
ejpam-6212	469	6	.	.	PUNCT
ejpam-6212	469	7	.	.	PUNCT
ejpam-6212	469	8	.	.	PUNCT
ejpam-6212	470	1	,	,	PUNCT
ejpam-6212	470	2	u2t1	u2t1	VERB
ejpam-6212	470	3	]	]	PUNCT
ejpam-6212	470	4	and	and	CCONJ
ejpam-6212	470	5	c2t2	c2t2	NOUN
ejpam-6212	471	1	=	=	PUNCT
ejpam-6212	472	1	[	[	X
ejpam-6212	472	2	u1	u1	NOUN
ejpam-6212	472	3	=	=	SYM
ejpam-6212	472	4	v1	v1	NOUN
ejpam-6212	472	5	,	,	PUNCT
ejpam-6212	472	6	v2	v2	NOUN
ejpam-6212	472	7	,	,	PUNCT
ejpam-6212	472	8	.	.	PUNCT
ejpam-6212	472	9	.	.	PUNCT
ejpam-6212	472	10	.	.	PUNCT
ejpam-6212	473	1	,	,	PUNCT
ejpam-6212	473	2	v2t2	v2t2	X
ejpam-6212	473	3	]	]	X
ejpam-6212	473	4	,	,	PUNCT
ejpam-6212	473	5	for	for	ADP
ejpam-6212	473	6	some	some	DET
ejpam-6212	473	7	natural	natural	ADJ
ejpam-6212	473	8	numbers	number	NOUN
ejpam-6212	473	9	t1	t1	PROPN
ejpam-6212	473	10	,	,	PUNCT
ejpam-6212	473	11	t2	t2	NOUN
ejpam-6212	473	12	≥	≥	NUM
ejpam-6212	473	13	2	2	NUM
ejpam-6212	473	14	.	.	PUNCT
ejpam-6212	474	1	then	then	ADV
ejpam-6212	474	2	1	1	NUM
ejpam-6212	474	3	∆2	∆2	PROPN
ejpam-6212	474	4	gut(g	gut(g	PROPN
ejpam-6212	474	5	)	)	PUNCT
ejpam-6212	475	1	+	+	NOUN
ejpam-6212	475	2	at1	at1	PROPN
ejpam-6212	475	3	+	+	PROPN
ejpam-6212	475	4	bt2	bt2	PROPN
ejpam-6212	475	5	<	<	X
ejpam-6212	475	6	wg(g	wg(g	PROPN
ejpam-6212	475	7	)	)	PUNCT
ejpam-6212	475	8	<	<	X
ejpam-6212	475	9	1	1	NUM
ejpam-6212	475	10	δ2	δ2	VERB
ejpam-6212	475	11	gut(g	gut(g	NOUN
ejpam-6212	475	12	)	)	PUNCT
ejpam-6212	475	13	+	+	NUM
ejpam-6212	475	14	cdiam(g	cdiam(g	X
ejpam-6212	475	15	)	)	PUNCT
ejpam-6212	475	16	,	,	PUNCT
ejpam-6212	475	17	where	where	SCONJ
ejpam-6212	475	18	{	{	PUNCT
ejpam-6212	475	19	u1	u1	NOUN
ejpam-6212	475	20	=	=	SYM
ejpam-6212	475	21	v1	v1	PROPN
ejpam-6212	475	22	,	,	PUNCT
ejpam-6212	475	23	u2	u2	NOUN
ejpam-6212	475	24	,	,	PUNCT
ejpam-6212	475	25	.	.	PUNCT
ejpam-6212	475	26	.	.	PUNCT
ejpam-6212	475	27	.	.	PUNCT
ejpam-6212	476	1	,	,	PUNCT
ejpam-6212	476	2	u2t1	u2t1	INTJ
ejpam-6212	476	3	,	,	PUNCT
ejpam-6212	476	4	v2	v2	PROPN
ejpam-6212	476	5	,	,	PUNCT
ejpam-6212	476	6	.	.	PUNCT
ejpam-6212	476	7	.	.	PUNCT
ejpam-6212	477	1	.	.	PUNCT
ejpam-6212	478	1	,	,	PUNCT
ejpam-6212	478	2	v2t2	v2t2	NOUN
ejpam-6212	478	3	}	}	PUNCT
ejpam-6212	478	4	is	be	AUX
ejpam-6212	478	5	the	the	DET
ejpam-6212	478	6	tree	tree	NOUN
ejpam-6212	478	7	-	-	PUNCT
ejpam-6212	478	8	partition	partition	NOUN
ejpam-6212	478	9	of	of	ADP
ejpam-6212	478	10	v	v	NOUN
ejpam-6212	478	11	(	(	PUNCT
ejpam-6212	478	12	g	g	NOUN
ejpam-6212	478	13	)	)	PUNCT
ejpam-6212	478	14	with	with	ADP
ejpam-6212	478	15	respect	respect	NOUN
ejpam-6212	478	16	to	to	ADP
ejpam-6212	478	17	the	the	DET
ejpam-6212	478	18	projection	projection	NOUN
ejpam-6212	478	19	of	of	ADP
ejpam-6212	478	20	v	v	NOUN
ejpam-6212	478	21	(	(	PUNCT
ejpam-6212	478	22	g	g	NOUN
ejpam-6212	478	23	)	)	PUNCT
ejpam-6212	478	24	onto	onto	ADP
ejpam-6212	478	25	the	the	DET
ejpam-6212	478	26	union	union	NOUN
ejpam-6212	478	27	of	of	ADP
ejpam-6212	478	28	the	the	DET
ejpam-6212	478	29	cycles	cycle	NOUN
ejpam-6212	478	30	c2t1	c2t1	NOUN
ejpam-6212	478	31	and	and	CCONJ
ejpam-6212	478	32	c2t2	c2t2	NOUN
ejpam-6212	478	33	,	,	PUNCT
ejpam-6212	478	34	and	and	CCONJ
ejpam-6212	479	1	a	a	DET
ejpam-6212	479	2	=	=	X
ejpam-6212	479	3	t1∑	t1∑	PROPN
ejpam-6212	479	4	i=1	i=1	PROPN
ejpam-6212	479	5	|ui||ui+t1	|ui||ui+t1	ADP
ejpam-6212	479	6	|+	|+	NOUN
ejpam-6212	479	7	2t2∑	2t2∑	NUM
ejpam-6212	479	8	j=2	j=2	NOUN
ejpam-6212	479	9	|ut1	|ut1	PUNCT
ejpam-6212	479	10	+	+	NOUN
ejpam-6212	479	11	1||vj	1||vj	NOUN
ejpam-6212	479	12	|+	|+	X
ejpam-6212	479	13	|ut1	|ut1	PUNCT
ejpam-6212	479	14	+	+	NOUN
ejpam-6212	479	15	1||vt2	1||vt2	NUM
ejpam-6212	479	16	+	+	NOUN
ejpam-6212	479	17	1|	1|	NUM
ejpam-6212	479	18	,	,	PUNCT
ejpam-6212	479	19	b	b	NOUN
ejpam-6212	479	20	=	=	SYM
ejpam-6212	479	21	t2∑	t2∑	PROPN
ejpam-6212	479	22	j=1	j=1	NOUN
ejpam-6212	479	23	|vj	|vj	X
ejpam-6212	479	24	||vj+t2	||vj+t2	PROPN
ejpam-6212	479	25	|+	|+	NOUN
ejpam-6212	479	26	2t1∑	2t1∑	NUM
ejpam-6212	479	27	i=2	i=2	PROPN
ejpam-6212	479	28	|vt2	|vt2	PROPN
ejpam-6212	480	1	+	+	NOUN
ejpam-6212	480	2	1||ui|+	1||ui|+	NOUN
ejpam-6212	480	3	|ut1	|ut1	NOUN
ejpam-6212	480	4	+	+	NOUN
ejpam-6212	480	5	1||vt2	1||vt2	NUM
ejpam-6212	480	6	+	+	NOUN
ejpam-6212	480	7	1|	1|	NUM
ejpam-6212	480	8	,	,	PUNCT
ejpam-6212	480	9	and	and	CCONJ
ejpam-6212	480	10	c	c	X
ejpam-6212	481	1	=	=	SYM
ejpam-6212	481	2	t1∑	t1∑	PROPN
ejpam-6212	481	3	i=1	i=1	PROPN
ejpam-6212	481	4	|ui||ui+t1	|ui||ui+t1	ADV
ejpam-6212	481	5	|+	|+	NOUN
ejpam-6212	481	6	t2∑	t2∑	PROPN
ejpam-6212	481	7	j=1	j=1	NOUN
ejpam-6212	482	1	|vj	|vj	X
ejpam-6212	482	2	||vj+t2	||vj+t2	PROPN
ejpam-6212	482	3	|+	|+	NOUN
ejpam-6212	482	4	2t2∑	2t2∑	NUM
ejpam-6212	482	5	j=2	j=2	NOUN
ejpam-6212	482	6	|ut1	|ut1	PUNCT
ejpam-6212	482	7	+	+	NOUN
ejpam-6212	482	8	1||vj	1||vj	PROPN
ejpam-6212	482	9	|+	|+	NOUN
ejpam-6212	482	10	2t1∑	2t1∑	NUM
ejpam-6212	482	11	i=2	i=2	PROPN
ejpam-6212	482	12	|vt2	|vt2	PROPN
ejpam-6212	483	1	+	+	NOUN
ejpam-6212	483	2	1||ui|+	1||ui|+	NOUN
ejpam-6212	483	3	|ut1	|ut1	NOUN
ejpam-6212	483	4	+	+	NOUN
ejpam-6212	483	5	1||vt2	1||vt2	NUM
ejpam-6212	483	6	+	+	NOUN
ejpam-6212	483	7	1|	1|	NUM
ejpam-6212	483	8	.	.	PUNCT
ejpam-6212	484	1	proof	proof	NOUN
ejpam-6212	484	2	.	.	PUNCT
ejpam-6212	485	1	it	it	PRON
ejpam-6212	485	2	’s	’	VERB
ejpam-6212	485	3	enough	enough	ADV
ejpam-6212	485	4	to	to	PART
ejpam-6212	485	5	show	show	VERB
ejpam-6212	485	6	the	the	DET
ejpam-6212	485	7	bounds	bound	NOUN
ejpam-6212	485	8	of	of	ADP
ejpam-6212	485	9	wiener	wiener	NOUN
ejpam-6212	485	10	index	index	NOUN
ejpam-6212	485	11	in	in	ADP
ejpam-6212	485	12	terms	term	NOUN
ejpam-6212	485	13	of	of	ADP
ejpam-6212	485	14	the	the	DET
ejpam-6212	485	15	gutman	gutman	NOUN
ejpam-6212	485	16	index	index	NOUN
ejpam-6212	485	17	and	and	CCONJ
ejpam-6212	485	18	use	use	VERB
ejpam-6212	485	19	lemma	lemma	PROPN
ejpam-6212	485	20	2	2	NUM
ejpam-6212	485	21	and	and	CCONJ
ejpam-6212	485	22	the	the	DET
ejpam-6212	485	23	proof	proof	NOUN
ejpam-6212	485	24	of	of	ADP
ejpam-6212	485	25	theorem	theorem	NOUN
ejpam-6212	485	26	1	1	NUM
ejpam-6212	485	27	.	.	PUNCT
ejpam-6212	486	1	now	now	ADV
ejpam-6212	486	2	,	,	PUNCT
ejpam-6212	486	3	w	w	PROPN
ejpam-6212	486	4	(	(	PUNCT
ejpam-6212	486	5	g	g	NOUN
ejpam-6212	486	6	)	)	PUNCT
ejpam-6212	486	7	=	=	PUNCT
ejpam-6212	486	8	∑	∑	PUNCT
ejpam-6212	486	9	{	{	PUNCT
ejpam-6212	486	10	u	u	NOUN
ejpam-6212	486	11	,	,	PUNCT
ejpam-6212	486	12	v}⊆v	v}⊆v	PROPN
ejpam-6212	486	13	(	(	PUNCT
ejpam-6212	486	14	g	g	NOUN
ejpam-6212	486	15	)	)	PUNCT
ejpam-6212	486	16	d(u	d(u	PROPN
ejpam-6212	486	17	,	,	PUNCT
ejpam-6212	486	18	v	v	NOUN
ejpam-6212	486	19	)	)	PUNCT
ejpam-6212	486	20	=	=	PUNCT
ejpam-6212	486	21	∑	∑	PUNCT
ejpam-6212	486	22	{	{	PUNCT
ejpam-6212	486	23	u	u	NOUN
ejpam-6212	486	24	,	,	PUNCT
ejpam-6212	486	25	v}⊆v	v}⊆v	PROPN
ejpam-6212	486	26	(	(	PUNCT
ejpam-6212	486	27	g	g	NOUN
ejpam-6212	486	28	)	)	PUNCT
ejpam-6212	486	29	d(u	d(u	PROPN
ejpam-6212	486	30	,	,	PUNCT
ejpam-6212	486	31	v	v	NOUN
ejpam-6212	486	32	)	)	PUNCT
ejpam-6212	486	33	·	·	PUNCT
ejpam-6212	487	1	dudv	dudv	ADV
ejpam-6212	487	2	dudv	dudv	NOUN
ejpam-6212	487	3	<	<	X
ejpam-6212	487	4	1	1	NUM
ejpam-6212	487	5	δ2	δ2	VERB
ejpam-6212	487	6	gut(g	gut(g	NOUN
ejpam-6212	487	7	)	)	PUNCT
ejpam-6212	487	8	.	.	PUNCT
ejpam-6212	488	1	moreover	moreover	ADV
ejpam-6212	488	2	,	,	PUNCT
ejpam-6212	488	3	w	w	PROPN
ejpam-6212	488	4	(	(	PUNCT
ejpam-6212	488	5	g	g	NOUN
ejpam-6212	488	6	)	)	PUNCT
ejpam-6212	488	7	=	=	PUNCT
ejpam-6212	488	8	∑	∑	PUNCT
ejpam-6212	488	9	{	{	PUNCT
ejpam-6212	488	10	u	u	NOUN
ejpam-6212	488	11	,	,	PUNCT
ejpam-6212	488	12	v}⊆v	v}⊆v	PROPN
ejpam-6212	488	13	(	(	PUNCT
ejpam-6212	488	14	g	g	NOUN
ejpam-6212	488	15	)	)	PUNCT
ejpam-6212	488	16	d(u	d(u	PROPN
ejpam-6212	488	17	,	,	PUNCT
ejpam-6212	488	18	v	v	NOUN
ejpam-6212	488	19	)	)	PUNCT
ejpam-6212	488	20	=	=	PUNCT
ejpam-6212	488	21	∑	∑	PUNCT
ejpam-6212	488	22	{	{	PUNCT
ejpam-6212	488	23	u	u	NOUN
ejpam-6212	488	24	,	,	PUNCT
ejpam-6212	488	25	v}⊆v	v}⊆v	PROPN
ejpam-6212	488	26	(	(	PUNCT
ejpam-6212	488	27	g	g	NOUN
ejpam-6212	488	28	)	)	PUNCT
ejpam-6212	488	29	d(u	d(u	PROPN
ejpam-6212	488	30	,	,	PUNCT
ejpam-6212	488	31	v	v	NOUN
ejpam-6212	488	32	)	)	PUNCT
ejpam-6212	488	33	·	·	PUNCT
ejpam-6212	489	1	dudv	dudv	ADP
ejpam-6212	489	2	dudv	dudv	NOUN
ejpam-6212	489	3	>	>	X
ejpam-6212	489	4	1	1	NUM
ejpam-6212	489	5	∆2	∆2	PROPN
ejpam-6212	489	6	gut(g	gut(g	PROPN
ejpam-6212	489	7	)	)	PUNCT
ejpam-6212	489	8	.	.	PUNCT
ejpam-6212	490	1	r.	r.	PROPN
ejpam-6212	490	2	g.	g.	PROPN
ejpam-6212	490	3	artes	artes	PROPN
ejpam-6212	490	4	jr	jr	PROPN
ejpam-6212	490	5	.	.	PROPN
ejpam-6212	490	6	et	et	PROPN
ejpam-6212	490	7	al	al	PROPN
ejpam-6212	490	8	.	.	PUNCT
ejpam-6212	490	9	/	/	SYM
ejpam-6212	490	10	eur	eur	PROPN
ejpam-6212	490	11	.	.	PUNCT
ejpam-6212	491	1	j.	j.	PROPN
ejpam-6212	491	2	pure	pure	PROPN
ejpam-6212	491	3	appl	appl	PROPN
ejpam-6212	491	4	.	.	PROPN
ejpam-6212	491	5	math	math	PROPN
ejpam-6212	491	6	,	,	PUNCT
ejpam-6212	491	7	18	18	NUM
ejpam-6212	491	8	(	(	PUNCT
ejpam-6212	491	9	4	4	NUM
ejpam-6212	491	10	)	)	PUNCT
ejpam-6212	491	11	(	(	PUNCT
ejpam-6212	491	12	2025	2025	NUM
ejpam-6212	491	13	)	)	PUNCT
ejpam-6212	491	14	,	,	PUNCT
ejpam-6212	491	15	6212	6212	NUM
ejpam-6212	491	16	12	12	NUM
ejpam-6212	491	17	of	of	ADP
ejpam-6212	491	18	20	20	NUM
ejpam-6212	491	19	the	the	DET
ejpam-6212	491	20	strict	strict	ADJ
ejpam-6212	491	21	inequalities	inequality	NOUN
ejpam-6212	491	22	in	in	ADP
ejpam-6212	491	23	the	the	DET
ejpam-6212	491	24	above	above	ADJ
ejpam-6212	491	25	result	result	NOUN
ejpam-6212	491	26	are	be	AUX
ejpam-6212	491	27	due	due	ADJ
ejpam-6212	491	28	to	to	ADP
ejpam-6212	491	29	the	the	DET
ejpam-6212	491	30	fact	fact	NOUN
ejpam-6212	491	31	that	that	SCONJ
ejpam-6212	491	32	there	there	PRON
ejpam-6212	491	33	exist	exist	VERB
ejpam-6212	491	34	u	u	NOUN
ejpam-6212	491	35	,	,	PUNCT
ejpam-6212	491	36	v	v	NOUN
ejpam-6212	491	37	∈	∈	PROPN
ejpam-6212	491	38	v	v	NOUN
ejpam-6212	491	39	(	(	PUNCT
ejpam-6212	491	40	g	g	NOUN
ejpam-6212	491	41	)	)	PUNCT
ejpam-6212	491	42	such	such	ADJ
ejpam-6212	491	43	that	that	DET
ejpam-6212	491	44	dudv	dudv	NOUN
ejpam-6212	491	45	>	>	X
ejpam-6212	491	46	δ2	δ2	PROPN
ejpam-6212	491	47	.	.	PUNCT
ejpam-6212	492	1	the	the	DET
ejpam-6212	492	2	following	follow	VERB
ejpam-6212	492	3	results	result	NOUN
ejpam-6212	492	4	uses	use	VERB
ejpam-6212	492	5	theorem	theorem	VERB
ejpam-6212	492	6	2	2	NUM
ejpam-6212	492	7	and	and	CCONJ
ejpam-6212	492	8	the	the	DET
ejpam-6212	492	9	proof	proof	NOUN
ejpam-6212	492	10	of	of	ADP
ejpam-6212	492	11	theorem	theorem	ADJ
ejpam-6212	492	12	3	3	NUM
ejpam-6212	492	13	.	.	PUNCT
ejpam-6212	492	14	corollary	corollary	ADJ
ejpam-6212	492	15	1	1	NUM
ejpam-6212	492	16	.	.	PUNCT
ejpam-6212	493	1	let	let	VERB
ejpam-6212	493	2	g	g	PRON
ejpam-6212	493	3	be	be	AUX
ejpam-6212	493	4	a	a	DET
ejpam-6212	493	5	simple	simple	ADJ
ejpam-6212	493	6	spirocyclic	spirocyclic	NOUN
ejpam-6212	493	7	graph	graph	NOUN
ejpam-6212	493	8	with	with	ADP
ejpam-6212	493	9	minimum	minimum	NOUN
ejpam-6212	493	10	degree	degree	NOUN
ejpam-6212	493	11	δ	δ	NOUN
ejpam-6212	493	12	=	=	SYM
ejpam-6212	493	13	2	2	NUM
ejpam-6212	493	14	and	and	CCONJ
ejpam-6212	493	15	with	with	ADP
ejpam-6212	493	16	even	even	ADV
ejpam-6212	493	17	cycles	cycle	NOUN
ejpam-6212	493	18	c2t1	c2t1	NOUN
ejpam-6212	493	19	and	and	CCONJ
ejpam-6212	493	20	c2t2	c2t2	PROPN
ejpam-6212	493	21	,	,	PUNCT
ejpam-6212	493	22	for	for	SCONJ
ejpam-6212	493	23	some	some	DET
ejpam-6212	493	24	natural	natural	ADJ
ejpam-6212	493	25	numbers	number	NOUN
ejpam-6212	493	26	t1	t1	PROPN
ejpam-6212	493	27	,	,	PUNCT
ejpam-6212	493	28	t2	t2	NOUN
ejpam-6212	493	29	≥	≥	NUM
ejpam-6212	493	30	2	2	NUM
ejpam-6212	493	31	.	.	PUNCT
ejpam-6212	494	1	then	then	ADV
ejpam-6212	494	2	1	1	NUM
ejpam-6212	494	3	16	16	NUM
ejpam-6212	494	4	gut(g	gut(g	PROPN
ejpam-6212	494	5	)	)	PUNCT
ejpam-6212	495	1	+	+	NUM
ejpam-6212	496	1	2(t1	2(t1	NUM
ejpam-6212	496	2	+	+	NUM
ejpam-6212	496	3	t2	t2	NOUN
ejpam-6212	496	4	)	)	PUNCT
ejpam-6212	496	5	2	2	NUM
ejpam-6212	496	6	<	<	X
ejpam-6212	496	7	wg(g	wg(g	NOUN
ejpam-6212	496	8	)	)	PUNCT
ejpam-6212	496	9	<	<	X
ejpam-6212	496	10	1	1	NUM
ejpam-6212	496	11	4	4	NUM
ejpam-6212	496	12	gut(g	gut(g	NOUN
ejpam-6212	496	13	)	)	PUNCT
ejpam-6212	496	14	+	+	NUM
ejpam-6212	497	1	2(t1	2(t1	NUM
ejpam-6212	497	2	+	+	NUM
ejpam-6212	497	3	t2	t2	NOUN
ejpam-6212	497	4	)	)	PUNCT
ejpam-6212	497	5	2	2	NUM
ejpam-6212	497	6	.	.	X
ejpam-6212	497	7	7	7	X
ejpam-6212	497	8	.	.	NUM
ejpam-6212	497	9	bounds	bound	NOUN
ejpam-6212	497	10	of	of	ADP
ejpam-6212	497	11	g	g	NOUN
ejpam-6212	497	12	-	-	PUNCT
ejpam-6212	497	13	wiener	wiener	NOUN
ejpam-6212	497	14	index	index	NOUN
ejpam-6212	497	15	with	with	ADP
ejpam-6212	497	16	schultz	schultz	PROPN
ejpam-6212	497	17	index	index	PROPN
ejpam-6212	497	18	the	the	DET
ejpam-6212	497	19	following	following	ADJ
ejpam-6212	497	20	result	result	NOUN
ejpam-6212	497	21	establishes	establish	VERB
ejpam-6212	497	22	the	the	DET
ejpam-6212	497	23	relation	relation	NOUN
ejpam-6212	497	24	between	between	ADP
ejpam-6212	497	25	geodetic	geodetic	ADJ
ejpam-6212	497	26	-	-	PUNCT
ejpam-6212	497	27	wiener	wiener	NOUN
ejpam-6212	497	28	and	and	CCONJ
ejpam-6212	497	29	schultz	schultz	PROPN
ejpam-6212	497	30	[	[	X
ejpam-6212	497	31	19	19	NUM
ejpam-6212	497	32	]	]	PUNCT
ejpam-6212	497	33	indices	index	NOUN
ejpam-6212	497	34	for	for	ADP
ejpam-6212	497	35	simple	simple	ADJ
ejpam-6212	497	36	spirocyclic	spirocyclic	NOUN
ejpam-6212	497	37	graphs	graph	NOUN
ejpam-6212	497	38	containing	contain	VERB
ejpam-6212	497	39	even	even	ADV
ejpam-6212	497	40	cycles	cycle	NOUN
ejpam-6212	497	41	.	.	PUNCT
ejpam-6212	498	1	theorem	theorem	ADJ
ejpam-6212	498	2	4	4	NUM
ejpam-6212	498	3	.	.	PUNCT
ejpam-6212	499	1	let	let	VERB
ejpam-6212	499	2	g	g	PRON
ejpam-6212	499	3	be	be	AUX
ejpam-6212	499	4	a	a	DET
ejpam-6212	499	5	simple	simple	ADJ
ejpam-6212	499	6	spirocyclic	spirocyclic	NOUN
ejpam-6212	499	7	graph	graph	NOUN
ejpam-6212	499	8	with	with	ADP
ejpam-6212	499	9	even	even	ADV
ejpam-6212	499	10	cycles	cycle	NOUN
ejpam-6212	499	11	c2t1	c2t1	NOUN
ejpam-6212	500	1	=	=	SYM
ejpam-6212	501	1	[	[	X
ejpam-6212	501	2	u1	u1	NOUN
ejpam-6212	501	3	,	,	PUNCT
ejpam-6212	501	4	u2	u2	NOUN
ejpam-6212	501	5	,	,	PUNCT
ejpam-6212	501	6	.	.	PUNCT
ejpam-6212	501	7	.	.	PUNCT
ejpam-6212	501	8	.	.	PUNCT
ejpam-6212	502	1	,	,	PUNCT
ejpam-6212	502	2	u2t1	u2t1	VERB
ejpam-6212	502	3	]	]	PUNCT
ejpam-6212	502	4	and	and	CCONJ
ejpam-6212	502	5	c2t2	c2t2	NOUN
ejpam-6212	503	1	=	=	PUNCT
ejpam-6212	504	1	[	[	X
ejpam-6212	504	2	u1	u1	NOUN
ejpam-6212	504	3	=	=	SYM
ejpam-6212	504	4	v1	v1	NOUN
ejpam-6212	504	5	,	,	PUNCT
ejpam-6212	504	6	v2	v2	NOUN
ejpam-6212	504	7	,	,	PUNCT
ejpam-6212	504	8	.	.	PUNCT
ejpam-6212	504	9	.	.	PUNCT
ejpam-6212	504	10	.	.	PUNCT
ejpam-6212	505	1	,	,	PUNCT
ejpam-6212	505	2	v2t2	v2t2	X
ejpam-6212	505	3	]	]	X
ejpam-6212	505	4	,	,	PUNCT
ejpam-6212	505	5	for	for	ADP
ejpam-6212	505	6	some	some	DET
ejpam-6212	505	7	natural	natural	ADJ
ejpam-6212	505	8	numbers	number	NOUN
ejpam-6212	505	9	t1	t1	PROPN
ejpam-6212	505	10	,	,	PUNCT
ejpam-6212	505	11	t2	t2	NOUN
ejpam-6212	505	12	≥	≥	NUM
ejpam-6212	505	13	2	2	NUM
ejpam-6212	505	14	.	.	PUNCT
ejpam-6212	506	1	then	then	ADV
ejpam-6212	506	2	1	1	NUM
ejpam-6212	506	3	2∆	2∆	NUM
ejpam-6212	506	4	s(g	s(g	PROPN
ejpam-6212	506	5	)	)	PUNCT
ejpam-6212	507	1	+	+	VERB
ejpam-6212	507	2	at1	at1	PROPN
ejpam-6212	507	3	+	+	PROPN
ejpam-6212	507	4	bt2	bt2	PROPN
ejpam-6212	507	5	<	<	X
ejpam-6212	507	6	wg(g	wg(g	PROPN
ejpam-6212	507	7	)	)	PUNCT
ejpam-6212	507	8	<	<	X
ejpam-6212	507	9	1	1	NUM
ejpam-6212	507	10	2δ	2δ	NUM
ejpam-6212	507	11	s(g	s(g	PROPN
ejpam-6212	507	12	)	)	PUNCT
ejpam-6212	507	13	+	+	NUM
ejpam-6212	508	1	cdiam(g	cdiam(g	X
ejpam-6212	508	2	)	)	PUNCT
ejpam-6212	508	3	,	,	PUNCT
ejpam-6212	508	4	where	where	SCONJ
ejpam-6212	508	5	{	{	PUNCT
ejpam-6212	508	6	u1	u1	NOUN
ejpam-6212	508	7	=	=	SYM
ejpam-6212	508	8	v1	v1	PROPN
ejpam-6212	508	9	,	,	PUNCT
ejpam-6212	508	10	u2	u2	NOUN
ejpam-6212	508	11	,	,	PUNCT
ejpam-6212	508	12	.	.	PUNCT
ejpam-6212	508	13	.	.	PUNCT
ejpam-6212	508	14	.	.	PUNCT
ejpam-6212	509	1	,	,	PUNCT
ejpam-6212	509	2	u2t1	u2t1	INTJ
ejpam-6212	509	3	,	,	PUNCT
ejpam-6212	509	4	v2	v2	PROPN
ejpam-6212	509	5	,	,	PUNCT
ejpam-6212	509	6	.	.	PUNCT
ejpam-6212	509	7	.	.	PUNCT
ejpam-6212	510	1	.	.	PUNCT
ejpam-6212	511	1	,	,	PUNCT
ejpam-6212	511	2	v2t2	v2t2	NOUN
ejpam-6212	511	3	}	}	PUNCT
ejpam-6212	511	4	is	be	AUX
ejpam-6212	511	5	the	the	DET
ejpam-6212	511	6	tree	tree	NOUN
ejpam-6212	511	7	-	-	PUNCT
ejpam-6212	511	8	partition	partition	NOUN
ejpam-6212	511	9	of	of	ADP
ejpam-6212	511	10	v	v	NOUN
ejpam-6212	511	11	(	(	PUNCT
ejpam-6212	511	12	g	g	NOUN
ejpam-6212	511	13	)	)	PUNCT
ejpam-6212	511	14	with	with	ADP
ejpam-6212	511	15	respect	respect	NOUN
ejpam-6212	511	16	to	to	ADP
ejpam-6212	511	17	the	the	DET
ejpam-6212	511	18	projection	projection	NOUN
ejpam-6212	511	19	of	of	ADP
ejpam-6212	511	20	v	v	NOUN
ejpam-6212	511	21	(	(	PUNCT
ejpam-6212	511	22	g	g	NOUN
ejpam-6212	511	23	)	)	PUNCT
ejpam-6212	511	24	onto	onto	ADP
ejpam-6212	511	25	the	the	DET
ejpam-6212	511	26	union	union	NOUN
ejpam-6212	511	27	of	of	ADP
ejpam-6212	511	28	the	the	DET
ejpam-6212	511	29	cycles	cycle	NOUN
ejpam-6212	511	30	c2t1	c2t1	NOUN
ejpam-6212	511	31	and	and	CCONJ
ejpam-6212	511	32	c2t2	c2t2	NOUN
ejpam-6212	511	33	,	,	PUNCT
ejpam-6212	511	34	and	and	CCONJ
ejpam-6212	512	1	a	a	DET
ejpam-6212	512	2	=	=	X
ejpam-6212	512	3	t1∑	t1∑	PROPN
ejpam-6212	512	4	i=1	i=1	PROPN
ejpam-6212	512	5	|ui||ui+t1	|ui||ui+t1	ADP
ejpam-6212	512	6	|+	|+	NOUN
ejpam-6212	512	7	2t2∑	2t2∑	NUM
ejpam-6212	512	8	j=2	j=2	NOUN
ejpam-6212	512	9	|ut1	|ut1	PUNCT
ejpam-6212	512	10	+	+	NOUN
ejpam-6212	512	11	1||vj	1||vj	NOUN
ejpam-6212	512	12	|+	|+	X
ejpam-6212	512	13	|ut1	|ut1	PUNCT
ejpam-6212	512	14	+	+	NOUN
ejpam-6212	512	15	1||vt2	1||vt2	NUM
ejpam-6212	512	16	+	+	NOUN
ejpam-6212	512	17	1|	1|	NUM
ejpam-6212	512	18	,	,	PUNCT
ejpam-6212	512	19	b	b	NOUN
ejpam-6212	512	20	=	=	SYM
ejpam-6212	512	21	t2∑	t2∑	PROPN
ejpam-6212	512	22	j=1	j=1	NOUN
ejpam-6212	512	23	|vj	|vj	X
ejpam-6212	512	24	||vj+t2	||vj+t2	PROPN
ejpam-6212	512	25	|+	|+	NOUN
ejpam-6212	512	26	2t1∑	2t1∑	NUM
ejpam-6212	512	27	i=2	i=2	PROPN
ejpam-6212	512	28	|vt2	|vt2	PROPN
ejpam-6212	513	1	+	+	NOUN
ejpam-6212	513	2	1||ui|+	1||ui|+	NOUN
ejpam-6212	513	3	|ut1	|ut1	NOUN
ejpam-6212	513	4	+	+	NOUN
ejpam-6212	513	5	1||vt2	1||vt2	NUM
ejpam-6212	513	6	+	+	NOUN
ejpam-6212	513	7	1|	1|	NUM
ejpam-6212	513	8	,	,	PUNCT
ejpam-6212	513	9	and	and	CCONJ
ejpam-6212	513	10	c	c	X
ejpam-6212	514	1	=	=	SYM
ejpam-6212	514	2	t1∑	t1∑	PROPN
ejpam-6212	514	3	i=1	i=1	PROPN
ejpam-6212	514	4	|ui||ui+t1	|ui||ui+t1	ADV
ejpam-6212	514	5	|+	|+	NOUN
ejpam-6212	514	6	t2∑	t2∑	PROPN
ejpam-6212	514	7	j=1	j=1	NOUN
ejpam-6212	515	1	|vj	|vj	X
ejpam-6212	515	2	||vj+t2	||vj+t2	PROPN
ejpam-6212	515	3	|+	|+	NOUN
ejpam-6212	515	4	2t2∑	2t2∑	NUM
ejpam-6212	515	5	j=2	j=2	NOUN
ejpam-6212	515	6	|ut1	|ut1	PUNCT
ejpam-6212	515	7	+	+	NOUN
ejpam-6212	515	8	1||vj	1||vj	PROPN
ejpam-6212	515	9	|+	|+	NOUN
ejpam-6212	515	10	2t1∑	2t1∑	NUM
ejpam-6212	515	11	i=2	i=2	PROPN
ejpam-6212	515	12	|vt2	|vt2	PROPN
ejpam-6212	516	1	+	+	NOUN
ejpam-6212	516	2	1||ui|+	1||ui|+	NOUN
ejpam-6212	516	3	|ut1	|ut1	NOUN
ejpam-6212	516	4	+	+	NOUN
ejpam-6212	516	5	1||vt2	1||vt2	NUM
ejpam-6212	516	6	+	+	NOUN
ejpam-6212	516	7	1|	1|	NUM
ejpam-6212	516	8	.	.	PUNCT
ejpam-6212	517	1	proof	proof	NOUN
ejpam-6212	517	2	.	.	PUNCT
ejpam-6212	518	1	we	we	PRON
ejpam-6212	518	2	will	will	AUX
ejpam-6212	518	3	establish	establish	VERB
ejpam-6212	518	4	the	the	DET
ejpam-6212	518	5	bounds	bound	NOUN
ejpam-6212	518	6	of	of	ADP
ejpam-6212	518	7	wiener	wiener	NOUN
ejpam-6212	518	8	index	index	NOUN
ejpam-6212	518	9	in	in	ADP
ejpam-6212	518	10	terms	term	NOUN
ejpam-6212	518	11	of	of	ADP
ejpam-6212	518	12	schultz	schultz	PROPN
ejpam-6212	518	13	index	index	NOUN
ejpam-6212	518	14	and	and	CCONJ
ejpam-6212	518	15	use	use	VERB
ejpam-6212	518	16	lemma	lemma	PROPN
ejpam-6212	518	17	2	2	NUM
ejpam-6212	518	18	together	together	ADV
ejpam-6212	518	19	with	with	ADP
ejpam-6212	518	20	the	the	DET
ejpam-6212	518	21	proof	proof	NOUN
ejpam-6212	518	22	of	of	ADP
ejpam-6212	518	23	theorem	theorem	NOUN
ejpam-6212	518	24	1	1	NUM
ejpam-6212	518	25	.	.	PUNCT
ejpam-6212	518	26	w	w	PROPN
ejpam-6212	518	27	(	(	PUNCT
ejpam-6212	518	28	g	g	NOUN
ejpam-6212	518	29	)	)	PUNCT
ejpam-6212	518	30	=	=	PUNCT
ejpam-6212	518	31	∑	∑	PUNCT
ejpam-6212	518	32	{	{	PUNCT
ejpam-6212	518	33	u	u	NOUN
ejpam-6212	518	34	,	,	PUNCT
ejpam-6212	518	35	v}⊆v	v}⊆v	PROPN
ejpam-6212	518	36	(	(	PUNCT
ejpam-6212	518	37	g	g	NOUN
ejpam-6212	518	38	)	)	PUNCT
ejpam-6212	518	39	d(u	d(u	PROPN
ejpam-6212	518	40	,	,	PUNCT
ejpam-6212	518	41	v	v	NOUN
ejpam-6212	518	42	)	)	PUNCT
ejpam-6212	518	43	=	=	SYM
ejpam-6212	518	44	∑	∑	PUNCT
ejpam-6212	518	45	u	u	PROPN
ejpam-6212	518	46	,	,	PUNCT
ejpam-6212	518	47	v∈v	v∈v	NOUN
ejpam-6212	518	48	(	(	PUNCT
ejpam-6212	518	49	g	g	NOUN
ejpam-6212	518	50	)	)	PUNCT
ejpam-6212	518	51	d(u	d(u	PROPN
ejpam-6212	518	52	,	,	PUNCT
ejpam-6212	518	53	v	v	NOUN
ejpam-6212	518	54	)	)	PUNCT
ejpam-6212	518	55	·	·	PUNCT
ejpam-6212	518	56	du	du	PROPN
ejpam-6212	519	1	+	+	CCONJ
ejpam-6212	519	2	dv	dv	PROPN
ejpam-6212	519	3	du	du	PROPN
ejpam-6212	519	4	+	+	CCONJ
ejpam-6212	519	5	dv	dv	PROPN
ejpam-6212	519	6	<	<	X
ejpam-6212	519	7	1	1	NUM
ejpam-6212	519	8	2δ	2δ	NUM
ejpam-6212	519	9	s(g	s(g	PROPN
ejpam-6212	519	10	)	)	PUNCT
ejpam-6212	519	11	.	.	PUNCT
ejpam-6212	520	1	r.	r.	PROPN
ejpam-6212	520	2	g.	g.	PROPN
ejpam-6212	520	3	artes	artes	PROPN
ejpam-6212	520	4	jr	jr	PROPN
ejpam-6212	520	5	.	.	PROPN
ejpam-6212	520	6	et	et	PROPN
ejpam-6212	520	7	al	al	PROPN
ejpam-6212	520	8	.	.	PUNCT
ejpam-6212	520	9	/	/	SYM
ejpam-6212	520	10	eur	eur	PROPN
ejpam-6212	520	11	.	.	PUNCT
ejpam-6212	521	1	j.	j.	PROPN
ejpam-6212	521	2	pure	pure	PROPN
ejpam-6212	521	3	appl	appl	PROPN
ejpam-6212	521	4	.	.	PROPN
ejpam-6212	521	5	math	math	PROPN
ejpam-6212	521	6	,	,	PUNCT
ejpam-6212	521	7	18	18	NUM
ejpam-6212	521	8	(	(	PUNCT
ejpam-6212	521	9	4	4	NUM
ejpam-6212	521	10	)	)	PUNCT
ejpam-6212	521	11	(	(	PUNCT
ejpam-6212	521	12	2025	2025	NUM
ejpam-6212	521	13	)	)	PUNCT
ejpam-6212	521	14	,	,	PUNCT
ejpam-6212	521	15	6212	6212	NUM
ejpam-6212	521	16	13	13	NUM
ejpam-6212	521	17	of	of	ADP
ejpam-6212	521	18	20	20	NUM
ejpam-6212	521	19	moreover	moreover	ADV
ejpam-6212	521	20	,	,	PUNCT
ejpam-6212	521	21	w	w	PROPN
ejpam-6212	521	22	(	(	PUNCT
ejpam-6212	521	23	g	g	NOUN
ejpam-6212	521	24	)	)	PUNCT
ejpam-6212	521	25	=	=	PUNCT
ejpam-6212	521	26	∑	∑	PUNCT
ejpam-6212	521	27	{	{	PUNCT
ejpam-6212	521	28	u	u	NOUN
ejpam-6212	521	29	,	,	PUNCT
ejpam-6212	521	30	v}⊆v	v}⊆v	PROPN
ejpam-6212	521	31	(	(	PUNCT
ejpam-6212	521	32	g	g	NOUN
ejpam-6212	521	33	)	)	PUNCT
ejpam-6212	521	34	d(u	d(u	PROPN
ejpam-6212	521	35	,	,	PUNCT
ejpam-6212	521	36	v	v	NOUN
ejpam-6212	521	37	)	)	PUNCT
ejpam-6212	521	38	=	=	PUNCT
ejpam-6212	521	39	∑	∑	PUNCT
ejpam-6212	521	40	{	{	PUNCT
ejpam-6212	521	41	u	u	NOUN
ejpam-6212	521	42	,	,	PUNCT
ejpam-6212	521	43	v}⊆v	v}⊆v	PROPN
ejpam-6212	521	44	(	(	PUNCT
ejpam-6212	521	45	g	g	NOUN
ejpam-6212	521	46	)	)	PUNCT
ejpam-6212	521	47	d(u	d(u	PROPN
ejpam-6212	521	48	,	,	PUNCT
ejpam-6212	521	49	v	v	NOUN
ejpam-6212	521	50	)	)	PUNCT
ejpam-6212	521	51	·	·	PUNCT
ejpam-6212	521	52	du	du	PROPN
ejpam-6212	522	1	+	+	CCONJ
ejpam-6212	522	2	dv	dv	PROPN
ejpam-6212	522	3	du	du	PROPN
ejpam-6212	522	4	+	+	CCONJ
ejpam-6212	522	5	dv	dv	PROPN
ejpam-6212	522	6	>	>	X
ejpam-6212	522	7	1	1	NUM
ejpam-6212	522	8	2∆	2∆	NUM
ejpam-6212	522	9	s(g	s(g	PROPN
ejpam-6212	522	10	)	)	PUNCT
ejpam-6212	522	11	.	.	PUNCT
ejpam-6212	523	1	using	use	VERB
ejpam-6212	523	2	theorem	theorem	NOUN
ejpam-6212	523	3	2	2	NUM
ejpam-6212	523	4	and	and	CCONJ
ejpam-6212	523	5	the	the	DET
ejpam-6212	523	6	proof	proof	NOUN
ejpam-6212	523	7	of	of	ADP
ejpam-6212	523	8	theorem	theorem	ADJ
ejpam-6212	523	9	4	4	NUM
ejpam-6212	523	10	,	,	PUNCT
ejpam-6212	523	11	the	the	DET
ejpam-6212	523	12	following	follow	VERB
ejpam-6212	523	13	is	be	AUX
ejpam-6212	523	14	immediate	immediate	ADJ
ejpam-6212	523	15	.	.	PUNCT
ejpam-6212	524	1	the	the	DET
ejpam-6212	524	2	strict	strict	ADJ
ejpam-6212	524	3	inequalities	inequality	NOUN
ejpam-6212	524	4	in	in	ADP
ejpam-6212	524	5	the	the	DET
ejpam-6212	524	6	above	above	ADJ
ejpam-6212	524	7	result	result	NOUN
ejpam-6212	524	8	are	be	AUX
ejpam-6212	524	9	due	due	ADJ
ejpam-6212	524	10	to	to	ADP
ejpam-6212	524	11	the	the	DET
ejpam-6212	524	12	fact	fact	NOUN
ejpam-6212	524	13	that	that	SCONJ
ejpam-6212	524	14	there	there	PRON
ejpam-6212	524	15	exist	exist	VERB
ejpam-6212	524	16	u	u	NOUN
ejpam-6212	524	17	,	,	PUNCT
ejpam-6212	524	18	v	v	NOUN
ejpam-6212	524	19	∈	∈	PROPN
ejpam-6212	524	20	v	v	NOUN
ejpam-6212	524	21	(	(	PUNCT
ejpam-6212	524	22	g	g	NOUN
ejpam-6212	524	23	)	)	PUNCT
ejpam-6212	524	24	such	such	ADJ
ejpam-6212	524	25	that	that	DET
ejpam-6212	524	26	du	du	PROPN
ejpam-6212	525	1	+	+	CCONJ
ejpam-6212	525	2	dv	dv	PROPN
ejpam-6212	525	3	>	>	X
ejpam-6212	525	4	2δ	2δ	PROPN
ejpam-6212	525	5	.	.	PUNCT
ejpam-6212	526	1	corollary	corollary	ADJ
ejpam-6212	526	2	2	2	NUM
ejpam-6212	526	3	.	.	PUNCT
ejpam-6212	527	1	let	let	VERB
ejpam-6212	527	2	g	g	PRON
ejpam-6212	527	3	be	be	AUX
ejpam-6212	527	4	a	a	DET
ejpam-6212	527	5	simple	simple	ADJ
ejpam-6212	527	6	spirocyclic	spirocyclic	NOUN
ejpam-6212	527	7	graph	graph	NOUN
ejpam-6212	527	8	with	with	ADP
ejpam-6212	527	9	minimum	minimum	NOUN
ejpam-6212	527	10	degree	degree	NOUN
ejpam-6212	527	11	δ	δ	NOUN
ejpam-6212	527	12	=	=	SYM
ejpam-6212	527	13	2	2	NUM
ejpam-6212	527	14	and	and	CCONJ
ejpam-6212	527	15	with	with	ADP
ejpam-6212	527	16	even	even	ADV
ejpam-6212	527	17	cycles	cycle	NOUN
ejpam-6212	527	18	c2t1	c2t1	NOUN
ejpam-6212	527	19	and	and	CCONJ
ejpam-6212	527	20	c2t2	c2t2	PROPN
ejpam-6212	527	21	,	,	PUNCT
ejpam-6212	527	22	for	for	SCONJ
ejpam-6212	527	23	some	some	DET
ejpam-6212	527	24	natural	natural	ADJ
ejpam-6212	527	25	numbers	number	NOUN
ejpam-6212	527	26	t1	t1	PROPN
ejpam-6212	527	27	,	,	PUNCT
ejpam-6212	527	28	t2	t2	NOUN
ejpam-6212	527	29	≥	≥	NUM
ejpam-6212	527	30	2	2	NUM
ejpam-6212	527	31	.	.	PUNCT
ejpam-6212	528	1	then	then	ADV
ejpam-6212	528	2	1	1	NUM
ejpam-6212	528	3	8	8	NUM
ejpam-6212	528	4	s(g	s(g	PROPN
ejpam-6212	528	5	)	)	PUNCT
ejpam-6212	529	1	+	+	CCONJ
ejpam-6212	530	1	2(t1	2(t1	NUM
ejpam-6212	530	2	+	+	NUM
ejpam-6212	530	3	t2	t2	NOUN
ejpam-6212	530	4	)	)	PUNCT
ejpam-6212	530	5	2	2	NUM
ejpam-6212	530	6	<	<	X
ejpam-6212	530	7	wg(g	wg(g	NOUN
ejpam-6212	530	8	)	)	PUNCT
ejpam-6212	530	9	<	<	X
ejpam-6212	530	10	1	1	NUM
ejpam-6212	530	11	4	4	NUM
ejpam-6212	530	12	s(g	s(g	PROPN
ejpam-6212	530	13	)	)	PUNCT
ejpam-6212	530	14	+	+	CCONJ
ejpam-6212	531	1	2(t1	2(t1	NUM
ejpam-6212	531	2	+	+	NUM
ejpam-6212	531	3	t2	t2	NOUN
ejpam-6212	531	4	)	)	PUNCT
ejpam-6212	531	5	2	2	NUM
ejpam-6212	531	6	.	.	NOUN
ejpam-6212	531	7	8	8	NUM
ejpam-6212	531	8	.	.	X
ejpam-6212	532	1	bounds	bound	NOUN
ejpam-6212	532	2	of	of	ADP
ejpam-6212	532	3	g	g	NOUN
ejpam-6212	532	4	-	-	PUNCT
ejpam-6212	532	5	wiener	wiener	NOUN
ejpam-6212	532	6	index	index	NOUN
ejpam-6212	532	7	with	with	ADP
ejpam-6212	532	8	hyper	hyper	ADJ
ejpam-6212	532	9	-	-	ADJ
ejpam-6212	532	10	wiener	wiener	NOUN
ejpam-6212	532	11	index	index	NOUN
ejpam-6212	532	12	the	the	DET
ejpam-6212	532	13	following	following	ADJ
ejpam-6212	532	14	result	result	NOUN
ejpam-6212	532	15	establishes	establish	VERB
ejpam-6212	532	16	the	the	DET
ejpam-6212	532	17	bounds	bound	NOUN
ejpam-6212	532	18	of	of	ADP
ejpam-6212	532	19	geodetic	geodetic	ADJ
ejpam-6212	532	20	-	-	PUNCT
ejpam-6212	532	21	wiener	wiener	NOUN
ejpam-6212	532	22	index	index	NOUN
ejpam-6212	532	23	in	in	ADP
ejpam-6212	532	24	terms	term	NOUN
ejpam-6212	532	25	of	of	ADP
ejpam-6212	532	26	hyperwiener	hyperwiener	NOUN
ejpam-6212	532	27	index	index	NOUN
ejpam-6212	532	28	as	as	SCONJ
ejpam-6212	532	29	defined	define	VERB
ejpam-6212	532	30	in	in	ADP
ejpam-6212	532	31	[	[	X
ejpam-6212	532	32	16	16	NUM
ejpam-6212	532	33	]	]	PUNCT
ejpam-6212	532	34	for	for	ADP
ejpam-6212	532	35	simple	simple	ADJ
ejpam-6212	532	36	spirocyclic	spirocyclic	NOUN
ejpam-6212	532	37	graphs	graph	NOUN
ejpam-6212	532	38	with	with	ADP
ejpam-6212	532	39	even	even	ADV
ejpam-6212	532	40	cycles	cycle	NOUN
ejpam-6212	532	41	.	.	PUNCT
ejpam-6212	533	1	theorem	theorem	NOUN
ejpam-6212	533	2	5	5	NUM
ejpam-6212	533	3	.	.	PUNCT
ejpam-6212	534	1	let	let	VERB
ejpam-6212	534	2	g	g	PRON
ejpam-6212	534	3	be	be	AUX
ejpam-6212	534	4	a	a	DET
ejpam-6212	534	5	simple	simple	ADJ
ejpam-6212	534	6	spirocyclic	spirocyclic	NOUN
ejpam-6212	534	7	graph	graph	NOUN
ejpam-6212	534	8	with	with	ADP
ejpam-6212	534	9	even	even	ADV
ejpam-6212	534	10	cycles	cycle	NOUN
ejpam-6212	534	11	c2t1	c2t1	NOUN
ejpam-6212	535	1	=	=	SYM
ejpam-6212	536	1	[	[	X
ejpam-6212	536	2	u1	u1	NOUN
ejpam-6212	536	3	,	,	PUNCT
ejpam-6212	536	4	u2	u2	NOUN
ejpam-6212	536	5	,	,	PUNCT
ejpam-6212	536	6	.	.	PUNCT
ejpam-6212	536	7	.	.	PUNCT
ejpam-6212	536	8	.	.	PUNCT
ejpam-6212	537	1	,	,	PUNCT
ejpam-6212	537	2	u2t1	u2t1	VERB
ejpam-6212	537	3	]	]	PUNCT
ejpam-6212	537	4	and	and	CCONJ
ejpam-6212	537	5	c2t2	c2t2	NOUN
ejpam-6212	538	1	=	=	PUNCT
ejpam-6212	539	1	[	[	X
ejpam-6212	539	2	u1	u1	NOUN
ejpam-6212	539	3	=	=	SYM
ejpam-6212	539	4	v1	v1	NOUN
ejpam-6212	539	5	,	,	PUNCT
ejpam-6212	539	6	v2	v2	NOUN
ejpam-6212	539	7	,	,	PUNCT
ejpam-6212	539	8	.	.	PUNCT
ejpam-6212	539	9	.	.	PUNCT
ejpam-6212	539	10	.	.	PUNCT
ejpam-6212	540	1	,	,	PUNCT
ejpam-6212	540	2	v2t2	v2t2	X
ejpam-6212	540	3	]	]	X
ejpam-6212	540	4	,	,	PUNCT
ejpam-6212	540	5	for	for	ADP
ejpam-6212	540	6	some	some	DET
ejpam-6212	540	7	natural	natural	ADJ
ejpam-6212	540	8	numbers	number	NOUN
ejpam-6212	540	9	t1	t1	PROPN
ejpam-6212	540	10	,	,	PUNCT
ejpam-6212	540	11	t2	t2	NOUN
ejpam-6212	540	12	≥	≥	NUM
ejpam-6212	540	13	2	2	NUM
ejpam-6212	540	14	.	.	PUNCT
ejpam-6212	541	1	then	then	ADV
ejpam-6212	541	2	ww	ww	PROPN
ejpam-6212	541	3	(	(	PUNCT
ejpam-6212	541	4	g	g	NOUN
ejpam-6212	541	5	)	)	PUNCT
ejpam-6212	541	6	+	+	NOUN
ejpam-6212	541	7	at1	at1	PROPN
ejpam-6212	541	8	+	+	PROPN
ejpam-6212	541	9	bt2	bt2	PROPN
ejpam-6212	541	10	<	<	X
ejpam-6212	541	11	wg(g	wg(g	PROPN
ejpam-6212	541	12	)	)	PUNCT
ejpam-6212	541	13	<	<	X
ejpam-6212	541	14	2	2	NUM
ejpam-6212	541	15	diam(g	diam(g	NOUN
ejpam-6212	541	16	)	)	PUNCT
ejpam-6212	542	1	+	+	CCONJ
ejpam-6212	542	2	1	1	NUM
ejpam-6212	542	3	ww	ww	PROPN
ejpam-6212	542	4	(	(	PUNCT
ejpam-6212	542	5	g	g	NOUN
ejpam-6212	542	6	)	)	PUNCT
ejpam-6212	542	7	+	+	CCONJ
ejpam-6212	543	1	cdiam(g	cdiam(g	X
ejpam-6212	543	2	)	)	PUNCT
ejpam-6212	543	3	where	where	SCONJ
ejpam-6212	543	4	{	{	PUNCT
ejpam-6212	543	5	u1	u1	NOUN
ejpam-6212	543	6	=	=	SYM
ejpam-6212	543	7	v1	v1	PROPN
ejpam-6212	543	8	,	,	PUNCT
ejpam-6212	543	9	u2	u2	NOUN
ejpam-6212	543	10	,	,	PUNCT
ejpam-6212	543	11	.	.	PUNCT
ejpam-6212	543	12	.	.	PUNCT
ejpam-6212	543	13	.	.	PUNCT
ejpam-6212	544	1	,	,	PUNCT
ejpam-6212	544	2	u2t1	u2t1	INTJ
ejpam-6212	544	3	,	,	PUNCT
ejpam-6212	544	4	v2	v2	PROPN
ejpam-6212	544	5	,	,	PUNCT
ejpam-6212	544	6	.	.	PUNCT
ejpam-6212	544	7	.	.	PUNCT
ejpam-6212	545	1	.	.	PUNCT
ejpam-6212	546	1	,	,	PUNCT
ejpam-6212	546	2	v2t2	v2t2	NOUN
ejpam-6212	546	3	}	}	PUNCT
ejpam-6212	546	4	is	be	AUX
ejpam-6212	546	5	the	the	DET
ejpam-6212	546	6	tree	tree	NOUN
ejpam-6212	546	7	-	-	PUNCT
ejpam-6212	546	8	partition	partition	NOUN
ejpam-6212	546	9	of	of	ADP
ejpam-6212	546	10	v	v	NOUN
ejpam-6212	546	11	(	(	PUNCT
ejpam-6212	546	12	g	g	NOUN
ejpam-6212	546	13	)	)	PUNCT
ejpam-6212	546	14	with	with	ADP
ejpam-6212	546	15	respect	respect	NOUN
ejpam-6212	546	16	to	to	ADP
ejpam-6212	546	17	the	the	DET
ejpam-6212	546	18	projection	projection	NOUN
ejpam-6212	546	19	of	of	ADP
ejpam-6212	546	20	v	v	NOUN
ejpam-6212	546	21	(	(	PUNCT
ejpam-6212	546	22	g	g	NOUN
ejpam-6212	546	23	)	)	PUNCT
ejpam-6212	546	24	onto	onto	ADP
ejpam-6212	546	25	the	the	DET
ejpam-6212	546	26	union	union	NOUN
ejpam-6212	546	27	of	of	ADP
ejpam-6212	546	28	the	the	DET
ejpam-6212	546	29	cycles	cycle	NOUN
ejpam-6212	546	30	c2t1	c2t1	NOUN
ejpam-6212	546	31	and	and	CCONJ
ejpam-6212	546	32	c2t2	c2t2	NOUN
ejpam-6212	546	33	,	,	PUNCT
ejpam-6212	546	34	and	and	CCONJ
ejpam-6212	547	1	a	a	DET
ejpam-6212	547	2	=	=	X
ejpam-6212	547	3	t1∑	t1∑	PROPN
ejpam-6212	547	4	i=1	i=1	PROPN
ejpam-6212	547	5	|ui||ui+t1	|ui||ui+t1	ADP
ejpam-6212	547	6	|+	|+	NOUN
ejpam-6212	547	7	2t2∑	2t2∑	NUM
ejpam-6212	547	8	j=2	j=2	NOUN
ejpam-6212	547	9	|ut1	|ut1	PUNCT
ejpam-6212	547	10	+	+	NOUN
ejpam-6212	547	11	1||vj	1||vj	NOUN
ejpam-6212	547	12	|+	|+	X
ejpam-6212	547	13	|ut1	|ut1	PUNCT
ejpam-6212	547	14	+	+	NOUN
ejpam-6212	547	15	1||vt2	1||vt2	NUM
ejpam-6212	547	16	+	+	NOUN
ejpam-6212	547	17	1|	1|	NUM
ejpam-6212	547	18	,	,	PUNCT
ejpam-6212	547	19	b	b	NOUN
ejpam-6212	547	20	=	=	SYM
ejpam-6212	547	21	t2∑	t2∑	PROPN
ejpam-6212	547	22	j=1	j=1	NOUN
ejpam-6212	547	23	|vj	|vj	X
ejpam-6212	547	24	||vj+t2	||vj+t2	PROPN
ejpam-6212	547	25	|+	|+	NOUN
ejpam-6212	547	26	2t1∑	2t1∑	NUM
ejpam-6212	547	27	i=2	i=2	PROPN
ejpam-6212	547	28	|vt2	|vt2	PROPN
ejpam-6212	548	1	+	+	NOUN
ejpam-6212	548	2	1||ui|+	1||ui|+	NOUN
ejpam-6212	548	3	|ut1	|ut1	NOUN
ejpam-6212	548	4	+	+	NOUN
ejpam-6212	548	5	1||vt2	1||vt2	NUM
ejpam-6212	548	6	+	+	NOUN
ejpam-6212	548	7	1|	1|	NUM
ejpam-6212	548	8	,	,	PUNCT
ejpam-6212	548	9	and	and	CCONJ
ejpam-6212	548	10	c	c	X
ejpam-6212	549	1	=	=	SYM
ejpam-6212	549	2	t1∑	t1∑	PROPN
ejpam-6212	549	3	i=1	i=1	PROPN
ejpam-6212	549	4	|ui||ui+t1	|ui||ui+t1	ADV
ejpam-6212	549	5	|+	|+	NOUN
ejpam-6212	549	6	t2∑	t2∑	PROPN
ejpam-6212	549	7	j=1	j=1	NOUN
ejpam-6212	550	1	|vj	|vj	X
ejpam-6212	550	2	||vj+t2	||vj+t2	PROPN
ejpam-6212	550	3	|+	|+	NOUN
ejpam-6212	550	4	2t2∑	2t2∑	NUM
ejpam-6212	550	5	j=2	j=2	NOUN
ejpam-6212	550	6	|ut1	|ut1	PUNCT
ejpam-6212	550	7	+	+	NOUN
ejpam-6212	550	8	1||vj	1||vj	PROPN
ejpam-6212	550	9	|+	|+	NOUN
ejpam-6212	550	10	2t1∑	2t1∑	NUM
ejpam-6212	550	11	i=2	i=2	PROPN
ejpam-6212	550	12	|vt2	|vt2	PROPN
ejpam-6212	551	1	+	+	NOUN
ejpam-6212	551	2	1||ui|+	1||ui|+	NOUN
ejpam-6212	551	3	|ut1	|ut1	NOUN
ejpam-6212	551	4	+	+	NOUN
ejpam-6212	551	5	1||vt2	1||vt2	NUM
ejpam-6212	551	6	+	+	NOUN
ejpam-6212	551	7	1|	1|	NUM
ejpam-6212	551	8	.	.	PUNCT
ejpam-6212	552	1	r.	r.	PROPN
ejpam-6212	552	2	g.	g.	PROPN
ejpam-6212	552	3	artes	artes	PROPN
ejpam-6212	552	4	jr	jr	PROPN
ejpam-6212	552	5	.	.	PROPN
ejpam-6212	552	6	et	et	PROPN
ejpam-6212	552	7	al	al	PROPN
ejpam-6212	552	8	.	.	PUNCT
ejpam-6212	552	9	/	/	SYM
ejpam-6212	552	10	eur	eur	PROPN
ejpam-6212	552	11	.	.	PUNCT
ejpam-6212	553	1	j.	j.	PROPN
ejpam-6212	553	2	pure	pure	PROPN
ejpam-6212	553	3	appl	appl	PROPN
ejpam-6212	553	4	.	.	PROPN
ejpam-6212	553	5	math	math	PROPN
ejpam-6212	553	6	,	,	PUNCT
ejpam-6212	553	7	18	18	NUM
ejpam-6212	553	8	(	(	PUNCT
ejpam-6212	553	9	4	4	NUM
ejpam-6212	553	10	)	)	PUNCT
ejpam-6212	553	11	(	(	PUNCT
ejpam-6212	553	12	2025	2025	NUM
ejpam-6212	553	13	)	)	PUNCT
ejpam-6212	553	14	,	,	PUNCT
ejpam-6212	553	15	6212	6212	NUM
ejpam-6212	553	16	14	14	NUM
ejpam-6212	553	17	of	of	ADP
ejpam-6212	553	18	20	20	NUM
ejpam-6212	553	19	proof	proof	NOUN
ejpam-6212	553	20	.	.	PUNCT
ejpam-6212	554	1	the	the	DET
ejpam-6212	554	2	proof	proof	NOUN
ejpam-6212	554	3	is	be	AUX
ejpam-6212	554	4	established	establish	VERB
ejpam-6212	554	5	by	by	ADP
ejpam-6212	554	6	taking	take	VERB
ejpam-6212	554	7	the	the	DET
ejpam-6212	554	8	bounds	bound	NOUN
ejpam-6212	554	9	of	of	ADP
ejpam-6212	554	10	wiener	wiener	NOUN
ejpam-6212	554	11	index	index	NOUN
ejpam-6212	554	12	in	in	ADP
ejpam-6212	554	13	terms	term	NOUN
ejpam-6212	554	14	of	of	ADP
ejpam-6212	554	15	hyper	hyper	ADJ
ejpam-6212	554	16	-	-	ADJ
ejpam-6212	554	17	wiener	wiener	NOUN
ejpam-6212	554	18	index	index	NOUN
ejpam-6212	554	19	and	and	CCONJ
ejpam-6212	554	20	using	use	VERB
ejpam-6212	554	21	lemma	lemma	PROPN
ejpam-6212	554	22	2	2	NUM
ejpam-6212	554	23	together	together	ADV
ejpam-6212	554	24	with	with	ADP
ejpam-6212	554	25	the	the	DET
ejpam-6212	554	26	proof	proof	NOUN
ejpam-6212	554	27	of	of	ADP
ejpam-6212	554	28	theorem	theorem	NOUN
ejpam-6212	554	29	1	1	NUM
ejpam-6212	554	30	.	.	PUNCT
ejpam-6212	554	31	w	w	PROPN
ejpam-6212	554	32	(	(	PUNCT
ejpam-6212	554	33	g	g	NOUN
ejpam-6212	554	34	)	)	PUNCT
ejpam-6212	554	35	=	=	PUNCT
ejpam-6212	554	36	∑	∑	PUNCT
ejpam-6212	554	37	{	{	PUNCT
ejpam-6212	554	38	u	u	NOUN
ejpam-6212	554	39	,	,	PUNCT
ejpam-6212	554	40	v}⊆v	v}⊆v	PROPN
ejpam-6212	554	41	(	(	PUNCT
ejpam-6212	554	42	g	g	NOUN
ejpam-6212	554	43	)	)	PUNCT
ejpam-6212	554	44	d(u	d(u	PROPN
ejpam-6212	554	45	,	,	PUNCT
ejpam-6212	554	46	v	v	NOUN
ejpam-6212	554	47	)	)	PUNCT
ejpam-6212	554	48	=	=	PUNCT
ejpam-6212	554	49	∑	∑	PUNCT
ejpam-6212	554	50	{	{	PUNCT
ejpam-6212	554	51	u	u	NOUN
ejpam-6212	554	52	,	,	PUNCT
ejpam-6212	554	53	v}⊆v	v}⊆v	PROPN
ejpam-6212	554	54	(	(	PUNCT
ejpam-6212	554	55	g	g	NOUN
ejpam-6212	554	56	)	)	PUNCT
ejpam-6212	554	57	d(u	d(u	PROPN
ejpam-6212	554	58	,	,	PUNCT
ejpam-6212	554	59	v	v	NOUN
ejpam-6212	554	60	)	)	PUNCT
ejpam-6212	554	61	·	·	PUNCT
ejpam-6212	555	1	d(u	d(u	PROPN
ejpam-6212	555	2	,	,	PUNCT
ejpam-6212	555	3	v	v	NOUN
ejpam-6212	555	4	)	)	PUNCT
ejpam-6212	555	5	+	+	CCONJ
ejpam-6212	555	6	1	1	NUM
ejpam-6212	555	7	d(u	d(u	PROPN
ejpam-6212	555	8	,	,	PUNCT
ejpam-6212	555	9	v	v	NOUN
ejpam-6212	555	10	)	)	PUNCT
ejpam-6212	555	11	+	+	CCONJ
ejpam-6212	555	12	1	1	NUM
ejpam-6212	555	13	<	<	SYM
ejpam-6212	555	14	2	2	NUM
ejpam-6212	555	15	diam(g	diam(g	NOUN
ejpam-6212	555	16	)	)	PUNCT
ejpam-6212	555	17	+	+	CCONJ
ejpam-6212	555	18	1	1	NUM
ejpam-6212	555	19	ww	ww	PROPN
ejpam-6212	555	20	(	(	PUNCT
ejpam-6212	555	21	g	g	NOUN
ejpam-6212	555	22	)	)	PUNCT
ejpam-6212	555	23	.	.	PUNCT
ejpam-6212	556	1	moreover	moreover	ADV
ejpam-6212	556	2	,	,	PUNCT
ejpam-6212	556	3	w	w	PROPN
ejpam-6212	556	4	(	(	PUNCT
ejpam-6212	556	5	g	g	NOUN
ejpam-6212	556	6	)	)	PUNCT
ejpam-6212	556	7	=	=	PUNCT
ejpam-6212	556	8	∑	∑	PUNCT
ejpam-6212	556	9	{	{	PUNCT
ejpam-6212	556	10	u	u	NOUN
ejpam-6212	556	11	,	,	PUNCT
ejpam-6212	556	12	v}⊆v	v}⊆v	PROPN
ejpam-6212	556	13	(	(	PUNCT
ejpam-6212	556	14	g	g	NOUN
ejpam-6212	556	15	)	)	PUNCT
ejpam-6212	556	16	d(u	d(u	PROPN
ejpam-6212	556	17	,	,	PUNCT
ejpam-6212	556	18	v	v	NOUN
ejpam-6212	556	19	)	)	PUNCT
ejpam-6212	556	20	=	=	PUNCT
ejpam-6212	556	21	∑	∑	PUNCT
ejpam-6212	556	22	{	{	PUNCT
ejpam-6212	556	23	u	u	NOUN
ejpam-6212	556	24	,	,	PUNCT
ejpam-6212	556	25	v}⊆v	v}⊆v	PROPN
ejpam-6212	556	26	(	(	PUNCT
ejpam-6212	556	27	g	g	NOUN
ejpam-6212	556	28	)	)	PUNCT
ejpam-6212	556	29	d(u	d(u	PROPN
ejpam-6212	556	30	,	,	PUNCT
ejpam-6212	556	31	v	v	NOUN
ejpam-6212	556	32	)	)	PUNCT
ejpam-6212	556	33	·	·	PUNCT
ejpam-6212	557	1	d(u	d(u	PROPN
ejpam-6212	557	2	,	,	PUNCT
ejpam-6212	557	3	v	v	NOUN
ejpam-6212	557	4	)	)	PUNCT
ejpam-6212	557	5	+	+	CCONJ
ejpam-6212	557	6	1	1	NUM
ejpam-6212	557	7	d(u	d(u	PROPN
ejpam-6212	557	8	,	,	PUNCT
ejpam-6212	557	9	v	v	NOUN
ejpam-6212	557	10	)	)	PUNCT
ejpam-6212	557	11	+	+	CCONJ
ejpam-6212	557	12	1	1	NUM
ejpam-6212	557	13	>	>	X
ejpam-6212	557	14	ww	ww	PROPN
ejpam-6212	557	15	(	(	PUNCT
ejpam-6212	557	16	g	g	NOUN
ejpam-6212	557	17	)	)	PUNCT
ejpam-6212	557	18	the	the	DET
ejpam-6212	557	19	proof	proof	NOUN
ejpam-6212	557	20	is	be	AUX
ejpam-6212	557	21	complete	complete	ADJ
ejpam-6212	557	22	.	.	PUNCT
ejpam-6212	558	1	an	an	DET
ejpam-6212	558	2	immediate	immediate	ADJ
ejpam-6212	558	3	result	result	NOUN
ejpam-6212	558	4	for	for	ADP
ejpam-6212	558	5	simple	simple	ADJ
ejpam-6212	558	6	spirocyclic	spirocyclic	NOUN
ejpam-6212	558	7	graph	graph	NOUN
ejpam-6212	558	8	with	with	ADP
ejpam-6212	558	9	minimum	minimum	NOUN
ejpam-6212	558	10	degree	degree	NOUN
ejpam-6212	558	11	δ	δ	NOUN
ejpam-6212	558	12	=	=	SYM
ejpam-6212	558	13	2	2	NUM
ejpam-6212	558	14	,	,	PUNCT
ejpam-6212	558	15	which	which	PRON
ejpam-6212	558	16	uses	use	VERB
ejpam-6212	558	17	theorem	theorem	NOUN
ejpam-6212	558	18	2	2	NUM
ejpam-6212	558	19	and	and	CCONJ
ejpam-6212	558	20	the	the	DET
ejpam-6212	558	21	proof	proof	NOUN
ejpam-6212	558	22	of	of	ADP
ejpam-6212	558	23	theorem	theorem	NOUN
ejpam-6212	558	24	5	5	NUM
ejpam-6212	558	25	,	,	PUNCT
ejpam-6212	558	26	is	be	AUX
ejpam-6212	558	27	shown	show	VERB
ejpam-6212	558	28	below	below	ADP
ejpam-6212	558	29	.	.	PUNCT
ejpam-6212	559	1	corollary	corollary	ADJ
ejpam-6212	559	2	3	3	X
ejpam-6212	559	3	.	.	PUNCT
ejpam-6212	560	1	let	let	VERB
ejpam-6212	560	2	g	g	PRON
ejpam-6212	560	3	be	be	AUX
ejpam-6212	560	4	a	a	DET
ejpam-6212	560	5	simple	simple	ADJ
ejpam-6212	560	6	spirocyclic	spirocyclic	NOUN
ejpam-6212	560	7	graph	graph	NOUN
ejpam-6212	560	8	with	with	ADP
ejpam-6212	560	9	minimum	minimum	NOUN
ejpam-6212	560	10	degree	degree	NOUN
ejpam-6212	560	11	δ	δ	NOUN
ejpam-6212	560	12	=	=	SYM
ejpam-6212	560	13	2	2	NUM
ejpam-6212	560	14	and	and	CCONJ
ejpam-6212	560	15	with	with	ADP
ejpam-6212	560	16	even	even	ADV
ejpam-6212	560	17	cycles	cycle	NOUN
ejpam-6212	560	18	c2t1	c2t1	NOUN
ejpam-6212	560	19	and	and	CCONJ
ejpam-6212	560	20	c2t2	c2t2	PROPN
ejpam-6212	560	21	,	,	PUNCT
ejpam-6212	560	22	for	for	SCONJ
ejpam-6212	560	23	some	some	DET
ejpam-6212	560	24	natural	natural	ADJ
ejpam-6212	560	25	numbers	number	NOUN
ejpam-6212	560	26	t1	t1	PROPN
ejpam-6212	560	27	,	,	PUNCT
ejpam-6212	560	28	t2	t2	NOUN
ejpam-6212	560	29	≥	≥	NUM
ejpam-6212	560	30	2	2	NUM
ejpam-6212	560	31	.	.	PUNCT
ejpam-6212	561	1	then	then	ADV
ejpam-6212	561	2	2	2	NUM
ejpam-6212	561	3	t1	t1	NOUN
ejpam-6212	561	4	+	+	CCONJ
ejpam-6212	561	5	t2	t2	NOUN
ejpam-6212	561	6	+	+	CCONJ
ejpam-6212	561	7	1	1	NUM
ejpam-6212	561	8	ww	ww	PROPN
ejpam-6212	561	9	(	(	PUNCT
ejpam-6212	561	10	g	g	NOUN
ejpam-6212	561	11	)	)	PUNCT
ejpam-6212	561	12	+	+	NOUN
ejpam-6212	562	1	2(t1	2(t1	NUM
ejpam-6212	562	2	+	+	NUM
ejpam-6212	562	3	t2	t2	NOUN
ejpam-6212	562	4	)	)	PUNCT
ejpam-6212	562	5	2	2	NUM
ejpam-6212	562	6	<	<	X
ejpam-6212	562	7	wg(g	wg(g	NOUN
ejpam-6212	562	8	)	)	PUNCT
ejpam-6212	562	9	<	<	X
ejpam-6212	563	1	ww	ww	PROPN
ejpam-6212	563	2	(	(	PUNCT
ejpam-6212	563	3	g	g	NOUN
ejpam-6212	563	4	)	)	PUNCT
ejpam-6212	563	5	+	+	NOUN
ejpam-6212	563	6	2(t1	2(t1	NUM
ejpam-6212	563	7	+	+	NUM
ejpam-6212	563	8	t2	t2	NOUN
ejpam-6212	563	9	)	)	PUNCT
ejpam-6212	563	10	2	2	NUM
ejpam-6212	563	11	.	.	NOUN
ejpam-6212	563	12	9	9	NUM
ejpam-6212	563	13	.	.	NUM
ejpam-6212	563	14	bounds	bound	NOUN
ejpam-6212	563	15	of	of	ADP
ejpam-6212	563	16	g	g	NOUN
ejpam-6212	563	17	-	-	PUNCT
ejpam-6212	563	18	wiener	wiener	NOUN
ejpam-6212	563	19	index	index	NOUN
ejpam-6212	563	20	with	with	ADP
ejpam-6212	563	21	harary	harary	PROPN
ejpam-6212	563	22	index	index	NOUN
ejpam-6212	563	23	the	the	DET
ejpam-6212	563	24	following	following	ADJ
ejpam-6212	563	25	result	result	NOUN
ejpam-6212	563	26	establishes	establish	VERB
ejpam-6212	563	27	the	the	DET
ejpam-6212	563	28	relation	relation	NOUN
ejpam-6212	563	29	between	between	ADP
ejpam-6212	563	30	g	g	NOUN
ejpam-6212	563	31	-	-	PUNCT
ejpam-6212	563	32	wiener	wiener	NOUN
ejpam-6212	563	33	index	index	NOUN
ejpam-6212	563	34	and	and	CCONJ
ejpam-6212	563	35	harary	harary	NOUN
ejpam-6212	563	36	index	index	NOUN
ejpam-6212	563	37	for	for	ADP
ejpam-6212	563	38	simple	simple	ADJ
ejpam-6212	563	39	spirocyclic	spirocyclic	NOUN
ejpam-6212	563	40	graphs	graph	NOUN
ejpam-6212	563	41	.	.	PUNCT
ejpam-6212	564	1	theorem	theorem	NOUN
ejpam-6212	564	2	6	6	NUM
ejpam-6212	564	3	.	.	PUNCT
ejpam-6212	565	1	let	let	VERB
ejpam-6212	565	2	g	g	PRON
ejpam-6212	565	3	be	be	AUX
ejpam-6212	565	4	a	a	DET
ejpam-6212	565	5	simple	simple	ADJ
ejpam-6212	565	6	spirocyclic	spirocyclic	NOUN
ejpam-6212	565	7	graph	graph	NOUN
ejpam-6212	565	8	with	with	ADP
ejpam-6212	565	9	even	even	ADV
ejpam-6212	565	10	cycles	cycle	NOUN
ejpam-6212	565	11	c2t1	c2t1	NOUN
ejpam-6212	566	1	=	=	SYM
ejpam-6212	567	1	[	[	X
ejpam-6212	567	2	u1	u1	NOUN
ejpam-6212	567	3	,	,	PUNCT
ejpam-6212	567	4	u2	u2	NOUN
ejpam-6212	567	5	,	,	PUNCT
ejpam-6212	567	6	.	.	PUNCT
ejpam-6212	567	7	.	.	PUNCT
ejpam-6212	567	8	.	.	PUNCT
ejpam-6212	568	1	,	,	PUNCT
ejpam-6212	568	2	u2t1	u2t1	VERB
ejpam-6212	568	3	]	]	PUNCT
ejpam-6212	568	4	and	and	CCONJ
ejpam-6212	568	5	c2t2	c2t2	NOUN
ejpam-6212	569	1	=	=	PUNCT
ejpam-6212	570	1	[	[	X
ejpam-6212	570	2	u1	u1	NOUN
ejpam-6212	570	3	=	=	SYM
ejpam-6212	570	4	v1	v1	NOUN
ejpam-6212	570	5	,	,	PUNCT
ejpam-6212	570	6	v2	v2	NOUN
ejpam-6212	570	7	,	,	PUNCT
ejpam-6212	570	8	.	.	PUNCT
ejpam-6212	570	9	.	.	PUNCT
ejpam-6212	570	10	.	.	PUNCT
ejpam-6212	571	1	,	,	PUNCT
ejpam-6212	571	2	v2t2	v2t2	X
ejpam-6212	571	3	]	]	X
ejpam-6212	571	4	,	,	PUNCT
ejpam-6212	571	5	for	for	ADP
ejpam-6212	571	6	some	some	DET
ejpam-6212	571	7	natural	natural	ADJ
ejpam-6212	571	8	numbers	number	NOUN
ejpam-6212	571	9	t1	t1	PROPN
ejpam-6212	571	10	,	,	PUNCT
ejpam-6212	571	11	t2	t2	NOUN
ejpam-6212	571	12	≥	≥	NUM
ejpam-6212	571	13	2	2	NUM
ejpam-6212	571	14	,	,	PUNCT
ejpam-6212	571	15	without	without	ADP
ejpam-6212	571	16	a	a	DET
ejpam-6212	571	17	common	common	ADJ
ejpam-6212	571	18	edge	edge	NOUN
ejpam-6212	571	19	.	.	PUNCT
ejpam-6212	572	1	then	then	ADV
ejpam-6212	572	2	h(g	h(g	VERB
ejpam-6212	572	3	)	)	PUNCT
ejpam-6212	573	1	+	+	ADP
ejpam-6212	573	2	at1	at1	PROPN
ejpam-6212	573	3	+	+	PROPN
ejpam-6212	573	4	bt2	bt2	PROPN
ejpam-6212	573	5	<	<	X
ejpam-6212	573	6	wg(g	wg(g	PROPN
ejpam-6212	573	7	)	)	PUNCT
ejpam-6212	573	8	<	<	X
ejpam-6212	573	9	(	(	PUNCT
ejpam-6212	573	10	diam(g))2h(g	diam(g))2h(g	NOUN
ejpam-6212	573	11	)	)	PUNCT
ejpam-6212	573	12	+	+	NUM
ejpam-6212	573	13	cdiam(g	cdiam(g	X
ejpam-6212	573	14	)	)	PUNCT
ejpam-6212	573	15	where	where	SCONJ
ejpam-6212	573	16	{	{	PUNCT
ejpam-6212	573	17	u1	u1	NOUN
ejpam-6212	573	18	=	=	SYM
ejpam-6212	573	19	v1	v1	PROPN
ejpam-6212	573	20	,	,	PUNCT
ejpam-6212	573	21	u2	u2	NOUN
ejpam-6212	573	22	,	,	PUNCT
ejpam-6212	573	23	.	.	PUNCT
ejpam-6212	573	24	.	.	PUNCT
ejpam-6212	573	25	.	.	PUNCT
ejpam-6212	574	1	,	,	PUNCT
ejpam-6212	574	2	u2t1	u2t1	INTJ
ejpam-6212	574	3	,	,	PUNCT
ejpam-6212	574	4	v2	v2	PROPN
ejpam-6212	574	5	,	,	PUNCT
ejpam-6212	574	6	.	.	PUNCT
ejpam-6212	574	7	.	.	PUNCT
ejpam-6212	575	1	.	.	PUNCT
ejpam-6212	576	1	,	,	PUNCT
ejpam-6212	576	2	v2t2	v2t2	NOUN
ejpam-6212	576	3	}	}	PUNCT
ejpam-6212	576	4	is	be	AUX
ejpam-6212	576	5	the	the	DET
ejpam-6212	576	6	tree	tree	NOUN
ejpam-6212	576	7	-	-	PUNCT
ejpam-6212	576	8	partition	partition	NOUN
ejpam-6212	576	9	of	of	ADP
ejpam-6212	576	10	v	v	NOUN
ejpam-6212	576	11	(	(	PUNCT
ejpam-6212	576	12	g	g	NOUN
ejpam-6212	576	13	)	)	PUNCT
ejpam-6212	576	14	with	with	ADP
ejpam-6212	576	15	respect	respect	NOUN
ejpam-6212	576	16	to	to	ADP
ejpam-6212	576	17	the	the	DET
ejpam-6212	576	18	projection	projection	NOUN
ejpam-6212	576	19	of	of	ADP
ejpam-6212	576	20	v	v	NOUN
ejpam-6212	576	21	(	(	PUNCT
ejpam-6212	576	22	g	g	NOUN
ejpam-6212	576	23	)	)	PUNCT
ejpam-6212	576	24	onto	onto	ADP
ejpam-6212	576	25	the	the	DET
ejpam-6212	576	26	union	union	NOUN
ejpam-6212	576	27	of	of	ADP
ejpam-6212	576	28	the	the	DET
ejpam-6212	576	29	cycles	cycle	NOUN
ejpam-6212	576	30	c2t1	c2t1	NOUN
ejpam-6212	576	31	and	and	CCONJ
ejpam-6212	576	32	c2t2	c2t2	NOUN
ejpam-6212	576	33	,	,	PUNCT
ejpam-6212	576	34	and	and	CCONJ
ejpam-6212	577	1	a	a	DET
ejpam-6212	577	2	=	=	X
ejpam-6212	577	3	t1∑	t1∑	PROPN
ejpam-6212	577	4	i=1	i=1	PROPN
ejpam-6212	577	5	|ui||ui+t1	|ui||ui+t1	ADP
ejpam-6212	577	6	|+	|+	NOUN
ejpam-6212	577	7	2t2∑	2t2∑	NUM
ejpam-6212	577	8	j=2	j=2	NOUN
ejpam-6212	577	9	|ut1	|ut1	PUNCT
ejpam-6212	577	10	+	+	NOUN
ejpam-6212	577	11	1||vj	1||vj	NOUN
ejpam-6212	577	12	|+	|+	X
ejpam-6212	577	13	|ut1	|ut1	PUNCT
ejpam-6212	577	14	+	+	NOUN
ejpam-6212	577	15	1||vt2	1||vt2	NUM
ejpam-6212	577	16	+	+	NOUN
ejpam-6212	577	17	1|	1|	NUM
ejpam-6212	577	18	,	,	PUNCT
ejpam-6212	577	19	r.	r.	PROPN
ejpam-6212	577	20	g.	g.	PROPN
ejpam-6212	577	21	artes	artes	PROPN
ejpam-6212	577	22	jr	jr	PROPN
ejpam-6212	577	23	.	.	PROPN
ejpam-6212	577	24	et	et	PROPN
ejpam-6212	577	25	al	al	PROPN
ejpam-6212	577	26	.	.	PUNCT
ejpam-6212	577	27	/	/	SYM
ejpam-6212	577	28	eur	eur	PROPN
ejpam-6212	577	29	.	.	PUNCT
ejpam-6212	578	1	j.	j.	PROPN
ejpam-6212	578	2	pure	pure	PROPN
ejpam-6212	578	3	appl	appl	PROPN
ejpam-6212	578	4	.	.	PROPN
ejpam-6212	578	5	math	math	PROPN
ejpam-6212	578	6	,	,	PUNCT
ejpam-6212	578	7	18	18	NUM
ejpam-6212	578	8	(	(	PUNCT
ejpam-6212	578	9	4	4	NUM
ejpam-6212	578	10	)	)	PUNCT
ejpam-6212	578	11	(	(	PUNCT
ejpam-6212	578	12	2025	2025	NUM
ejpam-6212	578	13	)	)	PUNCT
ejpam-6212	578	14	,	,	PUNCT
ejpam-6212	578	15	6212	6212	NUM
ejpam-6212	578	16	15	15	NUM
ejpam-6212	578	17	of	of	ADP
ejpam-6212	578	18	20	20	NUM
ejpam-6212	578	19	b	b	NOUN
ejpam-6212	578	20	=	=	SYM
ejpam-6212	578	21	t2∑	t2∑	PROPN
ejpam-6212	578	22	j=1	j=1	NOUN
ejpam-6212	579	1	|vj	|vj	X
ejpam-6212	579	2	||vj+t2	||vj+t2	PROPN
ejpam-6212	579	3	|+	|+	NOUN
ejpam-6212	579	4	2t1∑	2t1∑	NUM
ejpam-6212	579	5	i=2	i=2	PROPN
ejpam-6212	580	1	|vt2	|vt2	PROPN
ejpam-6212	581	1	+	+	NOUN
ejpam-6212	581	2	1||ui|+	1||ui|+	NOUN
ejpam-6212	581	3	|ut1	|ut1	NOUN
ejpam-6212	581	4	+	+	NOUN
ejpam-6212	581	5	1||vt2	1||vt2	NUM
ejpam-6212	581	6	+	+	NOUN
ejpam-6212	581	7	1|	1|	NUM
ejpam-6212	581	8	,	,	PUNCT
ejpam-6212	581	9	and	and	CCONJ
ejpam-6212	581	10	c	c	X
ejpam-6212	582	1	=	=	SYM
ejpam-6212	582	2	t1∑	t1∑	PROPN
ejpam-6212	582	3	i=1	i=1	PROPN
ejpam-6212	582	4	|ui||ui+t1	|ui||ui+t1	ADV
ejpam-6212	582	5	|+	|+	NOUN
ejpam-6212	582	6	t2∑	t2∑	PROPN
ejpam-6212	582	7	j=1	j=1	NOUN
ejpam-6212	583	1	|vj	|vj	X
ejpam-6212	583	2	||vj+t2	||vj+t2	PROPN
ejpam-6212	583	3	|+	|+	NOUN
ejpam-6212	583	4	2t2∑	2t2∑	NUM
ejpam-6212	583	5	j=2	j=2	NOUN
ejpam-6212	583	6	|ut1	|ut1	PUNCT
ejpam-6212	583	7	+	+	NOUN
ejpam-6212	583	8	1||vj	1||vj	PROPN
ejpam-6212	583	9	|+	|+	NOUN
ejpam-6212	583	10	2t1∑	2t1∑	NUM
ejpam-6212	583	11	i=2	i=2	PROPN
ejpam-6212	583	12	|vt2	|vt2	PROPN
ejpam-6212	584	1	+	+	NOUN
ejpam-6212	584	2	1||ui|+	1||ui|+	NOUN
ejpam-6212	584	3	|ut1	|ut1	NOUN
ejpam-6212	584	4	+	+	NOUN
ejpam-6212	584	5	1||vt2	1||vt2	NUM
ejpam-6212	584	6	+	+	NOUN
ejpam-6212	584	7	1|	1|	NUM
ejpam-6212	584	8	.	.	PUNCT
ejpam-6212	585	1	proof	proof	NOUN
ejpam-6212	585	2	.	.	PUNCT
ejpam-6212	586	1	it	it	PRON
ejpam-6212	586	2	suffices	suffice	VERB
ejpam-6212	586	3	to	to	PART
ejpam-6212	586	4	show	show	VERB
ejpam-6212	586	5	the	the	DET
ejpam-6212	586	6	bounds	bound	NOUN
ejpam-6212	586	7	of	of	ADP
ejpam-6212	586	8	wiener	wiener	NOUN
ejpam-6212	586	9	index	index	NOUN
ejpam-6212	586	10	in	in	ADP
ejpam-6212	586	11	terms	term	NOUN
ejpam-6212	586	12	harary	harary	PROPN
ejpam-6212	586	13	index	index	NOUN
ejpam-6212	586	14	and	and	CCONJ
ejpam-6212	586	15	use	use	VERB
ejpam-6212	586	16	lemma	lemma	PROPN
ejpam-6212	586	17	2	2	NUM
ejpam-6212	586	18	together	together	ADV
ejpam-6212	586	19	with	with	ADP
ejpam-6212	586	20	theorem	theorem	NOUN
ejpam-6212	586	21	1	1	NUM
ejpam-6212	586	22	.	.	PUNCT
ejpam-6212	587	1	w	w	PROPN
ejpam-6212	587	2	(	(	PUNCT
ejpam-6212	587	3	g	g	NOUN
ejpam-6212	587	4	)	)	PUNCT
ejpam-6212	587	5	=	=	PUNCT
ejpam-6212	587	6	∑	∑	PUNCT
ejpam-6212	587	7	{	{	PUNCT
ejpam-6212	587	8	u	u	NOUN
ejpam-6212	587	9	,	,	PUNCT
ejpam-6212	587	10	v}∈v	v}∈v	PROPN
ejpam-6212	587	11	(	(	PUNCT
ejpam-6212	587	12	g	g	NOUN
ejpam-6212	587	13	)	)	PUNCT
ejpam-6212	587	14	d(u	d(u	PROPN
ejpam-6212	587	15	,	,	PUNCT
ejpam-6212	587	16	v	v	NOUN
ejpam-6212	587	17	)	)	PUNCT
ejpam-6212	587	18	=	=	SYM
ejpam-6212	587	19	diam(g	diam(g	NOUN
ejpam-6212	587	20	)	)	PUNCT
ejpam-6212	587	21	∑	∑	PROPN
ejpam-6212	587	22	u	u	PROPN
ejpam-6212	587	23	,	,	PUNCT
ejpam-6212	587	24	v⊆v	v⊆v	PROPN
ejpam-6212	587	25	(	(	PUNCT
ejpam-6212	587	26	g	g	NOUN
ejpam-6212	587	27	)	)	PUNCT
ejpam-6212	587	28	d(u	d(u	PROPN
ejpam-6212	587	29	,	,	PUNCT
ejpam-6212	587	30	v	v	NOUN
ejpam-6212	587	31	)	)	PUNCT
ejpam-6212	587	32	d(u	d(u	PROPN
ejpam-6212	587	33	,	,	PUNCT
ejpam-6212	587	34	v	v	NOUN
ejpam-6212	587	35	)	)	PUNCT
ejpam-6212	587	36	<	<	X
ejpam-6212	587	37	diam(g)2h(g	diam(g)2h(g	NOUN
ejpam-6212	587	38	)	)	PUNCT
ejpam-6212	587	39	.	.	PUNCT
ejpam-6212	588	1	moreover	moreover	ADV
ejpam-6212	588	2	,	,	PUNCT
ejpam-6212	588	3	w	w	PROPN
ejpam-6212	588	4	(	(	PUNCT
ejpam-6212	588	5	g	g	NOUN
ejpam-6212	588	6	)	)	PUNCT
ejpam-6212	588	7	=	=	PUNCT
ejpam-6212	588	8	∑	∑	PUNCT
ejpam-6212	588	9	{	{	PUNCT
ejpam-6212	588	10	u	u	NOUN
ejpam-6212	588	11	,	,	PUNCT
ejpam-6212	588	12	v}⊆v	v}⊆v	PROPN
ejpam-6212	588	13	(	(	PUNCT
ejpam-6212	588	14	g	g	NOUN
ejpam-6212	588	15	)	)	PUNCT
ejpam-6212	588	16	d(u	d(u	PROPN
ejpam-6212	588	17	,	,	PUNCT
ejpam-6212	588	18	v	v	NOUN
ejpam-6212	588	19	)	)	PUNCT
ejpam-6212	588	20	=	=	PUNCT
ejpam-6212	588	21	∑	∑	PUNCT
ejpam-6212	588	22	{	{	PUNCT
ejpam-6212	588	23	u	u	NOUN
ejpam-6212	588	24	,	,	PUNCT
ejpam-6212	588	25	v}⊆v	v}⊆v	PROPN
ejpam-6212	588	26	(	(	PUNCT
ejpam-6212	588	27	g	g	NOUN
ejpam-6212	588	28	)	)	PUNCT
ejpam-6212	588	29	1	1	NUM
ejpam-6212	588	30	d(u	d(u	PROPN
ejpam-6212	588	31	,	,	PUNCT
ejpam-6212	588	32	v	v	NOUN
ejpam-6212	588	33	)	)	PUNCT
ejpam-6212	588	34	>	>	X
ejpam-6212	588	35	h(g	h(g	NOUN
ejpam-6212	588	36	)	)	PUNCT
ejpam-6212	588	37	.	.	PUNCT
ejpam-6212	589	1	the	the	DET
ejpam-6212	589	2	proof	proof	NOUN
ejpam-6212	589	3	is	be	AUX
ejpam-6212	589	4	complete	complete	ADJ
ejpam-6212	589	5	.	.	PUNCT
ejpam-6212	590	1	for	for	ADP
ejpam-6212	590	2	simple	simple	ADJ
ejpam-6212	590	3	spirocyclic	spirocyclic	NOUN
ejpam-6212	590	4	graphs	graph	NOUN
ejpam-6212	590	5	with	with	ADP
ejpam-6212	590	6	minimum	minimum	NOUN
ejpam-6212	590	7	degree	degree	NOUN
ejpam-6212	590	8	δ	δ	NOUN
ejpam-6212	590	9	=	=	SYM
ejpam-6212	590	10	2	2	NUM
ejpam-6212	590	11	,	,	PUNCT
ejpam-6212	590	12	the	the	DET
ejpam-6212	590	13	following	follow	VERB
ejpam-6212	590	14	bounds	bound	NOUN
ejpam-6212	590	15	of	of	ADP
ejpam-6212	590	16	harary	harary	PROPN
ejpam-6212	590	17	index	index	NOUN
ejpam-6212	590	18	follows	follow	VERB
ejpam-6212	590	19	by	by	ADP
ejpam-6212	590	20	using	use	VERB
ejpam-6212	590	21	theorem	theorem	ADJ
ejpam-6212	590	22	2	2	NUM
ejpam-6212	590	23	and	and	CCONJ
ejpam-6212	590	24	the	the	DET
ejpam-6212	590	25	proof	proof	NOUN
ejpam-6212	590	26	of	of	ADP
ejpam-6212	590	27	theorem	theorem	ADJ
ejpam-6212	590	28	6	6	NUM
ejpam-6212	590	29	.	.	PUNCT
ejpam-6212	590	30	corollary	corollary	ADJ
ejpam-6212	590	31	4	4	NUM
ejpam-6212	590	32	.	.	PUNCT
ejpam-6212	591	1	let	let	VERB
ejpam-6212	591	2	g	g	PRON
ejpam-6212	591	3	be	be	AUX
ejpam-6212	591	4	a	a	DET
ejpam-6212	591	5	simple	simple	ADJ
ejpam-6212	591	6	spirocyclic	spirocyclic	NOUN
ejpam-6212	591	7	graph	graph	NOUN
ejpam-6212	591	8	with	with	ADP
ejpam-6212	591	9	minimum	minimum	NOUN
ejpam-6212	591	10	degree	degree	NOUN
ejpam-6212	591	11	δ	δ	NOUN
ejpam-6212	591	12	=	=	SYM
ejpam-6212	591	13	2	2	NUM
ejpam-6212	591	14	and	and	CCONJ
ejpam-6212	591	15	with	with	ADP
ejpam-6212	591	16	even	even	ADV
ejpam-6212	591	17	cycles	cycle	NOUN
ejpam-6212	591	18	c2t1	c2t1	NOUN
ejpam-6212	591	19	and	and	CCONJ
ejpam-6212	591	20	c2t2	c2t2	PROPN
ejpam-6212	591	21	,	,	PUNCT
ejpam-6212	591	22	for	for	SCONJ
ejpam-6212	591	23	some	some	DET
ejpam-6212	591	24	natural	natural	ADJ
ejpam-6212	591	25	numbers	number	NOUN
ejpam-6212	591	26	t1	t1	PROPN
ejpam-6212	591	27	,	,	PUNCT
ejpam-6212	591	28	t2	t2	NOUN
ejpam-6212	591	29	≥	≥	NUM
ejpam-6212	591	30	2	2	NUM
ejpam-6212	591	31	.	.	PUNCT
ejpam-6212	592	1	then	then	ADV
ejpam-6212	592	2	(	(	PUNCT
ejpam-6212	592	3	t1	t1	NOUN
ejpam-6212	592	4	+	+	NUM
ejpam-6212	592	5	t2	t2	NOUN
ejpam-6212	592	6	)	)	PUNCT
ejpam-6212	592	7	2h(g	2h(g	NOUN
ejpam-6212	592	8	)	)	PUNCT
ejpam-6212	593	1	+	+	CCONJ
ejpam-6212	593	2	2(t1	2(t1	NUM
ejpam-6212	593	3	+	+	NUM
ejpam-6212	593	4	t2	t2	NOUN
ejpam-6212	593	5	)	)	PUNCT
ejpam-6212	593	6	2	2	NUM
ejpam-6212	593	7	<	<	X
ejpam-6212	593	8	wg(g	wg(g	NOUN
ejpam-6212	593	9	)	)	PUNCT
ejpam-6212	593	10	<	<	X
ejpam-6212	593	11	h(g	h(g	NOUN
ejpam-6212	593	12	)	)	PUNCT
ejpam-6212	594	1	+	+	CCONJ
ejpam-6212	595	1	2(t1	2(t1	NUM
ejpam-6212	595	2	+	+	NUM
ejpam-6212	595	3	t2	t2	NOUN
ejpam-6212	595	4	)	)	PUNCT
ejpam-6212	595	5	2	2	NUM
ejpam-6212	595	6	.	.	NOUN
ejpam-6212	595	7	10	10	NUM
ejpam-6212	595	8	.	.	PUNCT
ejpam-6212	596	1	bounds	bound	NOUN
ejpam-6212	596	2	of	of	ADP
ejpam-6212	596	3	g	g	NOUN
ejpam-6212	596	4	-	-	PUNCT
ejpam-6212	596	5	wiener	wiener	NOUN
ejpam-6212	596	6	index	index	NOUN
ejpam-6212	596	7	with	with	ADP
ejpam-6212	596	8	additively	additively	ADV
ejpam-6212	596	9	weighted	weight	VERB
ejpam-6212	596	10	harary	harary	PROPN
ejpam-6212	596	11	index	index	NOUN
ejpam-6212	596	12	the	the	DET
ejpam-6212	596	13	following	follow	VERB
ejpam-6212	596	14	result	result	NOUN
ejpam-6212	596	15	establishes	establish	VERB
ejpam-6212	596	16	bounds	bound	NOUN
ejpam-6212	596	17	of	of	ADP
ejpam-6212	596	18	g	g	NOUN
ejpam-6212	596	19	-	-	PUNCT
ejpam-6212	596	20	wiener	wiener	NOUN
ejpam-6212	596	21	index	index	NOUN
ejpam-6212	596	22	in	in	ADP
ejpam-6212	596	23	terms	term	NOUN
ejpam-6212	596	24	of	of	ADP
ejpam-6212	596	25	additively	additively	ADV
ejpam-6212	596	26	weighted	weight	VERB
ejpam-6212	596	27	harary	harary	ADJ
ejpam-6212	596	28	index	index	NOUN
ejpam-6212	596	29	as	as	SCONJ
ejpam-6212	596	30	defined	define	VERB
ejpam-6212	596	31	in	in	ADP
ejpam-6212	596	32	[	[	X
ejpam-6212	596	33	12	12	NUM
ejpam-6212	596	34	]	]	PUNCT
ejpam-6212	596	35	for	for	ADP
ejpam-6212	596	36	simple	simple	ADJ
ejpam-6212	596	37	spirocyclic	spirocyclic	NOUN
ejpam-6212	596	38	graph	graph	NOUN
ejpam-6212	596	39	g	g	NOUN
ejpam-6212	596	40	containing	contain	VERB
ejpam-6212	596	41	even	even	ADV
ejpam-6212	596	42	cycles	cycle	NOUN
ejpam-6212	596	43	.	.	PUNCT
ejpam-6212	597	1	theorem	theorem	ADJ
ejpam-6212	597	2	7	7	NUM
ejpam-6212	597	3	.	.	PUNCT
ejpam-6212	598	1	let	let	VERB
ejpam-6212	598	2	g	g	PRON
ejpam-6212	598	3	be	be	AUX
ejpam-6212	598	4	a	a	DET
ejpam-6212	598	5	simple	simple	ADJ
ejpam-6212	598	6	spirocyclic	spirocyclic	NOUN
ejpam-6212	598	7	graph	graph	NOUN
ejpam-6212	598	8	with	with	ADP
ejpam-6212	598	9	even	even	ADV
ejpam-6212	598	10	cycles	cycle	NOUN
ejpam-6212	598	11	c2t1	c2t1	NOUN
ejpam-6212	599	1	=	=	SYM
ejpam-6212	600	1	[	[	X
ejpam-6212	600	2	u1	u1	NOUN
ejpam-6212	600	3	,	,	PUNCT
ejpam-6212	600	4	u2	u2	NOUN
ejpam-6212	600	5	,	,	PUNCT
ejpam-6212	600	6	.	.	PUNCT
ejpam-6212	600	7	.	.	PUNCT
ejpam-6212	600	8	.	.	PUNCT
ejpam-6212	601	1	,	,	PUNCT
ejpam-6212	601	2	u2t1	u2t1	PROPN
ejpam-6212	601	3	]	]	PUNCT
ejpam-6212	601	4	r.	r.	PROPN
ejpam-6212	601	5	g.	g.	PROPN
ejpam-6212	601	6	artes	artes	PROPN
ejpam-6212	601	7	jr	jr	PROPN
ejpam-6212	601	8	.	.	PROPN
ejpam-6212	601	9	et	et	PROPN
ejpam-6212	601	10	al	al	PROPN
ejpam-6212	601	11	.	.	PUNCT
ejpam-6212	601	12	/	/	SYM
ejpam-6212	601	13	eur	eur	PROPN
ejpam-6212	601	14	.	.	PUNCT
ejpam-6212	602	1	j.	j.	PROPN
ejpam-6212	602	2	pure	pure	PROPN
ejpam-6212	602	3	appl	appl	PROPN
ejpam-6212	602	4	.	.	PROPN
ejpam-6212	602	5	math	math	PROPN
ejpam-6212	602	6	,	,	PUNCT
ejpam-6212	602	7	18	18	NUM
ejpam-6212	602	8	(	(	PUNCT
ejpam-6212	602	9	4	4	NUM
ejpam-6212	602	10	)	)	PUNCT
ejpam-6212	602	11	(	(	PUNCT
ejpam-6212	602	12	2025	2025	NUM
ejpam-6212	602	13	)	)	PUNCT
ejpam-6212	602	14	,	,	PUNCT
ejpam-6212	602	15	6212	6212	NUM
ejpam-6212	602	16	16	16	NUM
ejpam-6212	602	17	of	of	ADP
ejpam-6212	602	18	20	20	NUM
ejpam-6212	602	19	and	and	CCONJ
ejpam-6212	602	20	c2t2	c2t2	NOUN
ejpam-6212	602	21	=	=	PUNCT
ejpam-6212	603	1	[	[	X
ejpam-6212	603	2	u1	u1	NOUN
ejpam-6212	603	3	=	=	SYM
ejpam-6212	603	4	v1	v1	NOUN
ejpam-6212	603	5	,	,	PUNCT
ejpam-6212	603	6	v2	v2	NOUN
ejpam-6212	603	7	,	,	PUNCT
ejpam-6212	603	8	.	.	PUNCT
ejpam-6212	603	9	.	.	PUNCT
ejpam-6212	603	10	.	.	PUNCT
ejpam-6212	604	1	,	,	PUNCT
ejpam-6212	604	2	v2t2	v2t2	X
ejpam-6212	604	3	]	]	X
ejpam-6212	604	4	,	,	PUNCT
ejpam-6212	604	5	for	for	ADP
ejpam-6212	604	6	some	some	DET
ejpam-6212	604	7	natural	natural	ADJ
ejpam-6212	604	8	numbers	number	NOUN
ejpam-6212	604	9	t1	t1	PROPN
ejpam-6212	604	10	,	,	PUNCT
ejpam-6212	604	11	t2	t2	NOUN
ejpam-6212	604	12	≥	≥	NUM
ejpam-6212	604	13	2	2	NUM
ejpam-6212	604	14	.	.	PUNCT
ejpam-6212	605	1	then	then	ADV
ejpam-6212	605	2	1	1	NUM
ejpam-6212	605	3	2∆	2∆	NUM
ejpam-6212	605	4	ha(g	ha(g	NOUN
ejpam-6212	605	5	)	)	PUNCT
ejpam-6212	606	1	+	+	X
ejpam-6212	606	2	at1	at1	PROPN
ejpam-6212	606	3	+	+	PROPN
ejpam-6212	606	4	bt2	bt2	PROPN
ejpam-6212	606	5	<	<	X
ejpam-6212	606	6	wg(g	wg(g	PROPN
ejpam-6212	606	7	)	)	PUNCT
ejpam-6212	606	8	<	<	X
ejpam-6212	606	9	(	(	PUNCT
ejpam-6212	606	10	diam(g))2	diam(g))2	NOUN
ejpam-6212	606	11	2δ	2δ	NUM
ejpam-6212	606	12	ha(g	ha(g	X
ejpam-6212	606	13	)	)	PUNCT
ejpam-6212	606	14	+	+	NUM
ejpam-6212	607	1	cdiam(g	cdiam(g	X
ejpam-6212	607	2	)	)	PUNCT
ejpam-6212	607	3	where	where	SCONJ
ejpam-6212	607	4	{	{	PUNCT
ejpam-6212	607	5	u1	u1	NOUN
ejpam-6212	607	6	=	=	SYM
ejpam-6212	607	7	v1	v1	PROPN
ejpam-6212	607	8	,	,	PUNCT
ejpam-6212	607	9	u2	u2	NOUN
ejpam-6212	607	10	,	,	PUNCT
ejpam-6212	607	11	.	.	PUNCT
ejpam-6212	607	12	.	.	PUNCT
ejpam-6212	607	13	.	.	PUNCT
ejpam-6212	608	1	,	,	PUNCT
ejpam-6212	608	2	u2t1	u2t1	INTJ
ejpam-6212	608	3	,	,	PUNCT
ejpam-6212	608	4	v2	v2	PROPN
ejpam-6212	608	5	,	,	PUNCT
ejpam-6212	608	6	.	.	PUNCT
ejpam-6212	608	7	.	.	PUNCT
ejpam-6212	609	1	.	.	PUNCT
ejpam-6212	610	1	,	,	PUNCT
ejpam-6212	610	2	v2t2	v2t2	NOUN
ejpam-6212	610	3	}	}	PUNCT
ejpam-6212	610	4	is	be	AUX
ejpam-6212	610	5	the	the	DET
ejpam-6212	610	6	tree	tree	NOUN
ejpam-6212	610	7	-	-	PUNCT
ejpam-6212	610	8	partition	partition	NOUN
ejpam-6212	610	9	of	of	ADP
ejpam-6212	610	10	v	v	NOUN
ejpam-6212	610	11	(	(	PUNCT
ejpam-6212	610	12	g	g	NOUN
ejpam-6212	610	13	)	)	PUNCT
ejpam-6212	610	14	with	with	ADP
ejpam-6212	610	15	respect	respect	NOUN
ejpam-6212	610	16	to	to	ADP
ejpam-6212	610	17	the	the	DET
ejpam-6212	610	18	projection	projection	NOUN
ejpam-6212	610	19	of	of	ADP
ejpam-6212	610	20	v	v	NOUN
ejpam-6212	610	21	(	(	PUNCT
ejpam-6212	610	22	g	g	NOUN
ejpam-6212	610	23	)	)	PUNCT
ejpam-6212	610	24	onto	onto	ADP
ejpam-6212	610	25	the	the	DET
ejpam-6212	610	26	union	union	NOUN
ejpam-6212	610	27	of	of	ADP
ejpam-6212	610	28	the	the	DET
ejpam-6212	610	29	cycles	cycle	NOUN
ejpam-6212	610	30	c2t1	c2t1	NOUN
ejpam-6212	610	31	and	and	CCONJ
ejpam-6212	610	32	c2t2	c2t2	NOUN
ejpam-6212	610	33	,	,	PUNCT
ejpam-6212	610	34	and	and	CCONJ
ejpam-6212	611	1	a	a	DET
ejpam-6212	611	2	=	=	X
ejpam-6212	611	3	t1∑	t1∑	PROPN
ejpam-6212	611	4	i=1	i=1	PROPN
ejpam-6212	611	5	|ui||ui+t1	|ui||ui+t1	ADP
ejpam-6212	611	6	|+	|+	NOUN
ejpam-6212	611	7	2t2∑	2t2∑	NUM
ejpam-6212	611	8	j=2	j=2	NOUN
ejpam-6212	611	9	|ut1	|ut1	PUNCT
ejpam-6212	611	10	+	+	NOUN
ejpam-6212	611	11	1||vj	1||vj	NOUN
ejpam-6212	611	12	|+	|+	X
ejpam-6212	611	13	|ut1	|ut1	PUNCT
ejpam-6212	611	14	+	+	NOUN
ejpam-6212	611	15	1||vt2	1||vt2	NUM
ejpam-6212	611	16	+	+	NOUN
ejpam-6212	611	17	1|	1|	NUM
ejpam-6212	611	18	,	,	PUNCT
ejpam-6212	611	19	b	b	NOUN
ejpam-6212	611	20	=	=	SYM
ejpam-6212	611	21	t2∑	t2∑	PROPN
ejpam-6212	611	22	j=1	j=1	NOUN
ejpam-6212	611	23	|vj	|vj	X
ejpam-6212	611	24	||vj+t2	||vj+t2	PROPN
ejpam-6212	611	25	|+	|+	NOUN
ejpam-6212	611	26	2t1∑	2t1∑	NUM
ejpam-6212	611	27	i=2	i=2	PROPN
ejpam-6212	611	28	|vt2	|vt2	PROPN
ejpam-6212	612	1	+	+	NOUN
ejpam-6212	612	2	1||ui|+	1||ui|+	NOUN
ejpam-6212	612	3	|ut1	|ut1	NOUN
ejpam-6212	612	4	+	+	NOUN
ejpam-6212	612	5	1||vt2	1||vt2	NUM
ejpam-6212	612	6	+	+	NOUN
ejpam-6212	612	7	1|	1|	NUM
ejpam-6212	612	8	,	,	PUNCT
ejpam-6212	612	9	and	and	CCONJ
ejpam-6212	612	10	c	c	X
ejpam-6212	613	1	=	=	SYM
ejpam-6212	613	2	t1∑	t1∑	PROPN
ejpam-6212	613	3	i=1	i=1	PROPN
ejpam-6212	613	4	|ui||ui+t1	|ui||ui+t1	ADV
ejpam-6212	613	5	|+	|+	NOUN
ejpam-6212	613	6	t2∑	t2∑	PROPN
ejpam-6212	613	7	j=1	j=1	NOUN
ejpam-6212	614	1	|vj	|vj	X
ejpam-6212	614	2	||vj+t2	||vj+t2	PROPN
ejpam-6212	614	3	|+	|+	NOUN
ejpam-6212	614	4	2t2∑	2t2∑	NUM
ejpam-6212	614	5	j=2	j=2	NOUN
ejpam-6212	614	6	|ut1	|ut1	PUNCT
ejpam-6212	614	7	+	+	NOUN
ejpam-6212	614	8	1||vj	1||vj	PROPN
ejpam-6212	614	9	|+	|+	NOUN
ejpam-6212	614	10	2t1∑	2t1∑	NUM
ejpam-6212	614	11	i=2	i=2	PROPN
ejpam-6212	614	12	|vt2	|vt2	PROPN
ejpam-6212	615	1	+	+	NOUN
ejpam-6212	615	2	1||ui|+	1||ui|+	NOUN
ejpam-6212	615	3	|ut1	|ut1	NOUN
ejpam-6212	615	4	+	+	NOUN
ejpam-6212	615	5	1||vt2	1||vt2	NUM
ejpam-6212	615	6	+	+	NOUN
ejpam-6212	615	7	1|	1|	NUM
ejpam-6212	615	8	.	.	PUNCT
ejpam-6212	616	1	proof	proof	NOUN
ejpam-6212	616	2	.	.	PUNCT
ejpam-6212	617	1	we	we	PRON
ejpam-6212	617	2	use	use	VERB
ejpam-6212	617	3	lemma	lemma	PROPN
ejpam-6212	617	4	2	2	NUM
ejpam-6212	617	5	and	and	CCONJ
ejpam-6212	617	6	the	the	DET
ejpam-6212	617	7	proof	proof	NOUN
ejpam-6212	617	8	of	of	ADP
ejpam-6212	617	9	theorem	theorem	NOUN
ejpam-6212	617	10	1	1	NUM
ejpam-6212	617	11	to	to	PART
ejpam-6212	617	12	simplify	simplify	VERB
ejpam-6212	617	13	the	the	DET
ejpam-6212	617	14	proof	proof	NOUN
ejpam-6212	617	15	.	.	PUNCT
ejpam-6212	618	1	in	in	ADP
ejpam-6212	618	2	this	this	DET
ejpam-6212	618	3	case	case	NOUN
ejpam-6212	618	4	,	,	PUNCT
ejpam-6212	618	5	it	it	PRON
ejpam-6212	618	6	is	be	AUX
ejpam-6212	618	7	enough	enough	ADJ
ejpam-6212	618	8	to	to	PART
ejpam-6212	618	9	show	show	VERB
ejpam-6212	618	10	the	the	DET
ejpam-6212	618	11	bounds	bound	NOUN
ejpam-6212	618	12	of	of	ADP
ejpam-6212	618	13	wiener	wiener	NOUN
ejpam-6212	618	14	index	index	NOUN
ejpam-6212	618	15	in	in	ADP
ejpam-6212	618	16	terms	term	NOUN
ejpam-6212	618	17	of	of	ADP
ejpam-6212	618	18	additively	additively	ADV
ejpam-6212	618	19	weighted	weight	VERB
ejpam-6212	618	20	harary	harary	PROPN
ejpam-6212	618	21	index	index	PROPN
ejpam-6212	618	22	.	.	PUNCT
ejpam-6212	619	1	w	w	PROPN
ejpam-6212	619	2	(	(	PUNCT
ejpam-6212	619	3	g	g	NOUN
ejpam-6212	619	4	)	)	PUNCT
ejpam-6212	619	5	=	=	PUNCT
ejpam-6212	619	6	∑	∑	PUNCT
ejpam-6212	619	7	{	{	PUNCT
ejpam-6212	619	8	u	u	NOUN
ejpam-6212	619	9	,	,	PUNCT
ejpam-6212	619	10	v}⊆v	v}⊆v	PROPN
ejpam-6212	619	11	(	(	PUNCT
ejpam-6212	619	12	g	g	NOUN
ejpam-6212	619	13	)	)	PUNCT
ejpam-6212	619	14	d(u	d(u	PROPN
ejpam-6212	619	15	,	,	PUNCT
ejpam-6212	619	16	v	v	NOUN
ejpam-6212	619	17	)	)	PUNCT
ejpam-6212	619	18	=	=	SYM
ejpam-6212	619	19	diam(g	diam(g	NOUN
ejpam-6212	619	20	)	)	PUNCT
ejpam-6212	619	21	∑	∑	PUNCT
ejpam-6212	619	22	{	{	PUNCT
ejpam-6212	619	23	u	u	NOUN
ejpam-6212	619	24	,	,	PUNCT
ejpam-6212	619	25	v}⊆v	v}⊆v	PROPN
ejpam-6212	619	26	(	(	PUNCT
ejpam-6212	619	27	g	g	NOUN
ejpam-6212	619	28	)	)	PUNCT
ejpam-6212	619	29	du	du	PROPN
ejpam-6212	620	1	+	+	CCONJ
ejpam-6212	620	2	dv	dv	PROPN
ejpam-6212	620	3	d(u	d(u	PROPN
ejpam-6212	620	4	,	,	PUNCT
ejpam-6212	620	5	v	v	NOUN
ejpam-6212	620	6	)	)	PUNCT
ejpam-6212	620	7	·	·	PUNCT
ejpam-6212	621	1	d(u	d(u	PROPN
ejpam-6212	621	2	,	,	PUNCT
ejpam-6212	621	3	v	v	NOUN
ejpam-6212	621	4	)	)	PUNCT
ejpam-6212	621	5	du	du	PROPN
ejpam-6212	622	1	+	+	CCONJ
ejpam-6212	622	2	dv	dv	PROPN
ejpam-6212	622	3	<	<	X
ejpam-6212	622	4	(	(	PUNCT
ejpam-6212	622	5	diam(g))2	diam(g))2	NOUN
ejpam-6212	622	6	2δ	2δ	NUM
ejpam-6212	622	7	ha(g	ha(g	X
ejpam-6212	622	8	)	)	PUNCT
ejpam-6212	622	9	.	.	PUNCT
ejpam-6212	623	1	moreover	moreover	ADV
ejpam-6212	623	2	,	,	PUNCT
ejpam-6212	623	3	w	w	PROPN
ejpam-6212	623	4	(	(	PUNCT
ejpam-6212	623	5	g	g	NOUN
ejpam-6212	623	6	)	)	PUNCT
ejpam-6212	623	7	=	=	PUNCT
ejpam-6212	623	8	∑	∑	PUNCT
ejpam-6212	623	9	{	{	PUNCT
ejpam-6212	623	10	u	u	NOUN
ejpam-6212	623	11	,	,	PUNCT
ejpam-6212	623	12	v}⊆v	v}⊆v	PROPN
ejpam-6212	623	13	(	(	PUNCT
ejpam-6212	623	14	g	g	NOUN
ejpam-6212	623	15	)	)	PUNCT
ejpam-6212	623	16	d(u	d(u	PROPN
ejpam-6212	623	17	,	,	PUNCT
ejpam-6212	623	18	v	v	NOUN
ejpam-6212	623	19	)	)	PUNCT
ejpam-6212	623	20	=	=	PUNCT
ejpam-6212	623	21	∑	∑	PUNCT
ejpam-6212	623	22	{	{	PUNCT
ejpam-6212	623	23	u	u	NOUN
ejpam-6212	623	24	,	,	PUNCT
ejpam-6212	623	25	v}⊆v	v}⊆v	PROPN
ejpam-6212	623	26	(	(	PUNCT
ejpam-6212	623	27	g	g	NOUN
ejpam-6212	623	28	)	)	PUNCT
ejpam-6212	623	29	1	1	NUM
ejpam-6212	623	30	d(u	d(u	PROPN
ejpam-6212	623	31	,	,	PUNCT
ejpam-6212	623	32	v	v	NOUN
ejpam-6212	623	33	)	)	PUNCT
ejpam-6212	623	34	·	·	PUNCT
ejpam-6212	623	35	du	du	PROPN
ejpam-6212	623	36	+	+	CCONJ
ejpam-6212	623	37	dv	dv	PROPN
ejpam-6212	623	38	du	du	PROPN
ejpam-6212	623	39	+	+	CCONJ
ejpam-6212	623	40	dv	dv	PROPN
ejpam-6212	623	41	>	>	X
ejpam-6212	623	42	1	1	NUM
ejpam-6212	623	43	2∆	2∆	NUM
ejpam-6212	623	44	ha(g	ha(g	NOUN
ejpam-6212	623	45	)	)	PUNCT
ejpam-6212	623	46	.	.	PUNCT
ejpam-6212	624	1	this	this	PRON
ejpam-6212	624	2	completes	complete	VERB
ejpam-6212	624	3	the	the	DET
ejpam-6212	624	4	proof	proof	NOUN
ejpam-6212	624	5	.	.	PUNCT
ejpam-6212	625	1	the	the	DET
ejpam-6212	625	2	next	next	ADJ
ejpam-6212	625	3	corollary	corollary	NOUN
ejpam-6212	625	4	establishes	establish	VERB
ejpam-6212	625	5	the	the	DET
ejpam-6212	625	6	bounds	bound	NOUN
ejpam-6212	625	7	of	of	ADP
ejpam-6212	625	8	geodetic	geodetic	ADJ
ejpam-6212	625	9	-	-	PUNCT
ejpam-6212	625	10	wiener	wiener	NOUN
ejpam-6212	625	11	index	index	NOUN
ejpam-6212	625	12	with	with	ADP
ejpam-6212	625	13	additively	additively	ADV
ejpam-6212	625	14	weighted	weight	VERB
ejpam-6212	625	15	harary	harary	ADJ
ejpam-6212	625	16	index	index	NOUN
ejpam-6212	625	17	for	for	ADP
ejpam-6212	625	18	simple	simple	ADJ
ejpam-6212	625	19	spirocyclic	spirocyclic	NOUN
ejpam-6212	625	20	graphs	graph	NOUN
ejpam-6212	625	21	with	with	ADP
ejpam-6212	625	22	minimum	minimum	NOUN
ejpam-6212	625	23	degree	degree	NOUN
ejpam-6212	625	24	δ	δ	NOUN
ejpam-6212	625	25	=	=	SYM
ejpam-6212	625	26	2	2	NUM
ejpam-6212	625	27	by	by	ADP
ejpam-6212	625	28	r.	r.	PROPN
ejpam-6212	625	29	g.	g.	PROPN
ejpam-6212	625	30	artes	artes	PROPN
ejpam-6212	625	31	jr	jr	PROPN
ejpam-6212	625	32	.	.	PROPN
ejpam-6212	625	33	et	et	PROPN
ejpam-6212	625	34	al	al	PROPN
ejpam-6212	625	35	.	.	PUNCT
ejpam-6212	625	36	/	/	SYM
ejpam-6212	625	37	eur	eur	PROPN
ejpam-6212	625	38	.	.	PUNCT
ejpam-6212	626	1	j.	j.	PROPN
ejpam-6212	626	2	pure	pure	PROPN
ejpam-6212	626	3	appl	appl	PROPN
ejpam-6212	626	4	.	.	PROPN
ejpam-6212	626	5	math	math	PROPN
ejpam-6212	626	6	,	,	PUNCT
ejpam-6212	626	7	18	18	NUM
ejpam-6212	626	8	(	(	PUNCT
ejpam-6212	626	9	4	4	NUM
ejpam-6212	626	10	)	)	PUNCT
ejpam-6212	626	11	(	(	PUNCT
ejpam-6212	626	12	2025	2025	NUM
ejpam-6212	626	13	)	)	PUNCT
ejpam-6212	626	14	,	,	PUNCT
ejpam-6212	626	15	6212	6212	NUM
ejpam-6212	626	16	17	17	NUM
ejpam-6212	626	17	of	of	ADP
ejpam-6212	626	18	20	20	NUM
ejpam-6212	626	19	applying	apply	VERB
ejpam-6212	626	20	theorem	theorem	NOUN
ejpam-6212	626	21	2	2	NUM
ejpam-6212	626	22	and	and	CCONJ
ejpam-6212	626	23	the	the	DET
ejpam-6212	626	24	proof	proof	NOUN
ejpam-6212	626	25	of	of	ADP
ejpam-6212	626	26	theorem	theorem	ADJ
ejpam-6212	626	27	7	7	NUM
ejpam-6212	626	28	.	.	PUNCT
ejpam-6212	626	29	corollary	corollary	ADJ
ejpam-6212	626	30	5	5	NUM
ejpam-6212	626	31	.	.	PUNCT
ejpam-6212	627	1	let	let	VERB
ejpam-6212	627	2	g	g	PRON
ejpam-6212	627	3	be	be	AUX
ejpam-6212	627	4	a	a	DET
ejpam-6212	627	5	simple	simple	ADJ
ejpam-6212	627	6	spirocyclic	spirocyclic	NOUN
ejpam-6212	627	7	graph	graph	NOUN
ejpam-6212	627	8	with	with	ADP
ejpam-6212	627	9	minimum	minimum	NOUN
ejpam-6212	627	10	degree	degree	NOUN
ejpam-6212	627	11	δ	δ	NOUN
ejpam-6212	627	12	=	=	SYM
ejpam-6212	627	13	2	2	NUM
ejpam-6212	627	14	and	and	CCONJ
ejpam-6212	627	15	with	with	ADP
ejpam-6212	627	16	even	even	ADV
ejpam-6212	627	17	cycles	cycle	NOUN
ejpam-6212	627	18	c2t1	c2t1	NOUN
ejpam-6212	627	19	and	and	CCONJ
ejpam-6212	627	20	c2t2	c2t2	PROPN
ejpam-6212	627	21	,	,	PUNCT
ejpam-6212	627	22	for	for	SCONJ
ejpam-6212	627	23	some	some	DET
ejpam-6212	627	24	natural	natural	ADJ
ejpam-6212	627	25	numbers	number	NOUN
ejpam-6212	627	26	t1	t1	PROPN
ejpam-6212	627	27	,	,	PUNCT
ejpam-6212	627	28	t2	t2	NOUN
ejpam-6212	627	29	≥	≥	NUM
ejpam-6212	627	30	2	2	NUM
ejpam-6212	627	31	.	.	PUNCT
ejpam-6212	628	1	then	then	ADV
ejpam-6212	628	2	(	(	PUNCT
ejpam-6212	628	3	t1	t1	NOUN
ejpam-6212	628	4	+	+	NUM
ejpam-6212	628	5	t2	t2	NOUN
ejpam-6212	628	6	)	)	PUNCT
ejpam-6212	628	7	2	2	NUM
ejpam-6212	628	8	4	4	NUM
ejpam-6212	628	9	ha(g	ha(g	ADP
ejpam-6212	628	10	)	)	PUNCT
ejpam-6212	629	1	+	+	NUM
ejpam-6212	630	1	2(t1	2(t1	NUM
ejpam-6212	630	2	+	+	NUM
ejpam-6212	630	3	t2	t2	NOUN
ejpam-6212	630	4	)	)	PUNCT
ejpam-6212	630	5	2	2	NUM
ejpam-6212	630	6	<	<	X
ejpam-6212	630	7	wg(g	wg(g	NOUN
ejpam-6212	630	8	)	)	PUNCT
ejpam-6212	630	9	<	<	X
ejpam-6212	630	10	1	1	NUM
ejpam-6212	630	11	8	8	NUM
ejpam-6212	630	12	ha(g	ha(g	ADP
ejpam-6212	630	13	)	)	PUNCT
ejpam-6212	631	1	+	+	NUM
ejpam-6212	632	1	2(t1	2(t1	NUM
ejpam-6212	632	2	+	+	NUM
ejpam-6212	632	3	t2	t2	NOUN
ejpam-6212	632	4	)	)	PUNCT
ejpam-6212	632	5	2	2	NUM
ejpam-6212	632	6	.	.	NOUN
ejpam-6212	632	7	11	11	NUM
ejpam-6212	632	8	.	.	PUNCT
ejpam-6212	633	1	bounds	bound	NOUN
ejpam-6212	633	2	of	of	ADP
ejpam-6212	633	3	g	g	NOUN
ejpam-6212	633	4	-	-	PUNCT
ejpam-6212	633	5	wiener	wiener	NOUN
ejpam-6212	633	6	index	index	NOUN
ejpam-6212	633	7	with	with	ADP
ejpam-6212	633	8	multiplicatively	multiplicatively	ADV
ejpam-6212	633	9	weighted	weight	VERB
ejpam-6212	633	10	harary	harary	PROPN
ejpam-6212	633	11	index	index	NOUN
ejpam-6212	633	12	the	the	DET
ejpam-6212	633	13	following	follow	VERB
ejpam-6212	633	14	result	result	NOUN
ejpam-6212	633	15	establishes	establish	VERB
ejpam-6212	633	16	bounds	bound	NOUN
ejpam-6212	633	17	of	of	ADP
ejpam-6212	633	18	g	g	NOUN
ejpam-6212	633	19	-	-	PUNCT
ejpam-6212	633	20	wiener	wiener	NOUN
ejpam-6212	633	21	index	index	NOUN
ejpam-6212	633	22	in	in	ADP
ejpam-6212	633	23	terms	term	NOUN
ejpam-6212	633	24	of	of	ADP
ejpam-6212	633	25	the	the	DET
ejpam-6212	633	26	multiplicatively	multiplicatively	ADV
ejpam-6212	633	27	weighted	weight	VERB
ejpam-6212	633	28	harary	harary	PROPN
ejpam-6212	633	29	index	index	NOUN
ejpam-6212	633	30	as	as	SCONJ
ejpam-6212	633	31	defined	define	VERB
ejpam-6212	633	32	in	in	ADP
ejpam-6212	633	33	[	[	X
ejpam-6212	633	34	12	12	NUM
ejpam-6212	633	35	]	]	PUNCT
ejpam-6212	633	36	for	for	ADP
ejpam-6212	633	37	classes	class	NOUN
ejpam-6212	633	38	of	of	ADP
ejpam-6212	633	39	simple	simple	ADJ
ejpam-6212	633	40	spirocyclic	spirocyclic	NOUN
ejpam-6212	633	41	graphs	graph	NOUN
ejpam-6212	633	42	containing	contain	VERB
ejpam-6212	633	43	even	even	ADV
ejpam-6212	633	44	cycles	cycle	NOUN
ejpam-6212	633	45	.	.	PUNCT
ejpam-6212	634	1	theorem	theorem	ADJ
ejpam-6212	634	2	8	8	NUM
ejpam-6212	634	3	.	.	PUNCT
ejpam-6212	635	1	let	let	VERB
ejpam-6212	635	2	g	g	PRON
ejpam-6212	635	3	be	be	AUX
ejpam-6212	635	4	a	a	DET
ejpam-6212	635	5	simple	simple	ADJ
ejpam-6212	635	6	spirocyclic	spirocyclic	NOUN
ejpam-6212	635	7	graph	graph	NOUN
ejpam-6212	635	8	with	with	ADP
ejpam-6212	635	9	even	even	ADV
ejpam-6212	635	10	cycles	cycle	NOUN
ejpam-6212	635	11	c2t1	c2t1	NOUN
ejpam-6212	636	1	=	=	SYM
ejpam-6212	637	1	[	[	X
ejpam-6212	637	2	u1	u1	NOUN
ejpam-6212	637	3	,	,	PUNCT
ejpam-6212	637	4	u2	u2	NOUN
ejpam-6212	637	5	,	,	PUNCT
ejpam-6212	637	6	.	.	PUNCT
ejpam-6212	637	7	.	.	PUNCT
ejpam-6212	637	8	.	.	PUNCT
ejpam-6212	638	1	,	,	PUNCT
ejpam-6212	638	2	u2t1	u2t1	VERB
ejpam-6212	638	3	]	]	PUNCT
ejpam-6212	638	4	and	and	CCONJ
ejpam-6212	638	5	c2t2	c2t2	NOUN
ejpam-6212	639	1	=	=	PUNCT
ejpam-6212	640	1	[	[	X
ejpam-6212	640	2	v1	v1	NOUN
ejpam-6212	640	3	,	,	PUNCT
ejpam-6212	640	4	v2	v2	NOUN
ejpam-6212	640	5	,	,	PUNCT
ejpam-6212	640	6	.	.	PUNCT
ejpam-6212	640	7	.	.	PUNCT
ejpam-6212	640	8	.	.	PUNCT
ejpam-6212	641	1	,	,	PUNCT
ejpam-6212	641	2	v2t2	v2t2	X
ejpam-6212	641	3	]	]	X
ejpam-6212	641	4	,	,	PUNCT
ejpam-6212	641	5	for	for	ADP
ejpam-6212	641	6	some	some	DET
ejpam-6212	641	7	natural	natural	ADJ
ejpam-6212	641	8	numbers	number	NOUN
ejpam-6212	641	9	t1	t1	PROPN
ejpam-6212	641	10	,	,	PUNCT
ejpam-6212	641	11	t2	t2	NOUN
ejpam-6212	641	12	≥	≥	NUM
ejpam-6212	641	13	2	2	NUM
ejpam-6212	641	14	.	.	PUNCT
ejpam-6212	642	1	then	then	ADV
ejpam-6212	642	2	1	1	NUM
ejpam-6212	642	3	∆2	∆2	NOUN
ejpam-6212	642	4	hm	hm	INTJ
ejpam-6212	642	5	(	(	PUNCT
ejpam-6212	642	6	g	g	NOUN
ejpam-6212	642	7	)	)	PUNCT
ejpam-6212	643	1	+	+	NOUN
ejpam-6212	643	2	at1	at1	PROPN
ejpam-6212	643	3	+	+	PROPN
ejpam-6212	643	4	bt2	bt2	PROPN
ejpam-6212	643	5	<	<	X
ejpam-6212	643	6	wg(g	wg(g	PROPN
ejpam-6212	643	7	)	)	PUNCT
ejpam-6212	643	8	<	<	X
ejpam-6212	643	9	(	(	PUNCT
ejpam-6212	643	10	diam(g))2	diam(g))2	PROPN
ejpam-6212	643	11	δ2	δ2	VERB
ejpam-6212	643	12	hm	hm	INTJ
ejpam-6212	643	13	(	(	PUNCT
ejpam-6212	643	14	g	g	NOUN
ejpam-6212	643	15	)	)	PUNCT
ejpam-6212	644	1	+	+	CCONJ
ejpam-6212	644	2	cdiam(g	cdiam(g	X
ejpam-6212	644	3	)	)	PUNCT
ejpam-6212	644	4	where	where	SCONJ
ejpam-6212	644	5	{	{	PUNCT
ejpam-6212	644	6	u1	u1	NOUN
ejpam-6212	644	7	=	=	SYM
ejpam-6212	644	8	v1	v1	PROPN
ejpam-6212	644	9	,	,	PUNCT
ejpam-6212	644	10	u2	u2	NOUN
ejpam-6212	644	11	,	,	PUNCT
ejpam-6212	644	12	.	.	PUNCT
ejpam-6212	644	13	.	.	PUNCT
ejpam-6212	644	14	.	.	PUNCT
ejpam-6212	645	1	,	,	PUNCT
ejpam-6212	645	2	u2t1	u2t1	INTJ
ejpam-6212	645	3	,	,	PUNCT
ejpam-6212	645	4	v2	v2	PROPN
ejpam-6212	645	5	,	,	PUNCT
ejpam-6212	645	6	.	.	PUNCT
ejpam-6212	645	7	.	.	PUNCT
ejpam-6212	646	1	.	.	PUNCT
ejpam-6212	647	1	,	,	PUNCT
ejpam-6212	647	2	v2t2	v2t2	NOUN
ejpam-6212	647	3	}	}	PUNCT
ejpam-6212	647	4	is	be	AUX
ejpam-6212	647	5	the	the	DET
ejpam-6212	647	6	tree	tree	NOUN
ejpam-6212	647	7	-	-	PUNCT
ejpam-6212	647	8	partition	partition	NOUN
ejpam-6212	647	9	of	of	ADP
ejpam-6212	647	10	v	v	NOUN
ejpam-6212	647	11	(	(	PUNCT
ejpam-6212	647	12	g	g	NOUN
ejpam-6212	647	13	)	)	PUNCT
ejpam-6212	647	14	with	with	ADP
ejpam-6212	647	15	respect	respect	NOUN
ejpam-6212	647	16	to	to	ADP
ejpam-6212	647	17	the	the	DET
ejpam-6212	647	18	projection	projection	NOUN
ejpam-6212	647	19	of	of	ADP
ejpam-6212	647	20	v	v	NOUN
ejpam-6212	647	21	(	(	PUNCT
ejpam-6212	647	22	g	g	NOUN
ejpam-6212	647	23	)	)	PUNCT
ejpam-6212	647	24	onto	onto	ADP
ejpam-6212	647	25	the	the	DET
ejpam-6212	647	26	union	union	NOUN
ejpam-6212	647	27	of	of	ADP
ejpam-6212	647	28	the	the	DET
ejpam-6212	647	29	cycles	cycle	NOUN
ejpam-6212	647	30	c2t1	c2t1	NOUN
ejpam-6212	647	31	and	and	CCONJ
ejpam-6212	647	32	c2t2	c2t2	NOUN
ejpam-6212	647	33	,	,	PUNCT
ejpam-6212	647	34	and	and	CCONJ
ejpam-6212	648	1	a	a	DET
ejpam-6212	648	2	=	=	X
ejpam-6212	648	3	t1∑	t1∑	PROPN
ejpam-6212	648	4	i=1	i=1	PROPN
ejpam-6212	648	5	|ui||ui+t1	|ui||ui+t1	ADP
ejpam-6212	648	6	|+	|+	NOUN
ejpam-6212	648	7	2t2∑	2t2∑	NUM
ejpam-6212	648	8	j=2	j=2	NOUN
ejpam-6212	648	9	|ut1	|ut1	PUNCT
ejpam-6212	648	10	+	+	NOUN
ejpam-6212	648	11	1||vj	1||vj	NOUN
ejpam-6212	648	12	|+	|+	X
ejpam-6212	648	13	|ut1	|ut1	PUNCT
ejpam-6212	648	14	+	+	NOUN
ejpam-6212	648	15	1||vt2	1||vt2	NUM
ejpam-6212	648	16	+	+	NOUN
ejpam-6212	648	17	1|	1|	NUM
ejpam-6212	648	18	,	,	PUNCT
ejpam-6212	648	19	b	b	NOUN
ejpam-6212	648	20	=	=	SYM
ejpam-6212	648	21	t2∑	t2∑	PROPN
ejpam-6212	648	22	j=1	j=1	NOUN
ejpam-6212	648	23	|vj	|vj	X
ejpam-6212	648	24	||vj+t2	||vj+t2	PROPN
ejpam-6212	648	25	|+	|+	NOUN
ejpam-6212	648	26	2t1∑	2t1∑	NUM
ejpam-6212	648	27	i=2	i=2	PROPN
ejpam-6212	648	28	|vt2	|vt2	PROPN
ejpam-6212	649	1	+	+	NOUN
ejpam-6212	649	2	1||ui|+	1||ui|+	NOUN
ejpam-6212	649	3	|ut1	|ut1	NOUN
ejpam-6212	649	4	+	+	NOUN
ejpam-6212	649	5	1||vt2	1||vt2	NUM
ejpam-6212	649	6	+	+	NOUN
ejpam-6212	649	7	1|	1|	NUM
ejpam-6212	649	8	,	,	PUNCT
ejpam-6212	649	9	and	and	CCONJ
ejpam-6212	649	10	c	c	X
ejpam-6212	650	1	=	=	SYM
ejpam-6212	650	2	t1∑	t1∑	PROPN
ejpam-6212	650	3	i=1	i=1	PROPN
ejpam-6212	650	4	|ui||ui+t1	|ui||ui+t1	ADV
ejpam-6212	650	5	|+	|+	NOUN
ejpam-6212	650	6	t2∑	t2∑	PROPN
ejpam-6212	650	7	j=1	j=1	NOUN
ejpam-6212	651	1	|vj	|vj	X
ejpam-6212	651	2	||vj+t2	||vj+t2	PROPN
ejpam-6212	651	3	|+	|+	NOUN
ejpam-6212	651	4	2t2∑	2t2∑	NUM
ejpam-6212	651	5	j=2	j=2	NOUN
ejpam-6212	651	6	|ut1	|ut1	PUNCT
ejpam-6212	651	7	+	+	NOUN
ejpam-6212	651	8	1||vj	1||vj	PROPN
ejpam-6212	651	9	|+	|+	NOUN
ejpam-6212	651	10	2t1∑	2t1∑	NUM
ejpam-6212	651	11	i=2	i=2	PROPN
ejpam-6212	651	12	|vt2	|vt2	PROPN
ejpam-6212	652	1	+	+	NOUN
ejpam-6212	652	2	1||ui|+	1||ui|+	NOUN
ejpam-6212	652	3	|ut1	|ut1	NOUN
ejpam-6212	652	4	+	+	NOUN
ejpam-6212	652	5	1||vt2	1||vt2	NUM
ejpam-6212	652	6	+	+	NOUN
ejpam-6212	652	7	1|	1|	NUM
ejpam-6212	652	8	.	.	PUNCT
ejpam-6212	653	1	proof	proof	NOUN
ejpam-6212	653	2	.	.	PUNCT
ejpam-6212	654	1	it	it	PRON
ejpam-6212	654	2	suffices	suffice	VERB
ejpam-6212	654	3	to	to	PART
ejpam-6212	654	4	establish	establish	VERB
ejpam-6212	654	5	the	the	DET
ejpam-6212	654	6	bounds	bound	NOUN
ejpam-6212	654	7	of	of	ADP
ejpam-6212	654	8	wiener	wiener	NOUN
ejpam-6212	654	9	index	index	NOUN
ejpam-6212	654	10	in	in	ADP
ejpam-6212	654	11	terms	term	NOUN
ejpam-6212	654	12	of	of	ADP
ejpam-6212	654	13	multiplicatively	multiplicatively	ADV
ejpam-6212	654	14	weighted	weight	VERB
ejpam-6212	654	15	harary	harary	NOUN
ejpam-6212	654	16	and	and	CCONJ
ejpam-6212	654	17	use	use	VERB
ejpam-6212	654	18	lemma	lemma	PROPN
ejpam-6212	654	19	2	2	NUM
ejpam-6212	654	20	together	together	ADV
ejpam-6212	654	21	with	with	ADP
ejpam-6212	654	22	theorem	theorem	ADJ
ejpam-6212	654	23	1	1	NUM
ejpam-6212	654	24	.	.	PUNCT
ejpam-6212	654	25	note	note	VERB
ejpam-6212	654	26	that	that	SCONJ
ejpam-6212	654	27	in	in	ADP
ejpam-6212	654	28	simple	simple	ADJ
ejpam-6212	654	29	spirocyclic	spirocyclic	NOUN
ejpam-6212	654	30	graphs	graph	NOUN
ejpam-6212	654	31	,	,	PUNCT
ejpam-6212	654	32	δ	δ	X
ejpam-6212	654	33	<	<	X
ejpam-6212	654	34	∆.	∆.	X
ejpam-6212	654	35	hence	hence	ADV
ejpam-6212	654	36	,	,	PUNCT
ejpam-6212	654	37	w	w	PROPN
ejpam-6212	654	38	(	(	PUNCT
ejpam-6212	654	39	g	g	NOUN
ejpam-6212	654	40	)	)	PUNCT
ejpam-6212	654	41	=	=	PUNCT
ejpam-6212	654	42	∑	∑	PUNCT
ejpam-6212	654	43	{	{	PUNCT
ejpam-6212	654	44	u	u	NOUN
ejpam-6212	654	45	,	,	PUNCT
ejpam-6212	654	46	v}⊆v	v}⊆v	PROPN
ejpam-6212	654	47	(	(	PUNCT
ejpam-6212	654	48	g	g	NOUN
ejpam-6212	654	49	)	)	PUNCT
ejpam-6212	654	50	d(u	d(u	PROPN
ejpam-6212	654	51	,	,	PUNCT
ejpam-6212	654	52	v	v	NOUN
ejpam-6212	654	53	)	)	PUNCT
ejpam-6212	654	54	≤	≤	NUM
ejpam-6212	654	55	diam(g	diam(g	NOUN
ejpam-6212	654	56	)	)	PUNCT
ejpam-6212	654	57	∑	∑	PUNCT
ejpam-6212	654	58	{	{	PUNCT
ejpam-6212	654	59	u	u	NOUN
ejpam-6212	654	60	,	,	PUNCT
ejpam-6212	654	61	v}⊆v	v}⊆v	PROPN
ejpam-6212	654	62	(	(	PUNCT
ejpam-6212	654	63	g	g	NOUN
ejpam-6212	654	64	)	)	PUNCT
ejpam-6212	654	65	dudv	dudv	ADP
ejpam-6212	654	66	d(u	d(u	PROPN
ejpam-6212	654	67	,	,	PUNCT
ejpam-6212	654	68	v	v	NOUN
ejpam-6212	654	69	)	)	PUNCT
ejpam-6212	654	70	·	·	PUNCT
ejpam-6212	655	1	d(u	d(u	PROPN
ejpam-6212	655	2	,	,	PUNCT
ejpam-6212	655	3	v	v	NOUN
ejpam-6212	655	4	)	)	PUNCT
ejpam-6212	655	5	dudv	dudv	NOUN
ejpam-6212	655	6	<	<	X
ejpam-6212	656	1	[	[	X
ejpam-6212	656	2	diam(g)]2	diam(g)]2	X
ejpam-6212	656	3	δ2	δ2	VERB
ejpam-6212	656	4	hm	hm	INTJ
ejpam-6212	656	5	(	(	PUNCT
ejpam-6212	656	6	g	g	NOUN
ejpam-6212	656	7	)	)	PUNCT
ejpam-6212	656	8	.	.	PUNCT
ejpam-6212	657	1	r.	r.	PROPN
ejpam-6212	657	2	g.	g.	PROPN
ejpam-6212	657	3	artes	artes	PROPN
ejpam-6212	657	4	jr	jr	PROPN
ejpam-6212	657	5	.	.	PROPN
ejpam-6212	657	6	et	et	PROPN
ejpam-6212	657	7	al	al	PROPN
ejpam-6212	657	8	.	.	PUNCT
ejpam-6212	657	9	/	/	SYM
ejpam-6212	657	10	eur	eur	PROPN
ejpam-6212	657	11	.	.	PUNCT
ejpam-6212	658	1	j.	j.	PROPN
ejpam-6212	658	2	pure	pure	PROPN
ejpam-6212	658	3	appl	appl	PROPN
ejpam-6212	658	4	.	.	PROPN
ejpam-6212	658	5	math	math	PROPN
ejpam-6212	658	6	,	,	PUNCT
ejpam-6212	658	7	18	18	NUM
ejpam-6212	658	8	(	(	PUNCT
ejpam-6212	658	9	4	4	NUM
ejpam-6212	658	10	)	)	PUNCT
ejpam-6212	658	11	(	(	PUNCT
ejpam-6212	658	12	2025	2025	NUM
ejpam-6212	658	13	)	)	PUNCT
ejpam-6212	658	14	,	,	PUNCT
ejpam-6212	658	15	6212	6212	NUM
ejpam-6212	658	16	18	18	NUM
ejpam-6212	658	17	of	of	ADP
ejpam-6212	658	18	20	20	NUM
ejpam-6212	658	19	moreover	moreover	ADV
ejpam-6212	658	20	,	,	PUNCT
ejpam-6212	658	21	w	w	PROPN
ejpam-6212	658	22	(	(	PUNCT
ejpam-6212	658	23	g	g	NOUN
ejpam-6212	658	24	)	)	PUNCT
ejpam-6212	658	25	=	=	PUNCT
ejpam-6212	658	26	∑	∑	PUNCT
ejpam-6212	658	27	{	{	PUNCT
ejpam-6212	658	28	u	u	NOUN
ejpam-6212	658	29	,	,	PUNCT
ejpam-6212	658	30	v}⊆v	v}⊆v	PROPN
ejpam-6212	658	31	(	(	PUNCT
ejpam-6212	658	32	g	g	NOUN
ejpam-6212	658	33	)	)	PUNCT
ejpam-6212	658	34	d(u	d(u	PROPN
ejpam-6212	658	35	,	,	PUNCT
ejpam-6212	658	36	v	v	NOUN
ejpam-6212	658	37	)	)	PUNCT
ejpam-6212	658	38	=	=	PUNCT
ejpam-6212	658	39	∑	∑	PUNCT
ejpam-6212	658	40	{	{	PUNCT
ejpam-6212	658	41	u	u	NOUN
ejpam-6212	658	42	,	,	PUNCT
ejpam-6212	658	43	v}⊆v	v}⊆v	PROPN
ejpam-6212	658	44	(	(	PUNCT
ejpam-6212	658	45	g	g	NOUN
ejpam-6212	658	46	)	)	PUNCT
ejpam-6212	658	47	1	1	NUM
ejpam-6212	658	48	d(u	d(u	PROPN
ejpam-6212	658	49	,	,	PUNCT
ejpam-6212	658	50	v	v	NOUN
ejpam-6212	658	51	)	)	PUNCT
ejpam-6212	658	52	·	·	PUNCT
ejpam-6212	659	1	dudv	dudv	ADP
ejpam-6212	659	2	dudv	dudv	NOUN
ejpam-6212	659	3	>	>	X
ejpam-6212	659	4	1	1	NUM
ejpam-6212	659	5	∆2	∆2	X
ejpam-6212	659	6	hm	hm	INTJ
ejpam-6212	659	7	(	(	PUNCT
ejpam-6212	659	8	g	g	NOUN
ejpam-6212	659	9	)	)	PUNCT
ejpam-6212	659	10	.	.	PUNCT
ejpam-6212	660	1	the	the	DET
ejpam-6212	660	2	proof	proof	NOUN
ejpam-6212	660	3	is	be	AUX
ejpam-6212	660	4	complete	complete	ADJ
ejpam-6212	660	5	.	.	PUNCT
ejpam-6212	661	1	applying	apply	VERB
ejpam-6212	661	2	theorem	theorem	NOUN
ejpam-6212	661	3	2	2	NUM
ejpam-6212	661	4	and	and	CCONJ
ejpam-6212	661	5	the	the	DET
ejpam-6212	661	6	proof	proof	NOUN
ejpam-6212	661	7	of	of	ADP
ejpam-6212	661	8	theorem	theorem	ADJ
ejpam-6212	661	9	8	8	NUM
ejpam-6212	661	10	on	on	ADP
ejpam-6212	661	11	the	the	DET
ejpam-6212	661	12	bounds	bound	NOUN
ejpam-6212	661	13	of	of	ADP
ejpam-6212	661	14	wiener	wiener	NOUN
ejpam-6212	661	15	index	index	NOUN
ejpam-6212	661	16	with	with	ADP
ejpam-6212	661	17	multiplicatively	multiplicatively	ADV
ejpam-6212	661	18	weighted	weight	VERB
ejpam-6212	661	19	harary	harary	PROPN
ejpam-6212	661	20	index	index	NOUN
ejpam-6212	661	21	yields	yield	VERB
ejpam-6212	661	22	the	the	DET
ejpam-6212	661	23	following	follow	VERB
ejpam-6212	661	24	corollary	corollary	NOUN
ejpam-6212	661	25	.	.	PUNCT
ejpam-6212	662	1	corollary	corollary	ADJ
ejpam-6212	662	2	6	6	NUM
ejpam-6212	662	3	.	.	PUNCT
ejpam-6212	663	1	let	let	VERB
ejpam-6212	663	2	g	g	PRON
ejpam-6212	663	3	be	be	AUX
ejpam-6212	663	4	a	a	DET
ejpam-6212	663	5	simple	simple	ADJ
ejpam-6212	663	6	spirocyclic	spirocyclic	NOUN
ejpam-6212	663	7	graph	graph	NOUN
ejpam-6212	663	8	with	with	ADP
ejpam-6212	663	9	minimum	minimum	NOUN
ejpam-6212	663	10	degree	degree	NOUN
ejpam-6212	663	11	δ	δ	NOUN
ejpam-6212	663	12	=	=	SYM
ejpam-6212	663	13	2	2	NUM
ejpam-6212	663	14	and	and	CCONJ
ejpam-6212	663	15	with	with	ADP
ejpam-6212	663	16	even	even	ADV
ejpam-6212	663	17	cycles	cycle	NOUN
ejpam-6212	663	18	c2t1	c2t1	NOUN
ejpam-6212	663	19	and	and	CCONJ
ejpam-6212	663	20	c2t2	c2t2	PROPN
ejpam-6212	663	21	,	,	PUNCT
ejpam-6212	663	22	for	for	SCONJ
ejpam-6212	663	23	some	some	DET
ejpam-6212	663	24	natural	natural	ADJ
ejpam-6212	663	25	numbers	number	NOUN
ejpam-6212	663	26	t1	t1	PROPN
ejpam-6212	663	27	,	,	PUNCT
ejpam-6212	663	28	t2	t2	NOUN
ejpam-6212	663	29	≥	≥	NUM
ejpam-6212	663	30	2	2	NUM
ejpam-6212	663	31	.	.	PUNCT
ejpam-6212	664	1	then	then	ADV
ejpam-6212	664	2	1	1	NUM
ejpam-6212	664	3	16	16	NUM
ejpam-6212	664	4	hm	hm	INTJ
ejpam-6212	664	5	(	(	PUNCT
ejpam-6212	664	6	g	g	NOUN
ejpam-6212	664	7	)	)	PUNCT
ejpam-6212	665	1	+	+	NOUN
ejpam-6212	666	1	2(t1	2(t1	NUM
ejpam-6212	666	2	+	+	NUM
ejpam-6212	666	3	t2	t2	NOUN
ejpam-6212	666	4	)	)	PUNCT
ejpam-6212	666	5	2	2	NUM
ejpam-6212	666	6	<	<	X
ejpam-6212	666	7	wg(g	wg(g	NOUN
ejpam-6212	666	8	)	)	PUNCT
ejpam-6212	666	9	<	<	X
ejpam-6212	666	10	(	(	PUNCT
ejpam-6212	666	11	t1	t1	NOUN
ejpam-6212	666	12	+	+	NUM
ejpam-6212	666	13	t2	t2	NOUN
ejpam-6212	666	14	)	)	PUNCT
ejpam-6212	666	15	2	2	NUM
ejpam-6212	666	16	4	4	NUM
ejpam-6212	666	17	hm	hm	INTJ
ejpam-6212	666	18	(	(	PUNCT
ejpam-6212	666	19	g	g	NOUN
ejpam-6212	666	20	)	)	PUNCT
ejpam-6212	666	21	+	+	NOUN
ejpam-6212	667	1	2(t1	2(t1	NUM
ejpam-6212	667	2	+	+	NUM
ejpam-6212	667	3	t2	t2	NOUN
ejpam-6212	667	4	)	)	PUNCT
ejpam-6212	667	5	2	2	NUM
ejpam-6212	667	6	.	.	X
ejpam-6212	668	1	in	in	ADP
ejpam-6212	668	2	theorems	theorem	NOUN
ejpam-6212	668	3	5	5	NUM
ejpam-6212	668	4	-	-	SYM
ejpam-6212	668	5	8	8	NUM
ejpam-6212	668	6	,	,	PUNCT
ejpam-6212	668	7	the	the	DET
ejpam-6212	668	8	strict	strict	ADJ
ejpam-6212	668	9	inequalities	inequality	NOUN
ejpam-6212	668	10	are	be	AUX
ejpam-6212	668	11	due	due	ADJ
ejpam-6212	668	12	to	to	ADP
ejpam-6212	668	13	the	the	DET
ejpam-6212	668	14	fact	fact	NOUN
ejpam-6212	668	15	that	that	SCONJ
ejpam-6212	668	16	there	there	PRON
ejpam-6212	668	17	exist	exist	VERB
ejpam-6212	668	18	u	u	NOUN
ejpam-6212	668	19	,	,	PUNCT
ejpam-6212	668	20	v	v	NOUN
ejpam-6212	668	21	∈	∈	PROPN
ejpam-6212	668	22	v	v	NOUN
ejpam-6212	668	23	(	(	PUNCT
ejpam-6212	668	24	g	g	NOUN
ejpam-6212	668	25	)	)	PUNCT
ejpam-6212	668	26	such	such	ADJ
ejpam-6212	668	27	that	that	SCONJ
ejpam-6212	668	28	d(u	d(u	PROPN
ejpam-6212	668	29	,	,	PUNCT
ejpam-6212	668	30	v	v	NOUN
ejpam-6212	668	31	)	)	PUNCT
ejpam-6212	668	32	<	<	X
ejpam-6212	668	33	diam(g	diam(g	NOUN
ejpam-6212	668	34	)	)	PUNCT
ejpam-6212	668	35	.	.	PUNCT
ejpam-6212	669	1	in	in	ADP
ejpam-6212	669	2	particular	particular	ADJ
ejpam-6212	669	3	,	,	PUNCT
ejpam-6212	669	4	if	if	SCONJ
ejpam-6212	669	5	uv	uv	PROPN
ejpam-6212	669	6	∈	∈	PROPN
ejpam-6212	669	7	v	v	ADP
ejpam-6212	669	8	(	(	PUNCT
ejpam-6212	669	9	g	g	NOUN
ejpam-6212	669	10	)	)	PUNCT
ejpam-6212	669	11	,	,	PUNCT
ejpam-6212	669	12	then	then	ADV
ejpam-6212	669	13	d(u	d(u	PROPN
ejpam-6212	669	14	,	,	PUNCT
ejpam-6212	669	15	v	v	NOUN
ejpam-6212	669	16	)	)	PUNCT
ejpam-6212	669	17	=	=	SYM
ejpam-6212	669	18	1	1	NUM
ejpam-6212	669	19	<	<	X
ejpam-6212	669	20	diam(g	diam(g	NOUN
ejpam-6212	669	21	)	)	PUNCT
ejpam-6212	669	22	.	.	PUNCT
ejpam-6212	670	1	12	12	NUM
ejpam-6212	670	2	.	.	PUNCT
ejpam-6212	671	1	conclusion	conclusion	NOUN
ejpam-6212	671	2	in	in	ADP
ejpam-6212	671	3	this	this	DET
ejpam-6212	671	4	work	work	NOUN
ejpam-6212	671	5	,	,	PUNCT
ejpam-6212	671	6	we	we	PRON
ejpam-6212	671	7	found	find	VERB
ejpam-6212	671	8	some	some	DET
ejpam-6212	671	9	bounds	bound	NOUN
ejpam-6212	671	10	for	for	ADP
ejpam-6212	671	11	geodetic	geodetic	ADJ
ejpam-6212	671	12	-	-	PUNCT
ejpam-6212	671	13	wiener	wiener	NOUN
ejpam-6212	671	14	index	index	NOUN
ejpam-6212	671	15	in	in	ADP
ejpam-6212	671	16	terms	term	NOUN
ejpam-6212	671	17	of	of	ADP
ejpam-6212	671	18	other	other	ADJ
ejpam-6212	671	19	distance	distance	NOUN
ejpam-6212	671	20	-	-	PUNCT
ejpam-6212	671	21	based	base	VERB
ejpam-6212	671	22	topological	topological	ADJ
ejpam-6212	671	23	indices	index	NOUN
ejpam-6212	671	24	for	for	ADP
ejpam-6212	671	25	simple	simple	ADJ
ejpam-6212	671	26	spirocyclic	spirocyclic	NOUN
ejpam-6212	671	27	graphs	graph	NOUN
ejpam-6212	671	28	with	with	ADP
ejpam-6212	671	29	even	even	ADV
ejpam-6212	671	30	cycles	cycle	NOUN
ejpam-6212	671	31	by	by	ADP
ejpam-6212	671	32	decomposing	decompose	VERB
ejpam-6212	671	33	the	the	DET
ejpam-6212	671	34	structure	structure	NOUN
ejpam-6212	671	35	into	into	ADP
ejpam-6212	671	36	subtrees	subtree	NOUN
ejpam-6212	671	37	using	use	VERB
ejpam-6212	671	38	the	the	DET
ejpam-6212	671	39	concept	concept	NOUN
ejpam-6212	671	40	of	of	ADP
ejpam-6212	671	41	projection	projection	NOUN
ejpam-6212	671	42	of	of	ADP
ejpam-6212	671	43	v	v	NOUN
ejpam-6212	671	44	(	(	PUNCT
ejpam-6212	671	45	g	g	NOUN
ejpam-6212	671	46	)	)	PUNCT
ejpam-6212	671	47	onto	onto	ADP
ejpam-6212	671	48	the	the	DET
ejpam-6212	671	49	even	even	ADJ
ejpam-6212	671	50	cycles	cycle	NOUN
ejpam-6212	671	51	.	.	PUNCT
ejpam-6212	672	1	moreover	moreover	ADV
ejpam-6212	672	2	,	,	PUNCT
ejpam-6212	672	3	we	we	PRON
ejpam-6212	672	4	have	have	AUX
ejpam-6212	672	5	shown	show	VERB
ejpam-6212	672	6	that	that	SCONJ
ejpam-6212	672	7	the	the	DET
ejpam-6212	672	8	geodetic	geodetic	ADJ
ejpam-6212	672	9	-	-	PUNCT
ejpam-6212	672	10	wiener	wiener	NOUN
ejpam-6212	672	11	index	index	NOUN
ejpam-6212	672	12	of	of	ADP
ejpam-6212	672	13	spirocyclic	spirocyclic	ADJ
ejpam-6212	672	14	graphs	graph	NOUN
ejpam-6212	672	15	without	without	ADP
ejpam-6212	672	16	pendant	pendant	ADJ
ejpam-6212	672	17	vertices	vertex	NOUN
ejpam-6212	672	18	is	be	AUX
ejpam-6212	672	19	equal	equal	ADJ
ejpam-6212	672	20	to	to	ADP
ejpam-6212	672	21	the	the	DET
ejpam-6212	672	22	wiener	wiener	NOUN
ejpam-6212	672	23	index	index	NOUN
ejpam-6212	672	24	plus	plus	CCONJ
ejpam-6212	672	25	twice	twice	DET
ejpam-6212	672	26	the	the	DET
ejpam-6212	672	27	square	square	NOUN
ejpam-6212	672	28	of	of	ADP
ejpam-6212	672	29	the	the	DET
ejpam-6212	672	30	sum	sum	NOUN
ejpam-6212	672	31	of	of	ADP
ejpam-6212	672	32	the	the	DET
ejpam-6212	672	33	diameters	diameter	NOUN
ejpam-6212	672	34	of	of	ADP
ejpam-6212	672	35	the	the	DET
ejpam-6212	672	36	cycles	cycle	NOUN
ejpam-6212	672	37	.	.	PUNCT
ejpam-6212	673	1	the	the	DET
ejpam-6212	673	2	g	g	PROPN
ejpam-6212	673	3	-	-	PUNCT
ejpam-6212	673	4	wiener	wiener	NOUN
ejpam-6212	673	5	index	index	NOUN
ejpam-6212	673	6	captures	capture	VERB
ejpam-6212	673	7	more	more	ADJ
ejpam-6212	673	8	structural	structural	ADJ
ejpam-6212	673	9	information	information	NOUN
ejpam-6212	673	10	compared	compare	VERB
ejpam-6212	673	11	to	to	ADP
ejpam-6212	673	12	standard	standard	ADJ
ejpam-6212	673	13	wiener	wiener	NOUN
ejpam-6212	673	14	index	index	NOUN
ejpam-6212	673	15	.	.	PUNCT
ejpam-6212	674	1	a	a	DET
ejpam-6212	674	2	concrete	concrete	ADJ
ejpam-6212	674	3	example	example	NOUN
ejpam-6212	674	4	is	be	AUX
ejpam-6212	674	5	a	a	DET
ejpam-6212	674	6	spirocyclic	spirocyclic	ADJ
ejpam-6212	674	7	compound	compound	NOUN
ejpam-6212	674	8	with	with	ADP
ejpam-6212	674	9	even	even	ADV
ejpam-6212	674	10	connecting	connect	VERB
ejpam-6212	674	11	cycles	cycle	NOUN
ejpam-6212	674	12	,	,	PUNCT
ejpam-6212	674	13	such	such	ADJ
ejpam-6212	674	14	as	as	ADP
ejpam-6212	674	15	the	the	DET
ejpam-6212	674	16	spirobicyclohexane	spirobicyclohexane	NOUN
ejpam-6212	674	17	.	.	PUNCT
ejpam-6212	675	1	consider	consider	VERB
ejpam-6212	675	2	graphs	graph	NOUN
ejpam-6212	675	3	with	with	ADP
ejpam-6212	675	4	k	k	PROPN
ejpam-6212	675	5	even	even	ADV
ejpam-6212	675	6	cycles	cycle	NOUN
ejpam-6212	675	7	where	where	SCONJ
ejpam-6212	675	8	k	k	PROPN
ejpam-6212	675	9	≥	≥	NUM
ejpam-6212	675	10	3	3	X
ejpam-6212	675	11	.	.	PUNCT
ejpam-6212	676	1	this	this	PRON
ejpam-6212	676	2	will	will	AUX
ejpam-6212	676	3	increase	increase	VERB
ejpam-6212	676	4	the	the	DET
ejpam-6212	676	5	number	number	NOUN
ejpam-6212	676	6	of	of	ADP
ejpam-6212	676	7	geodesics	geodesic	NOUN
ejpam-6212	676	8	between	between	ADP
ejpam-6212	676	9	some	some	DET
ejpam-6212	676	10	vertex	vertex	NOUN
ejpam-6212	676	11	pairs	pair	NOUN
ejpam-6212	676	12	in	in	ADP
ejpam-6212	676	13	the	the	DET
ejpam-6212	676	14	graph	graph	NOUN
ejpam-6212	676	15	.	.	PUNCT
ejpam-6212	677	1	also	also	ADV
ejpam-6212	677	2	,	,	PUNCT
ejpam-6212	677	3	when	when	SCONJ
ejpam-6212	677	4	an	an	DET
ejpam-6212	677	5	odd	odd	ADJ
ejpam-6212	677	6	cycle	cycle	NOUN
ejpam-6212	677	7	is	be	AUX
ejpam-6212	677	8	attached	attach	VERB
ejpam-6212	677	9	to	to	ADP
ejpam-6212	677	10	the	the	DET
ejpam-6212	677	11	even	even	ADJ
ejpam-6212	677	12	cycle	cycle	NOUN
ejpam-6212	677	13	,	,	PUNCT
ejpam-6212	677	14	the	the	DET
ejpam-6212	677	15	projection	projection	NOUN
ejpam-6212	677	16	of	of	ADP
ejpam-6212	677	17	some	some	DET
ejpam-6212	677	18	vertices	vertex	NOUN
ejpam-6212	677	19	to	to	ADP
ejpam-6212	677	20	the	the	DET
ejpam-6212	677	21	even	even	ADJ
ejpam-6212	677	22	cycle	cycle	NOUN
ejpam-6212	677	23	may	may	AUX
ejpam-6212	677	24	not	not	PART
ejpam-6212	677	25	be	be	AUX
ejpam-6212	677	26	unique	unique	ADJ
ejpam-6212	677	27	.	.	PUNCT
ejpam-6212	678	1	this	this	PRON
ejpam-6212	678	2	will	will	AUX
ejpam-6212	678	3	be	be	AUX
ejpam-6212	678	4	another	another	DET
ejpam-6212	678	5	interesting	interesting	ADJ
ejpam-6212	678	6	and	and	CCONJ
ejpam-6212	678	7	challenging	challenging	ADJ
ejpam-6212	678	8	problem	problem	NOUN
ejpam-6212	678	9	that	that	PRON
ejpam-6212	678	10	could	could	AUX
ejpam-6212	678	11	be	be	AUX
ejpam-6212	678	12	considered	consider	VERB
ejpam-6212	678	13	.	.	PUNCT
ejpam-6212	679	1	furthermore	furthermore	ADV
ejpam-6212	679	2	,	,	PUNCT
ejpam-6212	679	3	evaluation	evaluation	NOUN
ejpam-6212	679	4	of	of	ADP
ejpam-6212	679	5	g	g	NOUN
ejpam-6212	679	6	-	-	PUNCT
ejpam-6212	679	7	wiener	wiener	NOUN
ejpam-6212	679	8	index	index	NOUN
ejpam-6212	679	9	of	of	ADP
ejpam-6212	679	10	graphs	graph	NOUN
ejpam-6212	679	11	resulting	result	VERB
ejpam-6212	679	12	from	from	ADP
ejpam-6212	679	13	some	some	DET
ejpam-6212	679	14	unary	unary	ADJ
ejpam-6212	679	15	and	and	CCONJ
ejpam-6212	679	16	binary	binary	ADJ
ejpam-6212	679	17	graph	graph	NOUN
ejpam-6212	679	18	operations	operation	NOUN
ejpam-6212	679	19	are	be	AUX
ejpam-6212	679	20	potential	potential	ADJ
ejpam-6212	679	21	problems	problem	NOUN
ejpam-6212	679	22	that	that	PRON
ejpam-6212	679	23	could	could	AUX
ejpam-6212	679	24	be	be	AUX
ejpam-6212	679	25	considered	consider	VERB
ejpam-6212	679	26	for	for	ADP
ejpam-6212	679	27	further	further	ADJ
ejpam-6212	679	28	investigations	investigation	NOUN
ejpam-6212	679	29	by	by	ADP
ejpam-6212	679	30	expressing	express	VERB
ejpam-6212	679	31	the	the	DET
ejpam-6212	679	32	g	g	PROPN
ejpam-6212	679	33	-	-	PUNCT
ejpam-6212	679	34	wiener	wiener	NOUN
ejpam-6212	679	35	index	index	NOUN
ejpam-6212	679	36	of	of	ADP
ejpam-6212	679	37	the	the	DET
ejpam-6212	679	38	graph	graph	NOUN
ejpam-6212	679	39	resulting	result	VERB
ejpam-6212	679	40	from	from	ADP
ejpam-6212	679	41	the	the	DET
ejpam-6212	679	42	graph	graph	NOUN
ejpam-6212	679	43	operations	operation	NOUN
ejpam-6212	679	44	in	in	ADP
ejpam-6212	679	45	terms	term	NOUN
ejpam-6212	679	46	of	of	ADP
ejpam-6212	679	47	the	the	DET
ejpam-6212	679	48	g	g	PROPN
ejpam-6212	679	49	-	-	PUNCT
ejpam-6212	679	50	wiener	wiener	NOUN
ejpam-6212	679	51	index	index	NOUN
ejpam-6212	679	52	of	of	ADP
ejpam-6212	679	53	the	the	DET
ejpam-6212	679	54	original	original	ADJ
ejpam-6212	679	55	graph	graph	NOUN
ejpam-6212	679	56	being	be	AUX
ejpam-6212	679	57	considered	consider	VERB
ejpam-6212	679	58	.	.	PUNCT
ejpam-6212	680	1	r.	r.	PROPN
ejpam-6212	680	2	g.	g.	PROPN
ejpam-6212	680	3	artes	artes	PROPN
ejpam-6212	680	4	jr	jr	PROPN
ejpam-6212	680	5	.	.	PROPN
ejpam-6212	680	6	et	et	PROPN
ejpam-6212	680	7	al	al	PROPN
ejpam-6212	680	8	.	.	PUNCT
ejpam-6212	680	9	/	/	SYM
ejpam-6212	680	10	eur	eur	PROPN
ejpam-6212	680	11	.	.	PUNCT
ejpam-6212	681	1	j.	j.	PROPN
ejpam-6212	681	2	pure	pure	PROPN
ejpam-6212	681	3	appl	appl	PROPN
ejpam-6212	681	4	.	.	PROPN
ejpam-6212	681	5	math	math	PROPN
ejpam-6212	681	6	,	,	PUNCT
ejpam-6212	681	7	18	18	NUM
ejpam-6212	681	8	(	(	PUNCT
ejpam-6212	681	9	4	4	NUM
ejpam-6212	681	10	)	)	PUNCT
ejpam-6212	681	11	(	(	PUNCT
ejpam-6212	681	12	2025	2025	NUM
ejpam-6212	681	13	)	)	PUNCT
ejpam-6212	681	14	,	,	PUNCT
ejpam-6212	681	15	6212	6212	NUM
ejpam-6212	681	16	19	19	NUM
ejpam-6212	681	17	of	of	ADP
ejpam-6212	681	18	20	20	NUM
ejpam-6212	681	19	acknowledgements	acknowledgement	NOUN
ejpam-6212	681	20	the	the	DET
ejpam-6212	681	21	first	first	ADJ
ejpam-6212	681	22	author	author	NOUN
ejpam-6212	681	23	is	be	AUX
ejpam-6212	681	24	supported	support	VERB
ejpam-6212	681	25	by	by	ADP
ejpam-6212	681	26	the	the	DET
ejpam-6212	681	27	msu	msu	PROPN
ejpam-6212	681	28	-	-	PUNCT
ejpam-6212	681	29	tcto	tcto	VERB
ejpam-6212	681	30	apdp	apdp	PROPN
ejpam-6212	681	31	grant	grant	PROPN
ejpam-6212	681	32	.	.	PUNCT
ejpam-6212	682	1	references	reference	NOUN
ejpam-6212	682	2	[	[	X
ejpam-6212	682	3	1	1	X
ejpam-6212	682	4	]	]	X
ejpam-6212	682	5	danishuddin	danishuddin	NOUN
ejpam-6212	682	6	and	and	CCONJ
ejpam-6212	682	7	a.	a.	NOUN
ejpam-6212	682	8	u.	u.	PROPN
ejpam-6212	682	9	khan	khan	PROPN
ejpam-6212	682	10	.	.	PUNCT
ejpam-6212	683	1	descriptors	descriptor	NOUN
ejpam-6212	683	2	and	and	CCONJ
ejpam-6212	683	3	their	their	PRON
ejpam-6212	683	4	selection	selection	NOUN
ejpam-6212	683	5	methods	method	NOUN
ejpam-6212	683	6	in	in	ADP
ejpam-6212	683	7	qsar	qsar	NOUN
ejpam-6212	683	8	analysis	analysis	NOUN
ejpam-6212	683	9	:	:	PUNCT
ejpam-6212	683	10	paradigm	paradigm	NOUN
ejpam-6212	683	11	for	for	ADP
ejpam-6212	683	12	drug	drug	NOUN
ejpam-6212	683	13	design	design	NOUN
ejpam-6212	683	14	.	.	PUNCT
ejpam-6212	684	1	drug	drug	NOUN
ejpam-6212	684	2	discovery	discovery	PROPN
ejpam-6212	684	3	today	today	NOUN
ejpam-6212	684	4	,	,	PUNCT
ejpam-6212	684	5	8(8):1291–1302	8(8):1291–1302	PROPN
ejpam-6212	684	6	,	,	PUNCT
ejpam-6212	684	7	2016	2016	NUM
ejpam-6212	684	8	.	.	PUNCT
ejpam-6212	685	1	[	[	X
ejpam-6212	685	2	2	2	X
ejpam-6212	685	3	]	]	PUNCT
ejpam-6212	685	4	h.	h.	PROPN
ejpam-6212	685	5	wiener	wiener	PROPN
ejpam-6212	685	6	.	.	PUNCT
ejpam-6212	686	1	structural	structural	ADJ
ejpam-6212	686	2	determination	determination	NOUN
ejpam-6212	686	3	of	of	ADP
ejpam-6212	686	4	paraffin	paraffin	NOUN
ejpam-6212	686	5	boiling	boiling	NOUN
ejpam-6212	686	6	points	point	NOUN
ejpam-6212	686	7	.	.	PUNCT
ejpam-6212	687	1	journal	journal	NOUN
ejpam-6212	687	2	of	of	ADP
ejpam-6212	687	3	the	the	DET
ejpam-6212	687	4	american	american	PROPN
ejpam-6212	687	5	chemical	chemical	PROPN
ejpam-6212	687	6	society	society	PROPN
ejpam-6212	687	7	,	,	PUNCT
ejpam-6212	687	8	69(1):17–20	69(1):17–20	NUM
ejpam-6212	687	9	,	,	PUNCT
ejpam-6212	687	10	1947	1947	NUM
ejpam-6212	687	11	.	.	PUNCT
ejpam-6212	688	1	[	[	X
ejpam-6212	688	2	3	3	NUM
ejpam-6212	688	3	]	]	X
ejpam-6212	688	4	m.	m.	NOUN
ejpam-6212	688	5	randić	randić	PROPN
ejpam-6212	688	6	.	.	PUNCT
ejpam-6212	689	1	novel	novel	ADJ
ejpam-6212	689	2	molecular	molecular	ADJ
ejpam-6212	689	3	descriptor	descriptor	NOUN
ejpam-6212	689	4	for	for	ADP
ejpam-6212	689	5	structure	structure	NOUN
ejpam-6212	689	6	-	-	PUNCT
ejpam-6212	689	7	property	property	NOUN
ejpam-6212	689	8	studies	study	NOUN
ejpam-6212	689	9	.	.	PUNCT
ejpam-6212	690	1	chemical	chemical	PROPN
ejpam-6212	690	2	physics	physics	PROPN
ejpam-6212	690	3	letters	letter	NOUN
ejpam-6212	690	4	,	,	PUNCT
ejpam-6212	690	5	211:478–483	211:478–483	NUM
ejpam-6212	690	6	,	,	PUNCT
ejpam-6212	690	7	1993	1993	NUM
ejpam-6212	690	8	.	.	PUNCT
ejpam-6212	691	1	[	[	X
ejpam-6212	691	2	4	4	NUM
ejpam-6212	691	3	]	]	X
ejpam-6212	691	4	i.	i.	PROPN
ejpam-6212	691	5	gutman	gutman	PROPN
ejpam-6212	691	6	.	.	PUNCT
ejpam-6212	691	7	degree	degree	NOUN
ejpam-6212	691	8	-	-	PUNCT
ejpam-6212	691	9	based	base	VERB
ejpam-6212	691	10	topological	topological	ADJ
ejpam-6212	691	11	indices	index	NOUN
ejpam-6212	691	12	.	.	PUNCT
ejpam-6212	692	1	croatica	croatica	PROPN
ejpam-6212	692	2	chemica	chemica	PROPN
ejpam-6212	692	3	acta	acta	PROPN
ejpam-6212	692	4	,	,	PUNCT
ejpam-6212	692	5	86(4):351–361	86(4):351–361	PROPN
ejpam-6212	692	6	,	,	PUNCT
ejpam-6212	692	7	2013	2013	NUM
ejpam-6212	692	8	.	.	PUNCT
ejpam-6212	693	1	[	[	X
ejpam-6212	693	2	5	5	X
ejpam-6212	693	3	]	]	PUNCT
ejpam-6212	693	4	s.	s.	PROPN
ejpam-6212	693	5	chen	chen	PROPN
ejpam-6212	693	6	.	.	PUNCT
ejpam-6212	694	1	modified	modify	VERB
ejpam-6212	694	2	schultz	schultz	PROPN
ejpam-6212	694	3	index	index	NOUN
ejpam-6212	694	4	of	of	ADP
ejpam-6212	694	5	zig	zig	PROPN
ejpam-6212	694	6	-	-	PUNCT
ejpam-6212	694	7	zag	zag	ADJ
ejpam-6212	694	8	polyhex	polyhex	NOUN
ejpam-6212	694	9	nanotubes	nanotube	NOUN
ejpam-6212	694	10	.	.	PUNCT
ejpam-6212	695	1	journal	journal	PROPN
ejpam-6212	695	2	of	of	ADP
ejpam-6212	695	3	computational	computational	ADJ
ejpam-6212	695	4	and	and	CCONJ
ejpam-6212	695	5	theoretical	theoretical	ADJ
ejpam-6212	695	6	nanoscience	nanoscience	NOUN
ejpam-6212	695	7	,	,	PUNCT
ejpam-6212	695	8	6(7):1499–1503	6(7):1499–1503	NOUN
ejpam-6212	695	9	,	,	PUNCT
ejpam-6212	695	10	2009	2009	NUM
ejpam-6212	695	11	.	.	PUNCT
ejpam-6212	696	1	[	[	X
ejpam-6212	696	2	6	6	NUM
ejpam-6212	696	3	]	]	PUNCT
ejpam-6212	696	4	m.	m.	PROPN
ejpam-6212	696	5	r.	r.	PROPN
ejpam-6212	696	6	farahani	farahani	PROPN
ejpam-6212	696	7	.	.	PUNCT
ejpam-6212	697	1	hosoya	hosoya	PROPN
ejpam-6212	697	2	,	,	PUNCT
ejpam-6212	697	3	schultz	schultz	PROPN
ejpam-6212	697	4	,	,	PUNCT
ejpam-6212	697	5	modified	modify	VERB
ejpam-6212	697	6	schultz	schultz	NOUN
ejpam-6212	697	7	polynomials	polynomial	NOUN
ejpam-6212	697	8	and	and	CCONJ
ejpam-6212	697	9	their	their	PRON
ejpam-6212	697	10	topological	topological	ADJ
ejpam-6212	697	11	indices	index	NOUN
ejpam-6212	697	12	of	of	ADP
ejpam-6212	697	13	benzene	benzene	NOUN
ejpam-6212	697	14	molecules	molecule	NOUN
ejpam-6212	697	15	:	:	PUNCT
ejpam-6212	697	16	first	first	ADJ
ejpam-6212	697	17	members	member	NOUN
ejpam-6212	697	18	of	of	ADP
ejpam-6212	697	19	polycyclic	polycyclic	ADJ
ejpam-6212	697	20	aromatic	aromatic	ADJ
ejpam-6212	697	21	hydrocarbons	hydrocarbon	NOUN
ejpam-6212	697	22	(	(	PUNCT
ejpam-6212	697	23	pahs	pahs	PROPN
ejpam-6212	697	24	)	)	PUNCT
ejpam-6212	697	25	.	.	PUNCT
ejpam-6212	698	1	international	international	ADJ
ejpam-6212	698	2	journal	journal	PROPN
ejpam-6212	698	3	of	of	ADP
ejpam-6212	698	4	theoretical	theoretical	ADJ
ejpam-6212	698	5	chemistry	chemistry	NOUN
ejpam-6212	698	6	,	,	PUNCT
ejpam-6212	698	7	1(2):9–16	1(2):9–16	NUM
ejpam-6212	698	8	,	,	PUNCT
ejpam-6212	698	9	2013	2013	NUM
ejpam-6212	698	10	.	.	PUNCT
ejpam-6212	699	1	[	[	X
ejpam-6212	699	2	7	7	NUM
ejpam-6212	699	3	]	]	PUNCT
ejpam-6212	699	4	a.	a.	NOUN
ejpam-6212	699	5	heydari	heydari	NOUN
ejpam-6212	699	6	.	.	PUNCT
ejpam-6212	700	1	on	on	ADP
ejpam-6212	700	2	the	the	DET
ejpam-6212	700	3	modified	modify	VERB
ejpam-6212	700	4	schultz	schultz	PROPN
ejpam-6212	700	5	index	index	NOUN
ejpam-6212	700	6	of	of	ADP
ejpam-6212	700	7	c4c8(s	c4c8(	NOUN
ejpam-6212	700	8	)	)	PUNCT
ejpam-6212	700	9	nanotubes	nanotube	NOUN
ejpam-6212	700	10	and	and	CCONJ
ejpam-6212	700	11	nanotorus	nanotorus	NOUN
ejpam-6212	700	12	.	.	PUNCT
ejpam-6212	701	1	digest	digest	PROPN
ejpam-6212	701	2	journal	journal	PROPN
ejpam-6212	701	3	of	of	ADP
ejpam-6212	701	4	nanomaterials	nanomaterial	NOUN
ejpam-6212	701	5	and	and	CCONJ
ejpam-6212	701	6	biostructures	biostructure	NOUN
ejpam-6212	701	7	,	,	PUNCT
ejpam-6212	701	8	5(1):51–56	5(1):51–56	NUM
ejpam-6212	701	9	,	,	PUNCT
ejpam-6212	701	10	2010	2010	NUM
ejpam-6212	701	11	.	.	PUNCT
ejpam-6212	702	1	[	[	X
ejpam-6212	702	2	8	8	X
ejpam-6212	702	3	]	]	X
ejpam-6212	702	4	s.	s.	PROPN
ejpam-6212	702	5	mukwembi	mukwembi	PROPN
ejpam-6212	702	6	and	and	CCONJ
ejpam-6212	702	7	s.	s.	PROPN
ejpam-6212	702	8	munyira	munyira	PROPN
ejpam-6212	702	9	.	.	PUNCT
ejpam-6212	702	10	degree	degree	NOUN
ejpam-6212	702	11	distance	distance	NOUN
ejpam-6212	702	12	and	and	CCONJ
ejpam-6212	702	13	minimum	minimum	NOUN
ejpam-6212	702	14	degree	degree	NOUN
ejpam-6212	702	15	.	.	PUNCT
ejpam-6212	703	1	bulletin	bulletin	NOUN
ejpam-6212	703	2	of	of	ADP
ejpam-6212	703	3	the	the	DET
ejpam-6212	703	4	australian	australian	ADJ
ejpam-6212	703	5	mathematical	mathematical	ADJ
ejpam-6212	703	6	society	society	NOUN
ejpam-6212	703	7	,	,	PUNCT
ejpam-6212	703	8	87:255–271	87:255–271	NOUN
ejpam-6212	703	9	,	,	PUNCT
ejpam-6212	703	10	2013	2013	NUM
ejpam-6212	703	11	.	.	PUNCT
ejpam-6212	704	1	[	[	X
ejpam-6212	704	2	9	9	NUM
ejpam-6212	704	3	]	]	PUNCT
ejpam-6212	704	4	z.	z.	PROPN
ejpam-6212	704	5	xiao	xiao	PROPN
ejpam-6212	704	6	and	and	CCONJ
ejpam-6212	704	7	s.	s.	PROPN
ejpam-6212	704	8	chen	chen	PROPN
ejpam-6212	704	9	.	.	PUNCT
ejpam-6212	705	1	the	the	DET
ejpam-6212	705	2	modified	modify	VERB
ejpam-6212	705	3	schultz	schultz	PROPN
ejpam-6212	705	4	index	index	NOUN
ejpam-6212	705	5	of	of	ADP
ejpam-6212	705	6	armchair	armchair	NOUN
ejpam-6212	705	7	polyhex	polyhex	NOUN
ejpam-6212	705	8	nanotubes	nanotube	NOUN
ejpam-6212	705	9	.	.	PUNCT
ejpam-6212	706	1	journal	journal	PROPN
ejpam-6212	706	2	of	of	ADP
ejpam-6212	706	3	computational	computational	ADJ
ejpam-6212	706	4	and	and	CCONJ
ejpam-6212	706	5	theoretical	theoretical	ADJ
ejpam-6212	706	6	nanoscience	nanoscience	NOUN
ejpam-6212	706	7	,	,	PUNCT
ejpam-6212	706	8	6(5):1109–1114	6(5):1109–1114	NOUN
ejpam-6212	706	9	,	,	PUNCT
ejpam-6212	706	10	2009	2009	NUM
ejpam-6212	706	11	.	.	PUNCT
ejpam-6212	707	1	[	[	X
ejpam-6212	707	2	10	10	NUM
ejpam-6212	707	3	]	]	X
ejpam-6212	707	4	o.	o.	NOUN
ejpam-6212	707	5	ivanciuc	ivanciuc	PROPN
ejpam-6212	707	6	,	,	PUNCT
ejpam-6212	707	7	t.	t.	PROPN
ejpam-6212	707	8	s.	s.	PROPN
ejpam-6212	707	9	balaban	balaban	PROPN
ejpam-6212	707	10	,	,	PUNCT
ejpam-6212	707	11	and	and	CCONJ
ejpam-6212	707	12	a.	a.	NOUN
ejpam-6212	707	13	t.	t.	PROPN
ejpam-6212	707	14	balaban	balaban	PROPN
ejpam-6212	707	15	.	.	PUNCT
ejpam-6212	708	1	design	design	NOUN
ejpam-6212	708	2	of	of	ADP
ejpam-6212	708	3	topological	topological	ADJ
ejpam-6212	708	4	indices	index	NOUN
ejpam-6212	708	5	.	.	PUNCT
ejpam-6212	709	1	journal	journal	NOUN
ejpam-6212	709	2	of	of	ADP
ejpam-6212	709	3	mathematical	mathematical	ADJ
ejpam-6212	709	4	chemistry	chemistry	NOUN
ejpam-6212	709	5	,	,	PUNCT
ejpam-6212	709	6	12(1):309–318	12(1):309–318	PROPN
ejpam-6212	709	7	,	,	PUNCT
ejpam-6212	709	8	1993	1993	NUM
ejpam-6212	709	9	.	.	PUNCT
ejpam-6212	710	1	[	[	X
ejpam-6212	710	2	11	11	NUM
ejpam-6212	710	3	]	]	PUNCT
ejpam-6212	710	4	d.	d.	PROPN
ejpam-6212	710	5	plavšić	plavšić	PROPN
ejpam-6212	710	6	,	,	PUNCT
ejpam-6212	710	7	s.	s.	PROPN
ejpam-6212	710	8	nikolić	nikolić	PROPN
ejpam-6212	710	9	,	,	PUNCT
ejpam-6212	710	10	and	and	CCONJ
ejpam-6212	710	11	n.	n.	PROPN
ejpam-6212	710	12	trinajstić	trinajstić	PROPN
ejpam-6212	710	13	.	.	PUNCT
ejpam-6212	711	1	on	on	ADP
ejpam-6212	711	2	the	the	DET
ejpam-6212	711	3	harary	harary	PROPN
ejpam-6212	711	4	index	index	NOUN
ejpam-6212	711	5	for	for	ADP
ejpam-6212	711	6	the	the	DET
ejpam-6212	711	7	characterization	characterization	NOUN
ejpam-6212	711	8	of	of	ADP
ejpam-6212	711	9	chemical	chemical	NOUN
ejpam-6212	711	10	graphs	graph	NOUN
ejpam-6212	711	11	.	.	PUNCT
ejpam-6212	712	1	journal	journal	NOUN
ejpam-6212	712	2	of	of	ADP
ejpam-6212	712	3	mathematical	mathematical	ADJ
ejpam-6212	712	4	chemistry	chemistry	NOUN
ejpam-6212	712	5	,	,	PUNCT
ejpam-6212	712	6	12:235–250	12:235–250	NUM
ejpam-6212	712	7	,	,	PUNCT
ejpam-6212	712	8	1993	1993	NUM
ejpam-6212	712	9	.	.	PUNCT
ejpam-6212	713	1	[	[	X
ejpam-6212	713	2	12	12	NUM
ejpam-6212	713	3	]	]	X
ejpam-6212	713	4	y.	y.	NOUN
ejpam-6212	713	5	alizadeh	alizadeh	PROPN
ejpam-6212	713	6	,	,	PUNCT
ejpam-6212	713	7	a.	a.	NOUN
ejpam-6212	713	8	iranmanesh	iranmanesh	PROPN
ejpam-6212	713	9	,	,	PUNCT
ejpam-6212	713	10	and	and	CCONJ
ejpam-6212	713	11	t.	t.	PROPN
ejpam-6212	713	12	došlić	došlić	NOUN
ejpam-6212	713	13	.	.	PUNCT
ejpam-6212	714	1	additively	additively	PROPN
ejpam-6212	714	2	weighted	weight	VERB
ejpam-6212	714	3	harary	harary	ADJ
ejpam-6212	714	4	index	index	NOUN
ejpam-6212	714	5	of	of	ADP
ejpam-6212	714	6	some	some	DET
ejpam-6212	714	7	composite	composite	ADJ
ejpam-6212	714	8	graphs	graph	NOUN
ejpam-6212	714	9	.	.	PUNCT
ejpam-6212	715	1	discrete	discrete	ADJ
ejpam-6212	715	2	mathematics	mathematic	NOUN
ejpam-6212	715	3	,	,	PUNCT
ejpam-6212	715	4	33(1):26–34	33(1):26–34	NUM
ejpam-6212	715	5	,	,	PUNCT
ejpam-6212	715	6	2023	2023	NUM
ejpam-6212	715	7	.	.	PUNCT
ejpam-6212	716	1	[	[	X
ejpam-6212	716	2	13	13	NUM
ejpam-6212	716	3	]	]	X
ejpam-6212	716	4	h.	h.	PROPN
ejpam-6212	716	5	deng	deng	PROPN
ejpam-6212	716	6	,	,	PUNCT
ejpam-6212	716	7	b.	b.	PROPN
ejpam-6212	716	8	krishnakumari	krishnakumari	PROPN
ejpam-6212	716	9	,	,	PUNCT
ejpam-6212	716	10	y.	y.	PROPN
ejpam-6212	716	11	b.	b.	PROPN
ejpam-6212	716	12	venkatakrishnan	venkatakrishnan	PROPN
ejpam-6212	716	13	,	,	PUNCT
ejpam-6212	716	14	and	and	CCONJ
ejpam-6212	716	15	s.	s.	PROPN
ejpam-6212	716	16	balachandran	balachandran	PROPN
ejpam-6212	716	17	.	.	PUNCT
ejpam-6212	717	1	multiplicatively	multiplicatively	ADV
ejpam-6212	717	2	weighted	weight	VERB
ejpam-6212	717	3	harary	harary	ADJ
ejpam-6212	717	4	index	index	NOUN
ejpam-6212	717	5	of	of	ADP
ejpam-6212	717	6	graphs	graph	NOUN
ejpam-6212	717	7	.	.	PUNCT
ejpam-6212	718	1	journal	journal	NOUN
ejpam-6212	718	2	of	of	ADP
ejpam-6212	718	3	combinatorial	combinatorial	ADJ
ejpam-6212	718	4	optimization	optimization	NOUN
ejpam-6212	718	5	,	,	PUNCT
ejpam-6212	718	6	30:1125–1137	30:1125–1137	NUM
ejpam-6212	718	7	,	,	PUNCT
ejpam-6212	718	8	2015	2015	NUM
ejpam-6212	718	9	.	.	PUNCT
ejpam-6212	719	1	[	[	X
ejpam-6212	719	2	14	14	NUM
ejpam-6212	719	3	]	]	X
ejpam-6212	719	4	h.	h.	PROPN
ejpam-6212	719	5	lin	lin	PROPN
ejpam-6212	719	6	.	.	PUNCT
ejpam-6212	720	1	a	a	DET
ejpam-6212	720	2	survey	survey	NOUN
ejpam-6212	720	3	of	of	ADP
ejpam-6212	720	4	recent	recent	ADJ
ejpam-6212	720	5	extremal	extremal	ADJ
ejpam-6212	720	6	results	result	NOUN
ejpam-6212	720	7	on	on	ADP
ejpam-6212	720	8	the	the	DET
ejpam-6212	720	9	wiener	wiener	NOUN
ejpam-6212	720	10	index	index	NOUN
ejpam-6212	720	11	of	of	ADP
ejpam-6212	720	12	trees	tree	NOUN
ejpam-6212	720	13	.	.	PUNCT
ejpam-6212	721	1	match	match	VERB
ejpam-6212	721	2	communications	communication	NOUN
ejpam-6212	721	3	in	in	ADP
ejpam-6212	721	4	mathematical	mathematical	ADJ
ejpam-6212	721	5	and	and	CCONJ
ejpam-6212	721	6	in	in	ADP
ejpam-6212	721	7	computer	computer	NOUN
ejpam-6212	721	8	chemistry	chemistry	NOUN
ejpam-6212	721	9	,	,	PUNCT
ejpam-6212	721	10	92:253–270	92:253–270	NUM
ejpam-6212	721	11	,	,	PUNCT
ejpam-6212	721	12	2024	2024	NUM
ejpam-6212	721	13	.	.	PUNCT
ejpam-6212	722	1	[	[	X
ejpam-6212	722	2	15	15	NUM
ejpam-6212	722	3	]	]	X
ejpam-6212	722	4	a.	a.	PROPN
ejpam-6212	722	5	martinez	martinez	PROPN
ejpam-6212	722	6	-	-	PUNCT
ejpam-6212	722	7	perez	perez	PROPN
ejpam-6212	722	8	and	and	CCONJ
ejpam-6212	722	9	j.	j.	PROPN
ejpam-6212	722	10	m.	m.	PROPN
ejpam-6212	722	11	rodriguez	rodriguez	PROPN
ejpam-6212	722	12	.	.	PUNCT
ejpam-6212	723	1	upper	upper	ADJ
ejpam-6212	723	2	and	and	CCONJ
ejpam-6212	723	3	lower	low	ADJ
ejpam-6212	723	4	bounds	bound	NOUN
ejpam-6212	723	5	for	for	ADP
ejpam-6212	723	6	generalized	generalized	ADJ
ejpam-6212	723	7	wiener	wiener	NOUN
ejpam-6212	723	8	indices	index	NOUN
ejpam-6212	723	9	on	on	ADP
ejpam-6212	723	10	unicyclic	unicyclic	ADJ
ejpam-6212	723	11	graphs	graph	NOUN
ejpam-6212	723	12	.	.	PUNCT
ejpam-6212	724	1	match	match	VERB
ejpam-6212	724	2	communications	communication	NOUN
ejpam-6212	724	3	in	in	ADP
ejpam-6212	724	4	mathematical	mathematical	ADJ
ejpam-6212	724	5	and	and	CCONJ
ejpam-6212	724	6	in	in	ADP
ejpam-6212	724	7	computer	computer	NOUN
ejpam-6212	724	8	chemistry	chemistry	NOUN
ejpam-6212	724	9	,	,	PUNCT
ejpam-6212	724	10	88:179–198	88:179–198	PROPN
ejpam-6212	724	11	,	,	PUNCT
ejpam-6212	724	12	2022	2022	NUM
ejpam-6212	724	13	.	.	PUNCT
ejpam-6212	725	1	[	[	X
ejpam-6212	725	2	16	16	NUM
ejpam-6212	725	3	]	]	PUNCT
ejpam-6212	725	4	a.	a.	NOUN
ejpam-6212	725	5	alhevaz	alhevaz	PROPN
ejpam-6212	725	6	,	,	PUNCT
ejpam-6212	725	7	m.	m.	NOUN
ejpam-6212	725	8	baghipur	baghipur	NOUN
ejpam-6212	725	9	,	,	PUNCT
ejpam-6212	725	10	and	and	CCONJ
ejpam-6212	725	11	s.	s.	PROPN
ejpam-6212	725	12	rahimi	rahimi	PROPN
ejpam-6212	725	13	.	.	PUNCT
ejpam-6212	726	1	bounds	bound	NOUN
ejpam-6212	726	2	on	on	ADP
ejpam-6212	726	3	hyper	hyper	ADJ
ejpam-6212	726	4	-	-	ADJ
ejpam-6212	726	5	wiener	wiener	NOUN
ejpam-6212	726	6	index	index	NOUN
ejpam-6212	726	7	of	of	ADP
ejpam-6212	726	8	graphs	graph	NOUN
ejpam-6212	726	9	.	.	PUNCT
ejpam-6212	727	1	asian	asian	ADJ
ejpam-6212	727	2	-	-	PUNCT
ejpam-6212	727	3	european	european	ADJ
ejpam-6212	727	4	journal	journal	NOUN
ejpam-6212	727	5	of	of	ADP
ejpam-6212	727	6	mathematics	mathematic	NOUN
ejpam-6212	727	7	,	,	PUNCT
ejpam-6212	727	8	10(3):1750057	10(3):1750057	NUM
ejpam-6212	727	9	,	,	PUNCT
ejpam-6212	727	10	2017	2017	NUM
ejpam-6212	727	11	.	.	PUNCT
ejpam-6212	728	1	[	[	X
ejpam-6212	728	2	17	17	NUM
ejpam-6212	728	3	]	]	PUNCT
ejpam-6212	728	4	i.	i.	PROPN
ejpam-6212	728	5	gutman	gutman	PROPN
ejpam-6212	728	6	.	.	PUNCT
ejpam-6212	729	1	selected	select	VERB
ejpam-6212	729	2	properties	property	NOUN
ejpam-6212	729	3	of	of	ADP
ejpam-6212	729	4	the	the	DET
ejpam-6212	729	5	schultz	schultz	PROPN
ejpam-6212	729	6	molecular	molecular	PROPN
ejpam-6212	729	7	topological	topological	PROPN
ejpam-6212	729	8	index	index	NOUN
ejpam-6212	729	9	.	.	PUNCT
ejpam-6212	730	1	journal	journal	PROPN
ejpam-6212	730	2	of	of	ADP
ejpam-6212	730	3	chemical	chemical	ADJ
ejpam-6212	730	4	information	information	NOUN
ejpam-6212	730	5	and	and	CCONJ
ejpam-6212	730	6	computer	computer	NOUN
ejpam-6212	730	7	sciences	science	NOUN
ejpam-6212	730	8	,	,	PUNCT
ejpam-6212	730	9	34:1087–1089	34:1087–1089	NUM
ejpam-6212	730	10	,	,	PUNCT
ejpam-6212	730	11	1994	1994	NUM
ejpam-6212	730	12	.	.	PUNCT
ejpam-6212	731	1	r.	r.	PROPN
ejpam-6212	731	2	g.	g.	PROPN
ejpam-6212	731	3	artes	artes	PROPN
ejpam-6212	731	4	jr	jr	PROPN
ejpam-6212	731	5	.	.	PROPN
ejpam-6212	731	6	et	et	PROPN
ejpam-6212	731	7	al	al	PROPN
ejpam-6212	731	8	.	.	PUNCT
ejpam-6212	731	9	/	/	SYM
ejpam-6212	731	10	eur	eur	PROPN
ejpam-6212	731	11	.	.	PUNCT
ejpam-6212	732	1	j.	j.	PROPN
ejpam-6212	732	2	pure	pure	PROPN
ejpam-6212	732	3	appl	appl	PROPN
ejpam-6212	732	4	.	.	PROPN
ejpam-6212	732	5	math	math	PROPN
ejpam-6212	732	6	,	,	PUNCT
ejpam-6212	732	7	18	18	NUM
ejpam-6212	732	8	(	(	PUNCT
ejpam-6212	732	9	4	4	NUM
ejpam-6212	732	10	)	)	PUNCT
ejpam-6212	732	11	(	(	PUNCT
ejpam-6212	732	12	2025	2025	NUM
ejpam-6212	732	13	)	)	PUNCT
ejpam-6212	732	14	,	,	PUNCT
ejpam-6212	732	15	6212	6212	NUM
ejpam-6212	732	16	20	20	NUM
ejpam-6212	732	17	of	of	ADP
ejpam-6212	732	18	20	20	NUM
ejpam-6212	732	19	[	[	SYM
ejpam-6212	732	20	18	18	NUM
ejpam-6212	732	21	]	]	PUNCT
ejpam-6212	732	22	j.	j.	PROPN
ejpam-6212	732	23	p.	p.	PROPN
ejpam-6212	732	24	mazorodze	mazorodze	PROPN
ejpam-6212	732	25	,	,	PUNCT
ejpam-6212	732	26	s.	s.	PROPN
ejpam-6212	732	27	mukwembi	mukwembi	PROPN
ejpam-6212	732	28	,	,	PUNCT
ejpam-6212	732	29	and	and	CCONJ
ejpam-6212	732	30	t.	t.	PROPN
ejpam-6212	732	31	vetrík	vetrík	PROPN
ejpam-6212	732	32	.	.	PUNCT
ejpam-6212	733	1	on	on	ADP
ejpam-6212	733	2	the	the	DET
ejpam-6212	733	3	gutman	gutman	NOUN
ejpam-6212	733	4	index	index	NOUN
ejpam-6212	733	5	and	and	CCONJ
ejpam-6212	733	6	minimum	minimum	NOUN
ejpam-6212	733	7	degree	degree	NOUN
ejpam-6212	733	8	.	.	PUNCT
ejpam-6212	734	1	discrete	discrete	ADJ
ejpam-6212	734	2	applied	apply	VERB
ejpam-6212	734	3	mathematics	mathematic	NOUN
ejpam-6212	734	4	,	,	PUNCT
ejpam-6212	734	5	173:77–82	173:77–82	PROPN
ejpam-6212	734	6	,	,	PUNCT
ejpam-6212	734	7	2014	2014	NUM
ejpam-6212	734	8	.	.	PUNCT
ejpam-6212	735	1	[	[	X
ejpam-6212	735	2	19	19	NUM
ejpam-6212	735	3	]	]	PUNCT
ejpam-6212	735	4	h.	h.	PROPN
ejpam-6212	735	5	p.	p.	PROPN
ejpam-6212	735	6	schultz	schultz	PROPN
ejpam-6212	735	7	.	.	PUNCT
ejpam-6212	736	1	topological	topological	ADJ
ejpam-6212	736	2	organic	organic	ADJ
ejpam-6212	736	3	chemistry	chemistry	NOUN
ejpam-6212	736	4	1	1	NUM
ejpam-6212	736	5	.	.	PUNCT
ejpam-6212	736	6	graph	graph	NOUN
ejpam-6212	736	7	theory	theory	NOUN
ejpam-6212	736	8	and	and	CCONJ
ejpam-6212	736	9	topological	topological	ADJ
ejpam-6212	736	10	indices	index	NOUN
ejpam-6212	736	11	of	of	ADP
ejpam-6212	736	12	alkanes	alkane	NOUN
ejpam-6212	736	13	.	.	PUNCT
ejpam-6212	737	1	journal	journal	PROPN
ejpam-6212	737	2	of	of	ADP
ejpam-6212	737	3	chemical	chemical	ADJ
ejpam-6212	737	4	information	information	NOUN
ejpam-6212	737	5	and	and	CCONJ
ejpam-6212	737	6	computer	computer	NOUN
ejpam-6212	737	7	sciences	science	NOUN
ejpam-6212	737	8	,	,	PUNCT
ejpam-6212	737	9	29:227–228	29:227–228	PROPN
ejpam-6212	737	10	,	,	PUNCT
ejpam-6212	737	11	1989	1989	NUM
ejpam-6212	737	12	.	.	PUNCT
ejpam-6212	738	1	[	[	X
ejpam-6212	738	2	20	20	NUM
ejpam-6212	738	3	]	]	PUNCT
ejpam-6212	738	4	i.	i.	PROPN
ejpam-6212	738	5	gutman	gutman	PROPN
ejpam-6212	738	6	,	,	PUNCT
ejpam-6212	738	7	w.	w.	PROPN
ejpam-6212	738	8	yan	yan	PROPN
ejpam-6212	738	9	,	,	PUNCT
ejpam-6212	738	10	y.	y.	PROPN
ejpam-6212	738	11	yeh	yeh	PROPN
ejpam-6212	738	12	,	,	PUNCT
ejpam-6212	738	13	and	and	CCONJ
ejpam-6212	738	14	b.	b.	PROPN
ejpam-6212	738	15	y.	y.	PROPN
ejpam-6212	738	16	yang	yang	PROPN
ejpam-6212	738	17	.	.	PUNCT
ejpam-6212	739	1	generalized	generalized	ADJ
ejpam-6212	739	2	wiener	wiener	NOUN
ejpam-6212	739	3	indices	index	NOUN
ejpam-6212	739	4	of	of	ADP
ejpam-6212	739	5	zigzagging	zigzag	VERB
ejpam-6212	739	6	pentachains	pentachain	NOUN
ejpam-6212	739	7	.	.	PUNCT
ejpam-6212	740	1	journal	journal	PROPN
ejpam-6212	740	2	of	of	ADP
ejpam-6212	740	3	mathematical	mathematical	ADJ
ejpam-6212	740	4	chemistry	chemistry	NOUN
ejpam-6212	740	5	,	,	PUNCT
ejpam-6212	740	6	42(2):103–117	42(2):103–117	NUM
ejpam-6212	740	7	,	,	PUNCT
ejpam-6212	740	8	2007	2007	NUM
ejpam-6212	740	9	.	.	PUNCT
ejpam-6212	741	1	[	[	X
ejpam-6212	741	2	21	21	NUM
ejpam-6212	741	3	]	]	PUNCT
ejpam-6212	741	4	m.	m.	PROPN
ejpam-6212	741	5	k.	k.	PROPN
ejpam-6212	741	6	jamil	jamil	PROPN
ejpam-6212	741	7	.	.	PUNCT
ejpam-6212	742	1	distance	distance	NOUN
ejpam-6212	742	2	-	-	PUNCT
ejpam-6212	742	3	based	base	VERB
ejpam-6212	742	4	topological	topological	ADJ
ejpam-6212	742	5	indices	index	NOUN
ejpam-6212	742	6	and	and	CCONJ
ejpam-6212	742	7	double	double	ADJ
ejpam-6212	742	8	graph	graph	NOUN
ejpam-6212	742	9	.	.	PUNCT
ejpam-6212	743	1	iranian	iranian	ADJ
ejpam-6212	743	2	journal	journal	PROPN
ejpam-6212	743	3	of	of	ADP
ejpam-6212	743	4	mathematical	mathematical	ADJ
ejpam-6212	743	5	chemistry	chemistry	NOUN
ejpam-6212	743	6	,	,	PUNCT
ejpam-6212	743	7	8(1):83–91	8(1):83–91	NUM
ejpam-6212	743	8	,	,	PUNCT
ejpam-6212	743	9	2017	2017	NUM
ejpam-6212	743	10	.	.	PUNCT
ejpam-6212	744	1	[	[	X
ejpam-6212	744	2	22	22	NUM
ejpam-6212	744	3	]	]	PUNCT
ejpam-6212	744	4	a.	a.	NOUN
ejpam-6212	744	5	a.	a.	PROPN
ejpam-6212	744	6	dobrynin	dobrynin	PROPN
ejpam-6212	744	7	.	.	PUNCT
ejpam-6212	745	1	wiener	wiener	NOUN
ejpam-6212	745	2	index	index	NOUN
ejpam-6212	745	3	of	of	ADP
ejpam-6212	745	4	uniform	uniform	ADJ
ejpam-6212	745	5	hypergraphs	hypergraph	NOUN
ejpam-6212	745	6	induced	induce	VERB
ejpam-6212	745	7	by	by	ADP
ejpam-6212	745	8	trees	tree	NOUN
ejpam-6212	745	9	.	.	PUNCT
ejpam-6212	746	1	open	open	ADJ
ejpam-6212	746	2	journal	journal	NOUN
ejpam-6212	746	3	of	of	ADP
ejpam-6212	746	4	discrete	discrete	ADJ
ejpam-6212	746	5	and	and	CCONJ
ejpam-6212	746	6	applied	apply	VERB
ejpam-6212	746	7	mathematics	mathematic	NOUN
ejpam-6212	746	8	,	,	PUNCT
ejpam-6212	746	9	2(3):19–22	2(3):19–22	NUM
ejpam-6212	746	10	,	,	PUNCT
ejpam-6212	746	11	2019	2019	NUM
ejpam-6212	746	12	.	.	PUNCT
ejpam-6212	747	1	[	[	X
ejpam-6212	747	2	23	23	NUM
ejpam-6212	747	3	]	]	PUNCT
ejpam-6212	747	4	a.	a.	NOUN
ejpam-6212	747	5	a.	a.	PROPN
ejpam-6212	747	6	dobrynin	dobrynin	PROPN
ejpam-6212	747	7	and	and	CCONJ
ejpam-6212	747	8	e.	e.	PROPN
ejpam-6212	747	9	estaji	estaji	PROPN
ejpam-6212	747	10	.	.	PROPN
ejpam-6212	748	1	wiener	wiener	PROPN
ejpam-6212	748	2	index	index	NOUN
ejpam-6212	748	3	of	of	ADP
ejpam-6212	748	4	hexagonal	hexagonal	ADJ
ejpam-6212	748	5	chains	chain	NOUN
ejpam-6212	748	6	under	under	ADP
ejpam-6212	748	7	some	some	DET
ejpam-6212	748	8	transformations	transformation	NOUN
ejpam-6212	748	9	.	.	PUNCT
ejpam-6212	749	1	open	open	ADJ
ejpam-6212	749	2	journal	journal	NOUN
ejpam-6212	749	3	of	of	ADP
ejpam-6212	749	4	discrete	discrete	ADJ
ejpam-6212	749	5	and	and	CCONJ
ejpam-6212	749	6	applied	apply	VERB
ejpam-6212	749	7	mathematics	mathematic	NOUN
ejpam-6212	749	8	,	,	PUNCT
ejpam-6212	749	9	3(1):28–36	3(1):28–36	NUM
ejpam-6212	749	10	,	,	PUNCT
ejpam-6212	749	11	2020	2020	NUM
ejpam-6212	749	12	.	.	PUNCT
ejpam-6212	750	1	[	[	X
ejpam-6212	750	2	24	24	NUM
ejpam-6212	750	3	]	]	PUNCT
ejpam-6212	750	4	k.	k.	PROPN
ejpam-6212	750	5	thulasiraman	thulasiraman	PROPN
ejpam-6212	750	6	,	,	PUNCT
ejpam-6212	750	7	s.	s.	PROPN
ejpam-6212	750	8	arumugam	arumugam	PROPN
ejpam-6212	750	9	,	,	PUNCT
ejpam-6212	750	10	and	and	CCONJ
ejpam-6212	750	11	a.	a.	NOUN
ejpam-6212	750	12	brandstädt	brandstädt	PROPN
ejpam-6212	750	13	.	.	PUNCT
ejpam-6212	751	1	handbook	handbook	NOUN
ejpam-6212	751	2	of	of	ADP
ejpam-6212	751	3	graph	graph	NOUN
ejpam-6212	751	4	theory	theory	NOUN
ejpam-6212	751	5	,	,	PUNCT
ejpam-6212	751	6	combinatorial	combinatorial	ADJ
ejpam-6212	751	7	optimization	optimization	NOUN
ejpam-6212	751	8	,	,	PUNCT
ejpam-6212	751	9	and	and	CCONJ
ejpam-6212	751	10	algorithms	algorithm	NOUN
ejpam-6212	751	11	.	.	PUNCT
ejpam-6212	752	1	chapman	chapman	NOUN
ejpam-6212	752	2	and	and	CCONJ
ejpam-6212	752	3	hall	hall	PROPN
ejpam-6212	752	4	,	,	PUNCT
ejpam-6212	752	5	new	new	PROPN
ejpam-6212	752	6	york	york	PROPN
ejpam-6212	752	7	,	,	PUNCT
ejpam-6212	752	8	2016	2016	NUM
ejpam-6212	752	9	.	.	PUNCT
ejpam-6212	753	1	[	[	X
ejpam-6212	753	2	25	25	NUM
ejpam-6212	753	3	]	]	PUNCT
ejpam-6212	753	4	chembridge	chembridge	NOUN
ejpam-6212	753	5	spirocycles	spirocycle	NOUN
ejpam-6212	753	6	library	library	NOUN
ejpam-6212	753	7	.	.	PUNCT
ejpam-6212	754	1	https://chembridge.com/	https://chembridge.com/	ADJ
ejpam-6212	754	2	targeted	target	VERB
ejpam-6212	754	3	-	-	PUNCT
ejpam-6212	754	4	and	and	CCONJ
ejpam-6212	754	5	-	-	PUNCT
ejpam-6212	754	6	specialty	specialty	NOUN
ejpam-6212	754	7	-	-	PUNCT
ejpam-6212	754	8	libraries	library	NOUN
ejpam-6212	754	9	/	/	SYM
ejpam-6212	754	10	spirocycles/	spirocycles/	NUM
ejpam-6212	754	11	,	,	PUNCT
ejpam-6212	754	12	2025	2025	NUM
ejpam-6212	754	13	.	.	PUNCT
ejpam-6212	755	1	[	[	X
ejpam-6212	755	2	26	26	NUM
ejpam-6212	755	3	]	]	X
ejpam-6212	755	4	b.	b.	PROPN
ejpam-6212	755	5	herman	herman	PROPN
ejpam-6212	755	6	.	.	PUNCT
ejpam-6212	756	1	spirobicyclohexane	spirobicyclohexane	PROPN
ejpam-6212	756	2	.	.	PUNCT
ejpam-6212	757	1	https://molview.org/	https://molview.org/	ADJ
ejpam-6212	757	2	,	,	PUNCT
ejpam-6212	757	3	2025	2025	NUM
ejpam-6212	757	4	.	.	PUNCT
ejpam-6212	758	1	[	[	X
ejpam-6212	758	2	27	27	NUM
ejpam-6212	758	3	]	]	X
ejpam-6212	758	4	chemical	chemical	NOUN
ejpam-6212	758	5	compound	compound	NOUN
ejpam-6212	758	6	database	database	NOUN
ejpam-6212	758	7	entry	entry	NOUN
ejpam-6212	758	8	for	for	ADP
ejpam-6212	758	9	spirobicyclohexane	spirobicyclohexane	NOUN
ejpam-6212	758	10	.	.	PUNCT
ejpam-6212	759	1	https://www.lookchem	https://www.lookchem	PROPN
ejpam-6212	759	2	.	.	PUNCT
ejpam-6212	759	3	com	com	NOUN
ejpam-6212	759	4	/	/	SYM
ejpam-6212	759	5	casno/180	casno/180	NOUN
ejpam-6212	759	6	-	-	PUNCT
ejpam-6212	759	7	43	43	NUM
ejpam-6212	759	8	-	-	PUNCT
ejpam-6212	759	9	8.html	8.html	NUM
ejpam-6212	759	10	,	,	PUNCT
ejpam-6212	759	11	2025	2025	NUM
ejpam-6212	759	12	.	.	PUNCT
ejpam-6212	760	1	[	[	X
ejpam-6212	760	2	28	28	NUM
ejpam-6212	760	3	]	]	X
ejpam-6212	760	4	d.	d.	PROPN
ejpam-6212	760	5	wang	wang	PROPN
ejpam-6212	760	6	and	and	CCONJ
ejpam-6212	760	7	s.	s.	PROPN
ejpam-6212	760	8	tan	tan	PROPN
ejpam-6212	760	9	.	.	PUNCT
ejpam-6212	761	1	the	the	DET
ejpam-6212	761	2	maximum	maximum	ADJ
ejpam-6212	761	3	hyper	hyper	ADJ
ejpam-6212	761	4	-	-	ADJ
ejpam-6212	761	5	wiener	wiener	NOUN
ejpam-6212	761	6	index	index	NOUN
ejpam-6212	761	7	of	of	ADP
ejpam-6212	761	8	cacti	cacti	PROPN
ejpam-6212	761	9	.	.	PUNCT
ejpam-6212	762	1	journal	journal	PROPN
ejpam-6212	762	2	of	of	ADP
ejpam-6212	762	3	applied	apply	VERB
ejpam-6212	762	4	mathematics	mathematic	NOUN
ejpam-6212	762	5	and	and	CCONJ
ejpam-6212	762	6	computing	computing	NOUN
ejpam-6212	762	7	,	,	PUNCT
ejpam-6212	762	8	47:91–102	47:91–102	NUM
ejpam-6212	762	9	,	,	PUNCT
ejpam-6212	762	10	2015	2015	NUM
ejpam-6212	762	11	.	.	PUNCT
ejpam-6212	763	1	[	[	X
ejpam-6212	763	2	29	29	NUM
ejpam-6212	763	3	]	]	PUNCT
ejpam-6212	763	4	e.	e.	PROPN
ejpam-6212	763	5	f.	f.	PROPN
ejpam-6212	763	6	moore	moore	PROPN
ejpam-6212	763	7	.	.	PUNCT
ejpam-6212	764	1	the	the	DET
ejpam-6212	764	2	shortest	short	ADJ
ejpam-6212	764	3	path	path	NOUN
ejpam-6212	764	4	through	through	ADP
ejpam-6212	764	5	a	a	DET
ejpam-6212	764	6	maze	maze	NOUN
ejpam-6212	764	7	.	.	PUNCT
ejpam-6212	765	1	in	in	ADP
ejpam-6212	765	2	proc	proc	PROPN
ejpam-6212	765	3	.	.	PUNCT
ejpam-6212	766	1	international	international	ADJ
ejpam-6212	766	2	symposium	symposium	NOUN
ejpam-6212	766	3	on	on	ADP
ejpam-6212	766	4	switching	switch	VERB
ejpam-6212	766	5	theory	theory	NOUN
ejpam-6212	766	6	,	,	PUNCT
ejpam-6212	766	7	part	part	PROPN
ejpam-6212	766	8	ii	ii	PROPN
ejpam-6212	766	9	,	,	PUNCT
ejpam-6212	766	10	pages	page	VERB
ejpam-6212	766	11	285–292	285–292	NUM
ejpam-6212	766	12	,	,	PUNCT
ejpam-6212	766	13	cambridge	cambridge	PROPN
ejpam-6212	766	14	,	,	PUNCT
ejpam-6212	766	15	ma	ma	PROPN
ejpam-6212	766	16	,	,	PUNCT
ejpam-6212	766	17	1959	1959	NUM
ejpam-6212	766	18	.	.	PUNCT
ejpam-6212	767	1	harvard	harvard	PROPN
ejpam-6212	767	2	university	university	PROPN
ejpam-6212	767	3	press	press	NOUN
ejpam-6212	767	4	.	.	PUNCT
ejpam-6212	768	1	[	[	X
ejpam-6212	768	2	30	30	NUM
ejpam-6212	768	3	]	]	X
ejpam-6212	768	4	r.	r.	PROPN
ejpam-6212	768	5	diestel	diestel	PROPN
ejpam-6212	768	6	.	.	PUNCT
ejpam-6212	769	1	graph	graph	NOUN
ejpam-6212	769	2	theory	theory	NOUN
ejpam-6212	769	3	.	.	PUNCT
ejpam-6212	770	1	springer	springer	NOUN
ejpam-6212	770	2	-	-	PUNCT
ejpam-6212	770	3	verlag	verlag	PROPN
ejpam-6212	770	4	,	,	PUNCT
ejpam-6212	770	5	berlin	berlin	PROPN
ejpam-6212	770	6	and	and	CCONJ
ejpam-6212	770	7	new	new	PROPN
ejpam-6212	770	8	york	york	PROPN
ejpam-6212	770	9	,	,	PUNCT
ejpam-6212	770	10	3rd	3rd	ADJ
ejpam-6212	770	11	edition	edition	NOUN
ejpam-6212	770	12	,	,	PUNCT
ejpam-6212	770	13	2005	2005	NUM
ejpam-6212	770	14	.	.	PUNCT
ejpam-6212	771	1	[	[	X
ejpam-6212	771	2	31	31	NUM
ejpam-6212	771	3	]	]	PUNCT
ejpam-6212	771	4	s.	s.	PROPN
ejpam-6212	771	5	skiena	skiena	PROPN
ejpam-6212	771	6	.	.	PUNCT
ejpam-6212	772	1	shortest	short	ADJ
ejpam-6212	772	2	paths	path	NOUN
ejpam-6212	772	3	,	,	PUNCT
ejpam-6212	772	4	pages	page	NOUN
ejpam-6212	772	5	225–253	225–253	NUM
ejpam-6212	772	6	.	.	PUNCT
ejpam-6212	773	1	addison	addison	PROPN
ejpam-6212	773	2	-	-	PUNCT
ejpam-6212	773	3	wesley	wesley	PROPN
ejpam-6212	773	4	,	,	PUNCT
ejpam-6212	773	5	reading	reading	NOUN
ejpam-6212	773	6	,	,	PUNCT
ejpam-6212	773	7	ma	ma	PROPN
ejpam-6212	773	8	,	,	PUNCT
ejpam-6212	773	9	1990	1990	NUM
ejpam-6212	773	10	.	.	PUNCT
ejpam-6212	774	1	[	[	X
ejpam-6212	774	2	32	32	NUM
ejpam-6212	774	3	]	]	PUNCT
ejpam-6212	774	4	r.	r.	PROPN
ejpam-6212	774	5	g.	g.	PROPN
ejpam-6212	774	6	artes	artes	PROPN
ejpam-6212	774	7	jr	jr	PROPN
ejpam-6212	774	8	.	.	PROPN
ejpam-6212	774	9	,	,	PUNCT
ejpam-6212	774	10	r.	r.	PROPN
ejpam-6212	774	11	u.	u.	PROPN
ejpam-6212	774	12	gobithaasan	gobithaasan	PROPN
ejpam-6212	774	13	,	,	PUNCT
ejpam-6212	774	14	r.	r.	PROPN
ejpam-6212	774	15	hasni	hasni	PROPN
ejpam-6212	774	16	,	,	PUNCT
ejpam-6212	774	17	and	and	CCONJ
ejpam-6212	774	18	n.	n.	PROPN
ejpam-6212	774	19	jafari	jafari	PROPN
ejpam-6212	774	20	rad	rad	PROPN
ejpam-6212	774	21	.	.	PROPN
ejpam-6212	774	22	extremal	extremal	ADJ
ejpam-6212	774	23	results	result	NOUN
ejpam-6212	774	24	and	and	CCONJ
ejpam-6212	774	25	bounds	bound	NOUN
ejpam-6212	774	26	for	for	ADP
ejpam-6212	774	27	geodetic	geodetic	ADJ
ejpam-6212	774	28	-	-	PUNCT
ejpam-6212	774	29	wiener	wiener	NOUN
ejpam-6212	774	30	index	index	NOUN
ejpam-6212	774	31	on	on	ADP
ejpam-6212	774	32	unicyclic	unicyclic	ADJ
ejpam-6212	774	33	graphs	graph	NOUN
ejpam-6212	774	34	.	.	PUNCT
ejpam-6212	775	1	preprint	preprint	NOUN
ejpam-6212	775	2	,	,	PUNCT
ejpam-6212	775	3	2025	2025	NUM
ejpam-6212	775	4	.	.	PUNCT
ejpam-6212	776	1	https://chembridge.com/targeted-and-specialty-libraries/spirocycles/	https://chembridge.com/targeted-and-specialty-libraries/spirocycles/	X
ejpam-6212	777	1	https://chembridge.com/targeted-and-specialty-libraries/spirocycles/	https://chembridge.com/targeted-and-specialty-libraries/spirocycles/	X
ejpam-6212	778	1	https://molview.org/	https://molview.org/	ADP
ejpam-6212	778	2	https://www.lookchem.com/casno/180-43-8.html	https://www.lookchem.com/casno/180-43-8.html	NOUN
ejpam-6212	778	3	https://www.lookchem.com/casno/180-43-8.html	https://www.lookchem.com/casno/180-43-8.html	PART
ejpam-6212	778	4	introduction	introduction	NOUN
ejpam-6212	778	5	spirocyclic	spirocyclic	NOUN
ejpam-6212	778	6	compounds	compound	NOUN
ejpam-6212	778	7	and	and	CCONJ
ejpam-6212	778	8	applications	application	NOUN
ejpam-6212	778	9	geodetic	geodetic	ADJ
ejpam-6212	778	10	-	-	PUNCT
ejpam-6212	778	11	wiener	wiener	NOUN
ejpam-6212	778	12	index	index	NOUN
ejpam-6212	778	13	formulation	formulation	NOUN
ejpam-6212	778	14	the	the	DET
ejpam-6212	778	15	partitioning	partition	VERB
ejpam-6212	778	16	bounds	bound	NOUN
ejpam-6212	778	17	of	of	ADP
ejpam-6212	778	18	g	g	NOUN
ejpam-6212	778	19	-	-	PUNCT
ejpam-6212	778	20	wiener	wiener	NOUN
ejpam-6212	778	21	index	index	NOUN
ejpam-6212	778	22	with	with	ADP
ejpam-6212	778	23	wiener	wiener	NOUN
ejpam-6212	778	24	index	index	NOUN
ejpam-6212	778	25	bounds	bound	NOUN
ejpam-6212	778	26	of	of	ADP
ejpam-6212	778	27	g	g	NOUN
ejpam-6212	778	28	-	-	PUNCT
ejpam-6212	778	29	wiener	wiener	NOUN
ejpam-6212	778	30	index	index	NOUN
ejpam-6212	778	31	with	with	ADP
ejpam-6212	778	32	gutman	gutman	NOUN
ejpam-6212	778	33	index	index	NOUN
ejpam-6212	778	34	bounds	bound	NOUN
ejpam-6212	778	35	of	of	ADP
ejpam-6212	778	36	g	g	NOUN
ejpam-6212	778	37	-	-	PUNCT
ejpam-6212	778	38	wiener	wiener	NOUN
ejpam-6212	778	39	index	index	NOUN
ejpam-6212	778	40	with	with	ADP
ejpam-6212	778	41	schultz	schultz	PROPN
ejpam-6212	778	42	index	index	NOUN
ejpam-6212	778	43	bounds	bound	NOUN
ejpam-6212	778	44	of	of	ADP
ejpam-6212	778	45	g	g	NOUN
ejpam-6212	778	46	-	-	PUNCT
ejpam-6212	778	47	wiener	wiener	NOUN
ejpam-6212	778	48	index	index	NOUN
ejpam-6212	778	49	with	with	ADP
ejpam-6212	778	50	hyper	hyper	ADJ
ejpam-6212	778	51	-	-	ADJ
ejpam-6212	778	52	wiener	wiener	NOUN
ejpam-6212	778	53	index	index	NOUN
ejpam-6212	778	54	bounds	bound	NOUN
ejpam-6212	778	55	of	of	ADP
ejpam-6212	778	56	g	g	NOUN
ejpam-6212	778	57	-	-	PUNCT
ejpam-6212	778	58	wiener	wiener	NOUN
ejpam-6212	778	59	index	index	NOUN
ejpam-6212	778	60	with	with	ADP
ejpam-6212	778	61	harary	harary	PROPN
ejpam-6212	778	62	index	index	NOUN
ejpam-6212	778	63	bounds	bound	NOUN
ejpam-6212	778	64	of	of	ADP
ejpam-6212	778	65	g	g	NOUN
ejpam-6212	778	66	-	-	PUNCT
ejpam-6212	778	67	wiener	wiener	NOUN
ejpam-6212	778	68	index	index	NOUN
ejpam-6212	778	69	with	with	ADP
ejpam-6212	778	70	additively	additively	ADV
ejpam-6212	778	71	weighted	weight	VERB
ejpam-6212	778	72	harary	harary	PROPN
ejpam-6212	778	73	index	index	NOUN
ejpam-6212	778	74	bounds	bound	NOUN
ejpam-6212	778	75	of	of	ADP
ejpam-6212	778	76	g	g	NOUN
ejpam-6212	778	77	-	-	PUNCT
ejpam-6212	778	78	wiener	wiener	NOUN
ejpam-6212	778	79	index	index	NOUN
ejpam-6212	778	80	with	with	ADP
ejpam-6212	778	81	multiplicatively	multiplicatively	ADV
ejpam-6212	778	82	weighted	weight	VERB
ejpam-6212	778	83	harary	harary	ADJ
ejpam-6212	778	84	index	index	NOUN
ejpam-6212	778	85	conclusion	conclusion	NOUN