id	sid	tid	token	lemma	pos
ejpam-524	1	1	14_524_germina.dvi	14_524_germina.dvi	NUM
ejpam-524	1	2	european	european	PROPN
ejpam-524	1	3	journal	journal	PROPN
ejpam-524	1	4	of	of	ADP
ejpam-524	1	5	pure	pure	ADJ
ejpam-524	1	6	and	and	CCONJ
ejpam-524	1	7	applied	apply	VERB
ejpam-524	1	8	mathematics	mathematic	NOUN
ejpam-524	1	9	vol	vol	NOUN
ejpam-524	1	10	.	.	PUNCT
ejpam-524	2	1	3	3	NUM
ejpam-524	2	2	,	,	PUNCT
ejpam-524	2	3	no	no	INTJ
ejpam-524	2	4	.	.	NOUN
ejpam-524	2	5	4	4	NUM
ejpam-524	2	6	,	,	PUNCT
ejpam-524	2	7	2010	2010	NUM
ejpam-524	2	8	,	,	PUNCT
ejpam-524	2	9	748	748	NUM
ejpam-524	2	10	-	-	SYM
ejpam-524	2	11	764	764	NUM
ejpam-524	2	12	issn	issn	PROPN
ejpam-524	2	13	1307	1307	NUM
ejpam-524	2	14	-	-	SYM
ejpam-524	2	15	5543	5543	NUM
ejpam-524	2	16	–	–	PUNCT
ejpam-524	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-524	2	18	distance	distance	NOUN
ejpam-524	2	19	neighbourhood	neighbourhood	NOUN
ejpam-524	2	20	pattern	pattern	NOUN
ejpam-524	2	21	matrices	matrice	VERB
ejpam-524	2	22	germina	germina	PROPN
ejpam-524	2	23	kizhekekunnel	kizhekekunnel	PROPN
ejpam-524	2	24	augustine1,2,∗	augustine1,2,∗	PROPN
ejpam-524	2	25	,	,	PUNCT
ejpam-524	2	26	alphy	alphy	NOUN
ejpam-524	2	27	joseph	joseph	PROPN
ejpam-524	2	28	2	2	NUM
ejpam-524	2	29	,	,	PUNCT
ejpam-524	2	30	sona	sona	PROPN
ejpam-524	2	31	jose	jose	PROPN
ejpam-524	2	32	2	2	NUM
ejpam-524	2	33	1	1	NUM
ejpam-524	2	34	p.g	p.g	PROPN
ejpam-524	2	35	.	.	PROPN
ejpam-524	2	36	&	&	CCONJ
ejpam-524	2	37	research	research	PROPN
ejpam-524	2	38	department	department	PROPN
ejpam-524	2	39	of	of	ADP
ejpam-524	2	40	mathematics	mathematics	PROPN
ejpam-524	2	41	,	,	PUNCT
ejpam-524	2	42	mary	mary	PROPN
ejpam-524	2	43	matha	matha	PROPN
ejpam-524	2	44	arts	arts	PROPN
ejpam-524	2	45	&	&	CCONJ
ejpam-524	2	46	science	science	PROPN
ejpam-524	2	47	college	college	PROPN
ejpam-524	2	48	(	(	PUNCT
ejpam-524	2	49	kannur	kannur	PROPN
ejpam-524	2	50	university	university	NOUN
ejpam-524	2	51	)	)	PUNCT
ejpam-524	2	52	,	,	PUNCT
ejpam-524	2	53	mananthavady-670645	mananthavady-670645	PROPN
ejpam-524	2	54	,	,	PUNCT
ejpam-524	2	55	india	india	PROPN
ejpam-524	2	56	2	2	NUM
ejpam-524	2	57	centre	centre	NOUN
ejpam-524	2	58	for	for	ADP
ejpam-524	2	59	mathematical	mathematical	ADJ
ejpam-524	2	60	sciences	science	NOUN
ejpam-524	2	61	,	,	PUNCT
ejpam-524	2	62	pala	pala	NOUN
ejpam-524	2	63	campus	campus	NOUN
ejpam-524	2	64	,	,	PUNCT
ejpam-524	2	65	arunapuram-686	arunapuram-686	ADJ
ejpam-524	2	66	574	574	NUM
ejpam-524	2	67	,	,	PUNCT
ejpam-524	2	68	kerala	kerala	PROPN
ejpam-524	2	69	,	,	PUNCT
ejpam-524	2	70	india	india	PROPN
ejpam-524	2	71	.	.	PUNCT
ejpam-524	3	1	abstract	abstract	PROPN
ejpam-524	3	2	.	.	PUNCT
ejpam-524	4	1	let	let	VERB
ejpam-524	4	2	g	g	PROPN
ejpam-524	4	3	=	=	SYM
ejpam-524	4	4	(	(	PUNCT
ejpam-524	4	5	v	v	NOUN
ejpam-524	4	6	,	,	PUNCT
ejpam-524	4	7	e	e	NOUN
ejpam-524	4	8	)	)	PUNCT
ejpam-524	4	9	be	be	AUX
ejpam-524	4	10	a	a	DET
ejpam-524	4	11	given	give	VERB
ejpam-524	4	12	connected	connect	VERB
ejpam-524	4	13	simple	simple	ADJ
ejpam-524	4	14	(	(	PUNCT
ejpam-524	4	15	p	p	NOUN
ejpam-524	4	16	,	,	PUNCT
ejpam-524	4	17	q)-graph	q)-graph	NOUN
ejpam-524	4	18	,	,	PUNCT
ejpam-524	4	19	and	and	CCONJ
ejpam-524	4	20	an	an	DET
ejpam-524	4	21	arbitrary	arbitrary	ADJ
ejpam-524	4	22	nonempty	nonempty	NOUN
ejpam-524	4	23	subset	subset	VERB
ejpam-524	4	24	m	m	VERB
ejpam-524	4	25	⊆	⊆	NUM
ejpam-524	4	26	v	v	NOUN
ejpam-524	4	27	(	(	PUNCT
ejpam-524	4	28	g	g	NOUN
ejpam-524	4	29	)	)	PUNCT
ejpam-524	4	30	of	of	ADP
ejpam-524	4	31	g	g	PROPN
ejpam-524	4	32	and	and	CCONJ
ejpam-524	4	33	for	for	ADP
ejpam-524	4	34	each	each	PRON
ejpam-524	4	35	v	v	NUM
ejpam-524	4	36	∈	∈	PROPN
ejpam-524	4	37	v	v	NOUN
ejpam-524	4	38	(	(	PUNCT
ejpam-524	4	39	g	g	NOUN
ejpam-524	4	40	)	)	PUNCT
ejpam-524	4	41	,	,	PUNCT
ejpam-524	4	42	define	define	VERB
ejpam-524	4	43	n	n	DET
ejpam-524	4	44	m	m	NOUN
ejpam-524	4	45	j	j	NOUN
ejpam-524	5	1	[	[	X
ejpam-524	5	2	u	u	X
ejpam-524	5	3	]	]	X
ejpam-524	5	4	=	=	SYM
ejpam-524	5	5	{	{	PUNCT
ejpam-524	5	6	v	v	NUM
ejpam-524	5	7	∈	∈	NOUN
ejpam-524	5	8	m	m	VERB
ejpam-524	5	9	:	:	PUNCT
ejpam-524	5	10	d(u	d(u	PROPN
ejpam-524	5	11	,	,	PUNCT
ejpam-524	5	12	v	v	NOUN
ejpam-524	5	13	)	)	PUNCT
ejpam-524	5	14	=	=	SYM
ejpam-524	5	15	j	j	PROPN
ejpam-524	5	16	}	}	PUNCT
ejpam-524	5	17	.	.	PUNCT
ejpam-524	6	1	clearly	clearly	ADV
ejpam-524	6	2	,	,	PUNCT
ejpam-524	6	3	then	then	ADV
ejpam-524	6	4	n	n	PROPN
ejpam-524	6	5	j[u	j[u	NOUN
ejpam-524	6	6	]	]	X
ejpam-524	6	7	=	=	SYM
ejpam-524	6	8	n	n	NUM
ejpam-524	6	9	v	v	NOUN
ejpam-524	6	10	(	(	PUNCT
ejpam-524	6	11	g	g	NOUN
ejpam-524	6	12	)	)	PUNCT
ejpam-524	6	13	j	j	NOUN
ejpam-524	7	1	[	[	X
ejpam-524	7	2	u	u	X
ejpam-524	7	3	]	]	X
ejpam-524	7	4	.	.	PUNCT
ejpam-524	8	1	b.d	b.d	PROPN
ejpam-524	8	2	.	.	PROPN
ejpam-524	8	3	acharya	acharya	PROPN
ejpam-524	9	1	[	[	X
ejpam-524	9	2	2	2	X
ejpam-524	9	3	]	]	PUNCT
ejpam-524	9	4	defined	define	VERB
ejpam-524	9	5	the	the	DET
ejpam-524	9	6	m	m	NOUN
ejpam-524	9	7	-	-	NOUN
ejpam-524	9	8	eccentricity	eccentricity	NOUN
ejpam-524	9	9	of	of	ADP
ejpam-524	9	10	u	u	NOUN
ejpam-524	9	11	as	as	ADP
ejpam-524	9	12	the	the	DET
ejpam-524	9	13	largest	large	ADJ
ejpam-524	9	14	integer	integer	NOUN
ejpam-524	9	15	for	for	ADP
ejpam-524	9	16	which	which	PRON
ejpam-524	9	17	n	n	NUM
ejpam-524	9	18	m	m	VERB
ejpam-524	9	19	j	j	NOUN
ejpam-524	10	1	[	[	X
ejpam-524	10	2	u	u	X
ejpam-524	10	3	]	]	X
ejpam-524	10	4	6=	6=	NUM
ejpam-524	10	5	;	;	PUNCT
ejpam-524	10	6	and	and	CCONJ
ejpam-524	10	7	the	the	DET
ejpam-524	10	8	p×	p×	PROPN
ejpam-524	10	9	(	(	PUNCT
ejpam-524	10	10	dg	dg	X
ejpam-524	10	11	+	+	CCONJ
ejpam-524	10	12	1	1	X
ejpam-524	10	13	)	)	PUNCT
ejpam-524	10	14	nonnegative	nonnegative	ADJ
ejpam-524	10	15	integer	integer	NOUN
ejpam-524	10	16	matrix	matrix	NOUN
ejpam-524	10	17	dm	dm	VERB
ejpam-524	10	18	g	g	NOUN
ejpam-524	10	19	=	=	PUNCT
ejpam-524	10	20	(	(	PUNCT
ejpam-524	10	21	|n	|n	NOUN
ejpam-524	10	22	m	m	PROPN
ejpam-524	10	23	j	j	NOUN
ejpam-524	11	1	[	[	X
ejpam-524	11	2	vi]|	vi]|	NOUN
ejpam-524	11	3	)	)	PUNCT
ejpam-524	11	4	,	,	PUNCT
ejpam-524	11	5	called	call	VERB
ejpam-524	11	6	the	the	DET
ejpam-524	11	7	m	m	NUM
ejpam-524	11	8	-distance	-distance	NOUN
ejpam-524	11	9	neighborhood	neighborhood	NOUN
ejpam-524	11	10	pattern	pattern	NOUN
ejpam-524	11	11	(	(	PUNCT
ejpam-524	11	12	or	or	CCONJ
ejpam-524	11	13	,	,	PUNCT
ejpam-524	11	14	m	m	PROPN
ejpam-524	11	15	-	-	PUNCT
ejpam-524	11	16	dnp	dnp	PROPN
ejpam-524	11	17	)	)	PUNCT
ejpam-524	11	18	matrix	matrix	NOUN
ejpam-524	11	19	of	of	ADP
ejpam-524	11	20	g.	g.	PROPN
ejpam-524	11	21	the	the	DET
ejpam-524	11	22	matrix	matrix	NOUN
ejpam-524	11	23	d∗m	d∗m	PUNCT
ejpam-524	11	24	g	g	NOUN
ejpam-524	11	25	is	be	AUX
ejpam-524	11	26	obtained	obtain	VERB
ejpam-524	11	27	from	from	ADP
ejpam-524	11	28	dm	dm	NUM
ejpam-524	11	29	g	g	NOUN
ejpam-524	11	30	by	by	ADP
ejpam-524	11	31	replacing	replace	VERB
ejpam-524	11	32	each	each	DET
ejpam-524	11	33	nonzero	nonzero	NOUN
ejpam-524	11	34	entry	entry	NOUN
ejpam-524	11	35	by	by	ADP
ejpam-524	11	36	1	1	NUM
ejpam-524	11	37	.	.	PUNCT
ejpam-524	12	1	clearly	clearly	ADV
ejpam-524	12	2	,	,	PUNCT
ejpam-524	12	3	fm	fm	PROPN
ejpam-524	12	4	(	(	PUNCT
ejpam-524	12	5	u	u	NOUN
ejpam-524	12	6	)	)	PUNCT
ejpam-524	12	7	=	=	SYM
ejpam-524	12	8	{	{	PUNCT
ejpam-524	12	9	j	j	NOUN
ejpam-524	12	10	:	:	PUNCT
ejpam-524	12	11	n	n	PROPN
ejpam-524	12	12	m	m	PROPN
ejpam-524	12	13	j	j	NOUN
ejpam-524	13	1	[	[	X
ejpam-524	13	2	u	u	X
ejpam-524	13	3	]	]	X
ejpam-524	13	4	6=	6=	NUM
ejpam-524	13	5	;	;	PUNCT
ejpam-524	13	6	}	}	PUNCT
ejpam-524	13	7	.	.	PUNCT
ejpam-524	14	1	hence	hence	ADV
ejpam-524	14	2	,	,	PUNCT
ejpam-524	14	3	in	in	ADP
ejpam-524	14	4	particular	particular	ADJ
ejpam-524	14	5	,	,	PUNCT
ejpam-524	14	6	if	if	SCONJ
ejpam-524	14	7	fm	fm	NOUN
ejpam-524	14	8	:	:	PUNCT
ejpam-524	14	9	u	u	PROPN
ejpam-524	14	10	7→	7→	NUM
ejpam-524	14	11	fm	fm	NOUN
ejpam-524	14	12	(	(	PUNCT
ejpam-524	14	13	u	u	NOUN
ejpam-524	14	14	)	)	PUNCT
ejpam-524	14	15	is	be	AUX
ejpam-524	14	16	an	an	DET
ejpam-524	14	17	injective	injective	ADJ
ejpam-524	14	18	function	function	NOUN
ejpam-524	14	19	,	,	PUNCT
ejpam-524	14	20	then	then	ADV
ejpam-524	14	21	the	the	DET
ejpam-524	14	22	set	set	NOUN
ejpam-524	14	23	m	m	VERB
ejpam-524	14	24	is	be	AUX
ejpam-524	14	25	a	a	DET
ejpam-524	14	26	distance	distance	NOUN
ejpam-524	14	27	-	-	PUNCT
ejpam-524	14	28	pattern	pattern	NOUN
ejpam-524	14	29	distinguishing	distinguish	VERB
ejpam-524	14	30	set	set	VERB
ejpam-524	14	31	(	(	PUNCT
ejpam-524	14	32	or	or	CCONJ
ejpam-524	14	33	,	,	PUNCT
ejpam-524	14	34	a	a	DET
ejpam-524	14	35	‘	'	PUNCT
ejpam-524	14	36	dpd	dpd	NOUN
ejpam-524	14	37	-	-	PUNCT
ejpam-524	14	38	set	set	NOUN
ejpam-524	14	39	’	'	PUNCT
ejpam-524	14	40	in	in	ADP
ejpam-524	14	41	short	short	ADJ
ejpam-524	14	42	)	)	PUNCT
ejpam-524	14	43	of	of	ADP
ejpam-524	14	44	g	g	PROPN
ejpam-524	14	45	and	and	CCONJ
ejpam-524	14	46	g	g	PROPN
ejpam-524	14	47	is	be	AUX
ejpam-524	14	48	a	a	DET
ejpam-524	14	49	dpd	dpd	NOUN
ejpam-524	14	50	-	-	PUNCT
ejpam-524	14	51	graph	graph	NOUN
ejpam-524	14	52	.	.	PUNCT
ejpam-524	15	1	if	if	SCONJ
ejpam-524	15	2	fm(u)−	fm(u)−	VERB
ejpam-524	15	3	{	{	PUNCT
ejpam-524	15	4	0	0	NUM
ejpam-524	15	5	}	}	PUNCT
ejpam-524	15	6	is	be	AUX
ejpam-524	15	7	independent	independent	ADJ
ejpam-524	15	8	of	of	ADP
ejpam-524	15	9	the	the	DET
ejpam-524	15	10	choice	choice	NOUN
ejpam-524	15	11	of	of	ADP
ejpam-524	15	12	u	u	NOUN
ejpam-524	15	13	in	in	ADP
ejpam-524	15	14	g	g	PROPN
ejpam-524	15	15	then	then	ADV
ejpam-524	15	16	m	m	PROPN
ejpam-524	15	17	is	be	AUX
ejpam-524	15	18	an	an	DET
ejpam-524	15	19	open	open	ADJ
ejpam-524	15	20	distance	distance	NOUN
ejpam-524	15	21	-	-	PUNCT
ejpam-524	15	22	pattern	pattern	NOUN
ejpam-524	15	23	uniform	uniform	NOUN
ejpam-524	15	24	(	(	PUNCT
ejpam-524	15	25	or	or	CCONJ
ejpam-524	15	26	,	,	PUNCT
ejpam-524	15	27	odpu	odpu	PROPN
ejpam-524	15	28	)	)	PUNCT
ejpam-524	15	29	set	set	NOUN
ejpam-524	15	30	of	of	ADP
ejpam-524	15	31	g.	g.	PROPN
ejpam-524	15	32	a	a	DET
ejpam-524	15	33	study	study	NOUN
ejpam-524	15	34	of	of	ADP
ejpam-524	15	35	these	these	DET
ejpam-524	15	36	sets	set	NOUN
ejpam-524	15	37	is	be	AUX
ejpam-524	15	38	expected	expect	VERB
ejpam-524	15	39	to	to	PART
ejpam-524	15	40	be	be	AUX
ejpam-524	15	41	useful	useful	ADJ
ejpam-524	15	42	in	in	ADP
ejpam-524	15	43	a	a	DET
ejpam-524	15	44	number	number	NOUN
ejpam-524	15	45	of	of	ADP
ejpam-524	15	46	areas	area	NOUN
ejpam-524	15	47	of	of	ADP
ejpam-524	15	48	practical	practical	ADJ
ejpam-524	15	49	importance	importance	NOUN
ejpam-524	15	50	such	such	ADJ
ejpam-524	15	51	as	as	ADP
ejpam-524	15	52	facility	facility	NOUN
ejpam-524	15	53	location	location	NOUN
ejpam-524	15	54	[	[	X
ejpam-524	15	55	5	5	NUM
ejpam-524	15	56	]	]	PUNCT
ejpam-524	15	57	and	and	CCONJ
ejpam-524	15	58	design	design	NOUN
ejpam-524	15	59	of	of	ADP
ejpam-524	15	60	indices	index	NOUN
ejpam-524	15	61	of	of	ADP
ejpam-524	15	62	“	"	PUNCT
ejpam-524	15	63	quantitative	quantitative	ADJ
ejpam-524	15	64	structureactivity	structureactivity	NOUN
ejpam-524	15	65	relationships	relationship	NOUN
ejpam-524	15	66	”	"	PUNCT
ejpam-524	15	67	(	(	PUNCT
ejpam-524	15	68	qsar	qsar	NOUN
ejpam-524	15	69	)	)	PUNCT
ejpam-524	15	70	in	in	ADP
ejpam-524	15	71	chemistry	chemistry	NOUN
ejpam-524	15	72	[	[	X
ejpam-524	15	73	3	3	NUM
ejpam-524	15	74	,	,	PUNCT
ejpam-524	15	75	10	10	NUM
ejpam-524	15	76	]	]	PUNCT
ejpam-524	15	77	.	.	PUNCT
ejpam-524	16	1	this	this	DET
ejpam-524	16	2	paper	paper	NOUN
ejpam-524	16	3	is	be	AUX
ejpam-524	16	4	a	a	DET
ejpam-524	16	5	study	study	NOUN
ejpam-524	16	6	of	of	ADP
ejpam-524	16	7	m	m	PROPN
ejpam-524	16	8	-dnp	-dnp	NOUN
ejpam-524	16	9	matrices	matrix	NOUN
ejpam-524	16	10	of	of	ADP
ejpam-524	16	11	a	a	DET
ejpam-524	16	12	dpd	dpd	NOUN
ejpam-524	16	13	-	-	PUNCT
ejpam-524	16	14	graph	graph	NOUN
ejpam-524	16	15	.	.	PUNCT
ejpam-524	17	1	2000	2000	NUM
ejpam-524	17	2	mathematics	mathematic	NOUN
ejpam-524	17	3	subject	subject	NOUN
ejpam-524	17	4	classifications	classification	NOUN
ejpam-524	17	5	:	:	PUNCT
ejpam-524	17	6	05c78	05c78	NUM
ejpam-524	17	7	key	key	ADJ
ejpam-524	17	8	words	word	NOUN
ejpam-524	17	9	and	and	CCONJ
ejpam-524	17	10	phrases	phrase	NOUN
ejpam-524	17	11	:	:	PUNCT
ejpam-524	17	12	distance	distance	NOUN
ejpam-524	17	13	-	-	PUNCT
ejpam-524	17	14	pattern	pattern	NOUN
ejpam-524	17	15	distinguishing	distinguish	VERB
ejpam-524	17	16	sets	set	NOUN
ejpam-524	17	17	,	,	PUNCT
ejpam-524	17	18	distance	distance	NOUN
ejpam-524	17	19	neighborhood	neighborhood	NOUN
ejpam-524	17	20	pattern	pattern	NOUN
ejpam-524	17	21	matrix	matrix	NOUN
ejpam-524	17	22	,	,	PUNCT
ejpam-524	17	23	m	m	NOUN
ejpam-524	17	24	-distance	-distance	ADJ
ejpam-524	17	25	neighborhood	neighborhood	NOUN
ejpam-524	17	26	pattern	pattern	NOUN
ejpam-524	17	27	matrix	matrix	NOUN
ejpam-524	17	28	.	.	PUNCT
ejpam-524	18	1	1	1	X
ejpam-524	18	2	.	.	X
ejpam-524	18	3	introduction	introduction	NOUN
ejpam-524	18	4	for	for	ADP
ejpam-524	18	5	all	all	DET
ejpam-524	18	6	terminology	terminology	NOUN
ejpam-524	18	7	which	which	PRON
ejpam-524	18	8	are	be	AUX
ejpam-524	18	9	not	not	PART
ejpam-524	18	10	defined	define	VERB
ejpam-524	18	11	in	in	ADP
ejpam-524	18	12	this	this	DET
ejpam-524	18	13	paper	paper	NOUN
ejpam-524	18	14	,	,	PUNCT
ejpam-524	18	15	we	we	PRON
ejpam-524	18	16	refer	refer	VERB
ejpam-524	18	17	the	the	DET
ejpam-524	18	18	reader	reader	NOUN
ejpam-524	18	19	to	to	ADP
ejpam-524	18	20	f.	f.	PROPN
ejpam-524	18	21	harary	harary	PROPN
ejpam-524	19	1	[	[	X
ejpam-524	19	2	5	5	NUM
ejpam-524	19	3	]	]	PUNCT
ejpam-524	19	4	.	.	PUNCT
ejpam-524	20	1	unless	unless	SCONJ
ejpam-524	20	2	mentioned	mention	VERB
ejpam-524	20	3	otherwise	otherwise	ADV
ejpam-524	20	4	,	,	PUNCT
ejpam-524	20	5	all	all	DET
ejpam-524	20	6	the	the	DET
ejpam-524	20	7	graphs	graph	NOUN
ejpam-524	20	8	considered	consider	VERB
ejpam-524	20	9	in	in	ADP
ejpam-524	20	10	this	this	DET
ejpam-524	20	11	paper	paper	NOUN
ejpam-524	20	12	are	be	AUX
ejpam-524	20	13	finite	finite	ADJ
ejpam-524	20	14	,	,	PUNCT
ejpam-524	20	15	simple	simple	ADJ
ejpam-524	20	16	and	and	CCONJ
ejpam-524	20	17	without	without	ADP
ejpam-524	20	18	self	self	NOUN
ejpam-524	20	19	loops	loop	NOUN
ejpam-524	20	20	.	.	PUNCT
ejpam-524	21	1	on	on	ADP
ejpam-524	21	2	26th	26th	NUM
ejpam-524	21	3	november	november	PROPN
ejpam-524	21	4	2006	2006	NUM
ejpam-524	21	5	,	,	PUNCT
ejpam-524	21	6	b.d	b.d	PROPN
ejpam-524	21	7	.	.	PROPN
ejpam-524	21	8	acharya	acharya	PROPN
ejpam-524	22	1	[	[	X
ejpam-524	22	2	2	2	NUM
ejpam-524	22	3	]	]	PUNCT
ejpam-524	22	4	conveyed	convey	VERB
ejpam-524	22	5	to	to	ADP
ejpam-524	22	6	the	the	DET
ejpam-524	22	7	first	first	ADJ
ejpam-524	22	8	author	author	NOUN
ejpam-524	22	9	the	the	DET
ejpam-524	22	10	following	follow	VERB
ejpam-524	22	11	definitions	definition	NOUN
ejpam-524	22	12	and	and	CCONJ
ejpam-524	22	13	problems	problem	NOUN
ejpam-524	22	14	for	for	ADP
ejpam-524	22	15	a	a	DET
ejpam-524	22	16	detailed	detailed	ADJ
ejpam-524	22	17	study	study	NOUN
ejpam-524	22	18	.	.	PUNCT
ejpam-524	23	1	∗corresponding	∗corresponde	VERB
ejpam-524	23	2	author	author	NOUN
ejpam-524	23	3	.	.	PUNCT
ejpam-524	24	1	email	email	NOUN
ejpam-524	24	2	addresses	address	NOUN
ejpam-524	24	3	:	:	PUNCT
ejpam-524	24	4	srgerminaka	srgerminaka	NOUN
ejpam-524	24	5	�	�	NOUN
ejpam-524	24	6	gmail	gmail	NOUN
ejpam-524	24	7	.	.	PUNCT
ejpam-524	25	1	om	om	PROPN
ejpam-524	25	2	(	(	PUNCT
ejpam-524	25	3	g.	g.	PROPN
ejpam-524	25	4	augustine	augustine	PROPN
ejpam-524	25	5	)	)	PUNCT
ejpam-524	25	6	,	,	PUNCT
ejpam-524	25	7	alphy22joseph	alphy22joseph	PROPN
ejpam-524	25	8	�	�	NOUN
ejpam-524	25	9	gmail	gmail	NOUN
ejpam-524	25	10	.	.	PUNCT
ejpam-524	26	1	om	om	PROPN
ejpam-524	26	2	(	(	PUNCT
ejpam-524	26	3	a.	a.	PROPN
ejpam-524	26	4	joseph),sonamaryjose	joseph),sonamaryjose	PROPN
ejpam-524	26	5	�	�	PROPN
ejpam-524	26	6	yahoo	yahoo	PROPN
ejpam-524	26	7	.	.	PUNCT
ejpam-524	26	8	om	om	PROPN
ejpam-524	26	9	(	(	PUNCT
ejpam-524	26	10	s.	s.	PROPN
ejpam-524	26	11	jose	jose	PROPN
ejpam-524	26	12	)	)	PUNCT
ejpam-524	26	13	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-524	27	1	748	748	NUM
ejpam-524	27	2	c	c	X
ejpam-524	27	3	©	©	PROPN
ejpam-524	27	4	2010	2010	NUM
ejpam-524	27	5	ejpam	ejpam	NOUN
ejpam-524	27	6	all	all	DET
ejpam-524	27	7	rights	right	NOUN
ejpam-524	27	8	reserved	reserve	VERB
ejpam-524	27	9	.	.	PUNCT
ejpam-524	28	1	g.	g.	PROPN
ejpam-524	28	2	augustine	augustine	PROPN
ejpam-524	28	3	,	,	PUNCT
ejpam-524	28	4	a.	a.	PROPN
ejpam-524	28	5	joseph	joseph	PROPN
ejpam-524	28	6	,	,	PUNCT
ejpam-524	28	7	s.	s.	PROPN
ejpam-524	28	8	jose	jose	PROPN
ejpam-524	28	9	/	/	SYM
ejpam-524	28	10	eur	eur	PROPN
ejpam-524	28	11	.	.	PUNCT
ejpam-524	29	1	j.	j.	PROPN
ejpam-524	29	2	pure	pure	PROPN
ejpam-524	29	3	appl	appl	PROPN
ejpam-524	29	4	.	.	PROPN
ejpam-524	29	5	math	math	PROPN
ejpam-524	29	6	,	,	PUNCT
ejpam-524	29	7	3	3	NUM
ejpam-524	29	8	(	(	PUNCT
ejpam-524	29	9	2010	2010	NUM
ejpam-524	29	10	)	)	PUNCT
ejpam-524	29	11	,	,	PUNCT
ejpam-524	29	12	748	748	NUM
ejpam-524	29	13	-	-	SYM
ejpam-524	29	14	764	764	NUM
ejpam-524	29	15	749	749	NUM
ejpam-524	29	16	definition	definition	NOUN
ejpam-524	29	17	1	1	NUM
ejpam-524	29	18	(	(	PUNCT
ejpam-524	29	19	[	[	X
ejpam-524	29	20	2	2	NUM
ejpam-524	29	21	,	,	PUNCT
ejpam-524	29	22	9	9	NUM
ejpam-524	29	23	]	]	PUNCT
ejpam-524	29	24	)	)	PUNCT
ejpam-524	29	25	.	.	PUNCT
ejpam-524	30	1	let	let	VERB
ejpam-524	30	2	g	g	PROPN
ejpam-524	30	3	=	=	SYM
ejpam-524	30	4	(	(	PUNCT
ejpam-524	30	5	v	v	NOUN
ejpam-524	30	6	,	,	PUNCT
ejpam-524	30	7	e	e	NOUN
ejpam-524	30	8	)	)	PUNCT
ejpam-524	30	9	be	be	AUX
ejpam-524	30	10	a	a	DET
ejpam-524	30	11	given	give	VERB
ejpam-524	30	12	connected	connect	VERB
ejpam-524	30	13	simple	simple	ADJ
ejpam-524	30	14	(	(	PUNCT
ejpam-524	30	15	p	p	NOUN
ejpam-524	30	16	,	,	PUNCT
ejpam-524	30	17	q)-graph	q)-graph	NOUN
ejpam-524	30	18	,	,	PUNCT
ejpam-524	30	19	m	m	VERB
ejpam-524	30	20	⊆	⊆	NUM
ejpam-524	30	21	v	v	NOUN
ejpam-524	30	22	(	(	PUNCT
ejpam-524	30	23	g	g	NOUN
ejpam-524	30	24	)	)	PUNCT
ejpam-524	30	25	and	and	CCONJ
ejpam-524	30	26	for	for	ADP
ejpam-524	30	27	each	each	DET
ejpam-524	30	28	u	u	PROPN
ejpam-524	30	29	∈	∈	PROPN
ejpam-524	30	30	v	v	NOUN
ejpam-524	30	31	(	(	PUNCT
ejpam-524	30	32	g	g	NOUN
ejpam-524	30	33	)	)	PUNCT
ejpam-524	30	34	,	,	PUNCT
ejpam-524	30	35	let	let	VERB
ejpam-524	30	36	fm	fm	PROPN
ejpam-524	30	37	(	(	PUNCT
ejpam-524	30	38	u	u	NOUN
ejpam-524	30	39	)	)	PUNCT
ejpam-524	30	40	=	=	SYM
ejpam-524	30	41	{	{	PUNCT
ejpam-524	30	42	d(u	d(u	PROPN
ejpam-524	30	43	,	,	PUNCT
ejpam-524	30	44	v	v	NOUN
ejpam-524	30	45	)	)	PUNCT
ejpam-524	30	46	:	:	PUNCT
ejpam-524	30	47	v	v	X
ejpam-524	30	48	∈	∈	PROPN
ejpam-524	30	49	m	m	AUX
ejpam-524	30	50	}	}	PUNCT
ejpam-524	30	51	be	be	AUX
ejpam-524	30	52	the	the	DET
ejpam-524	30	53	distance	distance	NOUN
ejpam-524	30	54	-	-	PUNCT
ejpam-524	30	55	pattern	pattern	NOUN
ejpam-524	30	56	of	of	ADP
ejpam-524	30	57	u	u	NOUN
ejpam-524	30	58	with	with	ADP
ejpam-524	30	59	respect	respect	NOUN
ejpam-524	30	60	to	to	ADP
ejpam-524	30	61	the	the	DET
ejpam-524	30	62	marker	marker	NOUN
ejpam-524	30	63	set	set	VERB
ejpam-524	30	64	m.	m.	NOUN
ejpam-524	30	65	if	if	SCONJ
ejpam-524	30	66	fm	fm	PROPN
ejpam-524	30	67	is	be	AUX
ejpam-524	30	68	injective	injective	ADJ
ejpam-524	30	69	then	then	ADV
ejpam-524	30	70	the	the	DET
ejpam-524	30	71	set	set	NOUN
ejpam-524	30	72	m	m	VERB
ejpam-524	30	73	is	be	AUX
ejpam-524	30	74	a	a	DET
ejpam-524	30	75	distance	distance	NOUN
ejpam-524	30	76	-	-	PUNCT
ejpam-524	30	77	pattern	pattern	NOUN
ejpam-524	30	78	distinguishing	distinguish	VERB
ejpam-524	30	79	set	set	VERB
ejpam-524	30	80	(	(	PUNCT
ejpam-524	30	81	or	or	CCONJ
ejpam-524	30	82	,	,	PUNCT
ejpam-524	30	83	a	a	DET
ejpam-524	30	84	“	"	PUNCT
ejpam-524	30	85	dpd	dpd	NOUN
ejpam-524	30	86	-	-	PUNCT
ejpam-524	30	87	set	set	NOUN
ejpam-524	30	88	”	"	PUNCT
ejpam-524	30	89	in	in	ADP
ejpam-524	30	90	short	short	ADJ
ejpam-524	30	91	)	)	PUNCT
ejpam-524	30	92	of	of	ADP
ejpam-524	30	93	g	g	PROPN
ejpam-524	30	94	and	and	CCONJ
ejpam-524	30	95	g	g	PROPN
ejpam-524	30	96	is	be	AUX
ejpam-524	30	97	a	a	DET
ejpam-524	30	98	dpd	dpd	NOUN
ejpam-524	30	99	-	-	PUNCT
ejpam-524	30	100	graph	graph	NOUN
ejpam-524	30	101	.	.	PUNCT
ejpam-524	31	1	if	if	SCONJ
ejpam-524	31	2	fm	fm	PROPN
ejpam-524	31	3	(	(	PUNCT
ejpam-524	31	4	u)−{0	u)−{0	NOUN
ejpam-524	31	5	}	}	PUNCT
ejpam-524	31	6	is	be	AUX
ejpam-524	31	7	independent	independent	ADJ
ejpam-524	31	8	of	of	ADP
ejpam-524	31	9	the	the	DET
ejpam-524	31	10	choice	choice	NOUN
ejpam-524	31	11	of	of	ADP
ejpam-524	31	12	u	u	NOUN
ejpam-524	31	13	in	in	ADP
ejpam-524	31	14	g	g	PROPN
ejpam-524	31	15	then	then	ADV
ejpam-524	31	16	m	m	PROPN
ejpam-524	31	17	is	be	AUX
ejpam-524	31	18	an	an	DET
ejpam-524	31	19	open	open	ADJ
ejpam-524	31	20	distance	distance	NOUN
ejpam-524	31	21	-	-	PUNCT
ejpam-524	31	22	pattern	pattern	NOUN
ejpam-524	31	23	uniform	uniform	NOUN
ejpam-524	31	24	(	(	PUNCT
ejpam-524	31	25	or	or	CCONJ
ejpam-524	31	26	,	,	PUNCT
ejpam-524	31	27	odpu	odpu	PROPN
ejpam-524	31	28	)	)	PUNCT
ejpam-524	31	29	set	set	NOUN
ejpam-524	31	30	of	of	ADP
ejpam-524	31	31	g	g	PROPN
ejpam-524	31	32	and	and	CCONJ
ejpam-524	31	33	g	g	PROPN
ejpam-524	31	34	is	be	AUX
ejpam-524	31	35	called	call	VERB
ejpam-524	31	36	an	an	DET
ejpam-524	31	37	odpu	odpu	NOUN
ejpam-524	31	38	-	-	PUNCT
ejpam-524	31	39	graph	graph	NOUN
ejpam-524	31	40	.	.	PUNCT
ejpam-524	32	1	the	the	DET
ejpam-524	32	2	minimum	minimum	ADJ
ejpam-524	32	3	cardinality	cardinality	NOUN
ejpam-524	32	4	of	of	ADP
ejpam-524	32	5	a	a	DET
ejpam-524	32	6	dpd	dpd	NOUN
ejpam-524	32	7	-	-	PUNCT
ejpam-524	32	8	set	set	VERB
ejpam-524	32	9	(	(	PUNCT
ejpam-524	32	10	odpu	odpu	NOUN
ejpam-524	32	11	-	-	PUNCT
ejpam-524	32	12	set	set	NOUN
ejpam-524	32	13	)	)	PUNCT
ejpam-524	32	14	in	in	ADP
ejpam-524	32	15	g	g	PROPN
ejpam-524	32	16	,	,	PUNCT
ejpam-524	32	17	if	if	SCONJ
ejpam-524	32	18	it	it	PRON
ejpam-524	32	19	exists	exist	VERB
ejpam-524	32	20	,	,	PUNCT
ejpam-524	32	21	is	be	AUX
ejpam-524	32	22	the	the	DET
ejpam-524	32	23	dpd	dpd	PROPN
ejpam-524	32	24	-	-	PUNCT
ejpam-524	32	25	number(odpunumber	number(odpunumber	PROPN
ejpam-524	32	26	)	)	PUNCT
ejpam-524	32	27	of	of	ADP
ejpam-524	32	28	g	g	PROPN
ejpam-524	32	29	and	and	CCONJ
ejpam-524	32	30	it	it	PRON
ejpam-524	32	31	is	be	AUX
ejpam-524	32	32	denoted	denote	VERB
ejpam-524	32	33	by	by	ADP
ejpam-524	32	34	̺(g	̺(g	NOUN
ejpam-524	32	35	)	)	PUNCT
ejpam-524	32	36	.	.	PUNCT
ejpam-524	33	1	b.d	b.d	PROPN
ejpam-524	33	2	.	.	PROPN
ejpam-524	33	3	acharya	acharya	PROPN
ejpam-524	34	1	[	[	X
ejpam-524	34	2	2	2	NUM
ejpam-524	34	3	]	]	PUNCT
ejpam-524	34	4	,	,	PUNCT
ejpam-524	34	5	raised	raise	VERB
ejpam-524	34	6	the	the	DET
ejpam-524	34	7	following	follow	VERB
ejpam-524	34	8	problems	problem	NOUN
ejpam-524	34	9	during	during	ADP
ejpam-524	34	10	the	the	DET
ejpam-524	34	11	conversation	conversation	NOUN
ejpam-524	34	12	.	.	PUNCT
ejpam-524	35	1	problem	problem	NOUN
ejpam-524	35	2	1	1	NUM
ejpam-524	35	3	.	.	PUNCT
ejpam-524	36	1	for	for	ADP
ejpam-524	36	2	what	what	PRON
ejpam-524	36	3	structural	structural	ADJ
ejpam-524	36	4	properties	property	NOUN
ejpam-524	36	5	of	of	ADP
ejpam-524	36	6	the	the	DET
ejpam-524	36	7	graph	graph	NOUN
ejpam-524	36	8	g	g	NOUN
ejpam-524	36	9	,	,	PUNCT
ejpam-524	36	10	the	the	DET
ejpam-524	36	11	function	function	NOUN
ejpam-524	36	12	fm	fm	PROPN
ejpam-524	36	13	is	be	AUX
ejpam-524	36	14	injective	injective	ADJ
ejpam-524	36	15	?	?	PUNCT
ejpam-524	37	1	problem	problem	NOUN
ejpam-524	37	2	2	2	NUM
ejpam-524	37	3	.	.	X
ejpam-524	37	4	characterize	characterize	VERB
ejpam-524	37	5	dpd	dpd	NOUN
ejpam-524	37	6	-	-	PUNCT
ejpam-524	37	7	graphs	graph	NOUN
ejpam-524	37	8	having	have	VERB
ejpam-524	37	9	the	the	DET
ejpam-524	37	10	given	give	VERB
ejpam-524	37	11	dpd	dpd	NOUN
ejpam-524	37	12	-	-	PUNCT
ejpam-524	37	13	number	number	NOUN
ejpam-524	37	14	.	.	PUNCT
ejpam-524	38	1	problem	problem	NOUN
ejpam-524	38	2	3	3	NUM
ejpam-524	38	3	.	.	NOUN
ejpam-524	38	4	which	which	PRON
ejpam-524	38	5	graphs	graph	VERB
ejpam-524	38	6	g	g	PROPN
ejpam-524	38	7	have	have	VERB
ejpam-524	38	8	the	the	DET
ejpam-524	38	9	property	property	NOUN
ejpam-524	38	10	that	that	PRON
ejpam-524	38	11	every	every	DET
ejpam-524	38	12	k	k	NOUN
ejpam-524	38	13	-	-	NOUN
ejpam-524	38	14	subset	subset	NOUN
ejpam-524	38	15	of	of	ADP
ejpam-524	38	16	v	v	NOUN
ejpam-524	38	17	(	(	PUNCT
ejpam-524	38	18	g	g	NOUN
ejpam-524	38	19	)	)	PUNCT
ejpam-524	38	20	is	be	AUX
ejpam-524	38	21	a	a	DET
ejpam-524	38	22	dpd	dpd	NOUN
ejpam-524	38	23	-	-	PUNCT
ejpam-524	38	24	set	set	NOUN
ejpam-524	38	25	of	of	ADP
ejpam-524	38	26	g.	g.	PROPN
ejpam-524	38	27	solve	solve	VERB
ejpam-524	38	28	this	this	DET
ejpam-524	38	29	problem	problem	NOUN
ejpam-524	38	30	in	in	ADP
ejpam-524	38	31	particular	particular	ADJ
ejpam-524	38	32	when	when	SCONJ
ejpam-524	38	33	k	k	PROPN
ejpam-524	38	34	=	=	PROPN
ejpam-524	38	35	̺(g	̺(g	NOUN
ejpam-524	38	36	)	)	PUNCT
ejpam-524	38	37	?	?	PUNCT
ejpam-524	39	1	problem	problem	NOUN
ejpam-524	39	2	4	4	NUM
ejpam-524	39	3	.	.	NOUN
ejpam-524	39	4	which	which	PRON
ejpam-524	39	5	graphs	graph	VERB
ejpam-524	39	6	g	g	PROPN
ejpam-524	39	7	have	have	VERB
ejpam-524	39	8	exactly	exactly	ADV
ejpam-524	39	9	one	one	NUM
ejpam-524	39	10	̺(g)-set	̺(g)-set	NUM
ejpam-524	39	11	?	?	PUNCT
ejpam-524	40	1	given	give	VERB
ejpam-524	40	2	a	a	DET
ejpam-524	40	3	positive	positive	ADJ
ejpam-524	40	4	integer	integer	NOUN
ejpam-524	40	5	n	n	CCONJ
ejpam-524	40	6	,	,	PUNCT
ejpam-524	40	7	an	an	DET
ejpam-524	40	8	n	n	CCONJ
ejpam-524	40	9	-	-	PUNCT
ejpam-524	40	10	distance	distance	NOUN
ejpam-524	40	11	coloring	coloring	NOUN
ejpam-524	40	12	of	of	ADP
ejpam-524	40	13	a	a	DET
ejpam-524	40	14	graph	graph	NOUN
ejpam-524	40	15	g	g	NOUN
ejpam-524	40	16	is	be	AUX
ejpam-524	40	17	a	a	DET
ejpam-524	40	18	coloring	coloring	NOUN
ejpam-524	40	19	of	of	ADP
ejpam-524	40	20	the	the	DET
ejpam-524	40	21	vertices	vertex	NOUN
ejpam-524	40	22	of	of	ADP
ejpam-524	40	23	g	g	NOUN
ejpam-524	40	24	in	in	ADP
ejpam-524	40	25	such	such	DET
ejpam-524	40	26	a	a	DET
ejpam-524	40	27	way	way	NOUN
ejpam-524	40	28	that	that	PRON
ejpam-524	40	29	no	no	DET
ejpam-524	40	30	two	two	NUM
ejpam-524	40	31	vertices	vertex	NOUN
ejpam-524	40	32	at	at	ADP
ejpam-524	40	33	distance	distance	NOUN
ejpam-524	40	34	n	n	NOUN
ejpam-524	40	35	are	be	AUX
ejpam-524	40	36	colored	color	VERB
ejpam-524	40	37	by	by	ADP
ejpam-524	40	38	the	the	DET
ejpam-524	40	39	same	same	ADJ
ejpam-524	40	40	color	color	NOUN
ejpam-524	40	41	;	;	PUNCT
ejpam-524	40	42	g	g	PROPN
ejpam-524	40	43	is	be	AUX
ejpam-524	40	44	n	n	CCONJ
ejpam-524	40	45	-	-	PUNCT
ejpam-524	40	46	distance	distance	NOUN
ejpam-524	40	47	colorable	colorable	ADJ
ejpam-524	40	48	if	if	SCONJ
ejpam-524	40	49	it	it	PRON
ejpam-524	40	50	indeed	indeed	ADV
ejpam-524	40	51	admits	admit	VERB
ejpam-524	40	52	such	such	DET
ejpam-524	40	53	a	a	DET
ejpam-524	40	54	coloring	coloring	NOUN
ejpam-524	40	55	(	(	PUNCT
ejpam-524	40	56	e.g.	e.g.	ADV
ejpam-524	40	57	,	,	PUNCT
ejpam-524	40	58	see	see	VERB
ejpam-524	40	59	sampathkumar	sampathkumar	PROPN
ejpam-524	40	60	,	,	PUNCT
ejpam-524	40	61	1977	1977	NUM
ejpam-524	40	62	[	[	X
ejpam-524	40	63	13	13	NUM
ejpam-524	40	64	]	]	PUNCT
ejpam-524	40	65	,	,	PUNCT
ejpam-524	40	66	1988	1988	NUM
ejpam-524	40	67	[	[	X
ejpam-524	40	68	14	14	NUM
ejpam-524	40	69	]	]	PUNCT
ejpam-524	40	70	)	)	PUNCT
ejpam-524	40	71	.	.	PUNCT
ejpam-524	41	1	clearly	clearly	ADV
ejpam-524	41	2	,	,	PUNCT
ejpam-524	41	3	if	if	SCONJ
ejpam-524	41	4	g	g	PROPN
ejpam-524	41	5	admits	admit	VERB
ejpam-524	41	6	an	an	DET
ejpam-524	41	7	n	n	NUM
ejpam-524	41	8	-	-	PUNCT
ejpam-524	41	9	distance	distance	NOUN
ejpam-524	41	10	coloring	coloring	NOUN
ejpam-524	41	11	then	then	ADV
ejpam-524	41	12	1≤	1≤	NUM
ejpam-524	41	13	n≤	n≤	PRON
ejpam-524	41	14	diam(g	diam(g	NOUN
ejpam-524	41	15	)	)	PUNCT
ejpam-524	41	16	.	.	PUNCT
ejpam-524	42	1	problem	problem	NOUN
ejpam-524	42	2	5	5	NUM
ejpam-524	42	3	.	.	PUNCT
ejpam-524	43	1	for	for	ADP
ejpam-524	43	2	which	which	PRON
ejpam-524	43	3	values	value	NOUN
ejpam-524	43	4	of	of	ADP
ejpam-524	43	5	n	n	PRON
ejpam-524	43	6	it	it	PRON
ejpam-524	43	7	is	be	AUX
ejpam-524	43	8	possible	possible	ADJ
ejpam-524	43	9	to	to	PART
ejpam-524	43	10	extract	extract	VERB
ejpam-524	43	11	a	a	DET
ejpam-524	43	12	proper	proper	ADJ
ejpam-524	43	13	n	n	CCONJ
ejpam-524	43	14	-	-	PUNCT
ejpam-524	43	15	distance	distance	NOUN
ejpam-524	43	16	coloring	coloring	NOUN
ejpam-524	43	17	of	of	ADP
ejpam-524	43	18	a	a	DET
ejpam-524	43	19	given	give	VERB
ejpam-524	43	20	graph	graph	NOUN
ejpam-524	43	21	g	g	NOUN
ejpam-524	43	22	using	use	VERB
ejpam-524	43	23	a	a	DET
ejpam-524	43	24	distance	distance	NOUN
ejpam-524	43	25	-	-	PUNCT
ejpam-524	43	26	pattern	pattern	NOUN
ejpam-524	43	27	function	function	NOUN
ejpam-524	43	28	as	as	ADP
ejpam-524	43	29	a	a	DET
ejpam-524	43	30	listing	listing	NOUN
ejpam-524	43	31	of	of	ADP
ejpam-524	43	32	colors	color	NOUN
ejpam-524	43	33	for	for	ADP
ejpam-524	43	34	the	the	DET
ejpam-524	43	35	vertices	vertex	NOUN
ejpam-524	43	36	?	?	PUNCT
ejpam-524	44	1	problem	problem	NOUN
ejpam-524	44	2	6	6	NUM
ejpam-524	44	3	.	.	PUNCT
ejpam-524	45	1	given	give	VERB
ejpam-524	45	2	any	any	DET
ejpam-524	45	3	positive	positive	ADJ
ejpam-524	45	4	integer	integer	NOUN
ejpam-524	45	5	k	k	PROPN
ejpam-524	45	6	,	,	PUNCT
ejpam-524	45	7	does	do	AUX
ejpam-524	45	8	there	there	PRON
ejpam-524	45	9	exist	exist	VERB
ejpam-524	45	10	a	a	DET
ejpam-524	45	11	graph	graph	NOUN
ejpam-524	45	12	g	g	NOUN
ejpam-524	45	13	with	with	ADP
ejpam-524	45	14	̺(g	̺(g	NOUN
ejpam-524	45	15	)	)	PUNCT
ejpam-524	46	1	=	=	PUNCT
ejpam-524	47	1	k	k	X
ejpam-524	47	2	?	?	PUNCT
ejpam-524	48	1	some	some	PRON
ejpam-524	48	2	of	of	ADP
ejpam-524	48	3	the	the	DET
ejpam-524	48	4	above	above	ADJ
ejpam-524	48	5	mentioned	mention	VERB
ejpam-524	48	6	problems	problem	NOUN
ejpam-524	48	7	studied	study	VERB
ejpam-524	48	8	are	be	AUX
ejpam-524	48	9	reported	report	VERB
ejpam-524	48	10	in	in	ADP
ejpam-524	48	11	the	the	DET
ejpam-524	48	12	technical	technical	ADJ
ejpam-524	48	13	report	report	NOUN
ejpam-524	48	14	[	[	X
ejpam-524	48	15	9	9	NUM
ejpam-524	48	16	]	]	PUNCT
ejpam-524	48	17	.	.	PUNCT
ejpam-524	49	1	b.d	b.d	PROPN
ejpam-524	49	2	.	.	PROPN
ejpam-524	49	3	acharya	acharya	PROPN
ejpam-524	49	4	,	,	PUNCT
ejpam-524	49	5	while	while	SCONJ
ejpam-524	49	6	sharing	share	VERB
ejpam-524	49	7	his	his	PRON
ejpam-524	49	8	many	many	ADJ
ejpam-524	49	9	incisive	incisive	ADJ
ejpam-524	49	10	thoughts	thought	NOUN
ejpam-524	49	11	,	,	PUNCT
ejpam-524	49	12	during	during	ADP
ejpam-524	49	13	the	the	DET
ejpam-524	49	14	discussion	discussion	NOUN
ejpam-524	49	15	,	,	PUNCT
ejpam-524	49	16	in	in	ADP
ejpam-524	49	17	june	june	PROPN
ejpam-524	49	18	2008	2008	NUM
ejpam-524	49	19	,	,	PUNCT
ejpam-524	49	20	introduced	introduce	VERB
ejpam-524	49	21	a	a	DET
ejpam-524	49	22	new	new	ADJ
ejpam-524	49	23	approach	approach	NOUN
ejpam-524	49	24	namely	namely	ADV
ejpam-524	49	25	,	,	PUNCT
ejpam-524	49	26	distance	distance	NOUN
ejpam-524	49	27	neighborhood	neighborhood	NOUN
ejpam-524	49	28	pattern	pattern	NOUN
ejpam-524	49	29	matrices	matrix	NOUN
ejpam-524	49	30	(	(	PUNCT
ejpam-524	49	31	dnp	dnp	NOUN
ejpam-524	49	32	-	-	PUNCT
ejpam-524	49	33	matrices	matrix	NOUN
ejpam-524	49	34	)	)	PUNCT
ejpam-524	49	35	,	,	PUNCT
ejpam-524	49	36	to	to	PART
ejpam-524	49	37	study	study	VERB
ejpam-524	49	38	dpd	dpd	NOUN
ejpam-524	49	39	-	-	PUNCT
ejpam-524	49	40	graphs	graph	NOUN
ejpam-524	49	41	.	.	PUNCT
ejpam-524	50	1	in	in	ADP
ejpam-524	50	2	this	this	DET
ejpam-524	50	3	paper	paper	NOUN
ejpam-524	50	4	we	we	PRON
ejpam-524	50	5	initiate	initiate	VERB
ejpam-524	50	6	a	a	DET
ejpam-524	50	7	study	study	NOUN
ejpam-524	50	8	of	of	ADP
ejpam-524	50	9	dnp	dnp	PROPN
ejpam-524	50	10	-	-	PUNCT
ejpam-524	50	11	matrices	matrix	NOUN
ejpam-524	50	12	of	of	ADP
ejpam-524	50	13	a	a	DET
ejpam-524	50	14	graph	graph	NOUN
ejpam-524	50	15	.	.	PUNCT
ejpam-524	51	1	for	for	ADP
ejpam-524	51	2	an	an	DET
ejpam-524	51	3	arbitrarily	arbitrarily	ADV
ejpam-524	51	4	fixed	fix	VERB
ejpam-524	51	5	vertex	vertex	NOUN
ejpam-524	51	6	u	u	NOUN
ejpam-524	51	7	in	in	ADP
ejpam-524	51	8	g	g	PROPN
ejpam-524	51	9	and	and	CCONJ
ejpam-524	51	10	for	for	ADP
ejpam-524	51	11	any	any	DET
ejpam-524	51	12	nonnegative	nonnegative	ADJ
ejpam-524	51	13	integer	integer	PROPN
ejpam-524	51	14	j	j	PROPN
ejpam-524	51	15	,	,	PUNCT
ejpam-524	51	16	we	we	PRON
ejpam-524	51	17	let	let	VERB
ejpam-524	51	18	n	n	PRON
ejpam-524	51	19	j[u	j[u	X
ejpam-524	51	20	]	]	X
ejpam-524	52	1	=	=	X
ejpam-524	52	2	{	{	PUNCT
ejpam-524	52	3	v	v	NUM
ejpam-524	52	4	∈	∈	NOUN
ejpam-524	52	5	v	v	NOUN
ejpam-524	52	6	(	(	PUNCT
ejpam-524	52	7	g	g	NOUN
ejpam-524	52	8	)	)	PUNCT
ejpam-524	52	9	:	:	PUNCT
ejpam-524	53	1	d(u	d(u	PROPN
ejpam-524	53	2	,	,	PUNCT
ejpam-524	53	3	v	v	NOUN
ejpam-524	53	4	)	)	PUNCT
ejpam-524	53	5	=	=	SYM
ejpam-524	53	6	j	j	PROPN
ejpam-524	53	7	}	}	PUNCT
ejpam-524	53	8	.	.	PUNCT
ejpam-524	54	1	clearly	clearly	ADV
ejpam-524	54	2	,	,	PUNCT
ejpam-524	54	3	n0[u	n0[u	NOUN
ejpam-524	54	4	]	]	PUNCT
ejpam-524	54	5	=	=	PUNCT
ejpam-524	54	6	{	{	PUNCT
ejpam-524	54	7	u	u	NOUN
ejpam-524	54	8	}	}	PUNCT
ejpam-524	54	9	,	,	PUNCT
ejpam-524	54	10	∀	∀	X
ejpam-524	54	11	u	u	NOUN
ejpam-524	54	12	∈	∈	PROPN
ejpam-524	54	13	v	v	NOUN
ejpam-524	54	14	(	(	PUNCT
ejpam-524	54	15	g	g	NOUN
ejpam-524	54	16	)	)	PUNCT
ejpam-524	54	17	and	and	CCONJ
ejpam-524	54	18	n	n	PRON
ejpam-524	54	19	j[u	j[u	NOUN
ejpam-524	54	20	]	]	X
ejpam-524	54	21	=	=	SYM
ejpam-524	54	22	v	v	X
ejpam-524	54	23	(	(	PUNCT
ejpam-524	54	24	g	g	NOUN
ejpam-524	54	25	)	)	PUNCT
ejpam-524	54	26	−	−	PROPN
ejpam-524	54	27	v	v	X
ejpam-524	54	28	(	(	PUNCT
ejpam-524	54	29	cu	cu	PROPN
ejpam-524	54	30	)	)	PUNCT
ejpam-524	54	31	whenever	whenever	SCONJ
ejpam-524	54	32	j	j	PROPN
ejpam-524	54	33	exceeds	exceed	VERB
ejpam-524	54	34	the	the	DET
ejpam-524	54	35	eccentricity	eccentricity	NOUN
ejpam-524	54	36	ǫ(u	ǫ(u	PROPN
ejpam-524	54	37	)	)	PUNCT
ejpam-524	54	38	of	of	ADP
ejpam-524	54	39	u	u	NOUN
ejpam-524	54	40	in	in	ADP
ejpam-524	54	41	the	the	DET
ejpam-524	54	42	component	component	NOUN
ejpam-524	54	43	cu	cu	PROPN
ejpam-524	54	44	to	to	PART
ejpam-524	54	45	which	which	PRON
ejpam-524	54	46	u	u	NOUN
ejpam-524	54	47	belongs	belong	VERB
ejpam-524	54	48	.	.	PUNCT
ejpam-524	55	1	thus	thus	ADV
ejpam-524	55	2	,	,	PUNCT
ejpam-524	55	3	if	if	SCONJ
ejpam-524	55	4	g	g	PROPN
ejpam-524	55	5	is	be	AUX
ejpam-524	55	6	connected	connect	VERB
ejpam-524	55	7	then	then	ADV
ejpam-524	55	8	,	,	PUNCT
ejpam-524	55	9	n	n	PROPN
ejpam-524	55	10	j[u	j[u	NOUN
ejpam-524	55	11	]	]	X
ejpam-524	56	1	=	=	X
ejpam-524	56	2	;	;	PUNCT
ejpam-524	56	3	if	if	SCONJ
ejpam-524	56	4	and	and	CCONJ
ejpam-524	56	5	only	only	ADV
ejpam-524	56	6	if	if	SCONJ
ejpam-524	56	7	j	j	PROPN
ejpam-524	56	8	>	>	X
ejpam-524	56	9	ǫ(u	ǫ(u	PROPN
ejpam-524	56	10	)	)	PUNCT
ejpam-524	56	11	.	.	PUNCT
ejpam-524	57	1	if	if	SCONJ
ejpam-524	57	2	g	g	PROPN
ejpam-524	57	3	is	be	AUX
ejpam-524	57	4	a	a	DET
ejpam-524	57	5	connected	connected	ADJ
ejpam-524	57	6	graph	graph	NOUN
ejpam-524	57	7	then	then	ADV
ejpam-524	57	8	the	the	DET
ejpam-524	57	9	vectors	vector	NOUN
ejpam-524	57	10	u	u	NOUN
ejpam-524	57	11	=	=	X
ejpam-524	57	12	(	(	PUNCT
ejpam-524	57	13	|n0[u]|	|n0[u]|	X
ejpam-524	57	14	,	,	PUNCT
ejpam-524	57	15	|n1[u]|	|n1[u]|	PRON
ejpam-524	57	16	,	,	PUNCT
ejpam-524	57	17	|n2[u]|	|n2[u]|	NUM
ejpam-524	57	18	,	,	PUNCT
ejpam-524	57	19	.	.	PUNCT
ejpam-524	57	20	.	.	PUNCT
ejpam-524	57	21	.	.	PUNCT
ejpam-524	58	1	,	,	PUNCT
ejpam-524	58	2	|nǫ(u)[u]|	|nǫ(u)[u]|	X
ejpam-524	58	3	)	)	PUNCT
ejpam-524	58	4	associated	associate	VERB
ejpam-524	58	5	with	with	ADP
ejpam-524	58	6	u	u	PROPN
ejpam-524	58	7	∈	∈	PROPN
ejpam-524	58	8	v	v	ADP
ejpam-524	58	9	(	(	PUNCT
ejpam-524	58	10	g	g	NOUN
ejpam-524	58	11	)	)	PUNCT
ejpam-524	58	12	can	can	AUX
ejpam-524	58	13	be	be	AUX
ejpam-524	58	14	arranged	arrange	VERB
ejpam-524	58	15	as	as	ADP
ejpam-524	58	16	a	a	DET
ejpam-524	58	17	p×	p×	NOUN
ejpam-524	58	18	(	(	PUNCT
ejpam-524	58	19	dg	dg	X
ejpam-524	58	20	+	+	NOUN
ejpam-524	58	21	1	1	X
ejpam-524	58	22	)	)	PUNCT
ejpam-524	58	23	nonnegative	nonnegative	ADJ
ejpam-524	58	24	integer	integer	NOUN
ejpam-524	58	25	matrix	matrix	NOUN
ejpam-524	58	26	dg	dg	NOUN
ejpam-524	58	27	given	give	VERB
ejpam-524	58	28	by	by	ADP
ejpam-524	58	29			NOUN
ejpam-524	58	30			NOUN
ejpam-524	58	31			NOUN
ejpam-524	58	32			NOUN
ejpam-524	58	33			NOUN
ejpam-524	58	34			NOUN
ejpam-524	58	35			NOUN
ejpam-524	58	36	1	1	NUM
ejpam-524	58	37	|n1[v1]|	|n1[v1]|	NUM
ejpam-524	58	38	|n2[v1]|	|n2[v1]|	PUNCT
ejpam-524	58	39	.	.	PUNCT
ejpam-524	58	40	.	.	PUNCT
ejpam-524	58	41	.	.	PUNCT
ejpam-524	59	1	|nǫ(v1	|nǫ(v1	X
ejpam-524	59	2	)	)	PUNCT
ejpam-524	60	1	[	[	X
ejpam-524	60	2	v1]|	v1]|	NOUN
ejpam-524	60	3	0	0	NUM
ejpam-524	60	4	0	0	NUM
ejpam-524	60	5	0	0	NUM
ejpam-524	60	6	1	1	NUM
ejpam-524	60	7	|n1[v2]|	|n1[v2]|	PROPN
ejpam-524	60	8	|n2[v2]|	|n2[v2]|	PROPN
ejpam-524	60	9	.	.	PUNCT
ejpam-524	60	10	.	.	PUNCT
ejpam-524	60	11	.	.	PUNCT
ejpam-524	60	12	.	.	PUNCT
ejpam-524	60	13	.	.	PUNCT
ejpam-524	60	14	.	.	PUNCT
ejpam-524	61	1	|nǫ(v2	|nǫ(v2	X
ejpam-524	61	2	)	)	PUNCT
ejpam-524	62	1	[	[	X
ejpam-524	62	2	v2]|	v2]|	PROPN
ejpam-524	62	3	0	0	NUM
ejpam-524	62	4	0	0	NUM
ejpam-524	62	5	.	.	PUNCT
ejpam-524	62	6	.	.	PUNCT
ejpam-524	62	7	.	.	PUNCT
ejpam-524	62	8	.	.	PUNCT
ejpam-524	62	9	.	.	PUNCT
ejpam-524	62	10	.	.	PUNCT
ejpam-524	62	11	.	.	PUNCT
ejpam-524	62	12	.	.	PUNCT
ejpam-524	62	13	.	.	PUNCT
ejpam-524	62	14	.	.	PUNCT
ejpam-524	62	15	.	.	PUNCT
ejpam-524	62	16	.	.	PUNCT
ejpam-524	62	17	.	.	PUNCT
ejpam-524	62	18	.	.	PUNCT
ejpam-524	62	19	.	.	PUNCT
ejpam-524	62	20	.	.	PUNCT
ejpam-524	62	21	.	.	PUNCT
ejpam-524	62	22	.	.	PUNCT
ejpam-524	62	23	.	.	PUNCT
ejpam-524	62	24	.	.	PUNCT
ejpam-524	62	25	.	.	PUNCT
ejpam-524	62	26	.	.	PUNCT
ejpam-524	62	27	.	.	PUNCT
ejpam-524	62	28	.	.	PUNCT
ejpam-524	62	29	.	.	PUNCT
ejpam-524	62	30	.	.	PUNCT
ejpam-524	62	31	.	.	PUNCT
ejpam-524	62	32	.	.	PUNCT
ejpam-524	62	33	.	.	PUNCT
ejpam-524	62	34	.	.	PUNCT
ejpam-524	62	35	.	.	PUNCT
ejpam-524	62	36	.	.	PUNCT
ejpam-524	62	37	.	.	PUNCT
ejpam-524	62	38	.	.	PUNCT
ejpam-524	62	39	.	.	PUNCT
ejpam-524	62	40	.	.	PUNCT
ejpam-524	62	41	.	.	PUNCT
ejpam-524	62	42	.	.	PUNCT
ejpam-524	62	43	.	.	PUNCT
ejpam-524	62	44	.	.	PUNCT
ejpam-524	62	45	.	.	PUNCT
ejpam-524	62	46	.	.	PUNCT
ejpam-524	62	47	.	.	PUNCT
ejpam-524	62	48	.	.	PUNCT
ejpam-524	62	49	.	.	PUNCT
ejpam-524	62	50	.	.	PUNCT
ejpam-524	62	51	.	.	PUNCT
ejpam-524	63	1	.	.	PUNCT
ejpam-524	64	1	1	1	NUM
ejpam-524	64	2	|n1[vp]|	|n1[vp]|	NOUN
ejpam-524	64	3	|n2[vp]|	|n2[vp]|	NOUN
ejpam-524	64	4	.	.	PUNCT
ejpam-524	64	5	.	.	PUNCT
ejpam-524	64	6	.	.	PUNCT
ejpam-524	64	7	.	.	PUNCT
ejpam-524	64	8	.	.	PUNCT
ejpam-524	64	9	.	.	PUNCT
ejpam-524	64	10	.	.	PUNCT
ejpam-524	64	11	.	.	PUNCT
ejpam-524	64	12	.	.	PUNCT
ejpam-524	64	13	.	.	PUNCT
ejpam-524	64	14	.	.	PUNCT
ejpam-524	64	15	.	.	PUNCT
ejpam-524	65	1	|nǫ(vp	|nǫ(vp	NOUN
ejpam-524	65	2	)	)	PUNCT
ejpam-524	66	1	[	[	X
ejpam-524	66	2	vp]|	vp]|	NOUN
ejpam-524	66	3			NOUN
ejpam-524	66	4			NOUN
ejpam-524	66	5			VERB
ejpam-524	66	6			NOUN
ejpam-524	66	7			NOUN
ejpam-524	66	8			NOUN
ejpam-524	66	9			PUNCT
ejpam-524	67	1	where	where	SCONJ
ejpam-524	67	2	dg	dg	PROPN
ejpam-524	67	3	denotes	denote	VERB
ejpam-524	67	4	the	the	DET
ejpam-524	67	5	diameter	diameter	NOUN
ejpam-524	67	6	of	of	ADP
ejpam-524	67	7	g	g	PROPN
ejpam-524	67	8	;	;	PUNCT
ejpam-524	67	9	we	we	PRON
ejpam-524	67	10	call	call	VERB
ejpam-524	67	11	dg	dg	PART
ejpam-524	67	12	distance	distance	NOUN
ejpam-524	67	13	neighborhood	neighborhood	NOUN
ejpam-524	67	14	pattern	pattern	NOUN
ejpam-524	67	15	(	(	PUNCT
ejpam-524	67	16	or	or	CCONJ
ejpam-524	67	17	,	,	PUNCT
ejpam-524	67	18	dnp-	dnp-	ADV
ejpam-524	67	19	)	)	PUNCT
ejpam-524	67	20	matrix	matrix	NOUN
ejpam-524	67	21	of	of	ADP
ejpam-524	67	22	g.	g.	PROPN
ejpam-524	67	23	for	for	ADP
ejpam-524	67	24	a	a	DET
ejpam-524	67	25	dnp	dnp	PROPN
ejpam-524	67	26	-	-	PUNCT
ejpam-524	67	27	matrix	matrix	NOUN
ejpam-524	67	28	the	the	DET
ejpam-524	67	29	following	follow	VERB
ejpam-524	67	30	observations	observation	NOUN
ejpam-524	67	31	are	be	AUX
ejpam-524	67	32	immediate	immediate	ADJ
ejpam-524	67	33	.	.	PUNCT
ejpam-524	68	1	g.	g.	PROPN
ejpam-524	68	2	augustine	augustine	PROPN
ejpam-524	68	3	,	,	PUNCT
ejpam-524	68	4	a.	a.	PROPN
ejpam-524	68	5	joseph	joseph	PROPN
ejpam-524	68	6	,	,	PUNCT
ejpam-524	68	7	s.	s.	PROPN
ejpam-524	68	8	jose	jose	PROPN
ejpam-524	68	9	/	/	SYM
ejpam-524	68	10	eur	eur	PROPN
ejpam-524	68	11	.	.	PUNCT
ejpam-524	69	1	j.	j.	PROPN
ejpam-524	69	2	pure	pure	PROPN
ejpam-524	69	3	appl	appl	PROPN
ejpam-524	69	4	.	.	PROPN
ejpam-524	69	5	math	math	PROPN
ejpam-524	69	6	,	,	PUNCT
ejpam-524	69	7	3	3	NUM
ejpam-524	69	8	(	(	PUNCT
ejpam-524	69	9	2010	2010	NUM
ejpam-524	69	10	)	)	PUNCT
ejpam-524	69	11	,	,	PUNCT
ejpam-524	69	12	748	748	NUM
ejpam-524	69	13	-	-	SYM
ejpam-524	69	14	764	764	NUM
ejpam-524	69	15	750	750	NUM
ejpam-524	69	16	observation	observation	NOUN
ejpam-524	69	17	7	7	NUM
ejpam-524	69	18	.	.	PUNCT
ejpam-524	70	1	since	since	SCONJ
ejpam-524	70	2	n0[u	n0[u	PROPN
ejpam-524	70	3	]	]	PUNCT
ejpam-524	70	4	=	=	PUNCT
ejpam-524	70	5	{	{	PUNCT
ejpam-524	70	6	u	u	NOUN
ejpam-524	70	7	}	}	PUNCT
ejpam-524	70	8	for	for	ADP
ejpam-524	70	9	all	all	PRON
ejpam-524	70	10	u	u	PROPN
ejpam-524	70	11	∈	∈	PROPN
ejpam-524	70	12	v	v	NOUN
ejpam-524	70	13	(	(	PUNCT
ejpam-524	70	14	g	g	NOUN
ejpam-524	70	15	)	)	PUNCT
ejpam-524	70	16	,	,	PUNCT
ejpam-524	70	17	each	each	DET
ejpam-524	70	18	entry	entry	NOUN
ejpam-524	70	19	in	in	ADP
ejpam-524	70	20	the	the	DET
ejpam-524	70	21	first	first	ADJ
ejpam-524	70	22	column	column	NOUN
ejpam-524	70	23	of	of	ADP
ejpam-524	70	24	dg	dg	PROPN
ejpam-524	70	25	is	be	AUX
ejpam-524	70	26	equal	equal	ADJ
ejpam-524	70	27	to	to	ADP
ejpam-524	70	28	1	1	NUM
ejpam-524	70	29	.	.	PUNCT
ejpam-524	70	30	observation	observation	NOUN
ejpam-524	70	31	8	8	NUM
ejpam-524	70	32	.	.	PUNCT
ejpam-524	71	1	entries	entry	NOUN
ejpam-524	71	2	in	in	ADP
ejpam-524	71	3	the	the	DET
ejpam-524	71	4	second	second	ADJ
ejpam-524	71	5	column	column	NOUN
ejpam-524	71	6	of	of	ADP
ejpam-524	71	7	dg	dg	PROPN
ejpam-524	71	8	corresponds	correspond	VERB
ejpam-524	71	9	to	to	ADP
ejpam-524	71	10	the	the	DET
ejpam-524	71	11	degree	degree	NOUN
ejpam-524	71	12	of	of	ADP
ejpam-524	71	13	the	the	DET
ejpam-524	71	14	corresponding	corresponding	ADJ
ejpam-524	71	15	vertices	vertex	NOUN
ejpam-524	71	16	in	in	ADP
ejpam-524	71	17	g.	g.	PROPN
ejpam-524	71	18	observation	observation	NOUN
ejpam-524	71	19	9	9	NUM
ejpam-524	71	20	.	.	PUNCT
ejpam-524	72	1	in	in	ADP
ejpam-524	72	2	each	each	DET
ejpam-524	72	3	row	row	NOUN
ejpam-524	72	4	of	of	ADP
ejpam-524	72	5	dg	dg	PROPN
ejpam-524	72	6	,	,	PUNCT
ejpam-524	72	7	the	the	DET
ejpam-524	72	8	entry	entry	NOUN
ejpam-524	72	9	zero	zero	NUM
ejpam-524	72	10	will	will	AUX
ejpam-524	72	11	be	be	AUX
ejpam-524	72	12	after	after	ADP
ejpam-524	72	13	the	the	DET
ejpam-524	72	14	nonzero	nonzero	PROPN
ejpam-524	72	15	entries	entry	NOUN
ejpam-524	72	16	.	.	PUNCT
ejpam-524	73	1	proposition	proposition	NOUN
ejpam-524	73	2	1	1	NUM
ejpam-524	73	3	.	.	PUNCT
ejpam-524	74	1	for	for	ADP
ejpam-524	74	2	each	each	DET
ejpam-524	74	3	u	u	PROPN
ejpam-524	74	4	∈	∈	PROPN
ejpam-524	74	5	v	v	NOUN
ejpam-524	74	6	(	(	PUNCT
ejpam-524	74	7	g	g	NOUN
ejpam-524	74	8	)	)	PUNCT
ejpam-524	74	9	of	of	ADP
ejpam-524	74	10	a	a	DET
ejpam-524	74	11	connected	connected	ADJ
ejpam-524	74	12	graph	graph	NOUN
ejpam-524	74	13	g	g	NOUN
ejpam-524	74	14	,	,	PUNCT
ejpam-524	74	15	{	{	PUNCT
ejpam-524	74	16	n	n	X
ejpam-524	74	17	j[u	j[u	PROPN
ejpam-524	74	18	]	]	X
ejpam-524	74	19	:	:	PUNCT
ejpam-524	74	20	n	n	X
ejpam-524	74	21	j[u	j[u	PROPN
ejpam-524	74	22	]	]	PUNCT
ejpam-524	74	23	6=	6=	NUM
ejpam-524	74	24	;	;	PUNCT
ejpam-524	74	25	,	,	PUNCT
ejpam-524	74	26	0	0	NUM
ejpam-524	74	27	≤	≤	NUM
ejpam-524	74	28	j	j	PROPN
ejpam-524	74	29	≤	≤	PROPN
ejpam-524	74	30	dg	dg	PROPN
ejpam-524	74	31	}	}	PUNCT
ejpam-524	74	32	gives	give	VERB
ejpam-524	74	33	a	a	DET
ejpam-524	74	34	partition	partition	NOUN
ejpam-524	74	35	of	of	ADP
ejpam-524	74	36	v	v	NOUN
ejpam-524	74	37	(	(	PUNCT
ejpam-524	74	38	g	g	NOUN
ejpam-524	74	39	)	)	PUNCT
ejpam-524	74	40	.	.	PUNCT
ejpam-524	75	1	proof	proof	NOUN
ejpam-524	75	2	.	.	PUNCT
ejpam-524	76	1	if	if	SCONJ
ejpam-524	76	2	possible	possible	ADJ
ejpam-524	76	3	,	,	PUNCT
ejpam-524	76	4	let	let	VERB
ejpam-524	76	5	n	n	PRON
ejpam-524	76	6	j[u	j[u	PROPN
ejpam-524	76	7	]	]	X
ejpam-524	76	8	⋂	⋂	PROPN
ejpam-524	76	9	nk[u	nk[u	PROPN
ejpam-524	76	10	]	]	X
ejpam-524	76	11	=	=	SYM
ejpam-524	76	12	v	v	NOUN
ejpam-524	76	13	,	,	PUNCT
ejpam-524	76	14	for	for	ADP
ejpam-524	76	15	some	some	DET
ejpam-524	76	16	u	u	NOUN
ejpam-524	76	17	,	,	PUNCT
ejpam-524	76	18	v	v	NOUN
ejpam-524	76	19	∈	∈	PROPN
ejpam-524	76	20	v	v	NOUN
ejpam-524	76	21	(	(	PUNCT
ejpam-524	76	22	g	g	NOUN
ejpam-524	76	23	)	)	PUNCT
ejpam-524	76	24	,	,	PUNCT
ejpam-524	76	25	which	which	PRON
ejpam-524	76	26	implies	imply	VERB
ejpam-524	76	27	d(u	d(u	PROPN
ejpam-524	76	28	,	,	PUNCT
ejpam-524	76	29	v	v	NOUN
ejpam-524	76	30	)	)	PUNCT
ejpam-524	76	31	=	=	SYM
ejpam-524	76	32	j	j	PROPN
ejpam-524	76	33	and	and	CCONJ
ejpam-524	76	34	d(u	d(u	PROPN
ejpam-524	76	35	,	,	PUNCT
ejpam-524	76	36	v	v	NOUN
ejpam-524	76	37	)	)	PUNCT
ejpam-524	77	1	=	=	SYM
ejpam-524	77	2	k	k	NOUN
ejpam-524	77	3	,	,	PUNCT
ejpam-524	77	4	and	and	CCONJ
ejpam-524	77	5	hence	hence	ADV
ejpam-524	77	6	j	j	PROPN
ejpam-524	77	7	=	=	PROPN
ejpam-524	77	8	k.	k.	PROPN
ejpam-524	78	1	therefore	therefore	ADV
ejpam-524	78	2	,	,	PUNCT
ejpam-524	78	3	n	n	PROPN
ejpam-524	78	4	j[u	j[u	PROPN
ejpam-524	78	5	]	]	X
ejpam-524	78	6	⋂	⋂	PROPN
ejpam-524	78	7	nk[u	nk[u	PROPN
ejpam-524	78	8	]	]	X
ejpam-524	78	9	=	=	PUNCT
ejpam-524	78	10	;	;	PUNCT
ejpam-524	78	11	for	for	ADP
ejpam-524	78	12	any	any	DET
ejpam-524	78	13	(	(	PUNCT
ejpam-524	78	14	j	j	PROPN
ejpam-524	78	15	,	,	PUNCT
ejpam-524	78	16	k	k	NOUN
ejpam-524	78	17	)	)	PUNCT
ejpam-524	78	18	with	with	ADP
ejpam-524	78	19	j	j	PROPN
ejpam-524	78	20	6=	6=	PROPN
ejpam-524	78	21	k.	k.	PROPN
ejpam-524	78	22	now	now	ADV
ejpam-524	78	23	,	,	PUNCT
ejpam-524	78	24	clearly	clearly	ADV
ejpam-524	78	25	,	,	PUNCT
ejpam-524	78	26	⋃dg	⋃dg	PROPN
ejpam-524	78	27	j=0	j=0	PROPN
ejpam-524	78	28	n	n	PROPN
ejpam-524	78	29	j[u	j[u	PROPN
ejpam-524	78	30	]	]	PUNCT
ejpam-524	78	31	⊆	⊆	NUM
ejpam-524	78	32	v	v	NOUN
ejpam-524	78	33	(	(	PUNCT
ejpam-524	78	34	g	g	NOUN
ejpam-524	78	35	)	)	PUNCT
ejpam-524	78	36	.	.	PUNCT
ejpam-524	79	1	also	also	ADV
ejpam-524	79	2	,	,	PUNCT
ejpam-524	79	3	for	for	ADP
ejpam-524	79	4	any	any	DET
ejpam-524	79	5	v	v	NUM
ejpam-524	79	6	∈	∈	NOUN
ejpam-524	79	7	v	v	NOUN
ejpam-524	79	8	(	(	PUNCT
ejpam-524	79	9	g	g	NOUN
ejpam-524	79	10	)	)	PUNCT
ejpam-524	79	11	,	,	PUNCT
ejpam-524	79	12	since	since	SCONJ
ejpam-524	79	13	g	g	PROPN
ejpam-524	79	14	is	be	AUX
ejpam-524	79	15	connected	connect	VERB
ejpam-524	79	16	,	,	PUNCT
ejpam-524	79	17	d(u	d(u	PROPN
ejpam-524	79	18	,	,	PUNCT
ejpam-524	79	19	v	v	NOUN
ejpam-524	79	20	)	)	PUNCT
ejpam-524	79	21	=	=	SYM
ejpam-524	80	1	k	k	NOUN
ejpam-524	80	2	,	,	PUNCT
ejpam-524	80	3	for	for	ADP
ejpam-524	80	4	some	some	DET
ejpam-524	80	5	k	k	PROPN
ejpam-524	80	6	∈	∈	PROPN
ejpam-524	80	7	{	{	PUNCT
ejpam-524	80	8	0,1,2	0,1,2	NOUN
ejpam-524	80	9	,	,	PUNCT
ejpam-524	80	10	.	.	PUNCT
ejpam-524	80	11	.	.	PUNCT
ejpam-524	80	12	.	.	PUNCT
ejpam-524	81	1	,	,	PUNCT
ejpam-524	81	2	dg	dg	PROPN
ejpam-524	81	3	}	}	PUNCT
ejpam-524	81	4	.	.	PUNCT
ejpam-524	82	1	that	that	PRON
ejpam-524	82	2	is	be	AUX
ejpam-524	82	3	,	,	PUNCT
ejpam-524	82	4	v	v	ADP
ejpam-524	82	5	∈	∈	PROPN
ejpam-524	82	6	nk[u	nk[u	NOUN
ejpam-524	82	7	]	]	PUNCT
ejpam-524	82	8	for	for	ADP
ejpam-524	82	9	some	some	DET
ejpam-524	82	10	k	k	PROPN
ejpam-524	82	11	∈	∈	PROPN
ejpam-524	82	12	{	{	PUNCT
ejpam-524	82	13	0,1,2	0,1,2	NOUN
ejpam-524	82	14	,	,	PUNCT
ejpam-524	82	15	.	.	PUNCT
ejpam-524	82	16	.	.	PUNCT
ejpam-524	82	17	.	.	PUNCT
ejpam-524	83	1	,	,	PUNCT
ejpam-524	83	2	dg	dg	PROPN
ejpam-524	83	3	}	}	PUNCT
ejpam-524	83	4	,	,	PUNCT
ejpam-524	83	5	which	which	PRON
ejpam-524	83	6	implies	imply	VERB
ejpam-524	83	7	v	v	NUM
ejpam-524	83	8	(	(	PUNCT
ejpam-524	83	9	g	g	NOUN
ejpam-524	83	10	)	)	PUNCT
ejpam-524	83	11	⊆	⊆	NUM
ejpam-524	83	12	⋃dg	⋃dg	X
ejpam-524	83	13	j=0	j=0	PROPN
ejpam-524	83	14	n	n	PROPN
ejpam-524	83	15	j[u	j[u	PROPN
ejpam-524	83	16	]	]	PUNCT
ejpam-524	83	17	.	.	PUNCT
ejpam-524	84	1	hence	hence	ADV
ejpam-524	84	2	,	,	PUNCT
ejpam-524	84	3	⋃dg	⋃dg	X
ejpam-524	84	4	j=0	j=0	PROPN
ejpam-524	84	5	n	n	PROPN
ejpam-524	84	6	j[u	j[u	PROPN
ejpam-524	84	7	]	]	X
ejpam-524	84	8	=	=	SYM
ejpam-524	84	9	v	v	X
ejpam-524	84	10	(	(	PUNCT
ejpam-524	84	11	g	g	NOUN
ejpam-524	84	12	)	)	PUNCT
ejpam-524	84	13	.	.	PUNCT
ejpam-524	85	1	corollary	corollary	ADJ
ejpam-524	85	2	1	1	NUM
ejpam-524	85	3	.	.	PUNCT
ejpam-524	85	4	each	each	DET
ejpam-524	85	5	row	row	NOUN
ejpam-524	85	6	of	of	ADP
ejpam-524	85	7	the	the	DET
ejpam-524	85	8	dnp	dnp	PROPN
ejpam-524	85	9	-	-	PUNCT
ejpam-524	85	10	matrix	matrix	NOUN
ejpam-524	85	11	dg	dg	NOUN
ejpam-524	85	12	of	of	ADP
ejpam-524	85	13	a	a	DET
ejpam-524	85	14	graph	graph	NOUN
ejpam-524	85	15	g	g	NOUN
ejpam-524	85	16	is	be	AUX
ejpam-524	85	17	the	the	DET
ejpam-524	85	18	partition	partition	NOUN
ejpam-524	85	19	of	of	ADP
ejpam-524	85	20	the	the	DET
ejpam-524	85	21	order	order	NOUN
ejpam-524	85	22	of	of	ADP
ejpam-524	85	23	g.	g.	PROPN
ejpam-524	85	24	hence	hence	ADV
ejpam-524	85	25	,	,	PUNCT
ejpam-524	85	26	sum	sum	NOUN
ejpam-524	85	27	of	of	ADP
ejpam-524	85	28	the	the	DET
ejpam-524	85	29	entries	entry	NOUN
ejpam-524	85	30	in	in	ADP
ejpam-524	85	31	each	each	DET
ejpam-524	85	32	row	row	NOUN
ejpam-524	85	33	of	of	ADP
ejpam-524	85	34	the	the	DET
ejpam-524	85	35	dnp	dnp	PROPN
ejpam-524	85	36	-	-	PUNCT
ejpam-524	85	37	matrix	matrix	NOUN
ejpam-524	85	38	dg	dg	NOUN
ejpam-524	85	39	of	of	ADP
ejpam-524	85	40	a	a	DET
ejpam-524	85	41	graph	graph	NOUN
ejpam-524	85	42	g	g	NOUN
ejpam-524	85	43	is	be	AUX
ejpam-524	85	44	equal	equal	ADJ
ejpam-524	85	45	to	to	ADP
ejpam-524	85	46	the	the	DET
ejpam-524	85	47	order	order	NOUN
ejpam-524	85	48	of	of	ADP
ejpam-524	85	49	g.	g.	PROPN
ejpam-524	85	50	2	2	NUM
ejpam-524	85	51	.	.	PUNCT
ejpam-524	86	1	m	m	NOUN
ejpam-524	86	2	-	-	PUNCT
ejpam-524	86	3	distance	distance	NOUN
ejpam-524	86	4	neighborhood	neighborhood	NOUN
ejpam-524	86	5	pattern	pattern	NOUN
ejpam-524	86	6	matrix	matrix	NOUN
ejpam-524	86	7	of	of	ADP
ejpam-524	86	8	a	a	DET
ejpam-524	86	9	graph	graph	NOUN
ejpam-524	86	10	given	give	VERB
ejpam-524	86	11	an	an	DET
ejpam-524	86	12	arbitrary	arbitrary	ADJ
ejpam-524	86	13	nonempty	nonempty	NOUN
ejpam-524	86	14	subset	subset	VERB
ejpam-524	86	15	m	m	VERB
ejpam-524	86	16	⊆	⊆	NUM
ejpam-524	86	17	v	v	NOUN
ejpam-524	86	18	(	(	PUNCT
ejpam-524	86	19	g	g	NOUN
ejpam-524	86	20	)	)	PUNCT
ejpam-524	86	21	of	of	ADP
ejpam-524	86	22	g	g	PROPN
ejpam-524	86	23	and	and	CCONJ
ejpam-524	86	24	for	for	ADP
ejpam-524	86	25	each	each	DET
ejpam-524	86	26	u	u	PROPN
ejpam-524	86	27	∈	∈	PROPN
ejpam-524	86	28	v	v	NOUN
ejpam-524	86	29	(	(	PUNCT
ejpam-524	86	30	g	g	NOUN
ejpam-524	86	31	)	)	PUNCT
ejpam-524	86	32	,	,	PUNCT
ejpam-524	86	33	define	define	VERB
ejpam-524	86	34	n	n	DET
ejpam-524	86	35	m	m	NOUN
ejpam-524	86	36	j	j	NOUN
ejpam-524	87	1	[	[	X
ejpam-524	87	2	u	u	X
ejpam-524	87	3	]	]	X
ejpam-524	87	4	=	=	SYM
ejpam-524	87	5	{	{	PUNCT
ejpam-524	87	6	v	v	NUM
ejpam-524	87	7	∈	∈	NOUN
ejpam-524	87	8	m	m	VERB
ejpam-524	87	9	:	:	PUNCT
ejpam-524	87	10	d(u	d(u	PROPN
ejpam-524	87	11	,	,	PUNCT
ejpam-524	87	12	v	v	NOUN
ejpam-524	87	13	)	)	PUNCT
ejpam-524	87	14	=	=	SYM
ejpam-524	87	15	j	j	PROPN
ejpam-524	87	16	}	}	PUNCT
ejpam-524	87	17	;	;	PUNCT
ejpam-524	87	18	clearly	clearly	ADV
ejpam-524	87	19	then	then	ADV
ejpam-524	87	20	n	n	ADV
ejpam-524	87	21	v	v	NOUN
ejpam-524	87	22	(	(	PUNCT
ejpam-524	87	23	g	g	NOUN
ejpam-524	87	24	)	)	PUNCT
ejpam-524	87	25	j	j	NOUN
ejpam-524	88	1	[	[	X
ejpam-524	88	2	u	u	X
ejpam-524	88	3	]	]	X
ejpam-524	88	4	=	=	PUNCT
ejpam-524	88	5	n	n	PRON
ejpam-524	88	6	j[u	j[u	NOUN
ejpam-524	88	7	]	]	PUNCT
ejpam-524	88	8	.	.	PUNCT
ejpam-524	89	1	one	one	PRON
ejpam-524	89	2	can	can	AUX
ejpam-524	89	3	define	define	VERB
ejpam-524	89	4	the	the	DET
ejpam-524	89	5	m	m	NOUN
ejpam-524	89	6	eccentricity	eccentricity	NOUN
ejpam-524	89	7	of	of	ADP
ejpam-524	89	8	u	u	NOUN
ejpam-524	89	9	as	as	ADP
ejpam-524	89	10	the	the	DET
ejpam-524	89	11	largest	large	ADJ
ejpam-524	89	12	integer	integer	NOUN
ejpam-524	89	13	for	for	ADP
ejpam-524	89	14	which	which	PRON
ejpam-524	89	15	n	n	NUM
ejpam-524	89	16	m	m	VERB
ejpam-524	89	17	j	j	NOUN
ejpam-524	90	1	[	[	X
ejpam-524	90	2	u	u	X
ejpam-524	90	3	]	]	X
ejpam-524	90	4	6=	6=	NUM
ejpam-524	90	5	;	;	PUNCT
ejpam-524	90	6	and	and	CCONJ
ejpam-524	90	7	the	the	DET
ejpam-524	90	8	p×	p×	PROPN
ejpam-524	90	9	(	(	PUNCT
ejpam-524	90	10	dg	dg	X
ejpam-524	90	11	+	+	CCONJ
ejpam-524	90	12	1	1	X
ejpam-524	90	13	)	)	PUNCT
ejpam-524	90	14	nonnegative	nonnegative	ADJ
ejpam-524	90	15	integer	integer	NOUN
ejpam-524	90	16	matrix	matrix	NOUN
ejpam-524	90	17	dm	dm	VERB
ejpam-524	90	18	g	g	NOUN
ejpam-524	90	19	=	=	PUNCT
ejpam-524	90	20	(	(	PUNCT
ejpam-524	90	21	|n	|n	NOUN
ejpam-524	90	22	m	m	VERB
ejpam-524	90	23	j	j	PROPN
ejpam-524	91	1	[	[	X
ejpam-524	91	2	u]|	u]|	X
ejpam-524	91	3	)	)	PUNCT
ejpam-524	91	4	is	be	AUX
ejpam-524	91	5	called	call	VERB
ejpam-524	91	6	the	the	DET
ejpam-524	91	7	m	m	NUM
ejpam-524	91	8	-distance	-distance	NOUN
ejpam-524	91	9	neighborhood	neighborhood	NOUN
ejpam-524	91	10	pattern	pattern	NOUN
ejpam-524	91	11	(	(	PUNCT
ejpam-524	91	12	or	or	CCONJ
ejpam-524	91	13	m	m	PROPN
ejpam-524	91	14	-dnp	-dnp	NUM
ejpam-524	91	15	)	)	PUNCT
ejpam-524	91	16	matrix	matrix	NOUN
ejpam-524	91	17	of	of	ADP
ejpam-524	91	18	g.	g.	PROPN
ejpam-524	91	19	d∗mg	d∗mg	PROPN
ejpam-524	91	20	is	be	AUX
ejpam-524	91	21	obtained	obtain	VERB
ejpam-524	91	22	from	from	ADP
ejpam-524	91	23	dm	dm	NUM
ejpam-524	91	24	g	g	NOUN
ejpam-524	91	25	by	by	ADP
ejpam-524	91	26	replacing	replace	VERB
ejpam-524	91	27	each	each	DET
ejpam-524	91	28	nonzero	nonzero	NOUN
ejpam-524	91	29	entry	entry	NOUN
ejpam-524	91	30	by	by	ADP
ejpam-524	91	31	1	1	NUM
ejpam-524	91	32	.	.	PUNCT
ejpam-524	91	33	acharya	acharya	PROPN
ejpam-524	92	1	[	[	X
ejpam-524	92	2	2	2	NUM
ejpam-524	92	3	]	]	PUNCT
ejpam-524	92	4	defined	define	VERB
ejpam-524	92	5	dnp	dnp	PROPN
ejpam-524	92	6	matrix	matrix	NOUN
ejpam-524	92	7	of	of	ADP
ejpam-524	92	8	any	any	DET
ejpam-524	92	9	graph	graph	NOUN
ejpam-524	92	10	and	and	CCONJ
ejpam-524	92	11	in	in	ADP
ejpam-524	92	12	particular	particular	ADJ
ejpam-524	92	13	,	,	PUNCT
ejpam-524	92	14	m	m	PROPN
ejpam-524	92	15	-	-	PUNCT
ejpam-524	92	16	dnp	dnp	PROPN
ejpam-524	92	17	matrix	matrix	NOUN
ejpam-524	92	18	of	of	ADP
ejpam-524	92	19	a	a	DET
ejpam-524	92	20	dpd	dpd	NOUN
ejpam-524	92	21	-	-	PUNCT
ejpam-524	92	22	graph	graph	NOUN
ejpam-524	92	23	as	as	SCONJ
ejpam-524	92	24	follows	follow	VERB
ejpam-524	92	25	:	:	PUNCT
ejpam-524	92	26	definition	definition	NOUN
ejpam-524	92	27	2	2	NUM
ejpam-524	92	28	.	.	PUNCT
ejpam-524	93	1	let	let	VERB
ejpam-524	93	2	g	g	PROPN
ejpam-524	93	3	=	=	SYM
ejpam-524	93	4	(	(	PUNCT
ejpam-524	93	5	v	v	NOUN
ejpam-524	93	6	,	,	PUNCT
ejpam-524	93	7	e	e	NOUN
ejpam-524	93	8	)	)	PUNCT
ejpam-524	93	9	be	be	AUX
ejpam-524	93	10	a	a	DET
ejpam-524	93	11	given	give	VERB
ejpam-524	93	12	connected	connect	VERB
ejpam-524	93	13	simple	simple	ADJ
ejpam-524	93	14	(	(	PUNCT
ejpam-524	93	15	p	p	NOUN
ejpam-524	93	16	,	,	PUNCT
ejpam-524	93	17	q)-graph	q)-graph	NOUN
ejpam-524	93	18	,	,	PUNCT
ejpam-524	93	19	;	;	PUNCT
ejpam-524	93	20	6=	6=	NUM
ejpam-524	93	21	m	m	PROPN
ejpam-524	93	22	⊆	⊆	NUM
ejpam-524	93	23	v	v	NOUN
ejpam-524	93	24	(	(	PUNCT
ejpam-524	93	25	g	g	NOUN
ejpam-524	93	26	)	)	PUNCT
ejpam-524	93	27	and	and	CCONJ
ejpam-524	93	28	u	u	PROPN
ejpam-524	93	29	∈	∈	PROPN
ejpam-524	93	30	v	v	NOUN
ejpam-524	93	31	(	(	PUNCT
ejpam-524	93	32	g	g	NOUN
ejpam-524	93	33	)	)	PUNCT
ejpam-524	93	34	.	.	PUNCT
ejpam-524	94	1	then	then	ADV
ejpam-524	94	2	,	,	PUNCT
ejpam-524	94	3	the	the	DET
ejpam-524	94	4	m	m	NOUN
ejpam-524	94	5	-	-	PUNCT
ejpam-524	94	6	distance	distance	NOUN
ejpam-524	94	7	-	-	PUNCT
ejpam-524	94	8	pattern	pattern	NOUN
ejpam-524	94	9	of	of	ADP
ejpam-524	94	10	u	u	NOUN
ejpam-524	94	11	is	be	AUX
ejpam-524	94	12	the	the	DET
ejpam-524	94	13	set	set	ADJ
ejpam-524	94	14	fm	fm	PROPN
ejpam-524	94	15	(	(	PUNCT
ejpam-524	94	16	u	u	NOUN
ejpam-524	94	17	)	)	PUNCT
ejpam-524	94	18	=	=	SYM
ejpam-524	94	19	{	{	PUNCT
ejpam-524	94	20	d(u	d(u	PROPN
ejpam-524	94	21	,	,	PUNCT
ejpam-524	94	22	v	v	NOUN
ejpam-524	94	23	)	)	PUNCT
ejpam-524	94	24	:	:	PUNCT
ejpam-524	94	25	v	v	X
ejpam-524	94	26	∈	∈	PROPN
ejpam-524	94	27	m	m	PRON
ejpam-524	94	28	}	}	PUNCT
ejpam-524	94	29	.	.	PUNCT
ejpam-524	95	1	clearly	clearly	ADV
ejpam-524	95	2	,	,	PUNCT
ejpam-524	95	3	fm	fm	PROPN
ejpam-524	95	4	(	(	PUNCT
ejpam-524	95	5	u	u	NOUN
ejpam-524	95	6	)	)	PUNCT
ejpam-524	95	7	=	=	SYM
ejpam-524	95	8	{	{	PUNCT
ejpam-524	95	9	j	j	NOUN
ejpam-524	95	10	:	:	PUNCT
ejpam-524	95	11	n	n	PROPN
ejpam-524	95	12	m	m	PROPN
ejpam-524	95	13	j	j	NOUN
ejpam-524	96	1	[	[	X
ejpam-524	96	2	u	u	X
ejpam-524	96	3	]	]	X
ejpam-524	96	4	6=	6=	NUM
ejpam-524	96	5	;	;	PUNCT
ejpam-524	96	6	}	}	PUNCT
ejpam-524	96	7	.	.	PUNCT
ejpam-524	97	1	hence	hence	ADV
ejpam-524	97	2	,	,	PUNCT
ejpam-524	97	3	in	in	ADP
ejpam-524	97	4	particular	particular	ADJ
ejpam-524	97	5	,	,	PUNCT
ejpam-524	97	6	if	if	SCONJ
ejpam-524	97	7	fm	fm	NOUN
ejpam-524	97	8	:	:	PUNCT
ejpam-524	97	9	u	u	PROPN
ejpam-524	97	10	7→	7→	NUM
ejpam-524	97	11	fm	fm	NOUN
ejpam-524	97	12	(	(	PUNCT
ejpam-524	97	13	u	u	NOUN
ejpam-524	97	14	)	)	PUNCT
ejpam-524	97	15	is	be	AUX
ejpam-524	97	16	an	an	DET
ejpam-524	97	17	injective	injective	ADJ
ejpam-524	97	18	function	function	NOUN
ejpam-524	97	19	then	then	ADV
ejpam-524	97	20	the	the	DET
ejpam-524	97	21	set	set	NOUN
ejpam-524	97	22	m	m	VERB
ejpam-524	97	23	is	be	AUX
ejpam-524	97	24	a	a	DET
ejpam-524	97	25	distance	distance	NOUN
ejpam-524	97	26	-	-	PUNCT
ejpam-524	97	27	pattern	pattern	NOUN
ejpam-524	97	28	distinguishing	distinguish	VERB
ejpam-524	97	29	set	set	VERB
ejpam-524	97	30	(	(	PUNCT
ejpam-524	97	31	or	or	CCONJ
ejpam-524	97	32	,	,	PUNCT
ejpam-524	97	33	a	a	DET
ejpam-524	97	34	“	"	PUNCT
ejpam-524	97	35	dpd	dpd	NOUN
ejpam-524	97	36	-	-	PUNCT
ejpam-524	97	37	set”in	set”in	NOUN
ejpam-524	97	38	short	short	ADJ
ejpam-524	97	39	)	)	PUNCT
ejpam-524	97	40	of	of	ADP
ejpam-524	97	41	g	g	PROPN
ejpam-524	97	42	and	and	CCONJ
ejpam-524	97	43	if	if	SCONJ
ejpam-524	97	44	fm	fm	PROPN
ejpam-524	97	45	(	(	PUNCT
ejpam-524	97	46	u)−{0	u)−{0	NOUN
ejpam-524	97	47	}	}	PUNCT
ejpam-524	97	48	is	be	AUX
ejpam-524	97	49	independent	independent	ADJ
ejpam-524	97	50	of	of	ADP
ejpam-524	97	51	the	the	DET
ejpam-524	97	52	choice	choice	NOUN
ejpam-524	97	53	of	of	ADP
ejpam-524	97	54	u	u	NOUN
ejpam-524	97	55	in	in	ADP
ejpam-524	97	56	g	g	PROPN
ejpam-524	97	57	then	then	ADV
ejpam-524	97	58	m	m	PROPN
ejpam-524	97	59	is	be	AUX
ejpam-524	97	60	an	an	DET
ejpam-524	97	61	open	open	ADJ
ejpam-524	97	62	distance	distance	NOUN
ejpam-524	97	63	-	-	PUNCT
ejpam-524	97	64	pattern	pattern	NOUN
ejpam-524	97	65	uniform	uniform	NOUN
ejpam-524	97	66	(	(	PUNCT
ejpam-524	97	67	or	or	CCONJ
ejpam-524	97	68	,	,	PUNCT
ejpam-524	97	69	odpu	odpu	PROPN
ejpam-524	97	70	)	)	PUNCT
ejpam-524	97	71	set	set	NOUN
ejpam-524	97	72	of	of	ADP
ejpam-524	97	73	g.	g.	PROPN
ejpam-524	97	74	a	a	DET
ejpam-524	97	75	graph	graph	NOUN
ejpam-524	97	76	g	g	NOUN
ejpam-524	97	77	with	with	ADP
ejpam-524	97	78	a	a	DET
ejpam-524	97	79	dpd	dpd	NOUN
ejpam-524	97	80	-	-	PUNCT
ejpam-524	97	81	set(odpu	set(odpu	NOUN
ejpam-524	97	82	-	-	PUNCT
ejpam-524	97	83	set	set	NOUN
ejpam-524	97	84	)	)	PUNCT
ejpam-524	97	85	is	be	AUX
ejpam-524	97	86	called	call	VERB
ejpam-524	97	87	a	a	DET
ejpam-524	97	88	dpd-(odpu-)graph	dpd-(odpu-)graph	NOUN
ejpam-524	97	89	.	.	PUNCT
ejpam-524	98	1	following	follow	VERB
ejpam-524	98	2	are	be	AUX
ejpam-524	98	3	some	some	DET
ejpam-524	98	4	interesting	interesting	ADJ
ejpam-524	98	5	results	result	NOUN
ejpam-524	98	6	on	on	ADP
ejpam-524	98	7	m	m	PROPN
ejpam-524	98	8	-dnp	-dnp	NOUN
ejpam-524	98	9	matrix	matrix	NOUN
ejpam-524	98	10	of	of	ADP
ejpam-524	98	11	a	a	DET
ejpam-524	98	12	connected	connected	ADJ
ejpam-524	98	13	graph	graph	NOUN
ejpam-524	98	14	g.	g.	NOUN
ejpam-524	98	15	observation	observation	NOUN
ejpam-524	98	16	10	10	NUM
ejpam-524	98	17	.	.	PUNCT
ejpam-524	99	1	both	both	DET
ejpam-524	99	2	dm	dm	PROPN
ejpam-524	99	3	g	g	NOUN
ejpam-524	99	4	and	and	CCONJ
ejpam-524	99	5	d∗mg	d∗mg	NOUN
ejpam-524	99	6	do	do	AUX
ejpam-524	99	7	not	not	PART
ejpam-524	99	8	admit	admit	VERB
ejpam-524	99	9	null	null	ADJ
ejpam-524	99	10	rows	row	NOUN
ejpam-524	99	11	.	.	PUNCT
ejpam-524	100	1	proposition	proposition	NOUN
ejpam-524	100	2	2	2	NUM
ejpam-524	100	3	.	.	X
ejpam-524	101	1	for	for	ADP
ejpam-524	101	2	each	each	DET
ejpam-524	101	3	ui	ui	PROPN
ejpam-524	101	4	∈	∈	PROPN
ejpam-524	101	5	v	v	ADP
ejpam-524	101	6	(	(	PUNCT
ejpam-524	101	7	g	g	NOUN
ejpam-524	101	8	)	)	PUNCT
ejpam-524	101	9	,	,	PUNCT
ejpam-524	101	10	n	n	PROPN
ejpam-524	101	11	m	m	VERB
ejpam-524	101	12	0	0	PUNCT
ejpam-524	102	1	[	[	X
ejpam-524	102	2	ui	ui	X
ejpam-524	102	3	]	]	X
ejpam-524	102	4	=	=	PUNCT
ejpam-524	102	5	¨	¨	NOUN
ejpam-524	102	6	ui	ui	NOUN
ejpam-524	102	7	if	if	SCONJ
ejpam-524	102	8	ui	ui	PROPN
ejpam-524	102	9	∈	∈	PROPN
ejpam-524	102	10	m	m	X
ejpam-524	102	11	;	;	PUNCT
ejpam-524	102	12	if	if	SCONJ
ejpam-524	102	13	ui	ui	PROPN
ejpam-524	102	14	6∈	6∈	PROPN
ejpam-524	102	15	m	m	VERB
ejpam-524	102	16	therefore	therefore	ADV
ejpam-524	102	17	,	,	PUNCT
ejpam-524	102	18	the	the	DET
ejpam-524	102	19	entries	entry	NOUN
ejpam-524	102	20	in	in	ADP
ejpam-524	102	21	the	the	DET
ejpam-524	102	22	first	first	ADJ
ejpam-524	102	23	column	column	NOUN
ejpam-524	102	24	of	of	ADP
ejpam-524	102	25	dm	dm	NUM
ejpam-524	102	26	g	g	NOUN
ejpam-524	102	27	and	and	CCONJ
ejpam-524	102	28	d∗mg	d∗mg	PROPN
ejpam-524	102	29	will	will	AUX
ejpam-524	102	30	either	either	CCONJ
ejpam-524	102	31	be	be	AUX
ejpam-524	102	32	0	0	NUM
ejpam-524	102	33	or	or	CCONJ
ejpam-524	102	34	1	1	NUM
ejpam-524	102	35	.	.	PUNCT
ejpam-524	102	36	g.	g.	PROPN
ejpam-524	102	37	augustine	augustine	PROPN
ejpam-524	102	38	,	,	PUNCT
ejpam-524	102	39	a.	a.	PROPN
ejpam-524	102	40	joseph	joseph	PROPN
ejpam-524	102	41	,	,	PUNCT
ejpam-524	102	42	s.	s.	PROPN
ejpam-524	102	43	jose	jose	PROPN
ejpam-524	102	44	/	/	SYM
ejpam-524	102	45	eur	eur	PROPN
ejpam-524	102	46	.	.	PUNCT
ejpam-524	103	1	j.	j.	PROPN
ejpam-524	103	2	pure	pure	PROPN
ejpam-524	103	3	appl	appl	PROPN
ejpam-524	103	4	.	.	PROPN
ejpam-524	103	5	math	math	PROPN
ejpam-524	103	6	,	,	PUNCT
ejpam-524	103	7	3	3	NUM
ejpam-524	103	8	(	(	PUNCT
ejpam-524	103	9	2010	2010	NUM
ejpam-524	103	10	)	)	PUNCT
ejpam-524	103	11	,	,	PUNCT
ejpam-524	103	12	748	748	NUM
ejpam-524	103	13	-	-	SYM
ejpam-524	103	14	764	764	NUM
ejpam-524	103	15	751	751	NUM
ejpam-524	103	16	remark	remark	NOUN
ejpam-524	103	17	1	1	NUM
ejpam-524	103	18	.	.	PUNCT
ejpam-524	104	1	it	it	PRON
ejpam-524	104	2	should	should	AUX
ejpam-524	104	3	note	note	VERB
ejpam-524	104	4	that	that	DET
ejpam-524	104	5	observation	observation	NOUN
ejpam-524	104	6	9	9	NUM
ejpam-524	104	7	is	be	AUX
ejpam-524	104	8	not	not	PART
ejpam-524	104	9	true	true	ADJ
ejpam-524	104	10	in	in	ADP
ejpam-524	104	11	the	the	DET
ejpam-524	104	12	case	case	NOUN
ejpam-524	104	13	of	of	ADP
ejpam-524	104	14	dm	dm	NUM
ejpam-524	104	15	g	g	NOUN
ejpam-524	104	16	.	.	PUNCT
ejpam-524	105	1	corollary	corollary	ADJ
ejpam-524	105	2	2	2	NUM
ejpam-524	105	3	.	.	PUNCT
ejpam-524	106	1	the	the	DET
ejpam-524	106	2	sum	sum	NOUN
ejpam-524	106	3	of	of	ADP
ejpam-524	106	4	the	the	DET
ejpam-524	106	5	entries	entry	NOUN
ejpam-524	106	6	in	in	ADP
ejpam-524	106	7	the	the	DET
ejpam-524	106	8	first	first	ADJ
ejpam-524	106	9	column	column	NOUN
ejpam-524	106	10	of	of	ADP
ejpam-524	106	11	dm	dm	NUM
ejpam-524	106	12	g	g	NOUN
ejpam-524	106	13	and	and	CCONJ
ejpam-524	106	14	d∗mg	d∗mg	NOUN
ejpam-524	106	15	is	be	AUX
ejpam-524	106	16	equal	equal	ADJ
ejpam-524	106	17	to	to	ADP
ejpam-524	106	18	|m	|m	NOUN
ejpam-524	106	19	|	|	ADV
ejpam-524	106	20	.	.	PUNCT
ejpam-524	107	1	lemma	lemma	PROPN
ejpam-524	107	2	1	1	NUM
ejpam-524	107	3	is	be	AUX
ejpam-524	107	4	similar	similar	ADJ
ejpam-524	107	5	to	to	ADP
ejpam-524	107	6	proposition	proposition	NOUN
ejpam-524	107	7	1	1	NUM
ejpam-524	107	8	.	.	PUNCT
ejpam-524	108	1	lemma	lemma	PROPN
ejpam-524	108	2	1	1	NUM
ejpam-524	108	3	.	.	PUNCT
ejpam-524	109	1	for	for	ADP
ejpam-524	109	2	each	each	DET
ejpam-524	109	3	u	u	PROPN
ejpam-524	109	4	∈	∈	PROPN
ejpam-524	109	5	v	v	NOUN
ejpam-524	109	6	(	(	PUNCT
ejpam-524	109	7	g	g	NOUN
ejpam-524	109	8	)	)	PUNCT
ejpam-524	109	9	,	,	PUNCT
ejpam-524	109	10	of	of	ADP
ejpam-524	109	11	a	a	DET
ejpam-524	109	12	connected	connected	ADJ
ejpam-524	109	13	graph	graph	NOUN
ejpam-524	109	14	g	g	NOUN
ejpam-524	109	15	,	,	PUNCT
ejpam-524	109	16	{	{	PUNCT
ejpam-524	109	17	n	n	NOUN
ejpam-524	109	18	m	m	PROPN
ejpam-524	109	19	j	j	NOUN
ejpam-524	110	1	[	[	X
ejpam-524	110	2	u	u	X
ejpam-524	110	3	]	]	X
ejpam-524	110	4	:	:	PUNCT
ejpam-524	110	5	n	n	PRON
ejpam-524	110	6	m	m	PROPN
ejpam-524	110	7	j	j	NOUN
ejpam-524	111	1	[	[	X
ejpam-524	111	2	u	u	X
ejpam-524	111	3	]	]	X
ejpam-524	111	4	6=	6=	NUM
ejpam-524	111	5	;	;	PUNCT
ejpam-524	111	6	,	,	PUNCT
ejpam-524	111	7	0	0	NUM
ejpam-524	111	8	≤	≤	NUM
ejpam-524	112	1	j	j	PROPN
ejpam-524	112	2	≤	≤	PROPN
ejpam-524	112	3	dg	dg	PROPN
ejpam-524	112	4	}	}	PUNCT
ejpam-524	112	5	is	be	AUX
ejpam-524	112	6	a	a	DET
ejpam-524	112	7	partition	partition	NOUN
ejpam-524	112	8	of	of	ADP
ejpam-524	112	9	m.	m.	NOUN
ejpam-524	112	10	proof	proof	NOUN
ejpam-524	112	11	.	.	PUNCT
ejpam-524	113	1	let	let	VERB
ejpam-524	113	2	n	n	PRON
ejpam-524	113	3	m	m	VERB
ejpam-524	113	4	j	j	NOUN
ejpam-524	114	1	[	[	X
ejpam-524	114	2	u	u	X
ejpam-524	114	3	]	]	X
ejpam-524	114	4	⋂	⋂	PROPN
ejpam-524	114	5	n	n	PRON
ejpam-524	114	6	m	m	PROPN
ejpam-524	114	7	k	k	NOUN
ejpam-524	115	1	[	[	X
ejpam-524	115	2	u	u	X
ejpam-524	115	3	]	]	X
ejpam-524	115	4	=	=	SYM
ejpam-524	115	5	v	v	NOUN
ejpam-524	115	6	,	,	PUNCT
ejpam-524	115	7	for	for	ADP
ejpam-524	115	8	some	some	DET
ejpam-524	115	9	u	u	NOUN
ejpam-524	115	10	∈	∈	PROPN
ejpam-524	115	11	v	v	NOUN
ejpam-524	115	12	(	(	PUNCT
ejpam-524	115	13	g	g	NOUN
ejpam-524	115	14	)	)	PUNCT
ejpam-524	115	15	,	,	PUNCT
ejpam-524	115	16	v	v	X
ejpam-524	115	17	∈	∈	NOUN
ejpam-524	115	18	m	m	NOUN
ejpam-524	115	19	.	.	PUNCT
ejpam-524	116	1	then	then	ADV
ejpam-524	116	2	d(u	d(u	PROPN
ejpam-524	116	3	,	,	PUNCT
ejpam-524	116	4	v	v	NOUN
ejpam-524	116	5	)	)	PUNCT
ejpam-524	116	6	=	=	SYM
ejpam-524	116	7	j	j	PROPN
ejpam-524	116	8	and	and	CCONJ
ejpam-524	116	9	d(u	d(u	PROPN
ejpam-524	116	10	,	,	PUNCT
ejpam-524	116	11	v	v	NOUN
ejpam-524	116	12	)	)	PUNCT
ejpam-524	116	13	=	=	SYM
ejpam-524	116	14	k	k	NOUN
ejpam-524	116	15	,	,	PUNCT
ejpam-524	116	16	and	and	CCONJ
ejpam-524	116	17	hence	hence	ADV
ejpam-524	116	18	j	j	PROPN
ejpam-524	116	19	=	=	PROPN
ejpam-524	116	20	k.	k.	PROPN
ejpam-524	116	21	therefore	therefore	ADV
ejpam-524	116	22	,	,	PUNCT
ejpam-524	116	23	n	n	PRON
ejpam-524	116	24	m	m	PROPN
ejpam-524	116	25	j	j	NOUN
ejpam-524	117	1	[	[	X
ejpam-524	117	2	u	u	X
ejpam-524	117	3	]	]	X
ejpam-524	117	4	⋂	⋂	PROPN
ejpam-524	117	5	n	n	PRON
ejpam-524	117	6	m	m	PROPN
ejpam-524	117	7	k	k	NOUN
ejpam-524	118	1	[	[	X
ejpam-524	118	2	u	u	X
ejpam-524	118	3	]	]	X
ejpam-524	118	4	=	=	X
ejpam-524	118	5	;	;	PUNCT
ejpam-524	118	6	for	for	ADP
ejpam-524	118	7	j	j	PROPN
ejpam-524	118	8	6=	6=	PROPN
ejpam-524	118	9	k.	k.	PROPN
ejpam-524	118	10	now	now	ADV
ejpam-524	118	11	,	,	PUNCT
ejpam-524	118	12	⋃dg	⋃dg	PROPN
ejpam-524	118	13	j=0	j=0	PROPN
ejpam-524	118	14	n	n	PROPN
ejpam-524	118	15	m	m	PROPN
ejpam-524	118	16	j	j	NOUN
ejpam-524	119	1	[	[	X
ejpam-524	119	2	u	u	X
ejpam-524	119	3	]	]	X
ejpam-524	119	4	⊆	⊆	NUM
ejpam-524	119	5	m	m	NOUN
ejpam-524	119	6	is	be	AUX
ejpam-524	119	7	trivial	trivial	ADJ
ejpam-524	119	8	.	.	PUNCT
ejpam-524	120	1	also	also	ADV
ejpam-524	120	2	,	,	PUNCT
ejpam-524	120	3	for	for	ADP
ejpam-524	120	4	any	any	DET
ejpam-524	120	5	vertex	vertex	NOUN
ejpam-524	120	6	v	v	ADP
ejpam-524	120	7	∈	∈	NOUN
ejpam-524	120	8	m	m	VERB
ejpam-524	120	9	,	,	PUNCT
ejpam-524	120	10	since	since	SCONJ
ejpam-524	120	11	g	g	PROPN
ejpam-524	120	12	is	be	AUX
ejpam-524	120	13	connected	connect	VERB
ejpam-524	120	14	d(u	d(u	PROPN
ejpam-524	120	15	,	,	PUNCT
ejpam-524	120	16	v	v	NOUN
ejpam-524	120	17	)	)	PUNCT
ejpam-524	120	18	=	=	SYM
ejpam-524	121	1	k	k	NOUN
ejpam-524	121	2	,	,	PUNCT
ejpam-524	121	3	for	for	ADP
ejpam-524	121	4	some	some	DET
ejpam-524	121	5	k	k	PROPN
ejpam-524	121	6	∈	∈	PROPN
ejpam-524	121	7	{	{	PUNCT
ejpam-524	121	8	0,1,2	0,1,2	NOUN
ejpam-524	121	9	,	,	PUNCT
ejpam-524	121	10	.	.	PUNCT
ejpam-524	121	11	.	.	PUNCT
ejpam-524	121	12	.	.	PUNCT
ejpam-524	122	1	,	,	PUNCT
ejpam-524	122	2	dg	dg	PROPN
ejpam-524	122	3	}	}	PUNCT
ejpam-524	122	4	.	.	PUNCT
ejpam-524	123	1	that	that	PRON
ejpam-524	123	2	is	be	AUX
ejpam-524	123	3	,	,	PUNCT
ejpam-524	123	4	v	v	PROPN
ejpam-524	123	5	∈	∈	PROPN
ejpam-524	123	6	n	n	PRON
ejpam-524	123	7	m	m	NOUN
ejpam-524	123	8	k	k	NOUN
ejpam-524	124	1	[	[	X
ejpam-524	124	2	u	u	X
ejpam-524	124	3	]	]	X
ejpam-524	124	4	for	for	ADP
ejpam-524	124	5	some	some	DET
ejpam-524	124	6	k	k	PROPN
ejpam-524	124	7	∈	∈	PROPN
ejpam-524	124	8	{	{	PUNCT
ejpam-524	124	9	0,1,2	0,1,2	NOUN
ejpam-524	124	10	,	,	PUNCT
ejpam-524	124	11	.	.	PUNCT
ejpam-524	124	12	.	.	PUNCT
ejpam-524	125	1	.	.	PUNCT
ejpam-524	126	1	,	,	PUNCT
ejpam-524	126	2	dg	dg	PROPN
ejpam-524	126	3	}	}	PUNCT
ejpam-524	126	4	.	.	PUNCT
ejpam-524	127	1	hence	hence	ADV
ejpam-524	127	2	,	,	PUNCT
ejpam-524	127	3	v	v	PROPN
ejpam-524	127	4	∈	∈	PROPN
ejpam-524	127	5	⋃dg	⋃dg	X
ejpam-524	127	6	j=0	j=0	PROPN
ejpam-524	127	7	n	n	PROPN
ejpam-524	127	8	m	m	PROPN
ejpam-524	127	9	j	j	NOUN
ejpam-524	128	1	[	[	X
ejpam-524	128	2	u	u	X
ejpam-524	128	3	]	]	X
ejpam-524	128	4	,	,	PUNCT
ejpam-524	128	5	which	which	PRON
ejpam-524	128	6	implies	imply	VERB
ejpam-524	128	7	m	m	PROPN
ejpam-524	128	8	⊆	⊆	NUM
ejpam-524	128	9	⋃dg	⋃dg	X
ejpam-524	128	10	j=0	j=0	PROPN
ejpam-524	128	11	n	n	PROPN
ejpam-524	128	12	m	m	PROPN
ejpam-524	128	13	j	j	NOUN
ejpam-524	129	1	[	[	X
ejpam-524	129	2	u	u	X
ejpam-524	129	3	]	]	X
ejpam-524	129	4	.	.	PUNCT
ejpam-524	130	1	hence	hence	ADV
ejpam-524	130	2	,	,	PUNCT
ejpam-524	130	3	⋃dg	⋃dg	X
ejpam-524	130	4	j=0	j=0	PROPN
ejpam-524	130	5	n	n	PROPN
ejpam-524	130	6	m	m	PROPN
ejpam-524	130	7	j	j	NOUN
ejpam-524	131	1	[	[	X
ejpam-524	131	2	u	u	X
ejpam-524	131	3	]	]	X
ejpam-524	131	4	=	=	NOUN
ejpam-524	131	5	m	m	NOUN
ejpam-524	131	6	.	.	PUNCT
ejpam-524	132	1	corollary	corollary	ADJ
ejpam-524	132	2	3	3	NUM
ejpam-524	132	3	.	.	PUNCT
ejpam-524	132	4	each	each	DET
ejpam-524	132	5	row	row	NOUN
ejpam-524	132	6	of	of	ADP
ejpam-524	132	7	dm	dm	PROPN
ejpam-524	132	8	g	g	PROPN
ejpam-524	132	9	is	be	AUX
ejpam-524	132	10	a	a	DET
ejpam-524	132	11	partition	partition	NOUN
ejpam-524	132	12	of	of	ADP
ejpam-524	132	13	|m	|m	NOUN
ejpam-524	132	14	|	|	ADV
ejpam-524	132	15	.	.	PUNCT
ejpam-524	133	1	corollary	corollary	ADJ
ejpam-524	133	2	4	4	NUM
ejpam-524	133	3	.	.	X
ejpam-524	133	4	sum	sum	NOUN
ejpam-524	133	5	of	of	ADP
ejpam-524	133	6	the	the	DET
ejpam-524	133	7	entries	entry	NOUN
ejpam-524	133	8	in	in	ADP
ejpam-524	133	9	each	each	DET
ejpam-524	133	10	row	row	NOUN
ejpam-524	133	11	of	of	ADP
ejpam-524	133	12	dm	dm	PROPN
ejpam-524	133	13	g	g	PROPN
ejpam-524	133	14	gives	give	VERB
ejpam-524	133	15	|m	|m	NOUN
ejpam-524	133	16	|	|	ADV
ejpam-524	133	17	and	and	CCONJ
ejpam-524	133	18	sum	sum	NOUN
ejpam-524	133	19	of	of	ADP
ejpam-524	133	20	the	the	DET
ejpam-524	133	21	entries	entry	NOUN
ejpam-524	133	22	in	in	ADP
ejpam-524	133	23	each	each	DET
ejpam-524	133	24	row	row	NOUN
ejpam-524	133	25	of	of	ADP
ejpam-524	133	26	d∗mg	d∗mg	NOUN
ejpam-524	133	27	is	be	AUX
ejpam-524	133	28	less	less	ADJ
ejpam-524	133	29	than	than	ADP
ejpam-524	133	30	or	or	CCONJ
ejpam-524	133	31	equal	equal	ADJ
ejpam-524	133	32	to	to	ADP
ejpam-524	133	33	|m	|m	NOUN
ejpam-524	133	34	|	|	ADV
ejpam-524	133	35	.	.	PUNCT
ejpam-524	134	1	3	3	X
ejpam-524	134	2	.	.	X
ejpam-524	134	3	m	m	PROPN
ejpam-524	134	4	-	-	PUNCT
ejpam-524	134	5	dnp	dnp	PROPN
ejpam-524	134	6	matrix	matrix	NOUN
ejpam-524	134	7	of	of	ADP
ejpam-524	134	8	a	a	DET
ejpam-524	134	9	dpd	dpd	NOUN
ejpam-524	134	10	-	-	PUNCT
ejpam-524	134	11	graph	graph	NOUN
ejpam-524	134	12	in	in	ADP
ejpam-524	134	13	this	this	DET
ejpam-524	134	14	section	section	NOUN
ejpam-524	134	15	we	we	PRON
ejpam-524	134	16	investigate	investigate	VERB
ejpam-524	134	17	some	some	DET
ejpam-524	134	18	interesting	interesting	ADJ
ejpam-524	134	19	results	result	NOUN
ejpam-524	134	20	of	of	ADP
ejpam-524	134	21	dm	dm	PRON
ejpam-524	134	22	g	g	PROPN
ejpam-524	134	23	(	(	PUNCT
ejpam-524	134	24	d	d	PROPN
ejpam-524	134	25	∗m	∗m	PROPN
ejpam-524	134	26	g	g	PROPN
ejpam-524	134	27	)	)	PUNCT
ejpam-524	134	28	of	of	ADP
ejpam-524	134	29	a	a	DET
ejpam-524	134	30	dpd	dpd	NOUN
ejpam-524	134	31	-	-	PUNCT
ejpam-524	134	32	graph	graph	NOUN
ejpam-524	134	33	.	.	PUNCT
ejpam-524	135	1	from	from	ADP
ejpam-524	135	2	the	the	DET
ejpam-524	135	3	definition	definition	NOUN
ejpam-524	135	4	of	of	ADP
ejpam-524	135	5	d∗mg	d∗mg	PROPN
ejpam-524	135	6	,	,	PUNCT
ejpam-524	135	7	we	we	PRON
ejpam-524	135	8	have	have	VERB
ejpam-524	135	9	the	the	DET
ejpam-524	135	10	following	follow	VERB
ejpam-524	135	11	important	important	ADJ
ejpam-524	135	12	observations	observation	NOUN
ejpam-524	135	13	.	.	PUNCT
ejpam-524	136	1	observation	observation	NOUN
ejpam-524	136	2	11	11	NUM
ejpam-524	136	3	.	.	PUNCT
ejpam-524	137	1	in	in	ADP
ejpam-524	137	2	any	any	DET
ejpam-524	137	3	graph	graph	NOUN
ejpam-524	137	4	g	g	NOUN
ejpam-524	137	5	,	,	PUNCT
ejpam-524	137	6	a	a	DET
ejpam-524	137	7	nonempty	nonempty	ADJ
ejpam-524	137	8	m	m	VERB
ejpam-524	137	9	⊆	⊆	NUM
ejpam-524	137	10	v	v	NOUN
ejpam-524	137	11	(	(	PUNCT
ejpam-524	137	12	g	g	NOUN
ejpam-524	137	13	)	)	PUNCT
ejpam-524	137	14	is	be	AUX
ejpam-524	137	15	a	a	DET
ejpam-524	137	16	dpd	dpd	NOUN
ejpam-524	137	17	-	-	PUNCT
ejpam-524	137	18	set	set	VERB
ejpam-524	137	19	if	if	SCONJ
ejpam-524	137	20	and	and	CCONJ
ejpam-524	137	21	only	only	ADV
ejpam-524	137	22	if	if	SCONJ
ejpam-524	137	23	no	no	DET
ejpam-524	137	24	two	two	NUM
ejpam-524	137	25	rows	row	NOUN
ejpam-524	137	26	of	of	ADP
ejpam-524	137	27	d∗mg	d∗mg	NOUN
ejpam-524	137	28	are	be	AUX
ejpam-524	137	29	identical	identical	ADJ
ejpam-524	137	30	.	.	PUNCT
ejpam-524	138	1	observation	observation	NOUN
ejpam-524	138	2	12	12	NUM
ejpam-524	138	3	.	.	PUNCT
ejpam-524	139	1	if	if	SCONJ
ejpam-524	139	2	m	m	NOUN
ejpam-524	139	3	is	be	AUX
ejpam-524	139	4	a	a	DET
ejpam-524	139	5	dpd	dpd	NOUN
ejpam-524	139	6	-	-	PUNCT
ejpam-524	139	7	set	set	NOUN
ejpam-524	139	8	of	of	ADP
ejpam-524	139	9	a	a	DET
ejpam-524	139	10	dpd	dpd	NOUN
ejpam-524	139	11	-	-	PUNCT
ejpam-524	139	12	graph	graph	NOUN
ejpam-524	139	13	g	g	NOUN
ejpam-524	139	14	,	,	PUNCT
ejpam-524	139	15	no	no	DET
ejpam-524	139	16	row	row	NOUN
ejpam-524	139	17	in	in	ADP
ejpam-524	139	18	d∗mg	d∗mg	PROPN
ejpam-524	139	19	is	be	AUX
ejpam-524	139	20	a	a	DET
ejpam-524	139	21	scalar	scalar	ADJ
ejpam-524	139	22	multiple	multiple	NOUN
ejpam-524	139	23	of	of	ADP
ejpam-524	139	24	any	any	DET
ejpam-524	139	25	other	other	ADJ
ejpam-524	139	26	row	row	NOUN
ejpam-524	139	27	.	.	PUNCT
ejpam-524	140	1	remark	remark	NOUN
ejpam-524	140	2	2	2	NUM
ejpam-524	140	3	.	.	PUNCT
ejpam-524	141	1	for	for	ADP
ejpam-524	141	2	any	any	PRON
ejpam-524	141	3	;	;	PUNCT
ejpam-524	141	4	6=	6=	NUM
ejpam-524	141	5	m	m	PROPN
ejpam-524	141	6	⊆	⊆	NUM
ejpam-524	141	7	v	v	NOUN
ejpam-524	141	8	(	(	PUNCT
ejpam-524	141	9	g	g	NOUN
ejpam-524	141	10	)	)	PUNCT
ejpam-524	141	11	,	,	PUNCT
ejpam-524	141	12	if	if	SCONJ
ejpam-524	141	13	the	the	DET
ejpam-524	141	14	rows	row	NOUN
ejpam-524	141	15	of	of	ADP
ejpam-524	141	16	d∗mg	d∗mg	NOUN
ejpam-524	141	17	are	be	AUX
ejpam-524	141	18	linearly	linearly	ADV
ejpam-524	141	19	independent	independent	ADJ
ejpam-524	141	20	,	,	PUNCT
ejpam-524	141	21	m	m	VERB
ejpam-524	141	22	is	be	AUX
ejpam-524	141	23	a	a	DET
ejpam-524	141	24	dpd	dpd	NOUN
ejpam-524	141	25	-	-	PUNCT
ejpam-524	141	26	set	set	NOUN
ejpam-524	141	27	.	.	PUNCT
ejpam-524	142	1	however	however	ADV
ejpam-524	142	2	,	,	PUNCT
ejpam-524	142	3	the	the	DET
ejpam-524	142	4	converse	converse	NOUN
ejpam-524	142	5	need	need	AUX
ejpam-524	142	6	not	not	PART
ejpam-524	142	7	be	be	AUX
ejpam-524	142	8	true	true	ADJ
ejpam-524	142	9	.	.	PUNCT
ejpam-524	143	1	for	for	ADP
ejpam-524	143	2	example	example	NOUN
ejpam-524	143	3	,	,	PUNCT
ejpam-524	143	4	let	let	VERB
ejpam-524	143	5	g	g	PRON
ejpam-524	143	6	be	be	AUX
ejpam-524	143	7	a	a	DET
ejpam-524	143	8	graph	graph	NOUN
ejpam-524	143	9	obtained	obtain	VERB
ejpam-524	143	10	by	by	ADP
ejpam-524	143	11	attaching	attach	VERB
ejpam-524	143	12	two	two	NUM
ejpam-524	143	13	vertices	vertex	NOUN
ejpam-524	143	14	u1	u1	NOUN
ejpam-524	143	15	and	and	CCONJ
ejpam-524	143	16	u2	u2	NOUN
ejpam-524	143	17	to	to	ADP
ejpam-524	143	18	two	two	NUM
ejpam-524	143	19	adjacent	adjacent	ADJ
ejpam-524	143	20	vertices	vertex	NOUN
ejpam-524	143	21	v4	v4	NOUN
ejpam-524	143	22	and	and	CCONJ
ejpam-524	143	23	v5	v5	VERB
ejpam-524	143	24	respectively	respectively	ADV
ejpam-524	143	25	of	of	ADP
ejpam-524	143	26	the	the	DET
ejpam-524	143	27	cycle	cycle	NOUN
ejpam-524	143	28	c5	c5	PROPN
ejpam-524	143	29	:	:	PUNCT
ejpam-524	143	30	v1v2v3v4v5	v1v2v3v4v5	NOUN
ejpam-524	143	31	.	.	PUNCT
ejpam-524	144	1	choose	choose	VERB
ejpam-524	144	2	m	m	NOUN
ejpam-524	144	3	=	=	SYM
ejpam-524	144	4	{	{	PUNCT
ejpam-524	144	5	v2	v2	PROPN
ejpam-524	144	6	,	,	PUNCT
ejpam-524	144	7	v3,u1	v3,u1	PROPN
ejpam-524	144	8	}	}	PUNCT
ejpam-524	144	9	.	.	PUNCT
ejpam-524	145	1	then	then	ADV
ejpam-524	145	2	,	,	PUNCT
ejpam-524	145	3	d∗mg	d∗mg	NOUN
ejpam-524	145	4	=	=	SYM
ejpam-524	145	5			PROPN
ejpam-524	145	6			NOUN
ejpam-524	145	7			NOUN
ejpam-524	145	8			NOUN
ejpam-524	145	9			NOUN
ejpam-524	145	10			NOUN
ejpam-524	145	11			NOUN
ejpam-524	145	12			NOUN
ejpam-524	145	13			NOUN
ejpam-524	145	14			NOUN
ejpam-524	145	15			NOUN
ejpam-524	145	16	1	1	NUM
ejpam-524	145	17	1	1	NUM
ejpam-524	145	18	1	1	NUM
ejpam-524	145	19	0	0	NUM
ejpam-524	145	20	1	1	NUM
ejpam-524	145	21	1	1	NUM
ejpam-524	145	22	0	0	NUM
ejpam-524	145	23	1	1	NUM
ejpam-524	145	24	0	0	NUM
ejpam-524	145	25	1	1	NUM
ejpam-524	145	26	1	1	NUM
ejpam-524	145	27	1	1	NUM
ejpam-524	145	28	1	1	NUM
ejpam-524	145	29	0	0	NUM
ejpam-524	145	30	1	1	NUM
ejpam-524	145	31	1	1	NUM
ejpam-524	145	32	0	0	NUM
ejpam-524	145	33	1	1	NUM
ejpam-524	145	34	1	1	NUM
ejpam-524	145	35	0	0	NUM
ejpam-524	145	36	0	0	NUM
ejpam-524	145	37	0	0	NUM
ejpam-524	145	38	1	1	NUM
ejpam-524	145	39	0	0	NUM
ejpam-524	145	40	0	0	NUM
ejpam-524	145	41	0	0	NUM
ejpam-524	145	42	0	0	NUM
ejpam-524	145	43	1	1	NUM
ejpam-524	145	44			NOUN
ejpam-524	145	45			NOUN
ejpam-524	145	46			VERB
ejpam-524	145	47			NOUN
ejpam-524	145	48			NOUN
ejpam-524	145	49			NOUN
ejpam-524	145	50			NOUN
ejpam-524	145	51			NOUN
ejpam-524	145	52			NOUN
ejpam-524	145	53			NOUN
ejpam-524	145	54			PUNCT
ejpam-524	146	1	in	in	ADP
ejpam-524	146	2	d∗mg	d∗mg	NOUN
ejpam-524	146	3	the	the	DET
ejpam-524	146	4	third	third	ADJ
ejpam-524	146	5	row	row	NOUN
ejpam-524	146	6	is	be	AUX
ejpam-524	146	7	the	the	DET
ejpam-524	146	8	sum	sum	NOUN
ejpam-524	146	9	of	of	ADP
ejpam-524	146	10	fifth	fifth	ADJ
ejpam-524	146	11	and	and	CCONJ
ejpam-524	146	12	seventh	seventh	ADJ
ejpam-524	146	13	rows	row	NOUN
ejpam-524	146	14	.	.	PUNCT
ejpam-524	147	1	g.	g.	PROPN
ejpam-524	147	2	augustine	augustine	PROPN
ejpam-524	147	3	,	,	PUNCT
ejpam-524	147	4	a.	a.	PROPN
ejpam-524	147	5	joseph	joseph	PROPN
ejpam-524	147	6	,	,	PUNCT
ejpam-524	147	7	s.	s.	PROPN
ejpam-524	147	8	jose	jose	PROPN
ejpam-524	147	9	/	/	SYM
ejpam-524	147	10	eur	eur	PROPN
ejpam-524	147	11	.	.	PUNCT
ejpam-524	148	1	j.	j.	PROPN
ejpam-524	148	2	pure	pure	PROPN
ejpam-524	148	3	appl	appl	PROPN
ejpam-524	148	4	.	.	PROPN
ejpam-524	148	5	math	math	PROPN
ejpam-524	148	6	,	,	PUNCT
ejpam-524	148	7	3	3	NUM
ejpam-524	148	8	(	(	PUNCT
ejpam-524	148	9	2010	2010	NUM
ejpam-524	148	10	)	)	PUNCT
ejpam-524	148	11	,	,	PUNCT
ejpam-524	148	12	748	748	NUM
ejpam-524	148	13	-	-	SYM
ejpam-524	148	14	764	764	NUM
ejpam-524	148	15	752	752	NUM
ejpam-524	148	16	lemma	lemma	PROPN
ejpam-524	148	17	2	2	NUM
ejpam-524	148	18	.	.	PUNCT
ejpam-524	149	1	let	let	VERB
ejpam-524	149	2	g	g	PRON
ejpam-524	149	3	be	be	AUX
ejpam-524	149	4	a	a	DET
ejpam-524	149	5	graph	graph	NOUN
ejpam-524	149	6	with	with	ADP
ejpam-524	149	7	dpd	dpd	NOUN
ejpam-524	149	8	-	-	PUNCT
ejpam-524	149	9	set	set	VERB
ejpam-524	149	10	m.	m.	NOUN
ejpam-524	149	11	if	if	SCONJ
ejpam-524	149	12	there	there	PRON
ejpam-524	149	13	exists	exist	VERB
ejpam-524	149	14	a	a	DET
ejpam-524	149	15	row	row	NOUN
ejpam-524	149	16	say	say	PROPN
ejpam-524	149	17	,	,	PUNCT
ejpam-524	149	18	rm	rm	PROPN
ejpam-524	149	19	,	,	PUNCT
ejpam-524	149	20	in	in	ADP
ejpam-524	149	21	d∗mg	d∗mg	NOUN
ejpam-524	149	22	as	as	ADP
ejpam-524	149	23	the	the	DET
ejpam-524	149	24	sum	sum	NOUN
ejpam-524	149	25	of	of	ADP
ejpam-524	149	26	any	any	DET
ejpam-524	149	27	other	other	ADJ
ejpam-524	149	28	rows	row	NOUN
ejpam-524	149	29	,	,	PUNCT
ejpam-524	149	30	say	say	INTJ
ejpam-524	149	31	,	,	PUNCT
ejpam-524	149	32	r1,r2	r1,r2	PROPN
ejpam-524	149	33	,	,	PUNCT
ejpam-524	149	34	.	.	PUNCT
ejpam-524	149	35	.	.	PUNCT
ejpam-524	150	1	.	.	PUNCT
ejpam-524	151	1	,	,	PUNCT
ejpam-524	151	2	rk	rk	NOUN
ejpam-524	151	3	then	then	ADV
ejpam-524	151	4	,	,	PUNCT
ejpam-524	151	5	each	each	DET
ejpam-524	151	6	column	column	NOUN
ejpam-524	151	7	sum	sum	NOUN
ejpam-524	151	8	of	of	ADP
ejpam-524	151	9	the	the	DET
ejpam-524	151	10	sub	sub	NOUN
ejpam-524	151	11	matrix	matrix	NOUN
ejpam-524	151	12	formed	form	VERB
ejpam-524	151	13	by	by	ADP
ejpam-524	151	14	r1,r2	r1,r2	PROPN
ejpam-524	151	15	,	,	PUNCT
ejpam-524	151	16	.	.	PUNCT
ejpam-524	151	17	.	.	PUNCT
ejpam-524	152	1	.	.	PUNCT
ejpam-524	153	1	,	,	PUNCT
ejpam-524	153	2	rk	rk	NOUN
ejpam-524	153	3	is	be	AUX
ejpam-524	153	4	either	either	CCONJ
ejpam-524	153	5	0	0	NUM
ejpam-524	153	6	or	or	CCONJ
ejpam-524	153	7	1	1	NUM
ejpam-524	153	8	.	.	PUNCT
ejpam-524	154	1	proof	proof	NOUN
ejpam-524	154	2	.	.	PUNCT
ejpam-524	155	1	let	let	VERB
ejpam-524	155	2	c	c	PROPN
ejpam-524	155	3	j	j	VERB
ejpam-524	155	4	:	:	PUNCT
ejpam-524	155	5	j	j	X
ejpam-524	155	6	=	=	SYM
ejpam-524	155	7	1,2	1,2	NUM
ejpam-524	155	8	,	,	PUNCT
ejpam-524	155	9	.	.	PUNCT
ejpam-524	155	10	.	.	PUNCT
ejpam-524	156	1	.	.	PUNCT
ejpam-524	157	1	,	,	PUNCT
ejpam-524	157	2	(	(	PUNCT
ejpam-524	157	3	dg	dg	X
ejpam-524	157	4	+	+	NOUN
ejpam-524	157	5	1	1	X
ejpam-524	157	6	)	)	PUNCT
ejpam-524	157	7	be	be	VERB
ejpam-524	157	8	the	the	DET
ejpam-524	157	9	j	j	PROPN
ejpam-524	157	10	th	th	X
ejpam-524	157	11	column	column	NOUN
ejpam-524	157	12	sum	sum	NOUN
ejpam-524	157	13	of	of	ADP
ejpam-524	157	14	the	the	DET
ejpam-524	157	15	sub	sub	NOUN
ejpam-524	157	16	-	-	NOUN
ejpam-524	157	17	matrix	matrix	NOUN
ejpam-524	157	18	formed	form	VERB
ejpam-524	157	19	by	by	ADP
ejpam-524	157	20	r1,r2	r1,r2	PROPN
ejpam-524	157	21	,	,	PUNCT
ejpam-524	157	22	.	.	PUNCT
ejpam-524	157	23	.	.	PUNCT
ejpam-524	158	1	.	.	PUNCT
ejpam-524	159	1	,	,	PUNCT
ejpam-524	159	2	rk	rk	PROPN
ejpam-524	159	3	.	.	PROPN
ejpam-524	159	4	assume	assume	VERB
ejpam-524	159	5	c	c	PROPN
ejpam-524	159	6	j	j	PROPN
ejpam-524	160	1	=	=	PUNCT
ejpam-524	160	2	c	c	PROPN
ejpam-524	160	3	where	where	SCONJ
ejpam-524	160	4	c	c	NOUN
ejpam-524	160	5	is	be	AUX
ejpam-524	160	6	a	a	DET
ejpam-524	160	7	constant	constant	ADJ
ejpam-524	160	8	not	not	PART
ejpam-524	160	9	equal	equal	ADJ
ejpam-524	160	10	to	to	ADP
ejpam-524	160	11	0	0	NUM
ejpam-524	160	12	or	or	CCONJ
ejpam-524	160	13	1	1	NUM
ejpam-524	160	14	for	for	ADP
ejpam-524	160	15	some	some	DET
ejpam-524	160	16	j.	j.	PROPN
ejpam-524	160	17	then	then	ADV
ejpam-524	160	18	the	the	DET
ejpam-524	160	19	j	j	PROPN
ejpam-524	160	20	th	th	X
ejpam-524	160	21	entry	entry	NOUN
ejpam-524	160	22	in	in	ADP
ejpam-524	160	23	row	row	NOUN
ejpam-524	160	24	rm	rm	PROPN
ejpam-524	160	25	is	be	AUX
ejpam-524	160	26	,	,	PUNCT
ejpam-524	160	27	c	c	PROPN
ejpam-524	160	28	6=	6=	PROPN
ejpam-524	160	29	0	0	NUM
ejpam-524	160	30	,	,	PUNCT
ejpam-524	160	31	1	1	NUM
ejpam-524	160	32	,	,	PUNCT
ejpam-524	160	33	which	which	PRON
ejpam-524	160	34	is	be	AUX
ejpam-524	160	35	a	a	DET
ejpam-524	160	36	contradiction	contradiction	NOUN
ejpam-524	160	37	to	to	ADP
ejpam-524	160	38	the	the	DET
ejpam-524	160	39	fact	fact	NOUN
ejpam-524	160	40	that	that	SCONJ
ejpam-524	160	41	d∗mg	d∗mg	NOUN
ejpam-524	160	42	is	be	AUX
ejpam-524	160	43	a	a	DET
ejpam-524	160	44	(	(	PUNCT
ejpam-524	160	45	0,1)−matrix	0,1)−matrix	NOUN
ejpam-524	160	46	.	.	PUNCT
ejpam-524	161	1	proposition	proposition	NOUN
ejpam-524	161	2	3	3	NUM
ejpam-524	161	3	.	.	PUNCT
ejpam-524	162	1	any	any	DET
ejpam-524	162	2	dpd	dpd	NOUN
ejpam-524	162	3	-	-	PUNCT
ejpam-524	162	4	graph	graph	NOUN
ejpam-524	162	5	g	g	NOUN
ejpam-524	162	6	,	,	PUNCT
ejpam-524	162	7	with	with	ADP
ejpam-524	162	8	dpd	dpd	NOUN
ejpam-524	162	9	-	-	PUNCT
ejpam-524	162	10	set	set	VERB
ejpam-524	162	11	m	m	NOUN
ejpam-524	162	12	and	and	CCONJ
ejpam-524	162	13	the	the	DET
ejpam-524	162	14	m	m	PROPN
ejpam-524	162	15	-	-	PROPN
ejpam-524	162	16	dnp	dnp	PROPN
ejpam-524	162	17	matrix	matrix	NOUN
ejpam-524	162	18	dm	dm	VERB
ejpam-524	162	19	g	g	NOUN
ejpam-524	162	20	as	as	ADP
ejpam-524	162	21	an	an	DET
ejpam-524	162	22	identity	identity	NOUN
ejpam-524	162	23	matrix	matrix	NOUN
ejpam-524	162	24	of	of	ADP
ejpam-524	162	25	order	order	NOUN
ejpam-524	162	26	n	n	PRON
ejpam-524	162	27	is	be	AUX
ejpam-524	162	28	isomorphic	isomorphic	ADJ
ejpam-524	162	29	to	to	ADP
ejpam-524	162	30	a	a	DET
ejpam-524	162	31	path	path	NOUN
ejpam-524	162	32	pn	pn	NOUN
ejpam-524	162	33	on	on	ADP
ejpam-524	162	34	n	n	PRON
ejpam-524	162	35	vertices	vertex	NOUN
ejpam-524	162	36	with	with	ADP
ejpam-524	162	37	dpd	dpd	NOUN
ejpam-524	162	38	-	-	PUNCT
ejpam-524	162	39	set	set	VERB
ejpam-524	162	40	m	m	NOUN
ejpam-524	162	41	as	as	ADP
ejpam-524	162	42	any	any	PRON
ejpam-524	162	43	of	of	ADP
ejpam-524	162	44	its	its	PRON
ejpam-524	162	45	pendent	pendent	ADJ
ejpam-524	162	46	vertices	vertex	NOUN
ejpam-524	162	47	.	.	PUNCT
ejpam-524	163	1	proof	proof	NOUN
ejpam-524	163	2	.	.	PUNCT
ejpam-524	164	1	let	let	VERB
ejpam-524	164	2	g	g	PRON
ejpam-524	164	3	be	be	AUX
ejpam-524	164	4	a	a	DET
ejpam-524	164	5	graph	graph	NOUN
ejpam-524	164	6	with	with	ADP
ejpam-524	164	7	dpd	dpd	NOUN
ejpam-524	164	8	-	-	PUNCT
ejpam-524	164	9	set	set	NOUN
ejpam-524	164	10	m	m	VERB
ejpam-524	164	11	such	such	ADJ
ejpam-524	164	12	that	that	SCONJ
ejpam-524	164	13	dm	dm	PROPN
ejpam-524	164	14	g	g	NOUN
ejpam-524	164	15	∼=	∼=	PROPN
ejpam-524	164	16	in	in	ADV
ejpam-524	164	17	,	,	PUNCT
ejpam-524	164	18	the	the	DET
ejpam-524	164	19	identity	identity	NOUN
ejpam-524	164	20	matrix	matrix	NOUN
ejpam-524	164	21	of	of	ADP
ejpam-524	164	22	order	order	NOUN
ejpam-524	164	23	n.	n.	NOUN
ejpam-524	164	24	from	from	ADP
ejpam-524	164	25	corollary	corollary	ADJ
ejpam-524	164	26	4	4	NUM
ejpam-524	164	27	,	,	PUNCT
ejpam-524	164	28	sum	sum	NOUN
ejpam-524	164	29	of	of	ADP
ejpam-524	164	30	the	the	DET
ejpam-524	164	31	entries	entry	NOUN
ejpam-524	164	32	in	in	ADP
ejpam-524	164	33	each	each	DET
ejpam-524	164	34	row	row	NOUN
ejpam-524	164	35	of	of	ADP
ejpam-524	164	36	dm	dm	NOUN
ejpam-524	164	37	g	g	NOUN
ejpam-524	164	38	=	=	PUNCT
ejpam-524	164	39	|m	|m	NOUN
ejpam-524	164	40	|	|	ADV
ejpam-524	164	41	.	.	PUNCT
ejpam-524	165	1	hence	hence	ADV
ejpam-524	165	2	|m	|m	NOUN
ejpam-524	165	3	|	|	ADV
ejpam-524	165	4	=	=	SYM
ejpam-524	165	5	1	1	NUM
ejpam-524	165	6	,	,	PUNCT
ejpam-524	165	7	since	since	ADV
ejpam-524	165	8	,	,	PUNCT
ejpam-524	165	9	dm	dm	PROPN
ejpam-524	165	10	g	g	NOUN
ejpam-524	165	11	∼=	∼=	ADV
ejpam-524	165	12	in	in	ADP
ejpam-524	165	13	.	.	PUNCT
ejpam-524	166	1	since	since	SCONJ
ejpam-524	166	2	|m	|m	NOUN
ejpam-524	166	3	|	|	NOUN
ejpam-524	166	4	=	=	SYM
ejpam-524	166	5	1	1	NUM
ejpam-524	166	6	,	,	PUNCT
ejpam-524	166	7	m	m	VERB
ejpam-524	166	8	=	=	SYM
ejpam-524	166	9	{	{	PUNCT
ejpam-524	166	10	x	x	NOUN
ejpam-524	166	11	}	}	PUNCT
ejpam-524	166	12	,	,	PUNCT
ejpam-524	166	13	where	where	SCONJ
ejpam-524	166	14	x	x	PRON
ejpam-524	166	15	is	be	AUX
ejpam-524	166	16	any	any	DET
ejpam-524	166	17	vertex	vertex	NOUN
ejpam-524	166	18	in	in	ADP
ejpam-524	166	19	g.	g.	PROPN
ejpam-524	166	20	we	we	PRON
ejpam-524	166	21	claim	claim	VERB
ejpam-524	166	22	that	that	SCONJ
ejpam-524	166	23	x	x	PRON
ejpam-524	166	24	is	be	AUX
ejpam-524	166	25	a	a	DET
ejpam-524	166	26	pendent	pendent	ADJ
ejpam-524	166	27	vertex	vertex	NOUN
ejpam-524	166	28	.	.	PUNCT
ejpam-524	167	1	if	if	SCONJ
ejpam-524	167	2	possible	possible	ADJ
ejpam-524	167	3	assume	assume	VERB
ejpam-524	167	4	there	there	PRON
ejpam-524	167	5	exists	exist	VERB
ejpam-524	167	6	at	at	ADP
ejpam-524	167	7	least	least	ADV
ejpam-524	167	8	two	two	NUM
ejpam-524	167	9	vertices	vertex	NOUN
ejpam-524	167	10	v1	v1	NOUN
ejpam-524	167	11	,	,	PUNCT
ejpam-524	167	12	v2	v2	PROPN
ejpam-524	167	13	∈	∈	PROPN
ejpam-524	167	14	v	v	NOUN
ejpam-524	167	15	(	(	PUNCT
ejpam-524	167	16	g	g	NOUN
ejpam-524	167	17	)	)	PUNCT
ejpam-524	167	18	adjacent	adjacent	ADJ
ejpam-524	167	19	to	to	ADP
ejpam-524	167	20	x	x	PROPN
ejpam-524	167	21	.	.	PUNCT
ejpam-524	168	1	then	then	ADV
ejpam-524	168	2	the	the	DET
ejpam-524	168	3	rows	row	NOUN
ejpam-524	168	4	corresponding	correspond	VERB
ejpam-524	168	5	to	to	PART
ejpam-524	168	6	v1	v1	VERB
ejpam-524	168	7	and	and	CCONJ
ejpam-524	168	8	v2	v2	VERB
ejpam-524	168	9	in	in	ADP
ejpam-524	168	10	dm	dm	PROPN
ejpam-524	168	11	g	g	NOUN
ejpam-524	168	12	will	will	AUX
ejpam-524	168	13	be	be	AUX
ejpam-524	168	14	�	�	PROPN
ejpam-524	168	15	0	0	NUM
ejpam-524	168	16	1	1	NUM
ejpam-524	168	17	0	0	NUM
ejpam-524	168	18	.	.	PUNCT
ejpam-524	168	19	.	.	PUNCT
ejpam-524	169	1	.	.	PUNCT
ejpam-524	170	1	0	0	NUM
ejpam-524	171	1	0	0	NUM
ejpam-524	171	2	0	0	NUM
ejpam-524	171	3	1	1	NUM
ejpam-524	171	4	0	0	NUM
ejpam-524	171	5	.	.	PUNCT
ejpam-524	171	6	.	.	PUNCT
ejpam-524	172	1	.	.	PUNCT
ejpam-524	173	1	0	0	NUM
ejpam-524	173	2	0	0	NUM
ejpam-524	173	3	�	�	PROPN
ejpam-524	173	4	,	,	PUNCT
ejpam-524	173	5	which	which	PRON
ejpam-524	173	6	is	be	AUX
ejpam-524	173	7	not	not	PART
ejpam-524	173	8	possible	possible	ADJ
ejpam-524	173	9	since	since	ADV
ejpam-524	173	10	,	,	PUNCT
ejpam-524	173	11	dm	dm	PROPN
ejpam-524	173	12	g	g	NOUN
ejpam-524	173	13	∼=	∼=	ADV
ejpam-524	173	14	in	in	ADP
ejpam-524	173	15	.	.	PUNCT
ejpam-524	174	1	therefore	therefore	ADV
ejpam-524	174	2	,	,	PUNCT
ejpam-524	174	3	x	x	X
ejpam-524	174	4	is	be	AUX
ejpam-524	174	5	a	a	DET
ejpam-524	174	6	pendent	pendent	ADJ
ejpam-524	174	7	vertex	vertex	NOUN
ejpam-524	174	8	.	.	PUNCT
ejpam-524	175	1	now	now	ADV
ejpam-524	175	2	we	we	PRON
ejpam-524	175	3	prove	prove	VERB
ejpam-524	175	4	that	that	SCONJ
ejpam-524	175	5	g	g	PROPN
ejpam-524	175	6	∼=	∼=	PROPN
ejpam-524	175	7	pn	pn	NOUN
ejpam-524	175	8	,	,	PUNCT
ejpam-524	175	9	a	a	DET
ejpam-524	175	10	path	path	NOUN
ejpam-524	175	11	on	on	ADP
ejpam-524	175	12	n	n	DET
ejpam-524	175	13	vertices	vertex	NOUN
ejpam-524	175	14	.	.	PUNCT
ejpam-524	176	1	since	since	ADV
ejpam-524	176	2	,	,	PUNCT
ejpam-524	176	3	dm	dm	PROPN
ejpam-524	176	4	g	g	NOUN
ejpam-524	176	5	∼=	∼=	PROPN
ejpam-524	176	6	in	in	ADP
ejpam-524	176	7	,	,	PUNCT
ejpam-524	176	8	o(g	o(g	PROPN
ejpam-524	176	9	)	)	PUNCT
ejpam-524	176	10	=	=	SYM
ejpam-524	177	1	n	n	PROPN
ejpam-524	177	2	and	and	CCONJ
ejpam-524	177	3	dg	dg	PROPN
ejpam-524	177	4	=	=	SYM
ejpam-524	177	5	n−	n−	NOUN
ejpam-524	177	6	1	1	NUM
ejpam-524	177	7	.	.	PUNCT
ejpam-524	178	1	since	since	SCONJ
ejpam-524	178	2	dg	dg	NOUN
ejpam-524	178	3	=	=	PUNCT
ejpam-524	178	4	n−	n−	NOUN
ejpam-524	178	5	1	1	NUM
ejpam-524	178	6	,	,	PUNCT
ejpam-524	178	7	g	g	PROPN
ejpam-524	178	8	contains	contain	VERB
ejpam-524	178	9	a	a	DET
ejpam-524	178	10	path	path	NOUN
ejpam-524	178	11	of	of	ADP
ejpam-524	178	12	length	length	NOUN
ejpam-524	178	13	n−	n−	NOUN
ejpam-524	178	14	1	1	NUM
ejpam-524	178	15	.	.	PUNCT
ejpam-524	178	16	since	since	SCONJ
ejpam-524	178	17	o(g	o(g	NOUN
ejpam-524	178	18	)	)	PUNCT
ejpam-524	178	19	=	=	SYM
ejpam-524	178	20	o(pn	o(pn	PROPN
ejpam-524	178	21	)	)	PUNCT
ejpam-524	178	22	=	=	SYM
ejpam-524	178	23	n	n	CCONJ
ejpam-524	178	24	,	,	PUNCT
ejpam-524	178	25	number	number	NOUN
ejpam-524	178	26	of	of	ADP
ejpam-524	178	27	vertices	vertex	NOUN
ejpam-524	178	28	of	of	ADP
ejpam-524	178	29	g	g	PROPN
ejpam-524	178	30	and	and	CCONJ
ejpam-524	178	31	pn	pn	PROPN
ejpam-524	178	32	are	be	AUX
ejpam-524	178	33	same	same	ADJ
ejpam-524	178	34	.	.	PUNCT
ejpam-524	179	1	now	now	ADV
ejpam-524	179	2	,	,	PUNCT
ejpam-524	179	3	if	if	SCONJ
ejpam-524	179	4	g	g	PROPN
ejpam-524	179	5	�	�	PROPN
ejpam-524	179	6	pn	pn	PROPN
ejpam-524	179	7	,	,	PUNCT
ejpam-524	179	8	g	g	PROPN
ejpam-524	179	9	contains	contain	VERB
ejpam-524	179	10	at	at	ADV
ejpam-524	179	11	least	least	ADV
ejpam-524	179	12	one	one	NUM
ejpam-524	179	13	edge	edge	NOUN
ejpam-524	179	14	other	other	ADJ
ejpam-524	179	15	than	than	ADP
ejpam-524	179	16	the	the	DET
ejpam-524	179	17	edges	edge	NOUN
ejpam-524	179	18	of	of	ADP
ejpam-524	179	19	pn	pn	NOUN
ejpam-524	179	20	,	,	PUNCT
ejpam-524	179	21	which	which	PRON
ejpam-524	179	22	is	be	AUX
ejpam-524	179	23	not	not	PART
ejpam-524	179	24	possible	possible	ADJ
ejpam-524	179	25	,	,	PUNCT
ejpam-524	179	26	since	since	SCONJ
ejpam-524	179	27	dg	dg	NOUN
ejpam-524	179	28	=	=	SYM
ejpam-524	179	29	n−	n−	NOUN
ejpam-524	179	30	1	1	NUM
ejpam-524	179	31	.	.	PUNCT
ejpam-524	180	1	hence	hence	ADV
ejpam-524	180	2	,	,	PUNCT
ejpam-524	180	3	g	g	PROPN
ejpam-524	180	4	∼=	∼=	PROPN
ejpam-524	180	5	pn	pn	NOUN
ejpam-524	180	6	,	,	PUNCT
ejpam-524	180	7	the	the	DET
ejpam-524	180	8	path	path	NOUN
ejpam-524	180	9	on	on	ADP
ejpam-524	180	10	n	n	DET
ejpam-524	180	11	vertices	vertex	NOUN
ejpam-524	180	12	.	.	PUNCT
ejpam-524	181	1	for	for	ADP
ejpam-524	181	2	the	the	DET
ejpam-524	181	3	converse	converse	NOUN
ejpam-524	181	4	,	,	PUNCT
ejpam-524	181	5	consider	consider	VERB
ejpam-524	181	6	the	the	DET
ejpam-524	181	7	path	path	NOUN
ejpam-524	181	8	pn	pn	PROPN
ejpam-524	181	9	=	=	PUNCT
ejpam-524	181	10	v1v2	v1v2	PROPN
ejpam-524	181	11	.	.	PUNCT
ejpam-524	181	12	.	.	PUNCT
ejpam-524	182	1	.	.	PUNCT
ejpam-524	183	1	vn	vn	VERB
ejpam-524	183	2	with	with	ADP
ejpam-524	183	3	dpd	dpd	NOUN
ejpam-524	183	4	-	-	PUNCT
ejpam-524	183	5	set	set	VERB
ejpam-524	183	6	m	m	NOUN
ejpam-524	183	7	as	as	ADP
ejpam-524	183	8	any	any	PRON
ejpam-524	183	9	of	of	ADP
ejpam-524	183	10	its	its	PRON
ejpam-524	183	11	pendent	pendent	ADJ
ejpam-524	183	12	vertices	vertex	NOUN
ejpam-524	183	13	.	.	PUNCT
ejpam-524	184	1	then	then	ADV
ejpam-524	184	2	,	,	PUNCT
ejpam-524	184	3	dm	dm	INTJ
ejpam-524	184	4	g	g	NOUN
ejpam-524	184	5	=	=	PUNCT
ejpam-524	184	6	in	in	ADP
ejpam-524	184	7	=	=	NOUN
ejpam-524	184	8			PROPN
ejpam-524	184	9			NOUN
ejpam-524	184	10			NOUN
ejpam-524	184	11			NOUN
ejpam-524	184	12			NOUN
ejpam-524	184	13	1	1	NUM
ejpam-524	184	14	0	0	NUM
ejpam-524	184	15	0	0	NUM
ejpam-524	184	16	.	.	PUNCT
ejpam-524	184	17	.	.	PUNCT
ejpam-524	184	18	.	.	PUNCT
ejpam-524	185	1	0	0	NUM
ejpam-524	186	1	0	0	NUM
ejpam-524	186	2	1	1	NUM
ejpam-524	186	3	0	0	NUM
ejpam-524	186	4	.	.	PUNCT
ejpam-524	186	5	.	.	PUNCT
ejpam-524	186	6	.	.	PUNCT
ejpam-524	187	1	0	0	PUNCT
ejpam-524	187	2	.	.	PUNCT
ejpam-524	187	3	.	.	PUNCT
ejpam-524	187	4	.	.	PUNCT
ejpam-524	187	5	.	.	PUNCT
ejpam-524	187	6	.	.	PUNCT
ejpam-524	187	7	.	.	PUNCT
ejpam-524	187	8	.	.	PUNCT
ejpam-524	187	9	.	.	PUNCT
ejpam-524	187	10	.	.	PUNCT
ejpam-524	187	11	.	.	PUNCT
ejpam-524	187	12	.	.	PUNCT
ejpam-524	187	13	.	.	PUNCT
ejpam-524	187	14	.	.	PUNCT
ejpam-524	187	15	.	.	PUNCT
ejpam-524	188	1	.	.	PUNCT
ejpam-524	189	1	0	0	NUM
ejpam-524	190	1	0	0	NUM
ejpam-524	190	2	0	0	NUM
ejpam-524	190	3	.	.	PUNCT
ejpam-524	190	4	.	.	PUNCT
ejpam-524	190	5	.	.	PUNCT
ejpam-524	191	1	1	1	NUM
ejpam-524	191	2			NOUN
ejpam-524	191	3			NOUN
ejpam-524	191	4			VERB
ejpam-524	191	5			NOUN
ejpam-524	191	6			PUNCT
ejpam-524	192	1	proposition	proposition	NOUN
ejpam-524	192	2	4	4	X
ejpam-524	192	3	.	.	PUNCT
ejpam-524	193	1	let	let	VERB
ejpam-524	193	2	g	g	PRON
ejpam-524	193	3	be	be	AUX
ejpam-524	193	4	a	a	DET
ejpam-524	193	5	dpd	dpd	NOUN
ejpam-524	193	6	-	-	PUNCT
ejpam-524	193	7	graph	graph	NOUN
ejpam-524	193	8	.	.	PUNCT
ejpam-524	194	1	then	then	ADV
ejpam-524	194	2	the	the	DET
ejpam-524	194	3	dnp	dnp	PROPN
ejpam-524	194	4	-	-	PUNCT
ejpam-524	194	5	matrix	matrix	NOUN
ejpam-524	194	6	dm	dm	X
ejpam-524	194	7	g	g	NOUN
ejpam-524	194	8	of	of	ADP
ejpam-524	194	9	g	g	PROPN
ejpam-524	194	10	is	be	AUX
ejpam-524	194	11	a	a	DET
ejpam-524	194	12	diagonal	diagonal	ADJ
ejpam-524	194	13	matrix	matrix	NOUN
ejpam-524	194	14	if	if	SCONJ
ejpam-524	194	15	and	and	CCONJ
ejpam-524	194	16	only	only	ADV
ejpam-524	194	17	if	if	SCONJ
ejpam-524	194	18	all	all	DET
ejpam-524	194	19	the	the	DET
ejpam-524	194	20	diagonal	diagonal	ADJ
ejpam-524	194	21	entries	entry	NOUN
ejpam-524	194	22	in	in	ADP
ejpam-524	194	23	dm	dm	PROPN
ejpam-524	194	24	g	g	PROPN
ejpam-524	194	25	are	be	AUX
ejpam-524	194	26	unity	unity	NOUN
ejpam-524	194	27	.	.	PUNCT
ejpam-524	195	1	also	also	ADV
ejpam-524	195	2	,	,	PUNCT
ejpam-524	195	3	dm	dm	PROPN
ejpam-524	195	4	g	g	PROPN
ejpam-524	195	5	can	can	AUX
ejpam-524	195	6	neither	neither	CCONJ
ejpam-524	195	7	be	be	AUX
ejpam-524	195	8	upper	upper	ADJ
ejpam-524	195	9	triangular	triangular	NOUN
ejpam-524	195	10	nor	nor	CCONJ
ejpam-524	195	11	lower	low	ADJ
ejpam-524	195	12	triangular	triangular	NOUN
ejpam-524	195	13	.	.	PUNCT
ejpam-524	196	1	proof	proof	NOUN
ejpam-524	196	2	.	.	PUNCT
ejpam-524	197	1	let	let	VERB
ejpam-524	197	2	g	g	PRON
ejpam-524	197	3	be	be	AUX
ejpam-524	197	4	graph	graph	NOUN
ejpam-524	197	5	with	with	ADP
ejpam-524	197	6	dpd	dpd	NOUN
ejpam-524	197	7	-	-	PUNCT
ejpam-524	197	8	set	set	VERB
ejpam-524	197	9	m	m	NOUN
ejpam-524	197	10	and	and	CCONJ
ejpam-524	197	11	m	m	PROPN
ejpam-524	197	12	-dnp	-dnp	NOUN
ejpam-524	197	13	matrix	matrix	NOUN
ejpam-524	197	14	dm	dm	VERB
ejpam-524	197	15	g	g	PROPN
ejpam-524	197	16	,	,	PUNCT
ejpam-524	197	17	a	a	DET
ejpam-524	197	18	diagonal	diagonal	ADJ
ejpam-524	197	19	matrix	matrix	NOUN
ejpam-524	197	20	say	say	VERB
ejpam-524	197	21	,	,	PUNCT
ejpam-524	197	22	d.	d.	PROPN
ejpam-524	197	23	by	by	ADP
ejpam-524	197	24	proposition	proposition	NOUN
ejpam-524	197	25	2	2	NUM
ejpam-524	197	26	,	,	PUNCT
ejpam-524	197	27	entries	entry	NOUN
ejpam-524	197	28	in	in	ADP
ejpam-524	197	29	the	the	DET
ejpam-524	197	30	first	first	ADJ
ejpam-524	197	31	column	column	NOUN
ejpam-524	197	32	of	of	ADP
ejpam-524	197	33	dm	dm	PROPN
ejpam-524	197	34	g	g	PROPN
ejpam-524	197	35	are	be	AUX
ejpam-524	197	36	0	0	NUM
ejpam-524	197	37	or	or	CCONJ
ejpam-524	197	38	1	1	NUM
ejpam-524	197	39	and	and	CCONJ
ejpam-524	197	40	by	by	ADP
ejpam-524	197	41	observation	observation	NOUN
ejpam-524	197	42	10	10	NUM
ejpam-524	197	43	,	,	PUNCT
ejpam-524	197	44	dm	dm	PRON
ejpam-524	197	45	g	g	PROPN
ejpam-524	197	46	does	do	AUX
ejpam-524	197	47	not	not	PART
ejpam-524	197	48	admit	admit	VERB
ejpam-524	197	49	null	null	ADJ
ejpam-524	197	50	rows	row	NOUN
ejpam-524	197	51	,	,	PUNCT
ejpam-524	197	52	hence	hence	ADV
ejpam-524	197	53	,	,	PUNCT
ejpam-524	197	54	a11	a11	PROPN
ejpam-524	197	55	=	=	SYM
ejpam-524	197	56	1	1	X
ejpam-524	197	57	.	.	PUNCT
ejpam-524	198	1	also	also	ADV
ejpam-524	198	2	,	,	PUNCT
ejpam-524	198	3	by	by	ADP
ejpam-524	198	4	corollary	corollary	ADJ
ejpam-524	198	5	4	4	NUM
ejpam-524	198	6	,	,	PUNCT
ejpam-524	198	7	the	the	DET
ejpam-524	198	8	sum	sum	NOUN
ejpam-524	198	9	of	of	ADP
ejpam-524	198	10	the	the	DET
ejpam-524	198	11	entries	entry	NOUN
ejpam-524	198	12	in	in	ADP
ejpam-524	198	13	each	each	DET
ejpam-524	198	14	row	row	NOUN
ejpam-524	198	15	of	of	ADP
ejpam-524	198	16	dm	dm	NOUN
ejpam-524	198	17	g	g	NOUN
ejpam-524	198	18	=	=	PUNCT
ejpam-524	198	19	|m	|m	NOUN
ejpam-524	198	20	|	|	ADV
ejpam-524	198	21	.	.	PUNCT
ejpam-524	199	1	therefore	therefore	ADV
ejpam-524	199	2	,	,	PUNCT
ejpam-524	199	3	from	from	ADP
ejpam-524	199	4	first	first	ADJ
ejpam-524	199	5	row	row	NOUN
ejpam-524	199	6	of	of	ADP
ejpam-524	199	7	d	d	PROPN
ejpam-524	199	8	,	,	PUNCT
ejpam-524	199	9	|m	|m	VERB
ejpam-524	199	10	|	|	NOUN
ejpam-524	199	11	=	=	SYM
ejpam-524	199	12	1	1	NUM
ejpam-524	199	13	and	and	CCONJ
ejpam-524	199	14	hence	hence	ADV
ejpam-524	199	15	aii	aii	X
ejpam-524	199	16	=	=	SYM
ejpam-524	199	17	1	1	NUM
ejpam-524	199	18	∀	∀	NOUN
ejpam-524	199	19	i	i	NOUN
ejpam-524	199	20	=	=	NOUN
ejpam-524	199	21	2,3	2,3	NUM
ejpam-524	199	22	,	,	PUNCT
ejpam-524	199	23	.	.	PUNCT
ejpam-524	199	24	.	.	PUNCT
ejpam-524	199	25	.	.	PUNCT
ejpam-524	200	1	,	,	PUNCT
ejpam-524	200	2	n.	n.	NOUN
ejpam-524	200	3	hence	hence	ADV
ejpam-524	200	4	d	d	X
ejpam-524	200	5	∼=	∼=	NOUN
ejpam-524	200	6	in	in	ADV
ejpam-524	200	7	.	.	PUNCT
ejpam-524	201	1	converse	converse	NOUN
ejpam-524	201	2	part	part	NOUN
ejpam-524	201	3	follows	follow	VERB
ejpam-524	201	4	from	from	ADP
ejpam-524	201	5	proposition	proposition	NOUN
ejpam-524	201	6	3	3	NUM
ejpam-524	201	7	.	.	X
ejpam-524	202	1	for	for	ADP
ejpam-524	202	2	the	the	DET
ejpam-524	202	3	second	second	ADJ
ejpam-524	202	4	part	part	NOUN
ejpam-524	202	5	of	of	ADP
ejpam-524	202	6	the	the	DET
ejpam-524	202	7	theorem	theorem	NOUN
ejpam-524	202	8	,	,	PUNCT
ejpam-524	202	9	assume	assume	VERB
ejpam-524	202	10	that	that	SCONJ
ejpam-524	202	11	g	g	PROPN
ejpam-524	202	12	is	be	AUX
ejpam-524	202	13	a	a	DET
ejpam-524	202	14	graph	graph	NOUN
ejpam-524	202	15	with	with	ADP
ejpam-524	202	16	dpd	dpd	NOUN
ejpam-524	202	17	-	-	PUNCT
ejpam-524	202	18	set	set	VERB
ejpam-524	202	19	m	m	NOUN
ejpam-524	202	20	and	and	CCONJ
ejpam-524	202	21	dm	dm	X
ejpam-524	202	22	g	g	NOUN
ejpam-524	202	23	as	as	ADP
ejpam-524	202	24	an	an	DET
ejpam-524	202	25	upper	upper	ADJ
ejpam-524	202	26	triangular	triangular	NOUN
ejpam-524	202	27	matrix	matrix	NOUN
ejpam-524	202	28	with	with	ADP
ejpam-524	202	29	atleast	atleast	ADJ
ejpam-524	202	30	one	one	NUM
ejpam-524	202	31	nonzero	nonzero	NOUN
ejpam-524	202	32	entry	entry	NOUN
ejpam-524	202	33	above	above	ADP
ejpam-524	202	34	the	the	DET
ejpam-524	202	35	main	main	ADJ
ejpam-524	202	36	diagonal	diagonal	NOUN
ejpam-524	202	37	.	.	PUNCT
ejpam-524	203	1	from	from	ADP
ejpam-524	203	2	g.	g.	PROPN
ejpam-524	203	3	augustine	augustine	PROPN
ejpam-524	203	4	,	,	PUNCT
ejpam-524	203	5	a.	a.	PROPN
ejpam-524	203	6	joseph	joseph	PROPN
ejpam-524	203	7	,	,	PUNCT
ejpam-524	203	8	s.	s.	PROPN
ejpam-524	203	9	jose	jose	PROPN
ejpam-524	203	10	/	/	SYM
ejpam-524	203	11	eur	eur	PROPN
ejpam-524	203	12	.	.	PUNCT
ejpam-524	204	1	j.	j.	PROPN
ejpam-524	204	2	pure	pure	PROPN
ejpam-524	204	3	appl	appl	PROPN
ejpam-524	204	4	.	.	PROPN
ejpam-524	204	5	math	math	PROPN
ejpam-524	204	6	,	,	PUNCT
ejpam-524	204	7	3	3	NUM
ejpam-524	204	8	(	(	PUNCT
ejpam-524	204	9	2010	2010	NUM
ejpam-524	204	10	)	)	PUNCT
ejpam-524	204	11	,	,	PUNCT
ejpam-524	204	12	748	748	NUM
ejpam-524	204	13	-	-	SYM
ejpam-524	204	14	764	764	NUM
ejpam-524	204	15	753	753	NUM
ejpam-524	204	16	proposition	proposition	NOUN
ejpam-524	204	17	2	2	NUM
ejpam-524	204	18	,	,	PUNCT
ejpam-524	204	19	the	the	DET
ejpam-524	204	20	entries	entry	NOUN
ejpam-524	204	21	in	in	ADP
ejpam-524	204	22	the	the	DET
ejpam-524	204	23	first	first	ADJ
ejpam-524	204	24	column	column	NOUN
ejpam-524	204	25	of	of	ADP
ejpam-524	204	26	dm	dm	PROPN
ejpam-524	204	27	g	g	PROPN
ejpam-524	204	28	are	be	AUX
ejpam-524	204	29	either	either	CCONJ
ejpam-524	204	30	0	0	NUM
ejpam-524	204	31	or	or	CCONJ
ejpam-524	204	32	1	1	NUM
ejpam-524	204	33	.	.	PUNCT
ejpam-524	205	1	also	also	ADV
ejpam-524	205	2	,	,	PUNCT
ejpam-524	205	3	from	from	ADP
ejpam-524	205	4	corollary	corollary	ADJ
ejpam-524	205	5	2	2	NUM
ejpam-524	205	6	sum	sum	NOUN
ejpam-524	205	7	of	of	ADP
ejpam-524	205	8	the	the	DET
ejpam-524	205	9	entries	entry	NOUN
ejpam-524	205	10	in	in	ADP
ejpam-524	205	11	the	the	DET
ejpam-524	205	12	first	first	ADJ
ejpam-524	205	13	column	column	NOUN
ejpam-524	205	14	of	of	ADP
ejpam-524	205	15	dm	dm	NUM
ejpam-524	205	16	g	g	NOUN
ejpam-524	205	17	=	=	PUNCT
ejpam-524	205	18	|m	|m	NOUN
ejpam-524	205	19	|	|	ADV
ejpam-524	205	20	.	.	PUNCT
ejpam-524	206	1	hence	hence	ADV
ejpam-524	206	2	a11	a11	PROPN
ejpam-524	206	3	=	=	SYM
ejpam-524	206	4	1	1	NUM
ejpam-524	206	5	and	and	CCONJ
ejpam-524	206	6	|m	|m	NOUN
ejpam-524	206	7	|	|	ADV
ejpam-524	206	8	=	=	NOUN
ejpam-524	206	9	1	1	X
ejpam-524	206	10	.	.	PUNCT
ejpam-524	206	11	from	from	ADP
ejpam-524	206	12	corollary	corollary	ADJ
ejpam-524	206	13	4	4	NUM
ejpam-524	206	14	,	,	PUNCT
ejpam-524	206	15	sum	sum	NOUN
ejpam-524	206	16	of	of	ADP
ejpam-524	206	17	the	the	DET
ejpam-524	206	18	entries	entry	NOUN
ejpam-524	206	19	in	in	ADP
ejpam-524	206	20	each	each	DET
ejpam-524	206	21	row	row	NOUN
ejpam-524	206	22	of	of	ADP
ejpam-524	206	23	dm	dm	NOUN
ejpam-524	206	24	g	g	NOUN
ejpam-524	206	25	=	=	PUNCT
ejpam-524	206	26	|m	|m	NOUN
ejpam-524	206	27	|	|	ADV
ejpam-524	206	28	.	.	PUNCT
ejpam-524	207	1	hence	hence	ADV
ejpam-524	207	2	,	,	PUNCT
ejpam-524	207	3	in	in	ADP
ejpam-524	207	4	each	each	DET
ejpam-524	207	5	row	row	NOUN
ejpam-524	207	6	,	,	PUNCT
ejpam-524	207	7	the	the	DET
ejpam-524	207	8	nonzero	nonzero	PROPN
ejpam-524	207	9	entry	entry	NOUN
ejpam-524	207	10	appears	appear	VERB
ejpam-524	207	11	in	in	ADP
ejpam-524	207	12	exactly	exactly	ADV
ejpam-524	207	13	one	one	NUM
ejpam-524	207	14	place	place	NOUN
ejpam-524	207	15	and	and	CCONJ
ejpam-524	207	16	is	be	AUX
ejpam-524	207	17	unity	unity	NOUN
ejpam-524	207	18	.	.	PUNCT
ejpam-524	208	1	dm	dm	AUX
ejpam-524	208	2	g	g	PROPN
ejpam-524	208	3	being	be	AUX
ejpam-524	208	4	an	an	DET
ejpam-524	208	5	upper	upper	ADJ
ejpam-524	208	6	triangular	triangular	NOUN
ejpam-524	208	7	matrix	matrix	NOUN
ejpam-524	208	8	,	,	PUNCT
ejpam-524	208	9	the	the	DET
ejpam-524	208	10	entry	entry	NOUN
ejpam-524	208	11	1	1	NUM
ejpam-524	208	12	can	can	AUX
ejpam-524	208	13	not	not	PART
ejpam-524	208	14	be	be	AUX
ejpam-524	208	15	below	below	ADP
ejpam-524	208	16	the	the	DET
ejpam-524	208	17	main	main	ADJ
ejpam-524	208	18	diagonal	diagonal	NOUN
ejpam-524	208	19	and	and	CCONJ
ejpam-524	208	20	dm	dm	PROPN
ejpam-524	208	21	g	g	PROPN
ejpam-524	208	22	contains	contain	VERB
ejpam-524	208	23	atleast	atleast	ADJ
ejpam-524	208	24	one	one	NUM
ejpam-524	208	25	nonzero	nonzero	NOUN
ejpam-524	208	26	entry	entry	NOUN
ejpam-524	208	27	above	above	ADP
ejpam-524	208	28	the	the	DET
ejpam-524	208	29	main	main	ADJ
ejpam-524	208	30	diagonal	diagonal	NOUN
ejpam-524	208	31	,	,	PUNCT
ejpam-524	208	32	which	which	PRON
ejpam-524	208	33	in	in	ADP
ejpam-524	208	34	turn	turn	NOUN
ejpam-524	208	35	implies	imply	VERB
ejpam-524	208	36	,	,	PUNCT
ejpam-524	208	37	dm	dm	NUM
ejpam-524	208	38	g	g	PROPN
ejpam-524	208	39	contains	contain	VERB
ejpam-524	208	40	identical	identical	ADJ
ejpam-524	208	41	rows	row	NOUN
ejpam-524	208	42	,	,	PUNCT
ejpam-524	208	43	a	a	DET
ejpam-524	208	44	contradiction	contradiction	NOUN
ejpam-524	208	45	.	.	PUNCT
ejpam-524	209	1	by	by	ADP
ejpam-524	209	2	a	a	DET
ejpam-524	209	3	similar	similar	ADJ
ejpam-524	209	4	argument	argument	NOUN
ejpam-524	209	5	,	,	PUNCT
ejpam-524	209	6	we	we	PRON
ejpam-524	209	7	can	can	AUX
ejpam-524	209	8	prove	prove	VERB
ejpam-524	209	9	that	that	SCONJ
ejpam-524	209	10	dm	dm	PROPN
ejpam-524	209	11	g	g	PROPN
ejpam-524	209	12	is	be	AUX
ejpam-524	209	13	not	not	PART
ejpam-524	209	14	a	a	DET
ejpam-524	209	15	lower	low	ADJ
ejpam-524	209	16	triangular	triangular	NOUN
ejpam-524	209	17	matrix	matrix	NOUN
ejpam-524	209	18	.	.	PUNCT
ejpam-524	210	1	4	4	X
ejpam-524	210	2	.	.	X
ejpam-524	210	3	main	main	ADJ
ejpam-524	210	4	results	result	NOUN
ejpam-524	210	5	theorem	theorem	VERB
ejpam-524	210	6	13	13	NUM
ejpam-524	210	7	.	.	PUNCT
ejpam-524	211	1	for	for	ADP
ejpam-524	211	2	any	any	DET
ejpam-524	211	3	graph	graph	NOUN
ejpam-524	211	4	g	g	NOUN
ejpam-524	211	5	=	=	SYM
ejpam-524	211	6	(	(	PUNCT
ejpam-524	211	7	v	v	NOUN
ejpam-524	211	8	,	,	PUNCT
ejpam-524	211	9	e	e	NOUN
ejpam-524	211	10	)	)	PUNCT
ejpam-524	211	11	,	,	PUNCT
ejpam-524	211	12	there	there	PRON
ejpam-524	211	13	exists	exist	VERB
ejpam-524	211	14	no	no	DET
ejpam-524	211	15	dpd	dpd	NOUN
ejpam-524	211	16	-	-	PUNCT
ejpam-524	211	17	set	set	VERB
ejpam-524	211	18	m	m	NOUN
ejpam-524	211	19	of	of	ADP
ejpam-524	211	20	cardinality	cardinality	NOUN
ejpam-524	211	21	2	2	NUM
ejpam-524	211	22	.	.	PUNCT
ejpam-524	212	1	proof	proof	NOUN
ejpam-524	212	2	.	.	PUNCT
ejpam-524	213	1	suppose	suppose	VERB
ejpam-524	213	2	there	there	PRON
ejpam-524	213	3	exists	exist	VERB
ejpam-524	213	4	a	a	DET
ejpam-524	213	5	dpd	dpd	NOUN
ejpam-524	213	6	-	-	PUNCT
ejpam-524	213	7	graph	graph	NOUN
ejpam-524	213	8	g	g	NOUN
ejpam-524	213	9	with	with	ADP
ejpam-524	213	10	a	a	DET
ejpam-524	213	11	dpd	dpd	NOUN
ejpam-524	213	12	-	-	PUNCT
ejpam-524	213	13	set	set	VERB
ejpam-524	213	14	m	m	NOUN
ejpam-524	213	15	of	of	ADP
ejpam-524	213	16	cardinality	cardinality	NOUN
ejpam-524	213	17	2	2	NUM
ejpam-524	213	18	.	.	PUNCT
ejpam-524	214	1	let	let	VERB
ejpam-524	214	2	us	we	PRON
ejpam-524	214	3	choose	choose	VERB
ejpam-524	214	4	m	m	NOUN
ejpam-524	214	5	=	=	SYM
ejpam-524	214	6	{	{	PUNCT
ejpam-524	214	7	x	x	INTJ
ejpam-524	214	8	,	,	PUNCT
ejpam-524	214	9	y	y	PROPN
ejpam-524	214	10	}	}	PUNCT
ejpam-524	214	11	,	,	PUNCT
ejpam-524	214	12	where	where	SCONJ
ejpam-524	214	13	x	x	PUNCT
ejpam-524	214	14	and	and	CCONJ
ejpam-524	214	15	y	y	PROPN
ejpam-524	214	16	are	be	AUX
ejpam-524	214	17	arbitrary	arbitrary	ADJ
ejpam-524	214	18	vertices	vertex	NOUN
ejpam-524	214	19	in	in	ADP
ejpam-524	214	20	g.	g.	PROPN
ejpam-524	214	21	then	then	ADV
ejpam-524	214	22	d∗mg	d∗mg	PROPN
ejpam-524	214	23	contains	contain	VERB
ejpam-524	214	24	2×	2×	NUM
ejpam-524	214	25	(	(	PUNCT
ejpam-524	214	26	dg	dg	X
ejpam-524	214	27	+	+	NOUN
ejpam-524	214	28	1	1	X
ejpam-524	214	29	)	)	PUNCT
ejpam-524	214	30	submatrix	submatrix	NOUN
ejpam-524	214	31	so	so	SCONJ
ejpam-524	214	32	that	that	SCONJ
ejpam-524	214	33	rows	row	NOUN
ejpam-524	214	34	of	of	ADP
ejpam-524	214	35	the	the	DET
ejpam-524	214	36	sub	sub	NOUN
ejpam-524	214	37	-	-	NOUN
ejpam-524	214	38	matrix	matrix	NOUN
ejpam-524	214	39	represent	represent	VERB
ejpam-524	214	40	the	the	DET
ejpam-524	214	41	m	m	NOUN
ejpam-524	214	42	-	-	PUNCT
ejpam-524	214	43	distance	distance	NOUN
ejpam-524	214	44	neighborhood	neighborhood	NOUN
ejpam-524	214	45	pattern(m	pattern(m	PROPN
ejpam-524	214	46	-	-	PUNCT
ejpam-524	214	47	dnp	dnp	NOUN
ejpam-524	214	48	)	)	PUNCT
ejpam-524	214	49	of	of	ADP
ejpam-524	214	50	x	x	SYM
ejpam-524	214	51	and	and	CCONJ
ejpam-524	214	52	m	m	NOUN
ejpam-524	214	53	-	-	PUNCT
ejpam-524	214	54	distance	distance	NOUN
ejpam-524	214	55	neighborhood	neighborhood	NOUN
ejpam-524	214	56	pattern(m	pattern(m	PROPN
ejpam-524	214	57	-	-	PUNCT
ejpam-524	214	58	dnp	dnp	PROPN
ejpam-524	214	59	)	)	PUNCT
ejpam-524	214	60	of	of	ADP
ejpam-524	214	61	y	y	PROPN
ejpam-524	214	62	in	in	ADP
ejpam-524	214	63	d∗mg	d∗mg	NOUN
ejpam-524	214	64	.	.	PUNCT
ejpam-524	215	1	hence	hence	ADV
ejpam-524	215	2	,	,	PUNCT
ejpam-524	215	3	the	the	DET
ejpam-524	215	4	entry	entry	NOUN
ejpam-524	215	5	1	1	NUM
ejpam-524	215	6	can	can	AUX
ejpam-524	215	7	be	be	AUX
ejpam-524	215	8	only	only	ADV
ejpam-524	215	9	at	at	ADP
ejpam-524	215	10	the	the	DET
ejpam-524	215	11	first	first	ADJ
ejpam-524	215	12	and	and	CCONJ
ejpam-524	215	13	(	(	PUNCT
ejpam-524	215	14	d(x	d(x	PROPN
ejpam-524	215	15	,	,	PUNCT
ejpam-524	215	16	y	y	PROPN
ejpam-524	215	17	)	)	PUNCT
ejpam-524	216	1	+	+	CCONJ
ejpam-524	217	1	1)th	1)th	NUM
ejpam-524	217	2	columns	column	NOUN
ejpam-524	217	3	,	,	PUNCT
ejpam-524	217	4	and	and	CCONJ
ejpam-524	217	5	the	the	DET
ejpam-524	217	6	rows	row	NOUN
ejpam-524	217	7	will	will	AUX
ejpam-524	217	8	be	be	AUX
ejpam-524	217	9	of	of	ADP
ejpam-524	217	10	the	the	DET
ejpam-524	217	11	following	follow	VERB
ejpam-524	217	12	form	form	NOUN
ejpam-524	217	13	�	�	PROPN
ejpam-524	217	14	1	1	NUM
ejpam-524	217	15	0	0	NUM
ejpam-524	217	16	0	0	NUM
ejpam-524	217	17	.	.	PUNCT
ejpam-524	217	18	.	.	PUNCT
ejpam-524	218	1	.	.	PUNCT
ejpam-524	219	1	1	1	NUM
ejpam-524	219	2	0	0	NUM
ejpam-524	219	3	.	.	PUNCT
ejpam-524	219	4	.	.	PUNCT
ejpam-524	219	5	.	.	PUNCT
ejpam-524	220	1	0	0	NUM
ejpam-524	221	1	1	1	NUM
ejpam-524	221	2	0	0	NUM
ejpam-524	221	3	0	0	NUM
ejpam-524	221	4	.	.	PUNCT
ejpam-524	221	5	.	.	PUNCT
ejpam-524	221	6	.	.	PUNCT
ejpam-524	222	1	1	1	NUM
ejpam-524	222	2	0	0	NUM
ejpam-524	222	3	.	.	PUNCT
ejpam-524	222	4	.	.	PUNCT
ejpam-524	222	5	.	.	PUNCT
ejpam-524	223	1	0	0	NUM
ejpam-524	223	2	�	�	PROPN
ejpam-524	223	3	hence	hence	ADV
ejpam-524	223	4	,	,	PUNCT
ejpam-524	223	5	d∗mg	d∗mg	PROPN
ejpam-524	223	6	contains	contain	VERB
ejpam-524	223	7	identical	identical	ADJ
ejpam-524	223	8	rows	row	NOUN
ejpam-524	223	9	and	and	CCONJ
ejpam-524	223	10	so	so	ADV
ejpam-524	223	11	m	m	VERB
ejpam-524	223	12	is	be	AUX
ejpam-524	223	13	not	not	PART
ejpam-524	223	14	a	a	DET
ejpam-524	223	15	dpd	dpd	NOUN
ejpam-524	223	16	-	-	PUNCT
ejpam-524	223	17	set	set	NOUN
ejpam-524	223	18	.	.	PUNCT
ejpam-524	224	1	theorem	theorem	VERB
ejpam-524	224	2	14	14	NUM
ejpam-524	224	3	.	.	PUNCT
ejpam-524	225	1	for	for	ADP
ejpam-524	225	2	any	any	DET
ejpam-524	225	3	(	(	PUNCT
ejpam-524	225	4	p	p	NOUN
ejpam-524	225	5	,	,	PUNCT
ejpam-524	225	6	q)-graph	q)-graph	NOUN
ejpam-524	225	7	g	g	NOUN
ejpam-524	225	8	,	,	PUNCT
ejpam-524	225	9	v	v	NOUN
ejpam-524	225	10	(	(	PUNCT
ejpam-524	225	11	g	g	NOUN
ejpam-524	225	12	)	)	PUNCT
ejpam-524	225	13	is	be	AUX
ejpam-524	225	14	a	a	DET
ejpam-524	225	15	dpd	dpd	NOUN
ejpam-524	225	16	-	-	PUNCT
ejpam-524	225	17	set	set	VERB
ejpam-524	225	18	if	if	SCONJ
ejpam-524	226	1	and	and	CCONJ
ejpam-524	226	2	only	only	ADV
ejpam-524	226	3	if	if	SCONJ
ejpam-524	226	4	g	g	PROPN
ejpam-524	226	5	is	be	AUX
ejpam-524	226	6	isomorphic	isomorphic	ADJ
ejpam-524	226	7	to	to	ADP
ejpam-524	226	8	k1	k1	NOUN
ejpam-524	226	9	,	,	PUNCT
ejpam-524	226	10	the	the	DET
ejpam-524	226	11	trivial	trivial	ADJ
ejpam-524	226	12	graph	graph	NOUN
ejpam-524	226	13	.	.	PUNCT
ejpam-524	227	1	proof	proof	NOUN
ejpam-524	227	2	.	.	PUNCT
ejpam-524	228	1	assume	assume	VERB
ejpam-524	228	2	that	that	SCONJ
ejpam-524	228	3	g	g	PROPN
ejpam-524	228	4	is	be	AUX
ejpam-524	228	5	isomorphic	isomorphic	ADJ
ejpam-524	228	6	to	to	ADP
ejpam-524	228	7	k1	k1	PROPN
ejpam-524	228	8	.	.	PUNCT
ejpam-524	229	1	clearly	clearly	ADV
ejpam-524	229	2	,	,	PUNCT
ejpam-524	229	3	k1	k1	PROPN
ejpam-524	229	4	has	have	VERB
ejpam-524	229	5	the	the	DET
ejpam-524	229	6	dpd	dpd	NOUN
ejpam-524	229	7	-	-	PUNCT
ejpam-524	229	8	set	set	NOUN
ejpam-524	229	9	m	m	NOUN
ejpam-524	229	10	=	=	SYM
ejpam-524	229	11	{	{	PUNCT
ejpam-524	229	12	v	v	NOUN
ejpam-524	229	13	}	}	PUNCT
ejpam-524	229	14	where	where	SCONJ
ejpam-524	229	15	v	v	NOUN
ejpam-524	229	16	(	(	PUNCT
ejpam-524	229	17	k1	k1	NOUN
ejpam-524	229	18	)	)	PUNCT
ejpam-524	229	19	=	=	SYM
ejpam-524	229	20	{	{	PUNCT
ejpam-524	229	21	v	v	NOUN
ejpam-524	229	22	}	}	PUNCT
ejpam-524	229	23	.	.	PUNCT
ejpam-524	230	1	converse	converse	NOUN
ejpam-524	230	2	follows	follow	VERB
ejpam-524	230	3	from	from	ADP
ejpam-524	230	4	the	the	DET
ejpam-524	230	5	fact	fact	NOUN
ejpam-524	230	6	when	when	SCONJ
ejpam-524	230	7	m	m	PROPN
ejpam-524	230	8	=	=	SYM
ejpam-524	230	9	v	v	ADJ
ejpam-524	230	10	(	(	PUNCT
ejpam-524	230	11	g	g	NOUN
ejpam-524	230	12	)	)	PUNCT
ejpam-524	230	13	,	,	PUNCT
ejpam-524	230	14	the	the	DET
ejpam-524	230	15	rows	row	NOUN
ejpam-524	230	16	in	in	ADP
ejpam-524	230	17	the	the	DET
ejpam-524	230	18	dnp	dnp	PROPN
ejpam-524	230	19	-	-	PUNCT
ejpam-524	230	20	matrix	matrix	NOUN
ejpam-524	230	21	d∗mg	d∗mg	NOUN
ejpam-524	230	22	corresponding	correspond	VERB
ejpam-524	230	23	to	to	ADP
ejpam-524	230	24	the	the	DET
ejpam-524	230	25	diametrically	diametrically	ADV
ejpam-524	230	26	opposite	opposite	ADJ
ejpam-524	230	27	vertices	vertex	NOUN
ejpam-524	230	28	are	be	AUX
ejpam-524	230	29	identical	identical	ADJ
ejpam-524	230	30	.	.	PUNCT
ejpam-524	231	1	hence	hence	ADV
ejpam-524	231	2	,	,	PUNCT
ejpam-524	231	3	g	g	PROPN
ejpam-524	231	4	can	can	AUX
ejpam-524	231	5	have	have	VERB
ejpam-524	231	6	exactly	exactly	ADV
ejpam-524	231	7	one	one	NUM
ejpam-524	231	8	row	row	NOUN
ejpam-524	231	9	and	and	CCONJ
ejpam-524	231	10	column	column	NOUN
ejpam-524	231	11	(	(	PUNCT
ejpam-524	231	12	i.e.	i.e.	X
ejpam-524	231	13	,	,	PUNCT
ejpam-524	231	14	exactly	exactly	ADV
ejpam-524	231	15	one	one	NUM
ejpam-524	231	16	vertex	vertex	NOUN
ejpam-524	231	17	)	)	PUNCT
ejpam-524	231	18	and	and	CCONJ
ejpam-524	231	19	hence	hence	ADV
ejpam-524	231	20	is	be	AUX
ejpam-524	231	21	isomorphic	isomorphic	ADJ
ejpam-524	231	22	to	to	ADP
ejpam-524	231	23	k1	k1	PROPN
ejpam-524	231	24	.	.	PUNCT
ejpam-524	232	1	theorem	theorem	PROPN
ejpam-524	232	2	15	15	NUM
ejpam-524	232	3	.	.	PUNCT
ejpam-524	233	1	the	the	DET
ejpam-524	233	2	complete	complete	ADJ
ejpam-524	233	3	graph	graph	NOUN
ejpam-524	233	4	kn	kn	PROPN
ejpam-524	233	5	possess	possess	VERB
ejpam-524	233	6	a	a	DET
ejpam-524	233	7	dpd	dpd	NOUN
ejpam-524	233	8	-	-	PUNCT
ejpam-524	233	9	set	set	VERB
ejpam-524	233	10	if	if	SCONJ
ejpam-524	233	11	and	and	CCONJ
ejpam-524	233	12	only	only	ADV
ejpam-524	233	13	if	if	SCONJ
ejpam-524	233	14	n≤	n≤	PRON
ejpam-524	233	15	2	2	X
ejpam-524	233	16	.	.	PUNCT
ejpam-524	234	1	proof	proof	NOUN
ejpam-524	234	2	.	.	PUNCT
ejpam-524	235	1	suppose	suppose	VERB
ejpam-524	235	2	g	g	PROPN
ejpam-524	235	3	∼=	∼=	PROPN
ejpam-524	235	4	kn	kn	NOUN
ejpam-524	235	5	has	have	VERB
ejpam-524	235	6	a	a	DET
ejpam-524	235	7	dpd	dpd	NOUN
ejpam-524	235	8	-	-	PUNCT
ejpam-524	235	9	set	set	VERB
ejpam-524	235	10	m	m	NOUN
ejpam-524	235	11	with	with	ADP
ejpam-524	235	12	cardinality	cardinality	PROPN
ejpam-524	236	1	k.	k.	PROPN
ejpam-524	236	2	then	then	ADV
ejpam-524	236	3	the	the	DET
ejpam-524	236	4	first	first	ADJ
ejpam-524	236	5	k	k	PROPN
ejpam-524	236	6	rows	row	NOUN
ejpam-524	236	7	of	of	ADP
ejpam-524	236	8	dm	dm	PROPN
ejpam-524	236	9	g	g	PROPN
ejpam-524	236	10	represent	represent	VERB
ejpam-524	236	11	the	the	DET
ejpam-524	236	12	m	m	PROPN
ejpam-524	236	13	-	-	PUNCT
ejpam-524	236	14	dnp	dnp	PROPN
ejpam-524	236	15	of	of	ADP
ejpam-524	236	16	those	those	DET
ejpam-524	236	17	vertices	vertex	NOUN
ejpam-524	236	18	which	which	PRON
ejpam-524	236	19	belongs	belong	VERB
ejpam-524	236	20	to	to	ADP
ejpam-524	236	21	m	m	PROPN
ejpam-524	236	22	and	and	CCONJ
ejpam-524	236	23	the	the	DET
ejpam-524	236	24	remaining	remain	VERB
ejpam-524	236	25	n−	n−	NOUN
ejpam-524	236	26	k	k	PROPN
ejpam-524	236	27	rows	row	NOUN
ejpam-524	236	28	represent	represent	VERB
ejpam-524	236	29	the	the	DET
ejpam-524	236	30	m	m	PROPN
ejpam-524	236	31	-	-	PUNCT
ejpam-524	236	32	dnp	dnp	PROPN
ejpam-524	236	33	of	of	ADP
ejpam-524	236	34	those	those	DET
ejpam-524	236	35	vertices	vertex	NOUN
ejpam-524	236	36	which	which	PRON
ejpam-524	236	37	are	be	AUX
ejpam-524	236	38	not	not	PART
ejpam-524	236	39	in	in	ADP
ejpam-524	236	40	m	m	PROPN
ejpam-524	236	41	.	.	PUNCT
ejpam-524	237	1	g.	g.	PROPN
ejpam-524	237	2	augustine	augustine	PROPN
ejpam-524	237	3	,	,	PUNCT
ejpam-524	237	4	a.	a.	PROPN
ejpam-524	237	5	joseph	joseph	PROPN
ejpam-524	237	6	,	,	PUNCT
ejpam-524	237	7	s.	s.	PROPN
ejpam-524	237	8	jose	jose	PROPN
ejpam-524	237	9	/	/	SYM
ejpam-524	237	10	eur	eur	PROPN
ejpam-524	237	11	.	.	PUNCT
ejpam-524	238	1	j.	j.	PROPN
ejpam-524	238	2	pure	pure	PROPN
ejpam-524	238	3	appl	appl	PROPN
ejpam-524	238	4	.	.	PROPN
ejpam-524	238	5	math	math	PROPN
ejpam-524	238	6	,	,	PUNCT
ejpam-524	238	7	3	3	NUM
ejpam-524	238	8	(	(	PUNCT
ejpam-524	238	9	2010	2010	NUM
ejpam-524	238	10	)	)	PUNCT
ejpam-524	238	11	,	,	PUNCT
ejpam-524	238	12	748	748	NUM
ejpam-524	238	13	-	-	SYM
ejpam-524	238	14	764	764	NUM
ejpam-524	238	15	754	754	NUM
ejpam-524	238	16	that	that	PRON
ejpam-524	238	17	is	be	AUX
ejpam-524	238	18	,	,	PUNCT
ejpam-524	238	19	dm	dm	PROPN
ejpam-524	238	20	g	g	NOUN
ejpam-524	238	21	=	=	PUNCT
ejpam-524	238	22			PROPN
ejpam-524	238	23			NOUN
ejpam-524	238	24			NOUN
ejpam-524	238	25			NOUN
ejpam-524	238	26			NOUN
ejpam-524	238	27			NOUN
ejpam-524	238	28			NOUN
ejpam-524	238	29			NOUN
ejpam-524	238	30			NOUN
ejpam-524	238	31			NOUN
ejpam-524	238	32			NOUN
ejpam-524	238	33			NOUN
ejpam-524	238	34			NOUN
ejpam-524	238	35			NOUN
ejpam-524	238	36			NOUN
ejpam-524	238	37			NOUN
ejpam-524	238	38			NOUN
ejpam-524	238	39	1	1	NUM
ejpam-524	238	40	k−	k−	NOUN
ejpam-524	238	41	1	1	NUM
ejpam-524	238	42	1	1	NUM
ejpam-524	238	43	k−	k−	PROPN
ejpam-524	238	44	1	1	NUM
ejpam-524	238	45	·	·	PUNCT
ejpam-524	238	46	·	·	PUNCT
ejpam-524	238	47	·	·	PUNCT
ejpam-524	238	48	·	·	PUNCT
ejpam-524	238	49	·	·	PUNCT
ejpam-524	238	50	·	·	PUNCT
ejpam-524	238	51	·	·	PUNCT
ejpam-524	238	52	·	·	PUNCT
ejpam-524	238	53	·	·	PUNCT
ejpam-524	238	54	·	·	PUNCT
ejpam-524	238	55	·	·	PUNCT
ejpam-524	239	1	·	·	PUNCT
ejpam-524	239	2	1	1	NUM
ejpam-524	239	3	k−	k−	NOUN
ejpam-524	239	4	1	1	NUM
ejpam-524	239	5	0	0	NUM
ejpam-524	240	1	k	k	NOUN
ejpam-524	240	2	0	0	PUNCT
ejpam-524	241	1	k	k	X
ejpam-524	241	2	·	·	PUNCT
ejpam-524	241	3	·	·	PUNCT
ejpam-524	241	4	·	·	PUNCT
ejpam-524	241	5	·	·	PUNCT
ejpam-524	241	6	·	·	PUNCT
ejpam-524	241	7	·	·	PUNCT
ejpam-524	241	8	·	·	PUNCT
ejpam-524	241	9	·	·	PUNCT
ejpam-524	241	10	·	·	PUNCT
ejpam-524	241	11	·	·	PUNCT
ejpam-524	241	12	·	·	PUNCT
ejpam-524	241	13	·	·	PUNCT
ejpam-524	241	14	0	0	NUM
ejpam-524	242	1	k	k	PRON
ejpam-524	242	2			PROPN
ejpam-524	242	3			NOUN
ejpam-524	242	4			VERB
ejpam-524	242	5			NOUN
ejpam-524	242	6			NOUN
ejpam-524	242	7			NOUN
ejpam-524	242	8			NOUN
ejpam-524	242	9			NOUN
ejpam-524	242	10			NOUN
ejpam-524	242	11			NOUN
ejpam-524	242	12			NOUN
ejpam-524	242	13			NOUN
ejpam-524	242	14			NOUN
ejpam-524	242	15			NOUN
ejpam-524	242	16			NOUN
ejpam-524	242	17			NOUN
ejpam-524	242	18			PUNCT
ejpam-524	243	1	hence	hence	ADV
ejpam-524	243	2	,	,	PUNCT
ejpam-524	243	3	d∗mg	d∗mg	NOUN
ejpam-524	243	4	=	=	SYM
ejpam-524	243	5			PROPN
ejpam-524	243	6			NOUN
ejpam-524	243	7			NOUN
ejpam-524	243	8			NOUN
ejpam-524	243	9			NOUN
ejpam-524	243	10			NOUN
ejpam-524	243	11			NOUN
ejpam-524	243	12			NOUN
ejpam-524	243	13			NOUN
ejpam-524	243	14			NOUN
ejpam-524	243	15			NOUN
ejpam-524	243	16			NOUN
ejpam-524	243	17			NOUN
ejpam-524	243	18			NOUN
ejpam-524	243	19			NOUN
ejpam-524	243	20	1	1	NUM
ejpam-524	243	21	1	1	NUM
ejpam-524	243	22	1	1	NUM
ejpam-524	243	23	1	1	NUM
ejpam-524	243	24	·	·	PUNCT
ejpam-524	243	25	·	·	PUNCT
ejpam-524	243	26	·	·	PUNCT
ejpam-524	243	27	·	·	PUNCT
ejpam-524	243	28	·	·	PUNCT
ejpam-524	243	29	·	·	PUNCT
ejpam-524	243	30	·	·	PUNCT
ejpam-524	243	31	·	·	PUNCT
ejpam-524	243	32	·	·	PUNCT
ejpam-524	243	33	·	·	PUNCT
ejpam-524	243	34	·	·	PUNCT
ejpam-524	244	1	·	·	PUNCT
ejpam-524	244	2	1	1	NUM
ejpam-524	244	3	1	1	NUM
ejpam-524	244	4	0	0	NUM
ejpam-524	244	5	1	1	NUM
ejpam-524	244	6	·	·	PUNCT
ejpam-524	244	7	·	·	PUNCT
ejpam-524	244	8	·	·	PUNCT
ejpam-524	244	9	·	·	PUNCT
ejpam-524	244	10	·	·	PUNCT
ejpam-524	244	11	·	·	PUNCT
ejpam-524	244	12	·	·	PUNCT
ejpam-524	244	13	·	·	PUNCT
ejpam-524	244	14	·	·	PUNCT
ejpam-524	244	15	·	·	PUNCT
ejpam-524	244	16	·	·	PUNCT
ejpam-524	244	17	·	·	PUNCT
ejpam-524	244	18	0	0	NUM
ejpam-524	244	19	1	1	NUM
ejpam-524	244	20			NOUN
ejpam-524	244	21			NOUN
ejpam-524	244	22			VERB
ejpam-524	244	23			NOUN
ejpam-524	244	24			NOUN
ejpam-524	244	25			NOUN
ejpam-524	244	26			NOUN
ejpam-524	244	27			NOUN
ejpam-524	244	28			NOUN
ejpam-524	244	29			NOUN
ejpam-524	244	30			NOUN
ejpam-524	244	31			NOUN
ejpam-524	244	32			NOUN
ejpam-524	244	33			NOUN
ejpam-524	244	34			PUNCT
ejpam-524	245	1	clearly	clearly	ADV
ejpam-524	245	2	,	,	PUNCT
ejpam-524	245	3	when	when	SCONJ
ejpam-524	245	4	n	n	X
ejpam-524	245	5	≥	≥	NOUN
ejpam-524	245	6	3	3	NUM
ejpam-524	245	7	,	,	PUNCT
ejpam-524	245	8	d∗mg	d∗mg	NOUN
ejpam-524	245	9	contains	contain	VERB
ejpam-524	245	10	identical	identical	ADJ
ejpam-524	245	11	rows	row	NOUN
ejpam-524	245	12	and	and	CCONJ
ejpam-524	245	13	hence	hence	ADV
ejpam-524	245	14	m	m	VERB
ejpam-524	245	15	is	be	AUX
ejpam-524	245	16	not	not	PART
ejpam-524	245	17	a	a	DET
ejpam-524	245	18	dpd	dpd	NOUN
ejpam-524	245	19	-	-	PUNCT
ejpam-524	245	20	set	set	NOUN
ejpam-524	245	21	.	.	PUNCT
ejpam-524	246	1	converse	converse	NOUN
ejpam-524	246	2	follows	follow	VERB
ejpam-524	246	3	from	from	ADP
ejpam-524	246	4	theorem	theorem	ADJ
ejpam-524	246	5	14	14	NUM
ejpam-524	246	6	and	and	CCONJ
ejpam-524	246	7	proposition	proposition	NOUN
ejpam-524	246	8	3	3	NUM
ejpam-524	246	9	.	.	PUNCT
ejpam-524	246	10	theorem	theorem	VERB
ejpam-524	246	11	16	16	NUM
ejpam-524	246	12	.	.	PUNCT
ejpam-524	247	1	complete	complete	ADJ
ejpam-524	247	2	bipartite	bipartite	PROPN
ejpam-524	247	3	graph	graph	NOUN
ejpam-524	247	4	km	km	PROPN
ejpam-524	247	5	,	,	PUNCT
ejpam-524	247	6	n	n	PRON
ejpam-524	247	7	possess	possess	VERB
ejpam-524	247	8	a	a	DET
ejpam-524	247	9	dpd	dpd	NOUN
ejpam-524	247	10	-	-	PUNCT
ejpam-524	247	11	set	set	VERB
ejpam-524	247	12	m	m	NOUN
ejpam-524	247	13	if	if	SCONJ
ejpam-524	248	1	and	and	CCONJ
ejpam-524	248	2	only	only	ADV
ejpam-524	248	3	if	if	SCONJ
ejpam-524	248	4	either	either	PRON
ejpam-524	248	5	m	m	PROPN
ejpam-524	248	6	=	=	SYM
ejpam-524	248	7	n=	n=	ADJ
ejpam-524	248	8	1	1	NUM
ejpam-524	248	9	or	or	CCONJ
ejpam-524	248	10	m=	m=	ADJ
ejpam-524	248	11	1	1	NUM
ejpam-524	248	12	,	,	PUNCT
ejpam-524	248	13	n=	n=	ADJ
ejpam-524	248	14	2	2	NUM
ejpam-524	248	15	.	.	PUNCT
ejpam-524	249	1	proof	proof	NOUN
ejpam-524	249	2	.	.	PUNCT
ejpam-524	250	1	let	let	VERB
ejpam-524	250	2	g	g	PRON
ejpam-524	250	3	∼=	∼=	PROPN
ejpam-524	250	4	km	km	NOUN
ejpam-524	250	5	,	,	PUNCT
ejpam-524	250	6	n	n	PRON
ejpam-524	250	7	be	be	VERB
ejpam-524	250	8	a	a	DET
ejpam-524	250	9	complete	complete	ADJ
ejpam-524	250	10	bipartite	bipartite	NOUN
ejpam-524	250	11	graph	graph	NOUN
ejpam-524	250	12	with	with	ADP
ejpam-524	250	13	partition	partition	NOUN
ejpam-524	250	14	of	of	ADP
ejpam-524	250	15	the	the	DET
ejpam-524	250	16	vertex	vertex	NOUN
ejpam-524	250	17	set	set	VERB
ejpam-524	250	18	as	as	ADP
ejpam-524	250	19	p1	p1	NOUN
ejpam-524	250	20	and	and	CCONJ
ejpam-524	250	21	p2	p2	NOUN
ejpam-524	250	22	with	with	ADP
ejpam-524	250	23	|p1|	|p1|	NOUN
ejpam-524	250	24	=	=	PUNCT
ejpam-524	250	25	m	m	PROPN
ejpam-524	250	26	and	and	CCONJ
ejpam-524	250	27	|p2|	|p2|	PROPN
ejpam-524	250	28	=	=	SYM
ejpam-524	250	29	n.	n.	PROPN
ejpam-524	250	30	assume	assume	VERB
ejpam-524	250	31	km	km	PROPN
ejpam-524	250	32	,	,	PUNCT
ejpam-524	250	33	n	n	PRON
ejpam-524	250	34	possess	possess	VERB
ejpam-524	250	35	a	a	DET
ejpam-524	250	36	dpd	dpd	NOUN
ejpam-524	250	37	-	-	PUNCT
ejpam-524	250	38	set	set	NOUN
ejpam-524	250	39	m	m	VERB
ejpam-524	250	40	such	such	ADJ
ejpam-524	250	41	that	that	SCONJ
ejpam-524	250	42	|m	|m	NOUN
ejpam-524	250	43	|	|	NOUN
ejpam-524	250	44	=	=	SYM
ejpam-524	250	45	k.	k.	PROPN
ejpam-524	250	46	let	let	VERB
ejpam-524	250	47	m	m	AUX
ejpam-524	250	48	=	=	PUNCT
ejpam-524	250	49	{	{	PUNCT
ejpam-524	250	50	v1	v1	PROPN
ejpam-524	250	51	,	,	PUNCT
ejpam-524	250	52	v2	v2	PROPN
ejpam-524	250	53	,	,	PUNCT
ejpam-524	250	54	.	.	PUNCT
ejpam-524	250	55	.	.	PUNCT
ejpam-524	251	1	.	.	PUNCT
ejpam-524	252	1	,	,	PUNCT
ejpam-524	252	2	vk	vk	ADP
ejpam-524	252	3	}	}	PUNCT
ejpam-524	252	4	where	where	SCONJ
ejpam-524	252	5	{	{	PUNCT
ejpam-524	252	6	v1	v1	NOUN
ejpam-524	252	7	,	,	PUNCT
ejpam-524	252	8	v2	v2	NOUN
ejpam-524	252	9	,	,	PUNCT
ejpam-524	252	10	.	.	PUNCT
ejpam-524	252	11	.	.	PUNCT
ejpam-524	253	1	.	.	PUNCT
ejpam-524	254	1	,	,	PUNCT
ejpam-524	254	2	vr	vr	PROPN
ejpam-524	254	3	}	}	PUNCT
ejpam-524	254	4	∈	∈	PROPN
ejpam-524	254	5	p1	p1	NOUN
ejpam-524	254	6	and	and	CCONJ
ejpam-524	254	7	{	{	PUNCT
ejpam-524	254	8	vr+1	vr+1	NOUN
ejpam-524	254	9	,	,	PUNCT
ejpam-524	254	10	vr+2	vr+2	NOUN
ejpam-524	254	11	,	,	PUNCT
ejpam-524	254	12	.	.	PUNCT
ejpam-524	254	13	.	.	PUNCT
ejpam-524	255	1	.	.	PUNCT
ejpam-524	256	1	,	,	PUNCT
ejpam-524	256	2	vk	vk	VERB
ejpam-524	256	3	}	}	PUNCT
ejpam-524	256	4	∈	∈	PROPN
ejpam-524	256	5	p2	p2	NOUN
ejpam-524	256	6	.	.	PUNCT
ejpam-524	257	1	then	then	ADV
ejpam-524	257	2	the	the	DET
ejpam-524	257	3	first	first	ADJ
ejpam-524	257	4	k	k	PROPN
ejpam-524	257	5	rows	row	NOUN
ejpam-524	257	6	of	of	ADP
ejpam-524	257	7	d∗mg	d∗mg	NOUN
ejpam-524	257	8	represent	represent	VERB
ejpam-524	257	9	the	the	DET
ejpam-524	257	10	m	m	PROPN
ejpam-524	257	11	-	-	PUNCT
ejpam-524	257	12	dnp	dnp	PROPN
ejpam-524	257	13	of	of	ADP
ejpam-524	257	14	the	the	DET
ejpam-524	257	15	vertices	vertex	NOUN
ejpam-524	257	16	in	in	ADP
ejpam-524	257	17	m	m	PROPN
ejpam-524	257	18	.	.	PUNCT
ejpam-524	258	1	in	in	ADP
ejpam-524	258	2	this	this	DET
ejpam-524	258	3	k	k	PROPN
ejpam-524	258	4	rows	row	NOUN
ejpam-524	258	5	,	,	PUNCT
ejpam-524	258	6	the	the	DET
ejpam-524	258	7	first	first	ADJ
ejpam-524	258	8	r	r	NOUN
ejpam-524	258	9	rows	row	NOUN
ejpam-524	258	10	represent	represent	VERB
ejpam-524	258	11	the	the	DET
ejpam-524	258	12	m	m	PROPN
ejpam-524	258	13	-	-	PUNCT
ejpam-524	258	14	dnp	dnp	PROPN
ejpam-524	258	15	of	of	ADP
ejpam-524	258	16	the	the	DET
ejpam-524	258	17	vertices	vertex	NOUN
ejpam-524	258	18	which	which	PRON
ejpam-524	258	19	are	be	AUX
ejpam-524	258	20	in	in	ADP
ejpam-524	258	21	p1	p1	NOUN
ejpam-524	258	22	and	and	CCONJ
ejpam-524	258	23	the	the	DET
ejpam-524	258	24	remaining	remain	VERB
ejpam-524	258	25	k−	k−	PROPN
ejpam-524	258	26	r	r	NOUN
ejpam-524	258	27	rows	row	NOUN
ejpam-524	258	28	represent	represent	VERB
ejpam-524	258	29	the	the	DET
ejpam-524	258	30	m	m	PROPN
ejpam-524	258	31	-	-	PUNCT
ejpam-524	258	32	dnp	dnp	PROPN
ejpam-524	258	33	of	of	ADP
ejpam-524	258	34	the	the	DET
ejpam-524	258	35	vertices	vertex	NOUN
ejpam-524	258	36	which	which	PRON
ejpam-524	258	37	are	be	AUX
ejpam-524	258	38	in	in	ADP
ejpam-524	258	39	p2	p2	NOUN
ejpam-524	258	40	.	.	PUNCT
ejpam-524	259	1	the	the	DET
ejpam-524	259	2	remaining	remain	VERB
ejpam-524	259	3	(	(	PUNCT
ejpam-524	259	4	m+	m+	PRON
ejpam-524	259	5	n)−	n)−	PROPN
ejpam-524	259	6	k	k	PROPN
ejpam-524	259	7	rows	row	NOUN
ejpam-524	259	8	represent	represent	VERB
ejpam-524	259	9	the	the	DET
ejpam-524	259	10	m	m	PROPN
ejpam-524	259	11	-	-	PUNCT
ejpam-524	259	12	dnp	dnp	PROPN
ejpam-524	259	13	of	of	ADP
ejpam-524	259	14	the	the	DET
ejpam-524	259	15	vertices	vertex	NOUN
ejpam-524	259	16	which	which	PRON
ejpam-524	259	17	are	be	AUX
ejpam-524	259	18	not	not	PART
ejpam-524	259	19	in	in	ADP
ejpam-524	259	20	m	m	PROPN
ejpam-524	259	21	.	.	PUNCT
ejpam-524	260	1	now	now	ADV
ejpam-524	260	2	,	,	PUNCT
ejpam-524	260	3	in	in	ADP
ejpam-524	260	4	this	this	PRON
ejpam-524	260	5	(	(	PUNCT
ejpam-524	260	6	m+	m+	NOUN
ejpam-524	260	7	n)−	n)−	PROPN
ejpam-524	260	8	k	k	PROPN
ejpam-524	260	9	rows	row	NOUN
ejpam-524	260	10	,	,	PUNCT
ejpam-524	260	11	the	the	DET
ejpam-524	260	12	first	first	ADJ
ejpam-524	260	13	m−	m−	PROPN
ejpam-524	260	14	r	r	NOUN
ejpam-524	260	15	rows	row	NOUN
ejpam-524	260	16	represent	represent	VERB
ejpam-524	260	17	the	the	DET
ejpam-524	260	18	m	m	PROPN
ejpam-524	260	19	-	-	PUNCT
ejpam-524	260	20	dnp	dnp	PROPN
ejpam-524	260	21	of	of	ADP
ejpam-524	260	22	the	the	DET
ejpam-524	260	23	vertices	vertex	NOUN
ejpam-524	260	24	in	in	ADP
ejpam-524	260	25	p1	p1	PROPN
ejpam-524	260	26	and	and	CCONJ
ejpam-524	260	27	the	the	DET
ejpam-524	260	28	remaining	remain	VERB
ejpam-524	260	29	n−(k−	n−(k−	PROPN
ejpam-524	260	30	r	r	NOUN
ejpam-524	260	31	)	)	PUNCT
ejpam-524	260	32	rows	row	NOUN
ejpam-524	260	33	represent	represent	VERB
ejpam-524	260	34	the	the	DET
ejpam-524	260	35	m	m	PROPN
ejpam-524	260	36	-	-	PUNCT
ejpam-524	260	37	dnp	dnp	PROPN
ejpam-524	260	38	of	of	ADP
ejpam-524	260	39	vertices	vertex	NOUN
ejpam-524	260	40	which	which	PRON
ejpam-524	260	41	are	be	AUX
ejpam-524	260	42	in	in	ADP
ejpam-524	260	43	p2	p2	NOUN
ejpam-524	260	44	.	.	PUNCT
ejpam-524	261	1	case	case	NOUN
ejpam-524	261	2	1	1	NUM
ejpam-524	261	3	:	:	PUNCT
ejpam-524	261	4	r	r	NOUN
ejpam-524	261	5	≥	≥	NUM
ejpam-524	261	6	2	2	NUM
ejpam-524	261	7	and	and	CCONJ
ejpam-524	261	8	k−	k−	PROPN
ejpam-524	261	9	r	r	NOUN
ejpam-524	261	10	≥	≥	NUM
ejpam-524	261	11	2	2	NUM
ejpam-524	261	12	g.	g.	PROPN
ejpam-524	261	13	augustine	augustine	PROPN
ejpam-524	261	14	,	,	PUNCT
ejpam-524	261	15	a.	a.	PROPN
ejpam-524	261	16	joseph	joseph	PROPN
ejpam-524	261	17	,	,	PUNCT
ejpam-524	261	18	s.	s.	PROPN
ejpam-524	261	19	jose	jose	PROPN
ejpam-524	261	20	/	/	SYM
ejpam-524	261	21	eur	eur	PROPN
ejpam-524	261	22	.	.	PUNCT
ejpam-524	262	1	j.	j.	PROPN
ejpam-524	262	2	pure	pure	PROPN
ejpam-524	262	3	appl	appl	PROPN
ejpam-524	262	4	.	.	PROPN
ejpam-524	262	5	math	math	PROPN
ejpam-524	262	6	,	,	PUNCT
ejpam-524	262	7	3	3	NUM
ejpam-524	262	8	(	(	PUNCT
ejpam-524	262	9	2010	2010	NUM
ejpam-524	262	10	)	)	PUNCT
ejpam-524	262	11	,	,	PUNCT
ejpam-524	262	12	748	748	NUM
ejpam-524	262	13	-	-	SYM
ejpam-524	262	14	764	764	NUM
ejpam-524	262	15	755	755	NUM
ejpam-524	262	16	then	then	ADV
ejpam-524	262	17	,	,	PUNCT
ejpam-524	262	18	d∗mg	d∗mg	NOUN
ejpam-524	262	19	=	=	SYM
ejpam-524	262	20			PROPN
ejpam-524	262	21			NOUN
ejpam-524	262	22			NOUN
ejpam-524	262	23			NOUN
ejpam-524	262	24			NOUN
ejpam-524	262	25			NOUN
ejpam-524	262	26			NOUN
ejpam-524	262	27			NOUN
ejpam-524	262	28			NOUN
ejpam-524	262	29			NOUN
ejpam-524	262	30			NOUN
ejpam-524	262	31	1	1	NUM
ejpam-524	262	32	1	1	NUM
ejpam-524	262	33	1	1	NUM
ejpam-524	262	34	1	1	NUM
ejpam-524	262	35	1	1	NUM
ejpam-524	262	36	1	1	NUM
ejpam-524	262	37	.	.	PUNCT
ejpam-524	262	38	.	.	PUNCT
ejpam-524	262	39	.	.	PUNCT
ejpam-524	262	40	.	.	PUNCT
ejpam-524	262	41	.	.	PUNCT
ejpam-524	262	42	.	.	PUNCT
ejpam-524	262	43	.	.	PUNCT
ejpam-524	262	44	.	.	PUNCT
ejpam-524	263	1	.	.	PUNCT
ejpam-524	264	1	1	1	NUM
ejpam-524	264	2	1	1	NUM
ejpam-524	264	3	1	1	NUM
ejpam-524	264	4	0	0	NUM
ejpam-524	264	5	1	1	NUM
ejpam-524	264	6	1	1	NUM
ejpam-524	264	7	.	.	PUNCT
ejpam-524	264	8	.	.	PUNCT
ejpam-524	264	9	.	.	PUNCT
ejpam-524	264	10	.	.	PUNCT
ejpam-524	264	11	.	.	PUNCT
ejpam-524	264	12	.	.	PUNCT
ejpam-524	264	13	.	.	PUNCT
ejpam-524	264	14	.	.	PUNCT
ejpam-524	265	1	.	.	PUNCT
ejpam-524	266	1	0	0	NUM
ejpam-524	266	2	1	1	NUM
ejpam-524	266	3	1	1	NUM
ejpam-524	266	4			NOUN
ejpam-524	266	5			NOUN
ejpam-524	266	6			VERB
ejpam-524	266	7			NOUN
ejpam-524	266	8			NOUN
ejpam-524	266	9			NOUN
ejpam-524	266	10			NOUN
ejpam-524	266	11			NOUN
ejpam-524	266	12			NOUN
ejpam-524	266	13			NOUN
ejpam-524	266	14			PUNCT
ejpam-524	267	1	since	since	SCONJ
ejpam-524	267	2	r	r	PROPN
ejpam-524	267	3	≥	≥	NUM
ejpam-524	267	4	2	2	NUM
ejpam-524	267	5	and	and	CCONJ
ejpam-524	267	6	k−	k−	PROPN
ejpam-524	267	7	r	r	NOUN
ejpam-524	267	8	≥	≥	NOUN
ejpam-524	267	9	2	2	NUM
ejpam-524	267	10	,	,	PUNCT
ejpam-524	267	11	d∗mg	d∗mg	NOUN
ejpam-524	267	12	contains	contain	VERB
ejpam-524	267	13	identical	identical	ADJ
ejpam-524	267	14	rows	row	NOUN
ejpam-524	267	15	and	and	CCONJ
ejpam-524	267	16	hence	hence	ADV
ejpam-524	267	17	,	,	PUNCT
ejpam-524	267	18	m	m	VERB
ejpam-524	267	19	is	be	AUX
ejpam-524	267	20	not	not	PART
ejpam-524	267	21	a	a	DET
ejpam-524	267	22	dpd	dpd	NOUN
ejpam-524	267	23	-	-	PUNCT
ejpam-524	267	24	set	set	NOUN
ejpam-524	267	25	.	.	PUNCT
ejpam-524	268	1	case	case	NOUN
ejpam-524	268	2	2	2	NUM
ejpam-524	268	3	:	:	PUNCT
ejpam-524	268	4	r	r	NOUN
ejpam-524	268	5	=	=	SYM
ejpam-524	268	6	1	1	NUM
ejpam-524	268	7	and	and	CCONJ
ejpam-524	268	8	k−	k−	PROPN
ejpam-524	268	9	r	r	NOUN
ejpam-524	268	10	≥	≥	NUM
ejpam-524	268	11	2	2	NUM
ejpam-524	268	12	d∗mg	d∗mg	NOUN
ejpam-524	268	13	=	=	SYM
ejpam-524	268	14			PROPN
ejpam-524	268	15			NOUN
ejpam-524	268	16			NOUN
ejpam-524	268	17			NOUN
ejpam-524	268	18			NOUN
ejpam-524	268	19			NOUN
ejpam-524	268	20			NOUN
ejpam-524	268	21			NOUN
ejpam-524	268	22			NOUN
ejpam-524	268	23			NOUN
ejpam-524	268	24			NOUN
ejpam-524	268	25	1	1	NUM
ejpam-524	268	26	1	1	NUM
ejpam-524	268	27	0	0	NUM
ejpam-524	268	28	1	1	NUM
ejpam-524	268	29	1	1	NUM
ejpam-524	268	30	1	1	NUM
ejpam-524	268	31	.	.	PUNCT
ejpam-524	268	32	.	.	PUNCT
ejpam-524	268	33	.	.	PUNCT
ejpam-524	268	34	.	.	PUNCT
ejpam-524	268	35	.	.	PUNCT
ejpam-524	268	36	.	.	PUNCT
ejpam-524	268	37	.	.	PUNCT
ejpam-524	268	38	.	.	PUNCT
ejpam-524	269	1	.	.	PUNCT
ejpam-524	270	1	1	1	NUM
ejpam-524	270	2	1	1	NUM
ejpam-524	270	3	1	1	NUM
ejpam-524	270	4	0	0	NUM
ejpam-524	270	5	1	1	NUM
ejpam-524	270	6	1	1	NUM
ejpam-524	270	7	.	.	PUNCT
ejpam-524	270	8	.	.	PUNCT
ejpam-524	270	9	.	.	PUNCT
ejpam-524	270	10	.	.	PUNCT
ejpam-524	270	11	.	.	PUNCT
ejpam-524	270	12	.	.	PUNCT
ejpam-524	270	13	.	.	PUNCT
ejpam-524	270	14	.	.	PUNCT
ejpam-524	271	1	.	.	PUNCT
ejpam-524	272	1	0	0	NUM
ejpam-524	272	2	1	1	NUM
ejpam-524	272	3	1	1	NUM
ejpam-524	272	4			NOUN
ejpam-524	272	5			NOUN
ejpam-524	272	6			VERB
ejpam-524	272	7			NOUN
ejpam-524	272	8			NOUN
ejpam-524	272	9			NOUN
ejpam-524	272	10			NOUN
ejpam-524	272	11			NOUN
ejpam-524	272	12			NOUN
ejpam-524	272	13			NOUN
ejpam-524	272	14			PUNCT
ejpam-524	273	1	since	since	ADV
ejpam-524	273	2	,	,	PUNCT
ejpam-524	273	3	k−	k−	PROPN
ejpam-524	273	4	r	r	NOUN
ejpam-524	273	5	≥	≥	NOUN
ejpam-524	273	6	2	2	NUM
ejpam-524	273	7	,	,	PUNCT
ejpam-524	273	8	d∗mg	d∗mg	NOUN
ejpam-524	273	9	contains	contain	VERB
ejpam-524	273	10	identical	identical	ADJ
ejpam-524	273	11	rows	row	NOUN
ejpam-524	273	12	and	and	CCONJ
ejpam-524	273	13	hence	hence	ADV
ejpam-524	273	14	,	,	PUNCT
ejpam-524	273	15	m	m	VERB
ejpam-524	273	16	is	be	AUX
ejpam-524	273	17	not	not	PART
ejpam-524	273	18	a	a	DET
ejpam-524	273	19	dpd	dpd	NOUN
ejpam-524	273	20	-	-	PUNCT
ejpam-524	273	21	set	set	NOUN
ejpam-524	273	22	.	.	PUNCT
ejpam-524	274	1	case	case	NOUN
ejpam-524	274	2	3	3	NUM
ejpam-524	274	3	:	:	PUNCT
ejpam-524	274	4	r	r	NOUN
ejpam-524	274	5	=	=	SYM
ejpam-524	274	6	0	0	NUM
ejpam-524	274	7	and	and	CCONJ
ejpam-524	274	8	k−	k−	PROPN
ejpam-524	275	1	r	r	NOUN
ejpam-524	275	2	≥	≥	NUM
ejpam-524	275	3	2	2	NUM
ejpam-524	275	4	d∗mg	d∗mg	NOUN
ejpam-524	275	5	=	=	SYM
ejpam-524	275	6			PROPN
ejpam-524	275	7			NOUN
ejpam-524	275	8			NOUN
ejpam-524	275	9			NOUN
ejpam-524	275	10			NOUN
ejpam-524	275	11			NOUN
ejpam-524	275	12			NOUN
ejpam-524	275	13			NOUN
ejpam-524	275	14			NOUN
ejpam-524	275	15			NOUN
ejpam-524	275	16			NOUN
ejpam-524	275	17			NOUN
ejpam-524	275	18			NOUN
ejpam-524	275	19			NOUN
ejpam-524	275	20			NOUN
ejpam-524	275	21	1	1	NUM
ejpam-524	275	22	0	0	NUM
ejpam-524	275	23	1	1	NUM
ejpam-524	275	24	.	.	PUNCT
ejpam-524	275	25	.	.	PUNCT
ejpam-524	275	26	.	.	PUNCT
ejpam-524	276	1	.	.	PUNCT
ejpam-524	276	2	.	.	PUNCT
ejpam-524	277	1	.	.	PUNCT
ejpam-524	277	2	.	.	PUNCT
ejpam-524	278	1	.	.	PUNCT
ejpam-524	279	1	.	.	PUNCT
ejpam-524	280	1	1	1	NUM
ejpam-524	280	2	0	0	NUM
ejpam-524	280	3	1	1	NUM
ejpam-524	280	4	0	0	NUM
ejpam-524	280	5	1	1	NUM
ejpam-524	280	6	0	0	NUM
ejpam-524	280	7	.	.	PUNCT
ejpam-524	280	8	.	.	PUNCT
ejpam-524	280	9	.	.	PUNCT
ejpam-524	280	10	.	.	PUNCT
ejpam-524	280	11	.	.	PUNCT
ejpam-524	280	12	.	.	PUNCT
ejpam-524	280	13	.	.	PUNCT
ejpam-524	280	14	.	.	PUNCT
ejpam-524	280	15	.	.	PUNCT
ejpam-524	281	1	0	0	NUM
ejpam-524	282	1	1	1	NUM
ejpam-524	282	2	0	0	NUM
ejpam-524	282	3	0	0	NUM
ejpam-524	282	4	0	0	NUM
ejpam-524	282	5	1	1	NUM
ejpam-524	282	6	.	.	PUNCT
ejpam-524	282	7	.	.	PUNCT
ejpam-524	282	8	.	.	PUNCT
ejpam-524	282	9	.	.	PUNCT
ejpam-524	282	10	.	.	PUNCT
ejpam-524	282	11	.	.	PUNCT
ejpam-524	282	12	.	.	PUNCT
ejpam-524	282	13	.	.	PUNCT
ejpam-524	282	14	.	.	PUNCT
ejpam-524	283	1	0	0	NUM
ejpam-524	283	2	0	0	NUM
ejpam-524	283	3	1	1	NUM
ejpam-524	283	4			NOUN
ejpam-524	283	5			NOUN
ejpam-524	283	6			VERB
ejpam-524	283	7			NOUN
ejpam-524	283	8			NOUN
ejpam-524	283	9			NOUN
ejpam-524	283	10			NOUN
ejpam-524	283	11			NOUN
ejpam-524	283	12			NOUN
ejpam-524	283	13			NOUN
ejpam-524	283	14			NOUN
ejpam-524	283	15			NOUN
ejpam-524	283	16			NOUN
ejpam-524	283	17			NOUN
ejpam-524	283	18			PUNCT
ejpam-524	284	1	since	since	ADV
ejpam-524	284	2	,	,	PUNCT
ejpam-524	284	3	k−	k−	PROPN
ejpam-524	284	4	r	r	NOUN
ejpam-524	284	5	≥	≥	NUM
ejpam-524	284	6	2	2	NUM
ejpam-524	284	7	,	,	PUNCT
ejpam-524	284	8	d∗mg	d∗mg	NOUN
ejpam-524	284	9	will	will	AUX
ejpam-524	284	10	have	have	VERB
ejpam-524	284	11	identical	identical	ADJ
ejpam-524	284	12	rows	row	NOUN
ejpam-524	284	13	and	and	CCONJ
ejpam-524	284	14	hence	hence	ADV
ejpam-524	284	15	,	,	PUNCT
ejpam-524	284	16	m	m	VERB
ejpam-524	284	17	is	be	AUX
ejpam-524	284	18	not	not	PART
ejpam-524	284	19	a	a	DET
ejpam-524	284	20	dpd	dpd	NOUN
ejpam-524	284	21	-	-	PUNCT
ejpam-524	284	22	set	set	NOUN
ejpam-524	284	23	.	.	PUNCT
ejpam-524	285	1	case	case	NOUN
ejpam-524	285	2	4	4	NUM
ejpam-524	285	3	:	:	PUNCT
ejpam-524	285	4	r	r	NOUN
ejpam-524	285	5	=	=	SYM
ejpam-524	285	6	1	1	NUM
ejpam-524	285	7	and	and	CCONJ
ejpam-524	285	8	k−	k−	NOUN
ejpam-524	285	9	r	r	NOUN
ejpam-524	285	10	=	=	NOUN
ejpam-524	285	11	1	1	NUM
ejpam-524	285	12	in	in	ADP
ejpam-524	285	13	this	this	DET
ejpam-524	285	14	case	case	NOUN
ejpam-524	285	15	,	,	PUNCT
ejpam-524	285	16	k	k	NOUN
ejpam-524	285	17	=	=	NOUN
ejpam-524	285	18	|m	|m	NOUN
ejpam-524	285	19	|=	|=	X
ejpam-524	285	20	2	2	X
ejpam-524	285	21	.	.	X
ejpam-524	285	22	therefore	therefore	ADV
ejpam-524	285	23	,	,	PUNCT
ejpam-524	285	24	by	by	ADP
ejpam-524	285	25	theorem	theorem	NOUN
ejpam-524	285	26	13	13	NUM
ejpam-524	285	27	,	,	PUNCT
ejpam-524	285	28	m	m	VERB
ejpam-524	285	29	is	be	AUX
ejpam-524	285	30	not	not	PART
ejpam-524	285	31	a	a	DET
ejpam-524	285	32	dpd	dpd	NOUN
ejpam-524	285	33	-	-	PUNCT
ejpam-524	285	34	set	set	NOUN
ejpam-524	285	35	.	.	PUNCT
ejpam-524	286	1	case	case	NOUN
ejpam-524	286	2	5	5	NUM
ejpam-524	286	3	:	:	PUNCT
ejpam-524	286	4	r	r	NOUN
ejpam-524	286	5	=	=	SYM
ejpam-524	286	6	0	0	NUM
ejpam-524	286	7	and	and	CCONJ
ejpam-524	286	8	k−	k−	PROPN
ejpam-524	287	1	r	r	NOUN
ejpam-524	287	2	=	=	SYM
ejpam-524	287	3	1	1	NUM
ejpam-524	287	4	d∗mg	d∗mg	NOUN
ejpam-524	287	5	=	=	SYM
ejpam-524	287	6			PROPN
ejpam-524	287	7			NOUN
ejpam-524	287	8			NOUN
ejpam-524	287	9			NOUN
ejpam-524	287	10			NOUN
ejpam-524	287	11			NOUN
ejpam-524	287	12			NOUN
ejpam-524	287	13			NOUN
ejpam-524	287	14			NOUN
ejpam-524	287	15			NOUN
ejpam-524	287	16			NOUN
ejpam-524	287	17	1	1	NUM
ejpam-524	287	18	0	0	NUM
ejpam-524	287	19	0	0	NUM
ejpam-524	287	20	0	0	NUM
ejpam-524	287	21	1	1	NUM
ejpam-524	287	22	0	0	NUM
ejpam-524	287	23	.	.	PUNCT
ejpam-524	287	24	.	.	PUNCT
ejpam-524	288	1	.	.	PUNCT
ejpam-524	288	2	.	.	PUNCT
ejpam-524	289	1	.	.	PUNCT
ejpam-524	289	2	.	.	PUNCT
ejpam-524	290	1	.	.	PUNCT
ejpam-524	290	2	.	.	PUNCT
ejpam-524	291	1	.	.	PUNCT
ejpam-524	292	1	0	0	NUM
ejpam-524	293	1	1	1	NUM
ejpam-524	293	2	0	0	NUM
ejpam-524	293	3	0	0	NUM
ejpam-524	293	4	0	0	NUM
ejpam-524	293	5	1	1	NUM
ejpam-524	293	6	.	.	PUNCT
ejpam-524	293	7	.	.	PUNCT
ejpam-524	293	8	.	.	PUNCT
ejpam-524	293	9	.	.	PUNCT
ejpam-524	293	10	.	.	PUNCT
ejpam-524	293	11	.	.	PUNCT
ejpam-524	293	12	.	.	PUNCT
ejpam-524	293	13	.	.	PUNCT
ejpam-524	293	14	.	.	PUNCT
ejpam-524	294	1	0	0	NUM
ejpam-524	294	2	0	0	NUM
ejpam-524	294	3	1	1	NUM
ejpam-524	294	4			NOUN
ejpam-524	294	5			NOUN
ejpam-524	294	6			VERB
ejpam-524	294	7			NOUN
ejpam-524	294	8			NOUN
ejpam-524	294	9			NOUN
ejpam-524	294	10			NOUN
ejpam-524	294	11			NOUN
ejpam-524	294	12			NOUN
ejpam-524	294	13			NOUN
ejpam-524	294	14			PUNCT
ejpam-524	295	1	g.	g.	PROPN
ejpam-524	295	2	augustine	augustine	PROPN
ejpam-524	295	3	,	,	PUNCT
ejpam-524	295	4	a.	a.	PROPN
ejpam-524	295	5	joseph	joseph	PROPN
ejpam-524	295	6	,	,	PUNCT
ejpam-524	295	7	s.	s.	PROPN
ejpam-524	295	8	jose	jose	PROPN
ejpam-524	295	9	/	/	SYM
ejpam-524	295	10	eur	eur	PROPN
ejpam-524	295	11	.	.	PUNCT
ejpam-524	296	1	j.	j.	PROPN
ejpam-524	296	2	pure	pure	PROPN
ejpam-524	296	3	appl	appl	PROPN
ejpam-524	296	4	.	.	PROPN
ejpam-524	296	5	math	math	PROPN
ejpam-524	296	6	,	,	PUNCT
ejpam-524	296	7	3	3	NUM
ejpam-524	296	8	(	(	PUNCT
ejpam-524	296	9	2010	2010	NUM
ejpam-524	296	10	)	)	PUNCT
ejpam-524	296	11	,	,	PUNCT
ejpam-524	296	12	748	748	NUM
ejpam-524	296	13	-	-	SYM
ejpam-524	296	14	764	764	NUM
ejpam-524	296	15	756	756	NUM
ejpam-524	296	16	hence	hence	ADV
ejpam-524	296	17	,	,	PUNCT
ejpam-524	296	18	from	from	ADP
ejpam-524	296	19	d∗mg	d∗mg	NOUN
ejpam-524	296	20	it	it	PRON
ejpam-524	296	21	is	be	AUX
ejpam-524	296	22	clear	clear	ADJ
ejpam-524	296	23	that	that	SCONJ
ejpam-524	296	24	d∗mg	d∗mg	NOUN
ejpam-524	296	25	contains	contain	VERB
ejpam-524	296	26	nonidentical	nonidentical	ADJ
ejpam-524	296	27	rows	row	NOUN
ejpam-524	296	28	only	only	ADV
ejpam-524	296	29	if	if	SCONJ
ejpam-524	296	30	either	either	DET
ejpam-524	296	31	m	m	VERB
ejpam-524	296	32	=	=	SYM
ejpam-524	296	33	1	1	NUM
ejpam-524	296	34	,	,	PUNCT
ejpam-524	296	35	n=	n=	ADJ
ejpam-524	296	36	1	1	NUM
ejpam-524	296	37	or	or	CCONJ
ejpam-524	296	38	m=	m=	ADJ
ejpam-524	296	39	1	1	NUM
ejpam-524	296	40	,	,	PUNCT
ejpam-524	296	41	n=	n=	ADJ
ejpam-524	296	42	2	2	NUM
ejpam-524	296	43	.	.	PUNCT
ejpam-524	296	44	converse	converse	NOUN
ejpam-524	296	45	follows	follow	VERB
ejpam-524	296	46	from	from	ADP
ejpam-524	296	47	proposition	proposition	NOUN
ejpam-524	296	48	3	3	NUM
ejpam-524	296	49	.	.	PUNCT
ejpam-524	296	50	corollary	corollary	ADJ
ejpam-524	296	51	5	5	NUM
ejpam-524	296	52	.	.	PUNCT
ejpam-524	297	1	the	the	DET
ejpam-524	297	2	star	star	NOUN
ejpam-524	297	3	graph	graph	NOUN
ejpam-524	297	4	k1,n	k1,n	PROPN
ejpam-524	297	5	admits	admit	VERB
ejpam-524	297	6	a	a	DET
ejpam-524	297	7	dpd	dpd	NOUN
ejpam-524	297	8	-	-	PUNCT
ejpam-524	297	9	set	set	VERB
ejpam-524	297	10	m	m	NOUN
ejpam-524	297	11	if	if	SCONJ
ejpam-524	297	12	and	and	CCONJ
ejpam-524	297	13	only	only	ADV
ejpam-524	298	1	if	if	SCONJ
ejpam-524	298	2	n≤	n≤	PRON
ejpam-524	298	3	2	2	NUM
ejpam-524	298	4	.	.	PUNCT
ejpam-524	298	5	theorem	theorem	VERB
ejpam-524	298	6	17	17	NUM
ejpam-524	298	7	.	.	PUNCT
ejpam-524	299	1	for	for	ADP
ejpam-524	299	2	a	a	DET
ejpam-524	299	3	dpd	dpd	NOUN
ejpam-524	299	4	-	-	PUNCT
ejpam-524	299	5	graph	graph	NOUN
ejpam-524	299	6	g	g	NOUN
ejpam-524	299	7	with	with	ADP
ejpam-524	299	8	a	a	DET
ejpam-524	299	9	dpd	dpd	NOUN
ejpam-524	299	10	-	-	PUNCT
ejpam-524	299	11	set	set	VERB
ejpam-524	299	12	m	m	NOUN
ejpam-524	299	13	of	of	ADP
ejpam-524	299	14	|m	|m	NOUN
ejpam-524	299	15	|	|	ADV
ejpam-524	299	16	=	=	SYM
ejpam-524	299	17	3	3	NUM
ejpam-524	299	18	,	,	PUNCT
ejpam-524	299	19	the	the	DET
ejpam-524	299	20	vertices	vertex	NOUN
ejpam-524	299	21	in	in	ADP
ejpam-524	299	22	m	m	PROPN
ejpam-524	299	23	should	should	AUX
ejpam-524	299	24	be	be	AUX
ejpam-524	299	25	at	at	ADP
ejpam-524	299	26	distinct	distinct	ADJ
ejpam-524	299	27	distances	distance	NOUN
ejpam-524	299	28	from	from	ADP
ejpam-524	299	29	each	each	DET
ejpam-524	299	30	other	other	ADJ
ejpam-524	299	31	.	.	PUNCT
ejpam-524	300	1	proof	proof	NOUN
ejpam-524	300	2	.	.	PUNCT
ejpam-524	301	1	let	let	VERB
ejpam-524	301	2	g	g	PRON
ejpam-524	301	3	be	be	AUX
ejpam-524	301	4	a	a	DET
ejpam-524	301	5	dpd	dpd	NOUN
ejpam-524	301	6	-	-	PUNCT
ejpam-524	301	7	graph	graph	NOUN
ejpam-524	301	8	with	with	ADP
ejpam-524	301	9	dpd	dpd	NOUN
ejpam-524	301	10	-	-	PUNCT
ejpam-524	301	11	set	set	NOUN
ejpam-524	301	12	m	m	NOUN
ejpam-524	301	13	=	=	SYM
ejpam-524	301	14	{	{	PUNCT
ejpam-524	301	15	v1	v1	PROPN
ejpam-524	301	16	,	,	PUNCT
ejpam-524	301	17	v2	v2	PROPN
ejpam-524	301	18	,	,	PUNCT
ejpam-524	301	19	v3	v3	PROPN
ejpam-524	301	20	}	}	PUNCT
ejpam-524	301	21	.	.	PUNCT
ejpam-524	302	1	let	let	VERB
ejpam-524	302	2	us	we	PRON
ejpam-524	302	3	denote	denote	VERB
ejpam-524	302	4	d(v1	d(v1	NOUN
ejpam-524	302	5	,	,	PUNCT
ejpam-524	302	6	v2	v2	NOUN
ejpam-524	302	7	)	)	PUNCT
ejpam-524	302	8	=	=	SYM
ejpam-524	302	9	k1	k1	PROPN
ejpam-524	302	10	,	,	PUNCT
ejpam-524	302	11	d(v2	d(v2	NOUN
ejpam-524	302	12	,	,	PUNCT
ejpam-524	302	13	v3	v3	PROPN
ejpam-524	302	14	)	)	PUNCT
ejpam-524	303	1	=	=	SYM
ejpam-524	303	2	k2	k2	PROPN
ejpam-524	303	3	and	and	CCONJ
ejpam-524	303	4	d(v1	d(v1	PROPN
ejpam-524	303	5	,	,	PUNCT
ejpam-524	303	6	v3	v3	PROPN
ejpam-524	303	7	)	)	PUNCT
ejpam-524	304	1	=	=	PUNCT
ejpam-524	304	2	k3	k3	VERB
ejpam-524	304	3	.	.	PUNCT
ejpam-524	305	1	case	case	NOUN
ejpam-524	305	2	1	1	NUM
ejpam-524	305	3	:	:	PUNCT
ejpam-524	305	4	d(v1	d(v1	NOUN
ejpam-524	305	5	,	,	PUNCT
ejpam-524	305	6	v2	v2	NOUN
ejpam-524	305	7	)	)	PUNCT
ejpam-524	305	8	=	=	SYM
ejpam-524	305	9	d(v2	d(v2	NOUN
ejpam-524	305	10	,	,	PUNCT
ejpam-524	305	11	v3	v3	PROPN
ejpam-524	305	12	)	)	PUNCT
ejpam-524	305	13	=	=	SYM
ejpam-524	305	14	d(v1	d(v1	PROPN
ejpam-524	305	15	,	,	PUNCT
ejpam-524	305	16	v3	v3	PROPN
ejpam-524	305	17	)	)	PUNCT
ejpam-524	306	1	=	=	SYM
ejpam-524	307	1	k	k	X
ejpam-524	307	2	in	in	ADP
ejpam-524	307	3	this	this	DET
ejpam-524	307	4	case	case	NOUN
ejpam-524	307	5	d∗mg	d∗mg	NOUN
ejpam-524	307	6	has	have	VERB
ejpam-524	307	7	a	a	DET
ejpam-524	307	8	3	3	NUM
ejpam-524	307	9	×	×	NOUN
ejpam-524	307	10	(	(	PUNCT
ejpam-524	307	11	dg	dg	X
ejpam-524	307	12	+	+	NOUN
ejpam-524	307	13	1	1	X
ejpam-524	307	14	)	)	PUNCT
ejpam-524	307	15	sub	sub	NOUN
ejpam-524	307	16	-	-	NOUN
ejpam-524	307	17	matrix	matrix	NOUN
ejpam-524	307	18	where	where	SCONJ
ejpam-524	307	19	the	the	DET
ejpam-524	307	20	rows	row	NOUN
ejpam-524	307	21	represent	represent	VERB
ejpam-524	307	22	the	the	DET
ejpam-524	307	23	m	m	PROPN
ejpam-524	307	24	-	-	PUNCT
ejpam-524	307	25	dnp	dnp	PROPN
ejpam-524	307	26	of	of	ADP
ejpam-524	307	27	the	the	DET
ejpam-524	307	28	vertices	vertex	NOUN
ejpam-524	307	29	v1	v1	NOUN
ejpam-524	307	30	,	,	PUNCT
ejpam-524	307	31	v2	v2	PROPN
ejpam-524	307	32	and	and	CCONJ
ejpam-524	307	33	v3	v3	PROPN
ejpam-524	307	34	respectively	respectively	ADV
ejpam-524	307	35	,	,	PUNCT
ejpam-524	307	36	with	with	ADP
ejpam-524	307	37	entries	entry	NOUN
ejpam-524	307	38	1	1	NUM
ejpam-524	307	39	only	only	ADV
ejpam-524	307	40	at	at	ADP
ejpam-524	307	41	the	the	DET
ejpam-524	307	42	first	first	ADJ
ejpam-524	307	43	and	and	CCONJ
ejpam-524	307	44	(	(	PUNCT
ejpam-524	307	45	k	k	PROPN
ejpam-524	307	46	+	+	PROPN
ejpam-524	307	47	1)th	1)th	NUM
ejpam-524	307	48	columns	column	NOUN
ejpam-524	307	49	.	.	PUNCT
ejpam-524	308	1			PROPN
ejpam-524	308	2			NOUN
ejpam-524	308	3			NOUN
ejpam-524	308	4	1	1	NUM
ejpam-524	308	5	0	0	NUM
ejpam-524	308	6	.	.	PUNCT
ejpam-524	308	7	.	.	PUNCT
ejpam-524	309	1	.	.	PUNCT
ejpam-524	310	1	0	0	NUM
ejpam-524	311	1	1	1	NUM
ejpam-524	311	2	0	0	NUM
ejpam-524	311	3	.	.	PUNCT
ejpam-524	311	4	.	.	PUNCT
ejpam-524	311	5	.	.	PUNCT
ejpam-524	312	1	0	0	NUM
ejpam-524	313	1	1	1	NUM
ejpam-524	313	2	0	0	NUM
ejpam-524	313	3	.	.	PUNCT
ejpam-524	313	4	.	.	PUNCT
ejpam-524	313	5	.	.	PUNCT
ejpam-524	314	1	0	0	NUM
ejpam-524	315	1	1	1	NUM
ejpam-524	315	2	0	0	NUM
ejpam-524	315	3	.	.	PUNCT
ejpam-524	315	4	.	.	PUNCT
ejpam-524	315	5	.	.	PUNCT
ejpam-524	316	1	0	0	NUM
ejpam-524	317	1	1	1	NUM
ejpam-524	317	2	0	0	NUM
ejpam-524	317	3	.	.	PUNCT
ejpam-524	317	4	.	.	PUNCT
ejpam-524	317	5	.	.	PUNCT
ejpam-524	318	1	0	0	NUM
ejpam-524	319	1	1	1	NUM
ejpam-524	319	2	0	0	NUM
ejpam-524	319	3	.	.	PUNCT
ejpam-524	319	4	.	.	PUNCT
ejpam-524	320	1	.	.	PUNCT
ejpam-524	320	2	0	0	NUM
ejpam-524	321	1			PROPN
ejpam-524	321	2			NOUN
ejpam-524	321	3			PUNCT
ejpam-524	322	1	therefore	therefore	ADV
ejpam-524	322	2	,	,	PUNCT
ejpam-524	322	3	d∗mg	d∗mg	NOUN
ejpam-524	322	4	contains	contain	VERB
ejpam-524	322	5	identical	identical	ADJ
ejpam-524	322	6	rows	row	NOUN
ejpam-524	322	7	and	and	CCONJ
ejpam-524	322	8	hence	hence	ADV
ejpam-524	322	9	,	,	PUNCT
ejpam-524	322	10	m	m	VERB
ejpam-524	322	11	is	be	AUX
ejpam-524	322	12	not	not	PART
ejpam-524	322	13	a	a	DET
ejpam-524	322	14	dpd	dpd	NOUN
ejpam-524	322	15	-	-	PUNCT
ejpam-524	322	16	set	set	NOUN
ejpam-524	322	17	.	.	PUNCT
ejpam-524	323	1	case	case	NOUN
ejpam-524	323	2	2	2	NUM
ejpam-524	323	3	:	:	PUNCT
ejpam-524	323	4	k1	k1	NOUN
ejpam-524	323	5	=	=	SYM
ejpam-524	323	6	k2	k2	PROPN
ejpam-524	323	7	6=	6=	PROPN
ejpam-524	323	8	k3	k3	PROPN
ejpam-524	323	9	in	in	ADP
ejpam-524	323	10	this	this	DET
ejpam-524	323	11	case	case	NOUN
ejpam-524	323	12	,	,	PUNCT
ejpam-524	323	13	d∗mg	d∗mg	PROPN
ejpam-524	323	14	has	have	VERB
ejpam-524	323	15	a	a	DET
ejpam-524	323	16	2×	2×	NUM
ejpam-524	323	17	(	(	PUNCT
ejpam-524	323	18	dg	dg	X
ejpam-524	323	19	+	+	NOUN
ejpam-524	323	20	1	1	X
ejpam-524	323	21	)	)	PUNCT
ejpam-524	323	22	sub	sub	NOUN
ejpam-524	323	23	-	-	NOUN
ejpam-524	323	24	matrix	matrix	NOUN
ejpam-524	323	25	where	where	SCONJ
ejpam-524	323	26	the	the	DET
ejpam-524	323	27	rows	row	NOUN
ejpam-524	323	28	represent	represent	VERB
ejpam-524	323	29	the	the	DET
ejpam-524	323	30	m	m	PROPN
ejpam-524	323	31	-	-	PUNCT
ejpam-524	323	32	dnp	dnp	PROPN
ejpam-524	323	33	of	of	ADP
ejpam-524	323	34	the	the	DET
ejpam-524	323	35	vertices	vertex	NOUN
ejpam-524	323	36	v1	v1	VERB
ejpam-524	323	37	and	and	CCONJ
ejpam-524	323	38	v3	v3	PROPN
ejpam-524	323	39	respectively	respectively	ADV
ejpam-524	323	40	with	with	ADP
ejpam-524	323	41	entries	entry	NOUN
ejpam-524	323	42	1	1	NUM
ejpam-524	323	43	only	only	ADV
ejpam-524	323	44	at	at	ADP
ejpam-524	323	45	the	the	DET
ejpam-524	323	46	first	first	ADJ
ejpam-524	323	47	,	,	PUNCT
ejpam-524	323	48	(	(	PUNCT
ejpam-524	323	49	k1	k1	X
ejpam-524	323	50	+	+	SYM
ejpam-524	323	51	1)th	1)th	NUM
ejpam-524	323	52	and	and	CCONJ
ejpam-524	323	53	(	(	PUNCT
ejpam-524	323	54	k3	k3	PROPN
ejpam-524	323	55	+	+	PROPN
ejpam-524	323	56	1)th	1)th	NOUN
ejpam-524	323	57	columns	column	NOUN
ejpam-524	323	58	.	.	PUNCT
ejpam-524	324	1	�	�	PROPN
ejpam-524	324	2	1	1	NUM
ejpam-524	324	3	0	0	NUM
ejpam-524	324	4	.	.	PUNCT
ejpam-524	324	5	.	.	PUNCT
ejpam-524	325	1	.	.	PUNCT
ejpam-524	326	1	0	0	NUM
ejpam-524	327	1	1	1	NUM
ejpam-524	327	2	0	0	NUM
ejpam-524	327	3	.	.	PUNCT
ejpam-524	327	4	.	.	PUNCT
ejpam-524	327	5	.	.	PUNCT
ejpam-524	328	1	0	0	NUM
ejpam-524	329	1	1	1	NUM
ejpam-524	329	2	0	0	NUM
ejpam-524	329	3	.	.	PUNCT
ejpam-524	329	4	.	.	PUNCT
ejpam-524	329	5	.	.	PUNCT
ejpam-524	330	1	0	0	NUM
ejpam-524	331	1	1	1	NUM
ejpam-524	331	2	0	0	NUM
ejpam-524	331	3	.	.	PUNCT
ejpam-524	331	4	.	.	PUNCT
ejpam-524	331	5	.	.	PUNCT
ejpam-524	332	1	0	0	NUM
ejpam-524	333	1	1	1	NUM
ejpam-524	333	2	0	0	NUM
ejpam-524	333	3	.	.	PUNCT
ejpam-524	333	4	.	.	PUNCT
ejpam-524	333	5	.	.	PUNCT
ejpam-524	334	1	0	0	NUM
ejpam-524	335	1	1	1	NUM
ejpam-524	335	2	0	0	NUM
ejpam-524	335	3	.	.	PUNCT
ejpam-524	335	4	.	.	PUNCT
ejpam-524	335	5	.	.	PUNCT
ejpam-524	336	1	0	0	NUM
ejpam-524	336	2	�	�	PROPN
ejpam-524	336	3	hence	hence	ADV
ejpam-524	336	4	,	,	PUNCT
ejpam-524	336	5	d∗mg	d∗mg	PROPN
ejpam-524	336	6	has	have	VERB
ejpam-524	336	7	identical	identical	ADJ
ejpam-524	336	8	rows	row	NOUN
ejpam-524	336	9	and	and	CCONJ
ejpam-524	336	10	m	m	NOUN
ejpam-524	336	11	is	be	AUX
ejpam-524	336	12	not	not	PART
ejpam-524	336	13	a	a	DET
ejpam-524	336	14	dpd	dpd	NOUN
ejpam-524	336	15	-	-	PUNCT
ejpam-524	336	16	set	set	NOUN
ejpam-524	336	17	.	.	PUNCT
ejpam-524	337	1	case	case	NOUN
ejpam-524	337	2	3	3	NUM
ejpam-524	337	3	:	:	PUNCT
ejpam-524	337	4	k1	k1	PROPN
ejpam-524	337	5	6=	6=	PROPN
ejpam-524	337	6	k2	k2	PROPN
ejpam-524	337	7	6=	6=	PROPN
ejpam-524	337	8	k3	k3	PROPN
ejpam-524	337	9	in	in	ADP
ejpam-524	337	10	this	this	DET
ejpam-524	337	11	case	case	NOUN
ejpam-524	337	12	,	,	PUNCT
ejpam-524	337	13	the	the	DET
ejpam-524	337	14	first	first	ADJ
ejpam-524	337	15	,	,	PUNCT
ejpam-524	337	16	second	second	ADJ
ejpam-524	337	17	and	and	CCONJ
ejpam-524	337	18	the	the	DET
ejpam-524	337	19	third	third	ADJ
ejpam-524	337	20	rows	row	NOUN
ejpam-524	337	21	represent	represent	VERB
ejpam-524	337	22	the	the	DET
ejpam-524	337	23	m	m	PROPN
ejpam-524	337	24	-	-	PUNCT
ejpam-524	337	25	dnp	dnp	PROPN
ejpam-524	337	26	of	of	ADP
ejpam-524	337	27	the	the	DET
ejpam-524	337	28	vertices	vertex	NOUN
ejpam-524	337	29	v1	v1	NOUN
ejpam-524	337	30	,	,	PUNCT
ejpam-524	337	31	v2	v2	PROPN
ejpam-524	337	32	and	and	CCONJ
ejpam-524	337	33	v3	v3	PROPN
ejpam-524	337	34	respectively	respectively	ADV
ejpam-524	337	35	in	in	ADP
ejpam-524	337	36	d∗mg	d∗mg	NOUN
ejpam-524	337	37	,	,	PUNCT
ejpam-524	337	38	with	with	ADP
ejpam-524	337	39	entries	entry	NOUN
ejpam-524	337	40	1	1	NUM
ejpam-524	337	41	only	only	ADV
ejpam-524	337	42	at	at	ADP
ejpam-524	337	43	the	the	DET
ejpam-524	337	44	first	first	ADJ
ejpam-524	337	45	,	,	PUNCT
ejpam-524	337	46	(	(	PUNCT
ejpam-524	337	47	k1	k1	NOUN
ejpam-524	337	48	+	+	CCONJ
ejpam-524	337	49	1)th	1)th	NUM
ejpam-524	337	50	,	,	PUNCT
ejpam-524	337	51	(	(	PUNCT
ejpam-524	337	52	k2	k2	X
ejpam-524	337	53	+	+	CCONJ
ejpam-524	337	54	1)th	1)th	PROPN
ejpam-524	337	55	and	and	CCONJ
ejpam-524	337	56	the	the	DET
ejpam-524	337	57	(	(	PUNCT
ejpam-524	337	58	k3	k3	ADJ
ejpam-524	337	59	+	+	NOUN
ejpam-524	337	60	1)th	1)th	NUM
ejpam-524	337	61	columns	column	NOUN
ejpam-524	337	62	.	.	PUNCT
ejpam-524	338	1			PROPN
ejpam-524	338	2			NOUN
ejpam-524	338	3			NOUN
ejpam-524	338	4	1	1	NUM
ejpam-524	338	5	0	0	NUM
ejpam-524	338	6	.	.	PUNCT
ejpam-524	338	7	.	.	PUNCT
ejpam-524	339	1	.	.	PUNCT
ejpam-524	340	1	0	0	NUM
ejpam-524	341	1	1	1	NUM
ejpam-524	341	2	0	0	NUM
ejpam-524	341	3	.	.	PUNCT
ejpam-524	341	4	.	.	PUNCT
ejpam-524	341	5	.	.	PUNCT
ejpam-524	342	1	0	0	NUM
ejpam-524	343	1	0	0	NUM
ejpam-524	343	2	0	0	NUM
ejpam-524	343	3	.	.	PUNCT
ejpam-524	343	4	.	.	PUNCT
ejpam-524	343	5	.	.	PUNCT
ejpam-524	344	1	0	0	NUM
ejpam-524	345	1	1	1	NUM
ejpam-524	345	2	0	0	NUM
ejpam-524	345	3	.	.	PUNCT
ejpam-524	345	4	.	.	PUNCT
ejpam-524	345	5	.	.	PUNCT
ejpam-524	346	1	0	0	NUM
ejpam-524	347	1	1	1	NUM
ejpam-524	347	2	0	0	NUM
ejpam-524	347	3	.	.	PUNCT
ejpam-524	347	4	.	.	PUNCT
ejpam-524	347	5	.	.	PUNCT
ejpam-524	348	1	0	0	NUM
ejpam-524	349	1	1	1	NUM
ejpam-524	349	2	0	0	NUM
ejpam-524	349	3	.	.	PUNCT
ejpam-524	349	4	.	.	PUNCT
ejpam-524	349	5	.	.	PUNCT
ejpam-524	350	1	0	0	NUM
ejpam-524	351	1	1	1	NUM
ejpam-524	351	2	0	0	NUM
ejpam-524	351	3	.	.	PUNCT
ejpam-524	351	4	.	.	PUNCT
ejpam-524	351	5	.	.	PUNCT
ejpam-524	352	1	0	0	NUM
ejpam-524	353	1	0	0	NUM
ejpam-524	353	2	0	0	NUM
ejpam-524	353	3	0	0	NUM
ejpam-524	353	4	0	0	NUM
ejpam-524	353	5	1	1	NUM
ejpam-524	353	6	0	0	NUM
ejpam-524	353	7	.	.	PUNCT
ejpam-524	353	8	.	.	PUNCT
ejpam-524	353	9	.	.	PUNCT
ejpam-524	354	1	0	0	NUM
ejpam-524	355	1	0	0	NUM
ejpam-524	355	2	0	0	NUM
ejpam-524	355	3	.	.	PUNCT
ejpam-524	355	4	.	.	PUNCT
ejpam-524	355	5	.	.	PUNCT
ejpam-524	356	1	0	0	NUM
ejpam-524	357	1	1	1	NUM
ejpam-524	357	2	0	0	NUM
ejpam-524	357	3	.	.	PUNCT
ejpam-524	357	4	.	.	PUNCT
ejpam-524	357	5	.	.	PUNCT
ejpam-524	358	1	0	0	NUM
ejpam-524	359	1	1	1	NUM
ejpam-524	359	2	0	0	NUM
ejpam-524	359	3	.	.	PUNCT
ejpam-524	359	4	.	.	PUNCT
ejpam-524	360	1	.	.	PUNCT
ejpam-524	360	2	0	0	NUM
ejpam-524	361	1			PROPN
ejpam-524	361	2			NOUN
ejpam-524	361	3			PUNCT
ejpam-524	362	1	hence	hence	ADV
ejpam-524	362	2	,	,	PUNCT
ejpam-524	362	3	it	it	PRON
ejpam-524	362	4	is	be	AUX
ejpam-524	362	5	possible	possible	ADJ
ejpam-524	362	6	to	to	PART
ejpam-524	362	7	form	form	VERB
ejpam-524	362	8	a	a	DET
ejpam-524	362	9	dpd	dpd	NOUN
ejpam-524	362	10	-	-	PUNCT
ejpam-524	362	11	set	set	VERB
ejpam-524	362	12	m	m	NOUN
ejpam-524	362	13	with	with	ADP
ejpam-524	362	14	|m	|m	NOUN
ejpam-524	362	15	|	|	ADV
ejpam-524	362	16	=	=	SYM
ejpam-524	362	17	3	3	NUM
ejpam-524	362	18	in	in	ADP
ejpam-524	362	19	this	this	DET
ejpam-524	362	20	case	case	NOUN
ejpam-524	362	21	.	.	PUNCT
ejpam-524	363	1	however	however	ADV
ejpam-524	363	2	,	,	PUNCT
ejpam-524	363	3	any	any	DET
ejpam-524	363	4	subset	subset	NOUN
ejpam-524	363	5	m	m	VERB
ejpam-524	363	6	=	=	SYM
ejpam-524	363	7	{	{	PUNCT
ejpam-524	363	8	v1	v1	PROPN
ejpam-524	363	9	,	,	PUNCT
ejpam-524	363	10	v2	v2	PROPN
ejpam-524	363	11	,	,	PUNCT
ejpam-524	363	12	v3	v3	PROPN
ejpam-524	363	13	}	}	PUNCT
ejpam-524	363	14	⊆	⊆	NUM
ejpam-524	363	15	v	v	NOUN
ejpam-524	363	16	(	(	PUNCT
ejpam-524	363	17	g	g	NOUN
ejpam-524	363	18	)	)	PUNCT
ejpam-524	363	19	,	,	PUNCT
ejpam-524	363	20	satisfying	satisfy	VERB
ejpam-524	363	21	the	the	DET
ejpam-524	363	22	condition	condition	NOUN
ejpam-524	363	23	stated	state	VERB
ejpam-524	363	24	in	in	ADP
ejpam-524	363	25	theorem	theorem	NOUN
ejpam-524	363	26	17	17	NUM
ejpam-524	363	27	,	,	PUNCT
ejpam-524	363	28	is	be	AUX
ejpam-524	363	29	not	not	PART
ejpam-524	363	30	a	a	DET
ejpam-524	363	31	sufficient	sufficient	ADJ
ejpam-524	363	32	condition	condition	NOUN
ejpam-524	363	33	for	for	SCONJ
ejpam-524	363	34	m	m	NOUN
ejpam-524	363	35	to	to	PART
ejpam-524	363	36	be	be	AUX
ejpam-524	363	37	a	a	DET
ejpam-524	363	38	dpd	dpd	NOUN
ejpam-524	363	39	-	-	PUNCT
ejpam-524	363	40	set	set	NOUN
ejpam-524	363	41	.	.	PUNCT
ejpam-524	364	1	consider	consider	VERB
ejpam-524	364	2	c6	c6	PROPN
ejpam-524	364	3	=	=	PUNCT
ejpam-524	364	4	(	(	PUNCT
ejpam-524	364	5	v1v2	v1v2	X
ejpam-524	364	6	.	.	PUNCT
ejpam-524	364	7	.	.	PUNCT
ejpam-524	364	8	.	.	PUNCT
ejpam-524	365	1	v6	v6	PROPN
ejpam-524	365	2	)	)	PUNCT
ejpam-524	365	3	,	,	PUNCT
ejpam-524	365	4	with	with	ADP
ejpam-524	365	5	m	m	PROPN
ejpam-524	365	6	=	=	SYM
ejpam-524	365	7	{	{	PUNCT
ejpam-524	365	8	v1	v1	PROPN
ejpam-524	365	9	,	,	PUNCT
ejpam-524	365	10	v2	v2	PROPN
ejpam-524	365	11	,	,	PUNCT
ejpam-524	365	12	v4	v4	PROPN
ejpam-524	365	13	}	}	PUNCT
ejpam-524	365	14	which	which	PRON
ejpam-524	365	15	are	be	AUX
ejpam-524	365	16	at	at	ADP
ejpam-524	365	17	distinct	distinct	ADJ
ejpam-524	365	18	distances	distance	NOUN
ejpam-524	365	19	,	,	PUNCT
ejpam-524	365	20	but	but	CCONJ
ejpam-524	365	21	clearly	clearly	ADV
ejpam-524	365	22	do	do	AUX
ejpam-524	365	23	not	not	PART
ejpam-524	365	24	form	form	VERB
ejpam-524	365	25	a	a	DET
ejpam-524	365	26	dpd	dpd	NOUN
ejpam-524	365	27	-	-	PUNCT
ejpam-524	365	28	set	set	NOUN
ejpam-524	365	29	.	.	PUNCT
ejpam-524	366	1	g.	g.	PROPN
ejpam-524	366	2	augustine	augustine	PROPN
ejpam-524	366	3	,	,	PUNCT
ejpam-524	366	4	a.	a.	PROPN
ejpam-524	366	5	joseph	joseph	PROPN
ejpam-524	366	6	,	,	PUNCT
ejpam-524	366	7	s.	s.	PROPN
ejpam-524	366	8	jose	jose	PROPN
ejpam-524	366	9	/	/	SYM
ejpam-524	366	10	eur	eur	PROPN
ejpam-524	366	11	.	.	PUNCT
ejpam-524	367	1	j.	j.	PROPN
ejpam-524	367	2	pure	pure	PROPN
ejpam-524	367	3	appl	appl	PROPN
ejpam-524	367	4	.	.	PROPN
ejpam-524	367	5	math	math	PROPN
ejpam-524	367	6	,	,	PUNCT
ejpam-524	367	7	3	3	NUM
ejpam-524	367	8	(	(	PUNCT
ejpam-524	367	9	2010	2010	NUM
ejpam-524	367	10	)	)	PUNCT
ejpam-524	367	11	,	,	PUNCT
ejpam-524	367	12	748	748	NUM
ejpam-524	367	13	-	-	SYM
ejpam-524	367	14	764	764	NUM
ejpam-524	367	15	757	757	NUM
ejpam-524	367	16	theorem	theorem	VERB
ejpam-524	367	17	18	18	NUM
ejpam-524	367	18	.	.	PUNCT
ejpam-524	368	1	a	a	DET
ejpam-524	368	2	cycle	cycle	NOUN
ejpam-524	368	3	g	g	NOUN
ejpam-524	368	4	∼=	∼=	PROPN
ejpam-524	368	5	cn	cn	NOUN
ejpam-524	368	6	of	of	ADP
ejpam-524	368	7	order	order	NOUN
ejpam-524	368	8	n	n	PRON
ejpam-524	368	9	admits	admit	VERB
ejpam-524	368	10	a	a	DET
ejpam-524	368	11	dpd	dpd	NOUN
ejpam-524	368	12	-	-	PUNCT
ejpam-524	368	13	set	set	VERB
ejpam-524	368	14	if	if	SCONJ
ejpam-524	368	15	and	and	CCONJ
ejpam-524	368	16	only	only	ADV
ejpam-524	368	17	if	if	SCONJ
ejpam-524	368	18	n≥	n≥	PROPN
ejpam-524	368	19	7	7	NUM
ejpam-524	368	20	.	.	PUNCT
ejpam-524	368	21	proof	proof	NOUN
ejpam-524	368	22	.	.	PUNCT
ejpam-524	369	1	let	let	VERB
ejpam-524	369	2	cn	cn	PROPN
ejpam-524	369	3	=	=	PRON
ejpam-524	369	4	(	(	PUNCT
ejpam-524	369	5	v1v2	v1v2	X
ejpam-524	369	6	.	.	PUNCT
ejpam-524	369	7	.	.	PUNCT
ejpam-524	369	8	.	.	PUNCT
ejpam-524	370	1	vnv1	vnv1	PROPN
ejpam-524	370	2	)	)	PUNCT
ejpam-524	370	3	be	be	VERB
ejpam-524	370	4	a	a	DET
ejpam-524	370	5	cycle	cycle	NOUN
ejpam-524	370	6	on	on	ADP
ejpam-524	370	7	n	n	DET
ejpam-524	370	8	vertices	vertex	NOUN
ejpam-524	370	9	.	.	PUNCT
ejpam-524	371	1	case	case	NOUN
ejpam-524	371	2	1	1	NUM
ejpam-524	371	3	:	:	SYM
ejpam-524	371	4	n	n	CCONJ
ejpam-524	371	5	,	,	PUNCT
ejpam-524	371	6	an	an	DET
ejpam-524	371	7	even	even	ADV
ejpam-524	371	8	integer	integer	NOUN
ejpam-524	371	9	and	and	CCONJ
ejpam-524	371	10	n≥	n≥	NOUN
ejpam-524	371	11	8	8	NUM
ejpam-524	371	12	let	let	VERB
ejpam-524	371	13	m	m	VERB
ejpam-524	371	14	=	=	PUNCT
ejpam-524	371	15	{	{	PUNCT
ejpam-524	371	16	v1	v1	PROPN
ejpam-524	371	17	,	,	PUNCT
ejpam-524	371	18	v2	v2	PROPN
ejpam-524	371	19	,	,	PUNCT
ejpam-524	371	20	v4	v4	NOUN
ejpam-524	371	21	}	}	PUNCT
ejpam-524	371	22	.	.	PUNCT
ejpam-524	372	1	then	then	ADV
ejpam-524	372	2	,	,	PUNCT
ejpam-524	372	3	d∗mg	d∗mg	NOUN
ejpam-524	372	4	=	=	SYM
ejpam-524	372	5			PROPN
ejpam-524	372	6			NOUN
ejpam-524	372	7			NOUN
ejpam-524	372	8			NOUN
ejpam-524	372	9			NOUN
ejpam-524	372	10			NOUN
ejpam-524	372	11			NOUN
ejpam-524	372	12			NOUN
ejpam-524	372	13			NOUN
ejpam-524	372	14			NOUN
ejpam-524	372	15			NOUN
ejpam-524	372	16			NOUN
ejpam-524	372	17			NOUN
ejpam-524	372	18			NOUN
ejpam-524	372	19			NOUN
ejpam-524	372	20			NOUN
ejpam-524	372	21			NOUN
ejpam-524	372	22			NOUN
ejpam-524	372	23			NOUN
ejpam-524	372	24			NOUN
ejpam-524	372	25			NOUN
ejpam-524	372	26			NOUN
ejpam-524	372	27			NOUN
ejpam-524	372	28			NOUN
ejpam-524	372	29			NOUN
ejpam-524	372	30			NOUN
ejpam-524	372	31			NOUN
ejpam-524	372	32			NOUN
ejpam-524	372	33	1	1	NUM
ejpam-524	372	34	1	1	NUM
ejpam-524	372	35	0	0	NUM
ejpam-524	372	36	1	1	NUM
ejpam-524	372	37	0	0	NUM
ejpam-524	372	38	0	0	NUM
ejpam-524	372	39	.	.	PUNCT
ejpam-524	372	40	.	.	PUNCT
ejpam-524	373	1	.	.	PUNCT
ejpam-524	374	1	0	0	NUM
ejpam-524	375	1	0	0	NUM
ejpam-524	375	2	0	0	NUM
ejpam-524	375	3	0	0	NUM
ejpam-524	375	4	0	0	NUM
ejpam-524	375	5	0	0	NUM
ejpam-524	375	6	1	1	NUM
ejpam-524	375	7	1	1	NUM
ejpam-524	375	8	1	1	NUM
ejpam-524	375	9	0	0	NUM
ejpam-524	375	10	0	0	NUM
ejpam-524	375	11	0	0	NUM
ejpam-524	375	12	.	.	PUNCT
ejpam-524	375	13	.	.	PUNCT
ejpam-524	375	14	.	.	PUNCT
ejpam-524	376	1	0	0	NUM
ejpam-524	377	1	0	0	NUM
ejpam-524	377	2	0	0	NUM
ejpam-524	377	3	0	0	NUM
ejpam-524	377	4	0	0	NUM
ejpam-524	377	5	0	0	NUM
ejpam-524	377	6	0	0	NUM
ejpam-524	377	7	1	1	NUM
ejpam-524	377	8	1	1	NUM
ejpam-524	377	9	0	0	NUM
ejpam-524	377	10	0	0	NUM
ejpam-524	377	11	0	0	NUM
ejpam-524	377	12	.	.	PUNCT
ejpam-524	377	13	.	.	PUNCT
ejpam-524	377	14	.	.	PUNCT
ejpam-524	378	1	0	0	NUM
ejpam-524	379	1	0	0	NUM
ejpam-524	379	2	0	0	NUM
ejpam-524	379	3	0	0	NUM
ejpam-524	379	4	0	0	NUM
ejpam-524	379	5	0	0	NUM
ejpam-524	379	6	1	1	NUM
ejpam-524	379	7	0	0	NUM
ejpam-524	379	8	1	1	NUM
ejpam-524	379	9	1	1	NUM
ejpam-524	379	10	0	0	NUM
ejpam-524	379	11	0	0	NUM
ejpam-524	379	12	.	.	PUNCT
ejpam-524	379	13	.	.	PUNCT
ejpam-524	379	14	.	.	PUNCT
ejpam-524	380	1	0	0	NUM
ejpam-524	381	1	0	0	NUM
ejpam-524	381	2	0	0	NUM
ejpam-524	381	3	0	0	NUM
ejpam-524	381	4	0	0	NUM
ejpam-524	381	5	0	0	NUM
ejpam-524	381	6	0	0	NUM
ejpam-524	381	7	1	1	NUM
ejpam-524	381	8	0	0	NUM
ejpam-524	381	9	1	1	NUM
ejpam-524	381	10	1	1	NUM
ejpam-524	381	11	0	0	NUM
ejpam-524	381	12	.	.	PUNCT
ejpam-524	381	13	.	.	PUNCT
ejpam-524	381	14	.	.	PUNCT
ejpam-524	382	1	0	0	NUM
ejpam-524	383	1	0	0	NUM
ejpam-524	383	2	0	0	NUM
ejpam-524	383	3	0	0	NUM
ejpam-524	383	4	0	0	NUM
ejpam-524	383	5	0	0	NUM
ejpam-524	383	6	0	0	NUM
ejpam-524	383	7	0	0	NUM
ejpam-524	383	8	1	1	NUM
ejpam-524	383	9	0	0	NUM
ejpam-524	383	10	1	1	NUM
ejpam-524	383	11	1	1	NUM
ejpam-524	383	12	.	.	PUNCT
ejpam-524	383	13	.	.	PUNCT
ejpam-524	383	14	.	.	PUNCT
ejpam-524	384	1	0	0	NUM
ejpam-524	385	1	0	0	NUM
ejpam-524	385	2	0	0	NUM
ejpam-524	385	3	0	0	NUM
ejpam-524	385	4	0	0	NUM
ejpam-524	385	5	0	0	NUM
ejpam-524	385	6	.	.	PUNCT
ejpam-524	385	7	.	.	PUNCT
ejpam-524	385	8	.	.	PUNCT
ejpam-524	385	9	.	.	PUNCT
ejpam-524	385	10	.	.	PUNCT
ejpam-524	385	11	.	.	PUNCT
ejpam-524	385	12	.	.	PUNCT
ejpam-524	385	13	.	.	PUNCT
ejpam-524	385	14	.	.	PUNCT
ejpam-524	385	15	.	.	PUNCT
ejpam-524	385	16	.	.	PUNCT
ejpam-524	385	17	.	.	PUNCT
ejpam-524	385	18	.	.	PUNCT
ejpam-524	385	19	.	.	PUNCT
ejpam-524	385	20	.	.	PUNCT
ejpam-524	385	21	.	.	PUNCT
ejpam-524	385	22	.	.	PUNCT
ejpam-524	385	23	.	.	PUNCT
ejpam-524	385	24	.	.	PUNCT
ejpam-524	385	25	.	.	PUNCT
ejpam-524	385	26	.	.	PUNCT
ejpam-524	385	27	.	.	PUNCT
ejpam-524	385	28	.	.	PUNCT
ejpam-524	385	29	.	.	PUNCT
ejpam-524	385	30	.	.	PUNCT
ejpam-524	385	31	.	.	PUNCT
ejpam-524	385	32	.	.	PUNCT
ejpam-524	385	33	.	.	PUNCT
ejpam-524	385	34	.	.	PUNCT
ejpam-524	385	35	.	.	PUNCT
ejpam-524	385	36	.	.	PUNCT
ejpam-524	385	37	.	.	PUNCT
ejpam-524	385	38	.	.	PUNCT
ejpam-524	385	39	.	.	PUNCT
ejpam-524	385	40	.	.	PUNCT
ejpam-524	385	41	.	.	PUNCT
ejpam-524	385	42	.	.	PUNCT
ejpam-524	385	43	.	.	PUNCT
ejpam-524	385	44	.	.	PUNCT
ejpam-524	386	1	0	0	NUM
ejpam-524	387	1	0	0	NUM
ejpam-524	387	2	0	0	NUM
ejpam-524	387	3	0	0	NUM
ejpam-524	387	4	0	0	NUM
ejpam-524	387	5	0	0	NUM
ejpam-524	387	6	.	.	PUNCT
ejpam-524	387	7	.	.	PUNCT
ejpam-524	387	8	.	.	PUNCT
ejpam-524	388	1	0	0	NUM
ejpam-524	389	1	1	1	NUM
ejpam-524	389	2	0	0	NUM
ejpam-524	389	3	1	1	NUM
ejpam-524	389	4	1	1	NUM
ejpam-524	389	5	0	0	NUM
ejpam-524	389	6	0	0	NUM
ejpam-524	389	7	0	0	NUM
ejpam-524	389	8	0	0	NUM
ejpam-524	389	9	0	0	NUM
ejpam-524	389	10	0	0	NUM
ejpam-524	389	11	0	0	NUM
ejpam-524	389	12	.	.	PUNCT
ejpam-524	389	13	.	.	PUNCT
ejpam-524	389	14	.	.	PUNCT
ejpam-524	390	1	0	0	NUM
ejpam-524	391	1	0	0	NUM
ejpam-524	391	2	1	1	NUM
ejpam-524	391	3	0	0	NUM
ejpam-524	391	4	1	1	NUM
ejpam-524	391	5	1	1	NUM
ejpam-524	391	6	0	0	NUM
ejpam-524	391	7	0	0	NUM
ejpam-524	391	8	0	0	NUM
ejpam-524	391	9	0	0	NUM
ejpam-524	391	10	0	0	NUM
ejpam-524	391	11	0	0	NUM
ejpam-524	391	12	.	.	PUNCT
ejpam-524	391	13	.	.	PUNCT
ejpam-524	391	14	.	.	PUNCT
ejpam-524	392	1	0	0	NUM
ejpam-524	393	1	0	0	NUM
ejpam-524	393	2	0	0	NUM
ejpam-524	393	3	1	1	NUM
ejpam-524	393	4	1	1	NUM
ejpam-524	393	5	1	1	NUM
ejpam-524	393	6	0	0	NUM
ejpam-524	393	7	0	0	NUM
ejpam-524	393	8	0	0	NUM
ejpam-524	393	9	0	0	NUM
ejpam-524	393	10	0	0	NUM
ejpam-524	393	11	0	0	NUM
ejpam-524	393	12	.	.	PUNCT
ejpam-524	393	13	.	.	PUNCT
ejpam-524	393	14	.	.	PUNCT
ejpam-524	394	1	0	0	NUM
ejpam-524	395	1	0	0	NUM
ejpam-524	395	2	0	0	NUM
ejpam-524	395	3	1	1	NUM
ejpam-524	395	4	1	1	NUM
ejpam-524	395	5	0	0	NUM
ejpam-524	395	6	0	0	NUM
ejpam-524	395	7	0	0	NUM
ejpam-524	395	8	0	0	NUM
ejpam-524	395	9	0	0	NUM
ejpam-524	395	10	0	0	NUM
ejpam-524	395	11	0	0	NUM
ejpam-524	395	12	.	.	PUNCT
ejpam-524	395	13	.	.	PUNCT
ejpam-524	396	1	.	.	PUNCT
ejpam-524	397	1	0	0	NUM
ejpam-524	398	1	0	0	NUM
ejpam-524	398	2	1	1	NUM
ejpam-524	398	3	1	1	NUM
ejpam-524	398	4	0	0	NUM
ejpam-524	398	5	1	1	NUM
ejpam-524	398	6	0	0	NUM
ejpam-524	398	7	0	0	NUM
ejpam-524	398	8	0	0	NUM
ejpam-524	398	9	0	0	NUM
ejpam-524	398	10	0	0	NUM
ejpam-524	398	11	0	0	NUM
ejpam-524	398	12	.	.	PUNCT
ejpam-524	398	13	.	.	PUNCT
ejpam-524	398	14	.	.	PUNCT
ejpam-524	399	1	0	0	NUM
ejpam-524	400	1	1	1	NUM
ejpam-524	400	2	1	1	NUM
ejpam-524	400	3	0	0	NUM
ejpam-524	400	4	1	1	NUM
ejpam-524	400	5	0	0	NUM
ejpam-524	400	6	0	0	NUM
ejpam-524	400	7	0	0	NUM
ejpam-524	400	8	0	0	NUM
ejpam-524	400	9	0	0	NUM
ejpam-524	400	10	0	0	NUM
ejpam-524	400	11	0	0	NUM
ejpam-524	400	12	.	.	PUNCT
ejpam-524	400	13	.	.	PUNCT
ejpam-524	400	14	.	.	PUNCT
ejpam-524	401	1	1	1	NUM
ejpam-524	401	2	1	1	NUM
ejpam-524	401	3	0	0	NUM
ejpam-524	401	4	1	1	NUM
ejpam-524	401	5	0	0	NUM
ejpam-524	401	6	0	0	NUM
ejpam-524	401	7	.	.	PUNCT
ejpam-524	401	8	.	.	PUNCT
ejpam-524	401	9	.	.	PUNCT
ejpam-524	401	10	.	.	PUNCT
ejpam-524	401	11	.	.	PUNCT
ejpam-524	401	12	.	.	PUNCT
ejpam-524	401	13	.	.	PUNCT
ejpam-524	401	14	.	.	PUNCT
ejpam-524	401	15	.	.	PUNCT
ejpam-524	401	16	.	.	PUNCT
ejpam-524	401	17	.	.	PUNCT
ejpam-524	401	18	.	.	PUNCT
ejpam-524	401	19	.	.	PUNCT
ejpam-524	401	20	.	.	PUNCT
ejpam-524	401	21	.	.	PUNCT
ejpam-524	401	22	.	.	PUNCT
ejpam-524	401	23	.	.	PUNCT
ejpam-524	401	24	.	.	PUNCT
ejpam-524	401	25	.	.	PUNCT
ejpam-524	401	26	.	.	PUNCT
ejpam-524	401	27	.	.	PUNCT
ejpam-524	401	28	.	.	PUNCT
ejpam-524	401	29	.	.	PUNCT
ejpam-524	401	30	.	.	PUNCT
ejpam-524	401	31	.	.	PUNCT
ejpam-524	401	32	.	.	PUNCT
ejpam-524	401	33	.	.	PUNCT
ejpam-524	401	34	.	.	PUNCT
ejpam-524	401	35	.	.	PUNCT
ejpam-524	401	36	.	.	PUNCT
ejpam-524	401	37	.	.	PUNCT
ejpam-524	401	38	.	.	PUNCT
ejpam-524	401	39	.	.	PUNCT
ejpam-524	401	40	.	.	PUNCT
ejpam-524	401	41	.	.	PUNCT
ejpam-524	401	42	.	.	PUNCT
ejpam-524	401	43	.	.	PUNCT
ejpam-524	401	44	.	.	PUNCT
ejpam-524	401	45	.	.	PUNCT
ejpam-524	402	1	0	0	NUM
ejpam-524	403	1	1	1	NUM
ejpam-524	403	2	1	1	NUM
ejpam-524	403	3	0	0	NUM
ejpam-524	403	4	1	1	NUM
ejpam-524	403	5	0	0	NUM
ejpam-524	403	6	.	.	PUNCT
ejpam-524	403	7	.	.	PUNCT
ejpam-524	403	8	.	.	PUNCT
ejpam-524	404	1	0	0	NUM
ejpam-524	404	2	0	0	NUM
ejpam-524	404	3	0	0	NUM
ejpam-524	404	4	0	0	NUM
ejpam-524	404	5	0	0	NUM
ejpam-524	404	6	0	0	NUM
ejpam-524	404	7			NOUN
ejpam-524	404	8			NOUN
ejpam-524	404	9			VERB
ejpam-524	404	10			NOUN
ejpam-524	404	11			NOUN
ejpam-524	404	12			NOUN
ejpam-524	404	13			NOUN
ejpam-524	404	14			NOUN
ejpam-524	404	15			NOUN
ejpam-524	404	16			NOUN
ejpam-524	404	17			NOUN
ejpam-524	404	18			NOUN
ejpam-524	404	19			NOUN
ejpam-524	404	20			NOUN
ejpam-524	404	21			NOUN
ejpam-524	404	22			NOUN
ejpam-524	404	23			NOUN
ejpam-524	404	24			NOUN
ejpam-524	404	25			NOUN
ejpam-524	404	26			NOUN
ejpam-524	404	27			NOUN
ejpam-524	404	28			NOUN
ejpam-524	404	29			NOUN
ejpam-524	404	30			NOUN
ejpam-524	404	31			NOUN
ejpam-524	404	32			NOUN
ejpam-524	404	33			NOUN
ejpam-524	404	34			PUNCT
ejpam-524	404	35	,	,	PUNCT
ejpam-524	404	36	where	where	SCONJ
ejpam-524	404	37	the	the	DET
ejpam-524	404	38	rows	row	NOUN
ejpam-524	404	39	of	of	ADP
ejpam-524	404	40	d∗mg	d∗mg	NOUN
ejpam-524	404	41	represent	represent	VERB
ejpam-524	404	42	the	the	DET
ejpam-524	404	43	m	m	NOUN
ejpam-524	404	44	-dnp	-dnp	NUM
ejpam-524	404	45	of	of	ADP
ejpam-524	404	46	the	the	DET
ejpam-524	404	47	vertices	vertex	NOUN
ejpam-524	404	48	v1	v1	NOUN
ejpam-524	404	49	,	,	PUNCT
ejpam-524	404	50	v2	v2	NOUN
ejpam-524	404	51	,	,	PUNCT
ejpam-524	404	52	.	.	PUNCT
ejpam-524	404	53	.	.	PUNCT
ejpam-524	405	1	.	.	PUNCT
ejpam-524	406	1	,	,	PUNCT
ejpam-524	406	2	vn	vn	AUX
ejpam-524	406	3	taken	take	VERB
ejpam-524	406	4	in	in	ADP
ejpam-524	406	5	order	order	NOUN
ejpam-524	406	6	.	.	PUNCT
ejpam-524	407	1	now	now	ADV
ejpam-524	407	2	,	,	PUNCT
ejpam-524	407	3	we	we	PRON
ejpam-524	407	4	can	can	AUX
ejpam-524	407	5	partition	partition	VERB
ejpam-524	407	6	d∗mg	d∗mg	NOUN
ejpam-524	407	7	in	in	ADP
ejpam-524	407	8	to	to	ADP
ejpam-524	407	9	two	two	NUM
ejpam-524	407	10	sub	sub	NOUN
ejpam-524	407	11	-	-	NOUN
ejpam-524	407	12	matrices	matrix	NOUN
ejpam-524	407	13	say	say	VERB
ejpam-524	407	14	,	,	PUNCT
ejpam-524	407	15	a	a	PRON
ejpam-524	407	16	and	and	CCONJ
ejpam-524	407	17	b	b	NOUN
ejpam-524	407	18	where	where	SCONJ
ejpam-524	407	19	a	a	PRON
ejpam-524	407	20	is	be	AUX
ejpam-524	407	21	a	a	DET
ejpam-524	407	22	n	n	NUM
ejpam-524	407	23	2	2	NUM
ejpam-524	407	24	×	×	NOUN
ejpam-524	407	25	(	(	PUNCT
ejpam-524	407	26	n	n	CCONJ
ejpam-524	407	27	2	2	NUM
ejpam-524	407	28	+	+	CCONJ
ejpam-524	407	29	1	1	NUM
ejpam-524	407	30	)	)	PUNCT
ejpam-524	407	31	sub	sub	NOUN
ejpam-524	407	32	-	-	NOUN
ejpam-524	407	33	matrix	matrix	NOUN
ejpam-524	407	34	of	of	ADP
ejpam-524	407	35	the	the	DET
ejpam-524	407	36	form	form	NOUN
ejpam-524	407	37			NOUN
ejpam-524	407	38			NOUN
ejpam-524	407	39			NOUN
ejpam-524	407	40			NOUN
ejpam-524	407	41			NOUN
ejpam-524	407	42			NOUN
ejpam-524	407	43			NOUN
ejpam-524	407	44			NOUN
ejpam-524	407	45			NOUN
ejpam-524	407	46			NOUN
ejpam-524	407	47			NOUN
ejpam-524	407	48			NOUN
ejpam-524	407	49			NOUN
ejpam-524	408	1	1	1	NUM
ejpam-524	408	2	1	1	NUM
ejpam-524	408	3	0	0	NUM
ejpam-524	408	4	1	1	NUM
ejpam-524	408	5	0	0	NUM
ejpam-524	408	6	0	0	NUM
ejpam-524	408	7	.	.	PUNCT
ejpam-524	408	8	.	.	PUNCT
ejpam-524	409	1	.	.	PUNCT
ejpam-524	410	1	0	0	NUM
ejpam-524	411	1	0	0	NUM
ejpam-524	411	2	0	0	NUM
ejpam-524	411	3	0	0	NUM
ejpam-524	411	4	0	0	NUM
ejpam-524	411	5	1	1	NUM
ejpam-524	411	6	1	1	NUM
ejpam-524	411	7	1	1	NUM
ejpam-524	411	8	0	0	NUM
ejpam-524	411	9	0	0	NUM
ejpam-524	411	10	0	0	NUM
ejpam-524	411	11	.	.	PUNCT
ejpam-524	411	12	.	.	PUNCT
ejpam-524	411	13	.	.	PUNCT
ejpam-524	412	1	0	0	NUM
ejpam-524	413	1	0	0	NUM
ejpam-524	413	2	0	0	NUM
ejpam-524	413	3	0	0	NUM
ejpam-524	413	4	0	0	NUM
ejpam-524	413	5	0	0	NUM
ejpam-524	413	6	1	1	NUM
ejpam-524	413	7	1	1	NUM
ejpam-524	413	8	0	0	NUM
ejpam-524	413	9	0	0	NUM
ejpam-524	413	10	0	0	NUM
ejpam-524	413	11	.	.	PUNCT
ejpam-524	413	12	.	.	PUNCT
ejpam-524	413	13	.	.	PUNCT
ejpam-524	414	1	0	0	NUM
ejpam-524	415	1	0	0	NUM
ejpam-524	415	2	0	0	NUM
ejpam-524	415	3	0	0	NUM
ejpam-524	415	4	0	0	NUM
ejpam-524	415	5	1	1	NUM
ejpam-524	415	6	0	0	NUM
ejpam-524	415	7	1	1	NUM
ejpam-524	415	8	1	1	NUM
ejpam-524	415	9	0	0	NUM
ejpam-524	415	10	0	0	NUM
ejpam-524	415	11	.	.	PUNCT
ejpam-524	415	12	.	.	PUNCT
ejpam-524	415	13	.	.	PUNCT
ejpam-524	416	1	0	0	NUM
ejpam-524	417	1	0	0	NUM
ejpam-524	417	2	0	0	NUM
ejpam-524	417	3	0	0	NUM
ejpam-524	417	4	0	0	NUM
ejpam-524	417	5	0	0	NUM
ejpam-524	417	6	1	1	NUM
ejpam-524	417	7	0	0	NUM
ejpam-524	417	8	1	1	NUM
ejpam-524	417	9	1	1	NUM
ejpam-524	417	10	0	0	NUM
ejpam-524	417	11	.	.	PUNCT
ejpam-524	417	12	.	.	PUNCT
ejpam-524	417	13	.	.	PUNCT
ejpam-524	418	1	0	0	NUM
ejpam-524	419	1	0	0	NUM
ejpam-524	419	2	0	0	NUM
ejpam-524	419	3	0	0	NUM
ejpam-524	419	4	0	0	NUM
ejpam-524	419	5	0	0	NUM
ejpam-524	419	6	0	0	NUM
ejpam-524	419	7	1	1	NUM
ejpam-524	419	8	0	0	NUM
ejpam-524	419	9	1	1	NUM
ejpam-524	419	10	1	1	NUM
ejpam-524	419	11	.	.	PUNCT
ejpam-524	419	12	.	.	PUNCT
ejpam-524	419	13	.	.	PUNCT
ejpam-524	420	1	0	0	NUM
ejpam-524	421	1	0	0	NUM
ejpam-524	421	2	0	0	NUM
ejpam-524	421	3	0	0	NUM
ejpam-524	421	4	0	0	NUM
ejpam-524	421	5	.	.	PUNCT
ejpam-524	421	6	.	.	PUNCT
ejpam-524	421	7	.	.	PUNCT
ejpam-524	421	8	.	.	PUNCT
ejpam-524	421	9	.	.	PUNCT
ejpam-524	421	10	.	.	PUNCT
ejpam-524	421	11	.	.	PUNCT
ejpam-524	421	12	.	.	PUNCT
ejpam-524	421	13	.	.	PUNCT
ejpam-524	421	14	.	.	PUNCT
ejpam-524	421	15	.	.	PUNCT
ejpam-524	421	16	.	.	PUNCT
ejpam-524	421	17	.	.	PUNCT
ejpam-524	421	18	.	.	PUNCT
ejpam-524	421	19	.	.	PUNCT
ejpam-524	421	20	.	.	PUNCT
ejpam-524	421	21	.	.	PUNCT
ejpam-524	421	22	.	.	PUNCT
ejpam-524	421	23	.	.	PUNCT
ejpam-524	421	24	.	.	PUNCT
ejpam-524	421	25	.	.	PUNCT
ejpam-524	421	26	.	.	PUNCT
ejpam-524	421	27	.	.	PUNCT
ejpam-524	421	28	.	.	PUNCT
ejpam-524	421	29	.	.	PUNCT
ejpam-524	421	30	.	.	PUNCT
ejpam-524	421	31	.	.	PUNCT
ejpam-524	421	32	.	.	PUNCT
ejpam-524	421	33	.	.	PUNCT
ejpam-524	421	34	.	.	PUNCT
ejpam-524	421	35	.	.	PUNCT
ejpam-524	421	36	.	.	PUNCT
ejpam-524	421	37	.	.	PUNCT
ejpam-524	421	38	.	.	PUNCT
ejpam-524	421	39	.	.	PUNCT
ejpam-524	421	40	.	.	PUNCT
ejpam-524	422	1	0	0	NUM
ejpam-524	423	1	0	0	NUM
ejpam-524	423	2	0	0	NUM
ejpam-524	423	3	0	0	NUM
ejpam-524	423	4	0	0	NUM
ejpam-524	423	5	0	0	NUM
ejpam-524	423	6	.	.	PUNCT
ejpam-524	423	7	.	.	PUNCT
ejpam-524	423	8	.	.	PUNCT
ejpam-524	424	1	1	1	NUM
ejpam-524	424	2	0	0	NUM
ejpam-524	424	3	1	1	NUM
ejpam-524	424	4	1	1	NUM
ejpam-524	424	5	0	0	NUM
ejpam-524	424	6			NOUN
ejpam-524	424	7			NOUN
ejpam-524	424	8			VERB
ejpam-524	424	9			NOUN
ejpam-524	424	10			NOUN
ejpam-524	424	11			NOUN
ejpam-524	424	12			NOUN
ejpam-524	424	13			NOUN
ejpam-524	424	14			NOUN
ejpam-524	424	15			NOUN
ejpam-524	424	16			NOUN
ejpam-524	424	17			NOUN
ejpam-524	424	18			PUNCT
ejpam-524	425	1	,	,	PUNCT
ejpam-524	425	2	if	if	SCONJ
ejpam-524	425	3	we	we	PRON
ejpam-524	425	4	denote	denote	VERB
ejpam-524	425	5	the	the	DET
ejpam-524	425	6	columns	column	NOUN
ejpam-524	425	7	of	of	ADP
ejpam-524	425	8	a	a	PRON
ejpam-524	425	9	as	as	ADP
ejpam-524	425	10	(	(	PUNCT
ejpam-524	425	11	c1	c1	PROPN
ejpam-524	425	12	,	,	PUNCT
ejpam-524	425	13	c2	c2	PROPN
ejpam-524	425	14	,	,	PUNCT
ejpam-524	425	15	.	.	PUNCT
ejpam-524	425	16	.	.	PUNCT
ejpam-524	426	1	.	.	PUNCT
ejpam-524	427	1	,	,	PUNCT
ejpam-524	427	2	cdg+1	cdg+1	NOUN
ejpam-524	427	3	)	)	PUNCT
ejpam-524	427	4	,	,	PUNCT
ejpam-524	427	5	then	then	ADV
ejpam-524	427	6	b	b	X
ejpam-524	427	7	is	be	AUX
ejpam-524	427	8	such	such	ADJ
ejpam-524	427	9	that	that	SCONJ
ejpam-524	427	10	,	,	PUNCT
ejpam-524	427	11	the	the	DET
ejpam-524	427	12	columns	column	NOUN
ejpam-524	427	13	of	of	ADP
ejpam-524	427	14	b	b	PROPN
ejpam-524	427	15	are	be	AUX
ejpam-524	427	16	(	(	PUNCT
ejpam-524	427	17	cdg+1	cdg+1	NOUN
ejpam-524	427	18	,	,	PUNCT
ejpam-524	427	19	.	.	PUNCT
ejpam-524	427	20	.	.	PUNCT
ejpam-524	428	1	.	.	PUNCT
ejpam-524	429	1	,	,	PUNCT
ejpam-524	429	2	c2	c2	PROPN
ejpam-524	429	3	,	,	PUNCT
ejpam-524	429	4	c1	c1	PROPN
ejpam-524	429	5	)	)	PUNCT
ejpam-524	429	6	.	.	PUNCT
ejpam-524	430	1	looking	look	VERB
ejpam-524	430	2	at	at	ADP
ejpam-524	430	3	the	the	DET
ejpam-524	430	4	rows	row	NOUN
ejpam-524	430	5	of	of	ADP
ejpam-524	430	6	a	a	PRON
ejpam-524	430	7	and	and	CCONJ
ejpam-524	430	8	b	b	NOUN
ejpam-524	430	9	,	,	PUNCT
ejpam-524	430	10	it	it	PRON
ejpam-524	430	11	is	be	AUX
ejpam-524	430	12	clear	clear	ADJ
ejpam-524	430	13	that	that	SCONJ
ejpam-524	430	14	the	the	DET
ejpam-524	430	15	rows	row	NOUN
ejpam-524	430	16	of	of	ADP
ejpam-524	430	17	d∗mg	d∗mg	NOUN
ejpam-524	430	18	are	be	AUX
ejpam-524	430	19	not	not	PART
ejpam-524	430	20	identical	identical	ADJ
ejpam-524	430	21	,	,	PUNCT
ejpam-524	430	22	and	and	CCONJ
ejpam-524	430	23	hence	hence	ADV
ejpam-524	430	24	,	,	PUNCT
ejpam-524	430	25	{	{	PUNCT
ejpam-524	430	26	v1	v1	NOUN
ejpam-524	430	27	,	,	PUNCT
ejpam-524	430	28	v2	v2	PROPN
ejpam-524	430	29	,	,	PUNCT
ejpam-524	430	30	v4	v4	NOUN
ejpam-524	430	31	}	}	PUNCT
ejpam-524	430	32	form	form	VERB
ejpam-524	430	33	a	a	DET
ejpam-524	430	34	dpd	dpd	NOUN
ejpam-524	430	35	-	-	PUNCT
ejpam-524	430	36	set	set	NOUN
ejpam-524	430	37	.	.	PUNCT
ejpam-524	431	1	case	case	NOUN
ejpam-524	431	2	2	2	NUM
ejpam-524	431	3	:	:	SYM
ejpam-524	431	4	n	n	CCONJ
ejpam-524	431	5	,	,	PUNCT
ejpam-524	431	6	an	an	DET
ejpam-524	431	7	odd	odd	ADJ
ejpam-524	431	8	integer	integer	NOUN
ejpam-524	431	9	and	and	CCONJ
ejpam-524	431	10	n≥	n≥	PROPN
ejpam-524	431	11	7	7	NUM
ejpam-524	431	12	g.	g.	PROPN
ejpam-524	431	13	augustine	augustine	PROPN
ejpam-524	431	14	,	,	PUNCT
ejpam-524	431	15	a.	a.	PROPN
ejpam-524	431	16	joseph	joseph	PROPN
ejpam-524	431	17	,	,	PUNCT
ejpam-524	431	18	s.	s.	PROPN
ejpam-524	431	19	jose	jose	PROPN
ejpam-524	431	20	/	/	SYM
ejpam-524	431	21	eur	eur	PROPN
ejpam-524	431	22	.	.	PUNCT
ejpam-524	432	1	j.	j.	PROPN
ejpam-524	432	2	pure	pure	PROPN
ejpam-524	432	3	appl	appl	PROPN
ejpam-524	432	4	.	.	PROPN
ejpam-524	432	5	math	math	PROPN
ejpam-524	432	6	,	,	PUNCT
ejpam-524	432	7	3	3	NUM
ejpam-524	432	8	(	(	PUNCT
ejpam-524	432	9	2010	2010	NUM
ejpam-524	432	10	)	)	PUNCT
ejpam-524	432	11	,	,	PUNCT
ejpam-524	432	12	748	748	NUM
ejpam-524	432	13	-	-	SYM
ejpam-524	432	14	764	764	NUM
ejpam-524	432	15	758	758	NUM
ejpam-524	432	16	let	let	VERB
ejpam-524	432	17	m	m	VERB
ejpam-524	432	18	=	=	PUNCT
ejpam-524	432	19	{	{	PUNCT
ejpam-524	432	20	v1	v1	PROPN
ejpam-524	432	21	,	,	PUNCT
ejpam-524	432	22	v2	v2	PROPN
ejpam-524	432	23	,	,	PUNCT
ejpam-524	432	24	v4	v4	NOUN
ejpam-524	432	25	}	}	PUNCT
ejpam-524	432	26	.	.	PUNCT
ejpam-524	433	1	then	then	ADV
ejpam-524	433	2	,	,	PUNCT
ejpam-524	433	3	d∗mg	d∗mg	NOUN
ejpam-524	433	4	=	=	SYM
ejpam-524	433	5			PROPN
ejpam-524	433	6			NOUN
ejpam-524	433	7			NOUN
ejpam-524	433	8			NOUN
ejpam-524	433	9			NOUN
ejpam-524	433	10			NOUN
ejpam-524	433	11			NOUN
ejpam-524	433	12			NOUN
ejpam-524	433	13			NOUN
ejpam-524	433	14			NOUN
ejpam-524	433	15			NOUN
ejpam-524	433	16			NOUN
ejpam-524	433	17			NOUN
ejpam-524	433	18			NOUN
ejpam-524	433	19			NOUN
ejpam-524	433	20			NOUN
ejpam-524	433	21			NOUN
ejpam-524	433	22			NOUN
ejpam-524	433	23			NOUN
ejpam-524	433	24			NOUN
ejpam-524	433	25			NOUN
ejpam-524	433	26			NOUN
ejpam-524	433	27			NOUN
ejpam-524	433	28			NOUN
ejpam-524	433	29			NOUN
ejpam-524	433	30			NOUN
ejpam-524	433	31			NOUN
ejpam-524	433	32			NOUN
ejpam-524	433	33	1	1	NUM
ejpam-524	433	34	1	1	NUM
ejpam-524	433	35	0	0	NUM
ejpam-524	433	36	1	1	NUM
ejpam-524	433	37	0	0	NUM
ejpam-524	433	38	0	0	NUM
ejpam-524	433	39	.	.	PUNCT
ejpam-524	433	40	.	.	PUNCT
ejpam-524	434	1	.	.	PUNCT
ejpam-524	435	1	0	0	NUM
ejpam-524	436	1	0	0	NUM
ejpam-524	436	2	0	0	NUM
ejpam-524	436	3	0	0	NUM
ejpam-524	436	4	0	0	NUM
ejpam-524	436	5	0	0	NUM
ejpam-524	436	6	1	1	NUM
ejpam-524	436	7	1	1	NUM
ejpam-524	436	8	1	1	NUM
ejpam-524	436	9	0	0	NUM
ejpam-524	436	10	0	0	NUM
ejpam-524	436	11	0	0	NUM
ejpam-524	436	12	.	.	PUNCT
ejpam-524	436	13	.	.	PUNCT
ejpam-524	436	14	.	.	PUNCT
ejpam-524	437	1	0	0	NUM
ejpam-524	438	1	0	0	NUM
ejpam-524	438	2	0	0	NUM
ejpam-524	438	3	0	0	NUM
ejpam-524	438	4	0	0	NUM
ejpam-524	438	5	0	0	NUM
ejpam-524	438	6	0	0	NUM
ejpam-524	438	7	1	1	NUM
ejpam-524	438	8	1	1	NUM
ejpam-524	438	9	0	0	NUM
ejpam-524	438	10	0	0	NUM
ejpam-524	438	11	0	0	NUM
ejpam-524	438	12	.	.	PUNCT
ejpam-524	438	13	.	.	PUNCT
ejpam-524	438	14	.	.	PUNCT
ejpam-524	439	1	0	0	NUM
ejpam-524	440	1	0	0	NUM
ejpam-524	440	2	0	0	NUM
ejpam-524	440	3	0	0	NUM
ejpam-524	440	4	0	0	NUM
ejpam-524	440	5	0	0	NUM
ejpam-524	440	6	1	1	NUM
ejpam-524	440	7	0	0	NUM
ejpam-524	440	8	1	1	NUM
ejpam-524	440	9	1	1	NUM
ejpam-524	440	10	0	0	NUM
ejpam-524	440	11	0	0	NUM
ejpam-524	440	12	.	.	PUNCT
ejpam-524	440	13	.	.	PUNCT
ejpam-524	440	14	.	.	PUNCT
ejpam-524	441	1	0	0	NUM
ejpam-524	442	1	0	0	NUM
ejpam-524	442	2	0	0	NUM
ejpam-524	442	3	0	0	NUM
ejpam-524	442	4	0	0	NUM
ejpam-524	442	5	0	0	NUM
ejpam-524	442	6	0	0	NUM
ejpam-524	442	7	1	1	NUM
ejpam-524	442	8	0	0	NUM
ejpam-524	442	9	1	1	NUM
ejpam-524	442	10	1	1	NUM
ejpam-524	442	11	0	0	NUM
ejpam-524	442	12	.	.	PUNCT
ejpam-524	442	13	.	.	PUNCT
ejpam-524	442	14	.	.	PUNCT
ejpam-524	443	1	0	0	NUM
ejpam-524	444	1	0	0	NUM
ejpam-524	444	2	0	0	NUM
ejpam-524	444	3	0	0	NUM
ejpam-524	444	4	0	0	NUM
ejpam-524	444	5	0	0	NUM
ejpam-524	444	6	0	0	NUM
ejpam-524	444	7	0	0	NUM
ejpam-524	444	8	1	1	NUM
ejpam-524	444	9	0	0	NUM
ejpam-524	444	10	1	1	NUM
ejpam-524	444	11	1	1	NUM
ejpam-524	444	12	.	.	PUNCT
ejpam-524	444	13	.	.	PUNCT
ejpam-524	444	14	.	.	PUNCT
ejpam-524	445	1	0	0	NUM
ejpam-524	446	1	0	0	NUM
ejpam-524	446	2	0	0	NUM
ejpam-524	446	3	0	0	NUM
ejpam-524	446	4	0	0	NUM
ejpam-524	446	5	0	0	NUM
ejpam-524	446	6	.	.	PUNCT
ejpam-524	446	7	.	.	PUNCT
ejpam-524	446	8	.	.	PUNCT
ejpam-524	446	9	.	.	PUNCT
ejpam-524	446	10	.	.	PUNCT
ejpam-524	446	11	.	.	PUNCT
ejpam-524	446	12	.	.	PUNCT
ejpam-524	446	13	.	.	PUNCT
ejpam-524	446	14	.	.	PUNCT
ejpam-524	446	15	.	.	PUNCT
ejpam-524	446	16	.	.	PUNCT
ejpam-524	446	17	.	.	PUNCT
ejpam-524	446	18	.	.	PUNCT
ejpam-524	446	19	.	.	PUNCT
ejpam-524	446	20	.	.	PUNCT
ejpam-524	446	21	.	.	PUNCT
ejpam-524	446	22	.	.	PUNCT
ejpam-524	446	23	.	.	PUNCT
ejpam-524	446	24	.	.	PUNCT
ejpam-524	446	25	.	.	PUNCT
ejpam-524	446	26	.	.	PUNCT
ejpam-524	446	27	.	.	PUNCT
ejpam-524	446	28	.	.	PUNCT
ejpam-524	446	29	.	.	PUNCT
ejpam-524	446	30	.	.	PUNCT
ejpam-524	446	31	.	.	PUNCT
ejpam-524	446	32	.	.	PUNCT
ejpam-524	446	33	.	.	PUNCT
ejpam-524	446	34	.	.	PUNCT
ejpam-524	446	35	.	.	PUNCT
ejpam-524	446	36	.	.	PUNCT
ejpam-524	446	37	.	.	PUNCT
ejpam-524	446	38	.	.	PUNCT
ejpam-524	446	39	.	.	PUNCT
ejpam-524	446	40	.	.	PUNCT
ejpam-524	446	41	.	.	PUNCT
ejpam-524	446	42	.	.	PUNCT
ejpam-524	446	43	.	.	PUNCT
ejpam-524	446	44	.	.	PUNCT
ejpam-524	447	1	0	0	NUM
ejpam-524	448	1	0	0	NUM
ejpam-524	448	2	0	0	NUM
ejpam-524	448	3	0	0	NUM
ejpam-524	448	4	0	0	NUM
ejpam-524	448	5	0	0	NUM
ejpam-524	448	6	.	.	PUNCT
ejpam-524	448	7	.	.	PUNCT
ejpam-524	448	8	.	.	PUNCT
ejpam-524	449	1	0	0	NUM
ejpam-524	450	1	0	0	NUM
ejpam-524	450	2	1	1	NUM
ejpam-524	450	3	0	0	NUM
ejpam-524	450	4	1	1	NUM
ejpam-524	450	5	1	1	NUM
ejpam-524	450	6	0	0	NUM
ejpam-524	450	7	0	0	NUM
ejpam-524	450	8	0	0	NUM
ejpam-524	450	9	0	0	NUM
ejpam-524	450	10	0	0	NUM
ejpam-524	450	11	0	0	NUM
ejpam-524	450	12	.	.	PUNCT
ejpam-524	450	13	.	.	PUNCT
ejpam-524	450	14	.	.	PUNCT
ejpam-524	451	1	0	0	NUM
ejpam-524	452	1	0	0	NUM
ejpam-524	452	2	0	0	NUM
ejpam-524	452	3	1	1	NUM
ejpam-524	452	4	0	0	NUM
ejpam-524	452	5	1	1	NUM
ejpam-524	452	6	0	0	NUM
ejpam-524	452	7	0	0	NUM
ejpam-524	452	8	0	0	NUM
ejpam-524	452	9	0	0	NUM
ejpam-524	452	10	0	0	NUM
ejpam-524	452	11	0	0	NUM
ejpam-524	452	12	.	.	PUNCT
ejpam-524	452	13	.	.	PUNCT
ejpam-524	452	14	.	.	PUNCT
ejpam-524	453	1	0	0	NUM
ejpam-524	454	1	0	0	NUM
ejpam-524	454	2	0	0	NUM
ejpam-524	454	3	0	0	NUM
ejpam-524	454	4	1	1	NUM
ejpam-524	454	5	1	1	NUM
ejpam-524	454	6	0	0	NUM
ejpam-524	454	7	0	0	NUM
ejpam-524	454	8	0	0	NUM
ejpam-524	454	9	0	0	NUM
ejpam-524	454	10	0	0	NUM
ejpam-524	454	11	0	0	NUM
ejpam-524	454	12	.	.	PUNCT
ejpam-524	454	13	.	.	PUNCT
ejpam-524	454	14	.	.	PUNCT
ejpam-524	455	1	0	0	NUM
ejpam-524	456	1	0	0	NUM
ejpam-524	456	2	0	0	NUM
ejpam-524	456	3	1	1	NUM
ejpam-524	456	4	1	1	NUM
ejpam-524	456	5	1	1	NUM
ejpam-524	456	6	0	0	NUM
ejpam-524	456	7	0	0	NUM
ejpam-524	456	8	0	0	NUM
ejpam-524	456	9	0	0	NUM
ejpam-524	456	10	0	0	NUM
ejpam-524	456	11	0	0	NUM
ejpam-524	456	12	.	.	PUNCT
ejpam-524	456	13	.	.	PUNCT
ejpam-524	457	1	.	.	PUNCT
ejpam-524	458	1	0	0	NUM
ejpam-524	459	1	0	0	NUM
ejpam-524	459	2	1	1	NUM
ejpam-524	459	3	1	1	NUM
ejpam-524	459	4	0	0	NUM
ejpam-524	459	5	1	1	NUM
ejpam-524	459	6	0	0	NUM
ejpam-524	459	7	0	0	NUM
ejpam-524	459	8	0	0	NUM
ejpam-524	459	9	0	0	NUM
ejpam-524	459	10	0	0	NUM
ejpam-524	459	11	0	0	NUM
ejpam-524	459	12	.	.	PUNCT
ejpam-524	459	13	.	.	PUNCT
ejpam-524	459	14	.	.	PUNCT
ejpam-524	460	1	0	0	NUM
ejpam-524	461	1	1	1	NUM
ejpam-524	461	2	1	1	NUM
ejpam-524	461	3	0	0	NUM
ejpam-524	461	4	1	1	NUM
ejpam-524	461	5	0	0	NUM
ejpam-524	461	6	0	0	NUM
ejpam-524	461	7	0	0	NUM
ejpam-524	461	8	0	0	NUM
ejpam-524	461	9	0	0	NUM
ejpam-524	461	10	0	0	NUM
ejpam-524	461	11	0	0	NUM
ejpam-524	461	12	.	.	PUNCT
ejpam-524	461	13	.	.	PUNCT
ejpam-524	461	14	.	.	PUNCT
ejpam-524	462	1	1	1	NUM
ejpam-524	462	2	1	1	NUM
ejpam-524	462	3	0	0	NUM
ejpam-524	462	4	1	1	NUM
ejpam-524	462	5	0	0	NUM
ejpam-524	462	6	0	0	NUM
ejpam-524	462	7	.	.	PUNCT
ejpam-524	462	8	.	.	PUNCT
ejpam-524	462	9	.	.	PUNCT
ejpam-524	462	10	.	.	PUNCT
ejpam-524	462	11	.	.	PUNCT
ejpam-524	462	12	.	.	PUNCT
ejpam-524	462	13	.	.	PUNCT
ejpam-524	462	14	.	.	PUNCT
ejpam-524	462	15	.	.	PUNCT
ejpam-524	462	16	.	.	PUNCT
ejpam-524	462	17	.	.	PUNCT
ejpam-524	462	18	.	.	PUNCT
ejpam-524	462	19	.	.	PUNCT
ejpam-524	462	20	.	.	PUNCT
ejpam-524	462	21	.	.	PUNCT
ejpam-524	462	22	.	.	PUNCT
ejpam-524	462	23	.	.	PUNCT
ejpam-524	462	24	.	.	PUNCT
ejpam-524	462	25	.	.	PUNCT
ejpam-524	462	26	.	.	PUNCT
ejpam-524	462	27	.	.	PUNCT
ejpam-524	462	28	.	.	PUNCT
ejpam-524	462	29	.	.	PUNCT
ejpam-524	462	30	.	.	PUNCT
ejpam-524	462	31	.	.	PUNCT
ejpam-524	462	32	.	.	PUNCT
ejpam-524	462	33	.	.	PUNCT
ejpam-524	462	34	.	.	PUNCT
ejpam-524	462	35	.	.	PUNCT
ejpam-524	462	36	.	.	PUNCT
ejpam-524	462	37	.	.	PUNCT
ejpam-524	462	38	.	.	PUNCT
ejpam-524	462	39	.	.	PUNCT
ejpam-524	462	40	.	.	PUNCT
ejpam-524	462	41	.	.	PUNCT
ejpam-524	462	42	.	.	PUNCT
ejpam-524	462	43	.	.	PUNCT
ejpam-524	462	44	.	.	PUNCT
ejpam-524	462	45	.	.	PUNCT
ejpam-524	463	1	0	0	NUM
ejpam-524	464	1	1	1	NUM
ejpam-524	464	2	1	1	NUM
ejpam-524	464	3	0	0	NUM
ejpam-524	464	4	1	1	NUM
ejpam-524	464	5	0	0	NUM
ejpam-524	464	6	.	.	PUNCT
ejpam-524	464	7	.	.	PUNCT
ejpam-524	464	8	.	.	PUNCT
ejpam-524	465	1	0	0	NUM
ejpam-524	465	2	0	0	NUM
ejpam-524	465	3	0	0	NUM
ejpam-524	465	4	0	0	NUM
ejpam-524	465	5	0	0	NUM
ejpam-524	465	6	0	0	NUM
ejpam-524	465	7			NOUN
ejpam-524	465	8			NOUN
ejpam-524	465	9			VERB
ejpam-524	465	10			NOUN
ejpam-524	465	11			NOUN
ejpam-524	465	12			NOUN
ejpam-524	465	13			NOUN
ejpam-524	465	14			NOUN
ejpam-524	465	15			NOUN
ejpam-524	465	16			NOUN
ejpam-524	465	17			NOUN
ejpam-524	465	18			NOUN
ejpam-524	465	19			NOUN
ejpam-524	465	20			NOUN
ejpam-524	465	21			NOUN
ejpam-524	465	22			NOUN
ejpam-524	465	23			NOUN
ejpam-524	465	24			NOUN
ejpam-524	465	25			NOUN
ejpam-524	465	26			NOUN
ejpam-524	465	27			NOUN
ejpam-524	465	28			NOUN
ejpam-524	465	29			NOUN
ejpam-524	465	30			NOUN
ejpam-524	465	31			NOUN
ejpam-524	465	32			NOUN
ejpam-524	465	33			NOUN
ejpam-524	465	34			PUNCT
ejpam-524	466	1	where	where	SCONJ
ejpam-524	466	2	rows	row	NOUN
ejpam-524	466	3	of	of	ADP
ejpam-524	466	4	d∗mg	d∗mg	NOUN
ejpam-524	466	5	represent	represent	VERB
ejpam-524	466	6	the	the	DET
ejpam-524	466	7	m	m	PROPN
ejpam-524	466	8	-	-	PUNCT
ejpam-524	466	9	dnp	dnp	PROPN
ejpam-524	466	10	of	of	ADP
ejpam-524	466	11	the	the	DET
ejpam-524	466	12	vertices	vertex	NOUN
ejpam-524	466	13	v1	v1	NOUN
ejpam-524	466	14	,	,	PUNCT
ejpam-524	466	15	v2	v2	NOUN
ejpam-524	466	16	,	,	PUNCT
ejpam-524	466	17	.	.	PUNCT
ejpam-524	466	18	.	.	PUNCT
ejpam-524	467	1	.	.	PUNCT
ejpam-524	468	1	,	,	PUNCT
ejpam-524	468	2	vn	vn	AUX
ejpam-524	468	3	taken	take	VERB
ejpam-524	468	4	in	in	ADP
ejpam-524	468	5	order	order	NOUN
ejpam-524	468	6	.	.	PUNCT
ejpam-524	469	1	in	in	ADP
ejpam-524	469	2	this	this	DET
ejpam-524	469	3	case	case	NOUN
ejpam-524	469	4	,	,	PUNCT
ejpam-524	469	5	d∗mg	d∗mg	NOUN
ejpam-524	469	6	can	can	AUX
ejpam-524	469	7	have	have	VERB
ejpam-524	469	8	three	three	NUM
ejpam-524	469	9	sub	sub	NOUN
ejpam-524	469	10	-	-	NOUN
ejpam-524	469	11	matrices	matrix	NOUN
ejpam-524	469	12	a	a	DET
ejpam-524	469	13	,	,	PUNCT
ejpam-524	469	14	b	b	NOUN
ejpam-524	469	15	,	,	PUNCT
ejpam-524	469	16	c	c	PROPN
ejpam-524	469	17	as	as	ADP
ejpam-524	469	18	its	its	PRON
ejpam-524	469	19	partition	partition	NOUN
ejpam-524	469	20	as	as	SCONJ
ejpam-524	469	21	described	describe	VERB
ejpam-524	469	22	below	below	ADV
ejpam-524	469	23	.	.	PUNCT
ejpam-524	470	1	choose	choose	VERB
ejpam-524	470	2	the	the	DET
ejpam-524	470	3	sub	sub	NOUN
ejpam-524	470	4	-	-	NOUN
ejpam-524	470	5	matrix	matrix	NOUN
ejpam-524	470	6	að	að	NOUN
ejpam-524	470	7	n	n	PROPN
ejpam-524	470	8	2	2	NUM
ejpam-524	470	9	ñ×	ñ×	PROPN
ejpam-524	470	10	(	(	PUNCT
ejpam-524	470	11	dg	dg	X
ejpam-524	470	12	+	+	NOUN
ejpam-524	470	13	1	1	NUM
ejpam-524	470	14	)	)	PUNCT
ejpam-524	470	15	as	as	ADP
ejpam-524	470	16			NOUN
ejpam-524	470	17			NOUN
ejpam-524	470	18			NOUN
ejpam-524	470	19			NOUN
ejpam-524	470	20			NOUN
ejpam-524	470	21			NOUN
ejpam-524	470	22			NOUN
ejpam-524	470	23			NOUN
ejpam-524	470	24			NOUN
ejpam-524	470	25			NOUN
ejpam-524	470	26			NOUN
ejpam-524	470	27			NOUN
ejpam-524	470	28			NOUN
ejpam-524	470	29	1	1	NUM
ejpam-524	470	30	1	1	NUM
ejpam-524	470	31	0	0	NUM
ejpam-524	470	32	1	1	NUM
ejpam-524	470	33	0	0	NUM
ejpam-524	470	34	0	0	NUM
ejpam-524	470	35	.	.	PUNCT
ejpam-524	470	36	.	.	PUNCT
ejpam-524	471	1	.	.	PUNCT
ejpam-524	472	1	0	0	NUM
ejpam-524	473	1	0	0	NUM
ejpam-524	473	2	0	0	NUM
ejpam-524	473	3	0	0	NUM
ejpam-524	473	4	0	0	NUM
ejpam-524	473	5	1	1	NUM
ejpam-524	473	6	1	1	NUM
ejpam-524	473	7	1	1	NUM
ejpam-524	473	8	0	0	NUM
ejpam-524	473	9	0	0	NUM
ejpam-524	473	10	0	0	NUM
ejpam-524	473	11	.	.	PUNCT
ejpam-524	473	12	.	.	PUNCT
ejpam-524	473	13	.	.	PUNCT
ejpam-524	474	1	0	0	NUM
ejpam-524	475	1	0	0	NUM
ejpam-524	475	2	0	0	NUM
ejpam-524	475	3	0	0	NUM
ejpam-524	475	4	0	0	NUM
ejpam-524	475	5	0	0	NUM
ejpam-524	475	6	1	1	NUM
ejpam-524	475	7	1	1	NUM
ejpam-524	475	8	0	0	NUM
ejpam-524	475	9	0	0	NUM
ejpam-524	475	10	0	0	NUM
ejpam-524	475	11	.	.	PUNCT
ejpam-524	475	12	.	.	PUNCT
ejpam-524	475	13	.	.	PUNCT
ejpam-524	476	1	0	0	NUM
ejpam-524	477	1	0	0	NUM
ejpam-524	477	2	0	0	NUM
ejpam-524	477	3	0	0	NUM
ejpam-524	477	4	0	0	NUM
ejpam-524	477	5	1	1	NUM
ejpam-524	477	6	0	0	NUM
ejpam-524	477	7	1	1	NUM
ejpam-524	477	8	1	1	NUM
ejpam-524	477	9	0	0	NUM
ejpam-524	477	10	0	0	NUM
ejpam-524	477	11	.	.	PUNCT
ejpam-524	477	12	.	.	PUNCT
ejpam-524	477	13	.	.	PUNCT
ejpam-524	478	1	0	0	NUM
ejpam-524	479	1	0	0	NUM
ejpam-524	479	2	0	0	NUM
ejpam-524	479	3	0	0	NUM
ejpam-524	479	4	0	0	NUM
ejpam-524	479	5	0	0	NUM
ejpam-524	479	6	1	1	NUM
ejpam-524	479	7	0	0	NUM
ejpam-524	479	8	1	1	NUM
ejpam-524	479	9	1	1	NUM
ejpam-524	479	10	0	0	NUM
ejpam-524	479	11	.	.	PUNCT
ejpam-524	479	12	.	.	PUNCT
ejpam-524	479	13	.	.	PUNCT
ejpam-524	480	1	0	0	NUM
ejpam-524	481	1	0	0	NUM
ejpam-524	481	2	0	0	NUM
ejpam-524	481	3	0	0	NUM
ejpam-524	481	4	0	0	NUM
ejpam-524	481	5	0	0	NUM
ejpam-524	481	6	0	0	NUM
ejpam-524	481	7	1	1	NUM
ejpam-524	481	8	0	0	NUM
ejpam-524	481	9	1	1	NUM
ejpam-524	481	10	1	1	NUM
ejpam-524	481	11	.	.	PUNCT
ejpam-524	481	12	.	.	PUNCT
ejpam-524	481	13	.	.	PUNCT
ejpam-524	482	1	0	0	NUM
ejpam-524	483	1	0	0	NUM
ejpam-524	483	2	0	0	NUM
ejpam-524	483	3	0	0	NUM
ejpam-524	483	4	0	0	NUM
ejpam-524	483	5	.	.	PUNCT
ejpam-524	483	6	.	.	PUNCT
ejpam-524	483	7	.	.	PUNCT
ejpam-524	483	8	.	.	PUNCT
ejpam-524	483	9	.	.	PUNCT
ejpam-524	483	10	.	.	PUNCT
ejpam-524	483	11	.	.	PUNCT
ejpam-524	483	12	.	.	PUNCT
ejpam-524	483	13	.	.	PUNCT
ejpam-524	483	14	.	.	PUNCT
ejpam-524	483	15	.	.	PUNCT
ejpam-524	483	16	.	.	PUNCT
ejpam-524	483	17	.	.	PUNCT
ejpam-524	483	18	.	.	PUNCT
ejpam-524	483	19	.	.	PUNCT
ejpam-524	483	20	.	.	PUNCT
ejpam-524	483	21	.	.	PUNCT
ejpam-524	483	22	.	.	PUNCT
ejpam-524	483	23	.	.	PUNCT
ejpam-524	483	24	.	.	PUNCT
ejpam-524	483	25	.	.	PUNCT
ejpam-524	483	26	.	.	PUNCT
ejpam-524	483	27	.	.	PUNCT
ejpam-524	483	28	.	.	PUNCT
ejpam-524	483	29	.	.	PUNCT
ejpam-524	483	30	.	.	PUNCT
ejpam-524	483	31	.	.	PUNCT
ejpam-524	483	32	.	.	PUNCT
ejpam-524	483	33	.	.	PUNCT
ejpam-524	483	34	.	.	PUNCT
ejpam-524	483	35	.	.	PUNCT
ejpam-524	483	36	.	.	PUNCT
ejpam-524	483	37	.	.	PUNCT
ejpam-524	483	38	.	.	PUNCT
ejpam-524	483	39	.	.	PUNCT
ejpam-524	483	40	.	.	PUNCT
ejpam-524	484	1	0	0	NUM
ejpam-524	485	1	0	0	NUM
ejpam-524	485	2	0	0	NUM
ejpam-524	485	3	0	0	NUM
ejpam-524	485	4	0	0	NUM
ejpam-524	485	5	0	0	NUM
ejpam-524	485	6	.	.	PUNCT
ejpam-524	485	7	.	.	PUNCT
ejpam-524	485	8	.	.	PUNCT
ejpam-524	486	1	0	0	NUM
ejpam-524	486	2	1	1	NUM
ejpam-524	486	3	0	0	NUM
ejpam-524	486	4	1	1	NUM
ejpam-524	486	5	1	1	NUM
ejpam-524	486	6			NOUN
ejpam-524	486	7			NOUN
ejpam-524	486	8			VERB
ejpam-524	486	9			NOUN
ejpam-524	486	10			NOUN
ejpam-524	486	11			NOUN
ejpam-524	486	12			NOUN
ejpam-524	486	13			NOUN
ejpam-524	486	14			NOUN
ejpam-524	486	15			NOUN
ejpam-524	486	16			NOUN
ejpam-524	486	17			NOUN
ejpam-524	486	18			PUNCT
ejpam-524	487	1	we	we	PRON
ejpam-524	487	2	choose	choose	VERB
ejpam-524	487	3	b	b	NOUN
ejpam-524	487	4	as	as	ADP
ejpam-524	487	5	3×	3×	NUM
ejpam-524	487	6	(	(	PUNCT
ejpam-524	487	7	dg	dg	X
ejpam-524	487	8	+	+	NOUN
ejpam-524	487	9	1	1	X
ejpam-524	487	10	)	)	PUNCT
ejpam-524	487	11	sub	sub	NOUN
ejpam-524	487	12	-	-	NOUN
ejpam-524	487	13	matrix	matrix	NOUN
ejpam-524	487	14	of	of	ADP
ejpam-524	487	15	d∗mg	d∗mg	NOUN
ejpam-524	487	16	,	,	PUNCT
ejpam-524	487	17	which	which	PRON
ejpam-524	487	18	is	be	AUX
ejpam-524	487	19	of	of	ADP
ejpam-524	487	20	the	the	DET
ejpam-524	487	21	form	form	NOUN
ejpam-524	487	22			NOUN
ejpam-524	487	23			NOUN
ejpam-524	487	24			NOUN
ejpam-524	487	25	0	0	NUM
ejpam-524	487	26	0	0	NUM
ejpam-524	487	27	0	0	NUM
ejpam-524	487	28	0	0	NUM
ejpam-524	487	29	0	0	NUM
ejpam-524	487	30	0	0	NUM
ejpam-524	487	31	.	.	PUNCT
ejpam-524	487	32	.	.	PUNCT
ejpam-524	488	1	.	.	PUNCT
ejpam-524	489	1	0	0	NUM
ejpam-524	490	1	0	0	NUM
ejpam-524	490	2	0	0	NUM
ejpam-524	490	3	1	1	NUM
ejpam-524	490	4	0	0	NUM
ejpam-524	490	5	1	1	NUM
ejpam-524	490	6	0	0	NUM
ejpam-524	490	7	0	0	NUM
ejpam-524	490	8	0	0	NUM
ejpam-524	490	9	0	0	NUM
ejpam-524	490	10	0	0	NUM
ejpam-524	490	11	0	0	NUM
ejpam-524	490	12	.	.	PUNCT
ejpam-524	490	13	.	.	PUNCT
ejpam-524	490	14	.	.	PUNCT
ejpam-524	491	1	0	0	NUM
ejpam-524	492	1	0	0	NUM
ejpam-524	492	2	0	0	NUM
ejpam-524	492	3	0	0	NUM
ejpam-524	492	4	1	1	NUM
ejpam-524	492	5	1	1	NUM
ejpam-524	492	6	0	0	NUM
ejpam-524	492	7	0	0	NUM
ejpam-524	492	8	0	0	NUM
ejpam-524	492	9	0	0	NUM
ejpam-524	492	10	0	0	NUM
ejpam-524	492	11	0	0	NUM
ejpam-524	492	12	.	.	PUNCT
ejpam-524	492	13	.	.	PUNCT
ejpam-524	492	14	.	.	PUNCT
ejpam-524	493	1	0	0	NUM
ejpam-524	493	2	0	0	NUM
ejpam-524	493	3	0	0	NUM
ejpam-524	493	4	1	1	NUM
ejpam-524	493	5	1	1	NUM
ejpam-524	493	6	1	1	NUM
ejpam-524	493	7			NOUN
ejpam-524	493	8			NOUN
ejpam-524	493	9			PUNCT
ejpam-524	494	1	also	also	ADV
ejpam-524	494	2	,	,	PUNCT
ejpam-524	494	3	choose	choose	VERB
ejpam-524	494	4	c	c	NOUN
ejpam-524	494	5	as	as	ADP
ejpam-524	494	6	(	(	PUNCT
ejpam-524	494	7	(	(	PUNCT
ejpam-524	494	8	n−	n−	NOUN
ejpam-524	494	9	3)−	3)−	NUM
ejpam-524	494	10	ð	ð	PROPN
ejpam-524	494	11	n	n	CCONJ
ejpam-524	494	12	2	2	NUM
ejpam-524	494	13	ñ)×	ñ)×	NOUN
ejpam-524	494	14	(	(	PUNCT
ejpam-524	494	15	dg	dg	X
ejpam-524	494	16	+	+	NOUN
ejpam-524	494	17	1	1	X
ejpam-524	494	18	)	)	PUNCT
ejpam-524	494	19	sub	sub	NOUN
ejpam-524	494	20	-	-	NOUN
ejpam-524	494	21	matrix	matrix	NOUN
ejpam-524	494	22	of	of	ADP
ejpam-524	494	23	d∗mg	d∗mg	NOUN
ejpam-524	494	24	,	,	PUNCT
ejpam-524	494	25	which	which	PRON
ejpam-524	494	26	is	be	AUX
ejpam-524	494	27	of	of	ADP
ejpam-524	494	28	the	the	DET
ejpam-524	494	29	form	form	NOUN
ejpam-524	494	30	,	,	PUNCT
ejpam-524	494	31			NOUN
ejpam-524	494	32			NOUN
ejpam-524	494	33			NOUN
ejpam-524	494	34			NOUN
ejpam-524	494	35			NOUN
ejpam-524	494	36			NOUN
ejpam-524	494	37			NOUN
ejpam-524	494	38	0	0	NUM
ejpam-524	494	39	0	0	NUM
ejpam-524	494	40	0	0	NUM
ejpam-524	494	41	0	0	NUM
ejpam-524	494	42	0	0	NUM
ejpam-524	494	43	0	0	NUM
ejpam-524	494	44	.	.	PUNCT
ejpam-524	494	45	.	.	PUNCT
ejpam-524	495	1	.	.	PUNCT
ejpam-524	496	1	0	0	NUM
ejpam-524	497	1	0	0	NUM
ejpam-524	497	2	1	1	NUM
ejpam-524	497	3	1	1	NUM
ejpam-524	497	4	0	0	NUM
ejpam-524	497	5	1	1	NUM
ejpam-524	497	6	0	0	NUM
ejpam-524	497	7	0	0	NUM
ejpam-524	497	8	0	0	NUM
ejpam-524	497	9	0	0	NUM
ejpam-524	497	10	0	0	NUM
ejpam-524	497	11	0	0	NUM
ejpam-524	497	12	.	.	PUNCT
ejpam-524	497	13	.	.	PUNCT
ejpam-524	497	14	.	.	PUNCT
ejpam-524	498	1	0	0	NUM
ejpam-524	499	1	1	1	NUM
ejpam-524	499	2	1	1	NUM
ejpam-524	499	3	0	0	NUM
ejpam-524	499	4	1	1	NUM
ejpam-524	499	5	0	0	NUM
ejpam-524	499	6	0	0	NUM
ejpam-524	499	7	0	0	NUM
ejpam-524	499	8	0	0	NUM
ejpam-524	499	9	0	0	NUM
ejpam-524	499	10	0	0	NUM
ejpam-524	499	11	0	0	NUM
ejpam-524	499	12	.	.	PUNCT
ejpam-524	499	13	.	.	PUNCT
ejpam-524	499	14	.	.	PUNCT
ejpam-524	500	1	1	1	NUM
ejpam-524	500	2	1	1	NUM
ejpam-524	500	3	0	0	NUM
ejpam-524	500	4	1	1	NUM
ejpam-524	500	5	0	0	NUM
ejpam-524	500	6	0	0	NUM
ejpam-524	500	7	.	.	PUNCT
ejpam-524	500	8	.	.	PUNCT
ejpam-524	500	9	.	.	PUNCT
ejpam-524	500	10	.	.	PUNCT
ejpam-524	500	11	.	.	PUNCT
ejpam-524	500	12	.	.	PUNCT
ejpam-524	500	13	.	.	PUNCT
ejpam-524	500	14	.	.	PUNCT
ejpam-524	500	15	.	.	PUNCT
ejpam-524	500	16	.	.	PUNCT
ejpam-524	500	17	.	.	PUNCT
ejpam-524	500	18	.	.	PUNCT
ejpam-524	500	19	.	.	PUNCT
ejpam-524	500	20	.	.	PUNCT
ejpam-524	500	21	.	.	PUNCT
ejpam-524	500	22	.	.	PUNCT
ejpam-524	500	23	.	.	PUNCT
ejpam-524	500	24	.	.	PUNCT
ejpam-524	500	25	.	.	PUNCT
ejpam-524	500	26	.	.	PUNCT
ejpam-524	500	27	.	.	PUNCT
ejpam-524	500	28	.	.	PUNCT
ejpam-524	500	29	.	.	PUNCT
ejpam-524	500	30	.	.	PUNCT
ejpam-524	500	31	.	.	PUNCT
ejpam-524	500	32	.	.	PUNCT
ejpam-524	500	33	.	.	PUNCT
ejpam-524	500	34	.	.	PUNCT
ejpam-524	500	35	.	.	PUNCT
ejpam-524	500	36	.	.	PUNCT
ejpam-524	500	37	.	.	PUNCT
ejpam-524	500	38	.	.	PUNCT
ejpam-524	500	39	.	.	PUNCT
ejpam-524	500	40	.	.	PUNCT
ejpam-524	500	41	.	.	PUNCT
ejpam-524	500	42	.	.	PUNCT
ejpam-524	500	43	.	.	PUNCT
ejpam-524	500	44	.	.	PUNCT
ejpam-524	500	45	.	.	PUNCT
ejpam-524	501	1	0	0	NUM
ejpam-524	502	1	1	1	NUM
ejpam-524	502	2	1	1	NUM
ejpam-524	502	3	0	0	NUM
ejpam-524	502	4	1	1	NUM
ejpam-524	502	5	0	0	NUM
ejpam-524	502	6	.	.	PUNCT
ejpam-524	502	7	.	.	PUNCT
ejpam-524	502	8	.	.	PUNCT
ejpam-524	503	1	0	0	NUM
ejpam-524	503	2	0	0	NUM
ejpam-524	503	3	0	0	NUM
ejpam-524	503	4	0	0	NUM
ejpam-524	503	5	0	0	NUM
ejpam-524	503	6	0	0	NUM
ejpam-524	503	7			NOUN
ejpam-524	503	8			NOUN
ejpam-524	503	9			VERB
ejpam-524	503	10			NOUN
ejpam-524	503	11			NOUN
ejpam-524	503	12			NOUN
ejpam-524	503	13			PUNCT
ejpam-524	504	1	g.	g.	PROPN
ejpam-524	504	2	augustine	augustine	PROPN
ejpam-524	504	3	,	,	PUNCT
ejpam-524	504	4	a.	a.	PROPN
ejpam-524	504	5	joseph	joseph	PROPN
ejpam-524	504	6	,	,	PUNCT
ejpam-524	504	7	s.	s.	PROPN
ejpam-524	504	8	jose	jose	PROPN
ejpam-524	504	9	/	/	SYM
ejpam-524	504	10	eur	eur	PROPN
ejpam-524	504	11	.	.	PUNCT
ejpam-524	505	1	j.	j.	PROPN
ejpam-524	505	2	pure	pure	PROPN
ejpam-524	505	3	appl	appl	PROPN
ejpam-524	505	4	.	.	PROPN
ejpam-524	505	5	math	math	PROPN
ejpam-524	505	6	,	,	PUNCT
ejpam-524	505	7	3	3	NUM
ejpam-524	505	8	(	(	PUNCT
ejpam-524	505	9	2010	2010	NUM
ejpam-524	505	10	)	)	PUNCT
ejpam-524	505	11	,	,	PUNCT
ejpam-524	505	12	748	748	NUM
ejpam-524	505	13	-	-	SYM
ejpam-524	505	14	764	764	NUM
ejpam-524	505	15	759	759	NUM
ejpam-524	505	16	none	none	NOUN
ejpam-524	505	17	of	of	ADP
ejpam-524	505	18	the	the	DET
ejpam-524	505	19	rows	row	NOUN
ejpam-524	505	20	of	of	ADP
ejpam-524	505	21	the	the	DET
ejpam-524	505	22	sub	sub	NOUN
ejpam-524	505	23	-	-	NOUN
ejpam-524	505	24	matrices	matrix	NOUN
ejpam-524	505	25	of	of	ADP
ejpam-524	505	26	a	a	DET
ejpam-524	505	27	,	,	PUNCT
ejpam-524	505	28	b	b	PROPN
ejpam-524	505	29	and	and	CCONJ
ejpam-524	505	30	c	c	PROPN
ejpam-524	505	31	are	be	AUX
ejpam-524	505	32	identical	identical	ADJ
ejpam-524	505	33	and	and	CCONJ
ejpam-524	505	34	hence	hence	ADV
ejpam-524	505	35	the	the	DET
ejpam-524	505	36	rows	row	NOUN
ejpam-524	505	37	of	of	ADP
ejpam-524	505	38	d∗mg	d∗mg	NOUN
ejpam-524	505	39	are	be	AUX
ejpam-524	505	40	not	not	PART
ejpam-524	505	41	identical	identical	ADJ
ejpam-524	505	42	.	.	PUNCT
ejpam-524	506	1	therefore	therefore	ADV
ejpam-524	506	2	,	,	PUNCT
ejpam-524	506	3	for	for	ADP
ejpam-524	506	4	any	any	DET
ejpam-524	506	5	cycle	cycle	NOUN
ejpam-524	506	6	cn	cn	PROPN
ejpam-524	506	7	,	,	PUNCT
ejpam-524	506	8	n≥	n≥	PROPN
ejpam-524	506	9	7	7	NUM
ejpam-524	506	10	there	there	PRON
ejpam-524	506	11	exist	exist	VERB
ejpam-524	506	12	a	a	DET
ejpam-524	506	13	dpd	dpd	NOUN
ejpam-524	506	14	-	-	PUNCT
ejpam-524	506	15	set	set	NOUN
ejpam-524	506	16	.	.	PUNCT
ejpam-524	507	1	now	now	ADV
ejpam-524	507	2	to	to	PART
ejpam-524	507	3	complete	complete	VERB
ejpam-524	507	4	the	the	DET
ejpam-524	507	5	proof	proof	NOUN
ejpam-524	507	6	of	of	ADP
ejpam-524	507	7	the	the	DET
ejpam-524	507	8	theorem	theorem	NOUN
ejpam-524	507	9	it	it	PRON
ejpam-524	507	10	is	be	AUX
ejpam-524	507	11	enough	enough	ADJ
ejpam-524	507	12	to	to	PART
ejpam-524	507	13	prove	prove	VERB
ejpam-524	507	14	that	that	SCONJ
ejpam-524	507	15	cn	cn	PROPN
ejpam-524	507	16	is	be	AUX
ejpam-524	507	17	not	not	PART
ejpam-524	507	18	a	a	DET
ejpam-524	507	19	dpdgraph	dpdgraph	NOUN
ejpam-524	507	20	for	for	ADP
ejpam-524	507	21	n≤	n≤	PRON
ejpam-524	507	22	6	6	NUM
ejpam-524	507	23	.	.	PUNCT
ejpam-524	507	24	case	case	NOUN
ejpam-524	507	25	3	3	NUM
ejpam-524	507	26	:	:	PUNCT
ejpam-524	507	27	n=	n=	ADJ
ejpam-524	507	28	3	3	X
ejpam-524	507	29	.	.	PUNCT
ejpam-524	507	30	since	since	SCONJ
ejpam-524	507	31	c3	c3	PROPN
ejpam-524	507	32	is	be	AUX
ejpam-524	507	33	a	a	DET
ejpam-524	507	34	complete	complete	ADJ
ejpam-524	507	35	graph	graph	NOUN
ejpam-524	507	36	by	by	ADP
ejpam-524	507	37	theorem	theorem	NOUN
ejpam-524	507	38	15	15	NUM
ejpam-524	507	39	,	,	PUNCT
ejpam-524	507	40	c3	c3	PROPN
ejpam-524	507	41	is	be	AUX
ejpam-524	507	42	not	not	PART
ejpam-524	507	43	a	a	DET
ejpam-524	507	44	dpd	dpd	NOUN
ejpam-524	507	45	-	-	PUNCT
ejpam-524	507	46	graph	graph	NOUN
ejpam-524	507	47	.	.	PUNCT
ejpam-524	507	48	case	case	NOUN
ejpam-524	507	49	4	4	NUM
ejpam-524	507	50	:	:	PUNCT
ejpam-524	507	51	n=	n=	ADJ
ejpam-524	507	52	4	4	NUM
ejpam-524	507	53	or	or	CCONJ
ejpam-524	507	54	n	n	NOUN
ejpam-524	507	55	=	=	SYM
ejpam-524	507	56	5	5	X
ejpam-524	507	57	.	.	X
ejpam-524	507	58	subcase	subcase	PROPN
ejpam-524	507	59	1	1	NUM
ejpam-524	507	60	:	:	PUNCT
ejpam-524	507	61	|m	|m	NOUN
ejpam-524	508	1	|	|	ADV
ejpam-524	508	2	=	=	NOUN
ejpam-524	508	3	1	1	X
ejpam-524	508	4	.	.	PUNCT
ejpam-524	508	5	let	let	VERB
ejpam-524	508	6	m	m	VERB
ejpam-524	508	7	=	=	PUNCT
ejpam-524	508	8	{	{	PUNCT
ejpam-524	508	9	v	v	NOUN
ejpam-524	508	10	}	}	PUNCT
ejpam-524	508	11	;	;	PUNCT
ejpam-524	508	12	v	v	X
ejpam-524	508	13	∈	∈	PROPN
ejpam-524	508	14	v	v	NOUN
ejpam-524	508	15	(	(	PUNCT
ejpam-524	508	16	g	g	NOUN
ejpam-524	508	17	)	)	PUNCT
ejpam-524	508	18	.	.	PUNCT
ejpam-524	509	1	then	then	ADV
ejpam-524	509	2	the	the	DET
ejpam-524	509	3	rows	row	NOUN
ejpam-524	509	4	represent	represent	VERB
ejpam-524	509	5	the	the	DET
ejpam-524	509	6	m	m	PROPN
ejpam-524	509	7	-	-	PUNCT
ejpam-524	509	8	dnp	dnp	PROPN
ejpam-524	509	9	of	of	ADP
ejpam-524	509	10	the	the	DET
ejpam-524	509	11	adjacent	adjacent	ADJ
ejpam-524	509	12	vertices	vertex	NOUN
ejpam-524	509	13	of	of	ADP
ejpam-524	509	14	v	v	NOUN
ejpam-524	509	15	gives	give	VERB
ejpam-524	509	16	a	a	DET
ejpam-524	509	17	2×	2×	NUM
ejpam-524	509	18	(	(	PUNCT
ejpam-524	509	19	dg	dg	X
ejpam-524	509	20	+	+	NOUN
ejpam-524	509	21	1	1	X
ejpam-524	509	22	)	)	PUNCT
ejpam-524	509	23	sub	sub	NOUN
ejpam-524	509	24	-	-	NOUN
ejpam-524	509	25	matrix	matrix	NOUN
ejpam-524	509	26	of	of	ADP
ejpam-524	509	27	d∗mg	d∗mg	NOUN
ejpam-524	509	28	of	of	ADP
ejpam-524	509	29	the	the	DET
ejpam-524	509	30	form	form	NOUN
ejpam-524	509	31	�	�	PROPN
ejpam-524	509	32	1	1	NUM
ejpam-524	510	1	1	1	NUM
ejpam-524	510	2	0	0	NUM
ejpam-524	510	3	0	0	NUM
ejpam-524	510	4	.	.	PUNCT
ejpam-524	510	5	.	.	PUNCT
ejpam-524	511	1	.	.	PUNCT
ejpam-524	512	1	0	0	NUM
ejpam-524	513	1	1	1	NUM
ejpam-524	513	2	1	1	NUM
ejpam-524	513	3	0	0	NUM
ejpam-524	513	4	0	0	NUM
ejpam-524	513	5	.	.	PUNCT
ejpam-524	513	6	.	.	PUNCT
ejpam-524	514	1	.	.	PUNCT
ejpam-524	515	1	0	0	NUM
ejpam-524	515	2	�	�	PROPN
ejpam-524	515	3	in	in	ADP
ejpam-524	515	4	which	which	PRON
ejpam-524	515	5	the	the	DET
ejpam-524	515	6	rows	row	NOUN
ejpam-524	515	7	are	be	AUX
ejpam-524	515	8	identical	identical	ADJ
ejpam-524	515	9	.	.	PUNCT
ejpam-524	516	1	hence	hence	ADV
ejpam-524	516	2	,	,	PUNCT
ejpam-524	516	3	m	m	VERB
ejpam-524	516	4	is	be	AUX
ejpam-524	516	5	not	not	PART
ejpam-524	516	6	a	a	DET
ejpam-524	516	7	dpd	dpd	NOUN
ejpam-524	516	8	-	-	PUNCT
ejpam-524	516	9	set	set	NOUN
ejpam-524	516	10	.	.	PUNCT
ejpam-524	517	1	subcase	subcase	PROPN
ejpam-524	517	2	2	2	NUM
ejpam-524	517	3	:	:	PUNCT
ejpam-524	517	4	|m	|m	NOUN
ejpam-524	517	5	|	|	ADV
ejpam-524	517	6	=	=	SYM
ejpam-524	517	7	2	2	X
ejpam-524	517	8	.	.	PUNCT
ejpam-524	517	9	by	by	ADP
ejpam-524	517	10	theorem	theorem	NOUN
ejpam-524	517	11	13	13	NUM
ejpam-524	517	12	,	,	PUNCT
ejpam-524	517	13	there	there	PRON
ejpam-524	517	14	exist	exist	VERB
ejpam-524	517	15	no	no	DET
ejpam-524	517	16	dpd	dpd	NOUN
ejpam-524	517	17	-	-	PUNCT
ejpam-524	517	18	set	set	VERB
ejpam-524	517	19	m	m	NOUN
ejpam-524	517	20	of	of	ADP
ejpam-524	517	21	cardinality	cardinality	PROPN
ejpam-524	517	22	2	2	NUM
ejpam-524	517	23	.	.	PUNCT
ejpam-524	517	24	subcase	subcase	PROPN
ejpam-524	517	25	3	3	NUM
ejpam-524	517	26	:	:	PUNCT
ejpam-524	517	27	|m	|m	NOUN
ejpam-524	518	1	|	|	ADV
ejpam-524	518	2	=	=	SYM
ejpam-524	518	3	3	3	NUM
ejpam-524	518	4	for	for	ADP
ejpam-524	518	5	c4	c4	NOUN
ejpam-524	518	6	and	and	CCONJ
ejpam-524	518	7	c5	c5	PROPN
ejpam-524	518	8	we	we	PRON
ejpam-524	518	9	can	can	AUX
ejpam-524	518	10	not	not	PART
ejpam-524	518	11	find	find	VERB
ejpam-524	518	12	a	a	DET
ejpam-524	518	13	dpd	dpd	NOUN
ejpam-524	518	14	-	-	PUNCT
ejpam-524	518	15	set	set	VERB
ejpam-524	518	16	m	m	NOUN
ejpam-524	518	17	with	with	ADP
ejpam-524	518	18	|m	|m	NOUN
ejpam-524	518	19	|	|	ADV
ejpam-524	518	20	=	=	SYM
ejpam-524	518	21	3	3	NUM
ejpam-524	518	22	,	,	PUNCT
ejpam-524	518	23	in	in	ADP
ejpam-524	518	24	which	which	PRON
ejpam-524	518	25	the	the	DET
ejpam-524	518	26	vertices	vertex	NOUN
ejpam-524	518	27	of	of	ADP
ejpam-524	518	28	m	m	NOUN
ejpam-524	518	29	are	be	AUX
ejpam-524	518	30	at	at	ADP
ejpam-524	518	31	distinct	distinct	ADJ
ejpam-524	518	32	distances	distance	NOUN
ejpam-524	518	33	from	from	ADP
ejpam-524	518	34	each	each	DET
ejpam-524	518	35	other	other	ADJ
ejpam-524	518	36	.	.	PUNCT
ejpam-524	519	1	hence	hence	ADV
ejpam-524	519	2	,	,	PUNCT
ejpam-524	519	3	by	by	ADP
ejpam-524	519	4	theorem	theorem	NOUN
ejpam-524	519	5	17	17	NUM
ejpam-524	519	6	there	there	PRON
ejpam-524	519	7	exist	exist	VERB
ejpam-524	519	8	no	no	DET
ejpam-524	519	9	dpd	dpd	NOUN
ejpam-524	519	10	-	-	PUNCT
ejpam-524	519	11	set	set	VERB
ejpam-524	519	12	m	m	NOUN
ejpam-524	519	13	with	with	ADP
ejpam-524	519	14	|m	|m	NOUN
ejpam-524	519	15	|	|	ADV
ejpam-524	519	16	=	=	SYM
ejpam-524	519	17	3	3	NUM
ejpam-524	519	18	for	for	ADP
ejpam-524	519	19	c4	c4	NOUN
ejpam-524	519	20	and	and	CCONJ
ejpam-524	519	21	c5	c5	PROPN
ejpam-524	519	22	.	.	PUNCT
ejpam-524	520	1	subcase	subcase	PROPN
ejpam-524	520	2	4	4	NUM
ejpam-524	520	3	:	:	PUNCT
ejpam-524	520	4	|m	|m	NOUN
ejpam-524	520	5	|	|	ADV
ejpam-524	520	6	=	=	SYM
ejpam-524	520	7	4	4	X
ejpam-524	520	8	.	.	PUNCT
ejpam-524	520	9	by	by	ADP
ejpam-524	520	10	theorem	theorem	NOUN
ejpam-524	520	11	14	14	NUM
ejpam-524	520	12	,	,	PUNCT
ejpam-524	520	13	c4	c4	NOUN
ejpam-524	520	14	does	do	AUX
ejpam-524	520	15	n’t	not	PART
ejpam-524	520	16	have	have	VERB
ejpam-524	520	17	a	a	DET
ejpam-524	520	18	dpd	dpd	NOUN
ejpam-524	520	19	-	-	PUNCT
ejpam-524	520	20	set	set	VERB
ejpam-524	520	21	m	m	NOUN
ejpam-524	520	22	with	with	ADP
ejpam-524	520	23	|m	|m	NOUN
ejpam-524	520	24	|	|	ADV
ejpam-524	520	25	=	=	SYM
ejpam-524	520	26	4	4	NUM
ejpam-524	520	27	and	and	CCONJ
ejpam-524	520	28	for	for	ADP
ejpam-524	520	29	c5	c5	PROPN
ejpam-524	520	30	,	,	PUNCT
ejpam-524	520	31	m	m	VERB
ejpam-524	520	32	with	with	ADP
ejpam-524	520	33	any	any	DET
ejpam-524	520	34	four	four	NUM
ejpam-524	520	35	vertices	vertex	NOUN
ejpam-524	520	36	of	of	ADP
ejpam-524	520	37	c5	c5	PROPN
ejpam-524	520	38	gives	give	VERB
ejpam-524	520	39	d∗mg	d∗mg	NOUN
ejpam-524	520	40	as	as	ADP
ejpam-524	520	41	:	:	PUNCT
ejpam-524	520	42	d∗mg	d∗mg	NOUN
ejpam-524	520	43	=	=	SYM
ejpam-524	520	44			PROPN
ejpam-524	520	45			NOUN
ejpam-524	520	46			NOUN
ejpam-524	520	47			NOUN
ejpam-524	520	48			NOUN
ejpam-524	520	49			NOUN
ejpam-524	520	50			NOUN
ejpam-524	520	51	1	1	NUM
ejpam-524	520	52	1	1	NUM
ejpam-524	520	53	1	1	NUM
ejpam-524	520	54	1	1	NUM
ejpam-524	520	55	1	1	NUM
ejpam-524	520	56	1	1	NUM
ejpam-524	520	57	1	1	NUM
ejpam-524	520	58	1	1	NUM
ejpam-524	520	59	1	1	NUM
ejpam-524	520	60	1	1	NUM
ejpam-524	520	61	1	1	NUM
ejpam-524	520	62	1	1	NUM
ejpam-524	520	63	0	0	NUM
ejpam-524	520	64	1	1	NUM
ejpam-524	520	65	1	1	NUM
ejpam-524	520	66			NOUN
ejpam-524	520	67			NOUN
ejpam-524	520	68			VERB
ejpam-524	520	69			NOUN
ejpam-524	520	70			NOUN
ejpam-524	520	71			NOUN
ejpam-524	520	72			PUNCT
ejpam-524	521	1	in	in	ADP
ejpam-524	521	2	which	which	PRON
ejpam-524	521	3	the	the	DET
ejpam-524	521	4	rows	row	NOUN
ejpam-524	521	5	are	be	AUX
ejpam-524	521	6	identical	identical	ADJ
ejpam-524	521	7	.	.	PUNCT
ejpam-524	522	1	hence	hence	ADV
ejpam-524	522	2	,	,	PUNCT
ejpam-524	522	3	m	m	VERB
ejpam-524	522	4	is	be	AUX
ejpam-524	522	5	not	not	PART
ejpam-524	522	6	a	a	DET
ejpam-524	522	7	dpd	dpd	NOUN
ejpam-524	522	8	-	-	PUNCT
ejpam-524	522	9	set	set	NOUN
ejpam-524	522	10	.	.	PUNCT
ejpam-524	523	1	subcase	subcase	PROPN
ejpam-524	523	2	5	5	NUM
ejpam-524	523	3	:	:	PUNCT
ejpam-524	523	4	|m	|m	NOUN
ejpam-524	523	5	|	|	ADV
ejpam-524	523	6	=	=	SYM
ejpam-524	523	7	5	5	X
ejpam-524	523	8	.	.	PUNCT
ejpam-524	523	9	by	by	ADP
ejpam-524	523	10	theorem	theorem	NOUN
ejpam-524	523	11	14	14	NUM
ejpam-524	524	1	,	,	PUNCT
ejpam-524	524	2	c5	c5	PROPN
ejpam-524	524	3	can	can	AUX
ejpam-524	524	4	not	not	PART
ejpam-524	524	5	have	have	VERB
ejpam-524	524	6	a	a	DET
ejpam-524	524	7	dpd	dpd	NOUN
ejpam-524	524	8	-	-	PUNCT
ejpam-524	524	9	set	set	VERB
ejpam-524	524	10	m	m	NOUN
ejpam-524	524	11	with	with	ADP
ejpam-524	524	12	|m	|m	NOUN
ejpam-524	524	13	|	|	ADV
ejpam-524	524	14	=	=	SYM
ejpam-524	524	15	5	5	NUM
ejpam-524	524	16	.	.	PUNCT
ejpam-524	524	17	thus	thus	ADV
ejpam-524	524	18	c4	c4	NOUN
ejpam-524	524	19	and	and	CCONJ
ejpam-524	524	20	c5	c5	PROPN
ejpam-524	524	21	are	be	AUX
ejpam-524	524	22	not	not	PART
ejpam-524	524	23	dpd	dpd	NOUN
ejpam-524	524	24	-	-	PUNCT
ejpam-524	524	25	graphs	graph	NOUN
ejpam-524	524	26	.	.	PUNCT
ejpam-524	525	1	case	case	NOUN
ejpam-524	525	2	5	5	NUM
ejpam-524	525	3	:	:	PUNCT
ejpam-524	525	4	n=	n=	ADJ
ejpam-524	525	5	6	6	X
ejpam-524	525	6	.	.	PUNCT
ejpam-524	526	1	as	as	ADP
ejpam-524	526	2	in	in	ADP
ejpam-524	526	3	case	case	NOUN
ejpam-524	526	4	4	4	NUM
ejpam-524	526	5	,	,	PUNCT
ejpam-524	526	6	m	m	VERB
ejpam-524	526	7	with	with	ADP
ejpam-524	526	8	|m	|m	NOUN
ejpam-524	526	9	|	|	ADV
ejpam-524	526	10	=	=	SYM
ejpam-524	526	11	1	1	NUM
ejpam-524	526	12	and	and	CCONJ
ejpam-524	526	13	|m	|m	NOUN
ejpam-524	527	1	|	|	ADV
ejpam-524	527	2	=	=	SYM
ejpam-524	527	3	2	2	NUM
ejpam-524	527	4	are	be	AUX
ejpam-524	527	5	not	not	PART
ejpam-524	527	6	possible	possible	ADJ
ejpam-524	527	7	.	.	PUNCT
ejpam-524	528	1	g.	g.	PROPN
ejpam-524	528	2	augustine	augustine	PROPN
ejpam-524	528	3	,	,	PUNCT
ejpam-524	528	4	a.	a.	PROPN
ejpam-524	528	5	joseph	joseph	PROPN
ejpam-524	528	6	,	,	PUNCT
ejpam-524	528	7	s.	s.	PROPN
ejpam-524	528	8	jose	jose	PROPN
ejpam-524	528	9	/	/	SYM
ejpam-524	528	10	eur	eur	PROPN
ejpam-524	528	11	.	.	PUNCT
ejpam-524	529	1	j.	j.	PROPN
ejpam-524	529	2	pure	pure	PROPN
ejpam-524	529	3	appl	appl	PROPN
ejpam-524	529	4	.	.	PROPN
ejpam-524	529	5	math	math	PROPN
ejpam-524	529	6	,	,	PUNCT
ejpam-524	529	7	3	3	NUM
ejpam-524	529	8	(	(	PUNCT
ejpam-524	529	9	2010	2010	NUM
ejpam-524	529	10	)	)	PUNCT
ejpam-524	529	11	,	,	PUNCT
ejpam-524	529	12	748	748	NUM
ejpam-524	529	13	-	-	SYM
ejpam-524	529	14	764	764	NUM
ejpam-524	529	15	760	760	NUM
ejpam-524	529	16	let	let	VERB
ejpam-524	529	17	|m	|m	NOUN
ejpam-524	529	18	|	|	ADV
ejpam-524	529	19	=	=	SYM
ejpam-524	529	20	3	3	X
ejpam-524	529	21	.	.	PUNCT
ejpam-524	530	1	then	then	ADV
ejpam-524	530	2	,	,	PUNCT
ejpam-524	530	3	any	any	DET
ejpam-524	530	4	dpd	dpd	NOUN
ejpam-524	530	5	-	-	PUNCT
ejpam-524	530	6	set	set	VERB
ejpam-524	530	7	m	m	PROPN
ejpam-524	530	8	satisfies	satisfie	NOUN
ejpam-524	530	9	theorem	theorem	VERB
ejpam-524	530	10	17	17	NUM
ejpam-524	530	11	,	,	PUNCT
ejpam-524	530	12	has	have	VERB
ejpam-524	530	13	d∗mg	d∗mg	NOUN
ejpam-524	530	14	as	as	ADP
ejpam-524	530	15	:	:	PUNCT
ejpam-524	530	16	d∗mg	d∗mg	NOUN
ejpam-524	530	17	=	=	SYM
ejpam-524	530	18			PROPN
ejpam-524	530	19			NOUN
ejpam-524	530	20			NOUN
ejpam-524	530	21			NOUN
ejpam-524	530	22			NOUN
ejpam-524	530	23			NOUN
ejpam-524	530	24			NOUN
ejpam-524	530	25			NOUN
ejpam-524	530	26			NOUN
ejpam-524	530	27	1	1	NUM
ejpam-524	530	28	1	1	NUM
ejpam-524	530	29	0	0	NUM
ejpam-524	530	30	1	1	NUM
ejpam-524	530	31	1	1	NUM
ejpam-524	530	32	1	1	NUM
ejpam-524	530	33	1	1	NUM
ejpam-524	530	34	0	0	NUM
ejpam-524	530	35	0	0	NUM
ejpam-524	530	36	1	1	NUM
ejpam-524	530	37	1	1	NUM
ejpam-524	530	38	0	0	NUM
ejpam-524	530	39	1	1	NUM
ejpam-524	530	40	0	0	NUM
ejpam-524	530	41	1	1	NUM
ejpam-524	530	42	1	1	NUM
ejpam-524	530	43	0	0	NUM
ejpam-524	530	44	1	1	NUM
ejpam-524	530	45	1	1	NUM
ejpam-524	530	46	1	1	NUM
ejpam-524	530	47	0	0	NUM
ejpam-524	530	48	1	1	NUM
ejpam-524	530	49	1	1	NUM
ejpam-524	530	50	0	0	NUM
ejpam-524	530	51			NOUN
ejpam-524	530	52			NOUN
ejpam-524	530	53			VERB
ejpam-524	530	54			NOUN
ejpam-524	530	55			NOUN
ejpam-524	530	56			NOUN
ejpam-524	530	57			NOUN
ejpam-524	530	58			NOUN
ejpam-524	530	59			PUNCT
ejpam-524	531	1	in	in	ADP
ejpam-524	531	2	which	which	PRON
ejpam-524	531	3	third	third	ADJ
ejpam-524	531	4	and	and	CCONJ
ejpam-524	531	5	sixth	sixth	ADJ
ejpam-524	531	6	rows	row	NOUN
ejpam-524	531	7	are	be	AUX
ejpam-524	531	8	identical	identical	ADJ
ejpam-524	531	9	.	.	PUNCT
ejpam-524	532	1	hence	hence	ADV
ejpam-524	532	2	,	,	PUNCT
ejpam-524	532	3	m	m	VERB
ejpam-524	532	4	with	with	ADP
ejpam-524	532	5	|m	|m	NOUN
ejpam-524	532	6	|	|	ADV
ejpam-524	532	7	=	=	SYM
ejpam-524	532	8	3	3	NUM
ejpam-524	532	9	,	,	PUNCT
ejpam-524	532	10	is	be	AUX
ejpam-524	532	11	not	not	PART
ejpam-524	532	12	a	a	DET
ejpam-524	532	13	dpd	dpd	NOUN
ejpam-524	532	14	-	-	PUNCT
ejpam-524	532	15	set	set	NOUN
ejpam-524	532	16	for	for	ADP
ejpam-524	532	17	c6	c6	PROPN
ejpam-524	532	18	.	.	PUNCT
ejpam-524	533	1	let	let	VERB
ejpam-524	533	2	c6	c6	PROPN
ejpam-524	533	3	has	have	VERB
ejpam-524	533	4	a	a	DET
ejpam-524	533	5	dpd	dpd	NOUN
ejpam-524	533	6	-	-	PUNCT
ejpam-524	533	7	set	set	VERB
ejpam-524	533	8	m	m	NOUN
ejpam-524	533	9	with	with	ADP
ejpam-524	533	10	|m	|m	NOUN
ejpam-524	534	1	|	|	ADV
ejpam-524	534	2	=	=	SYM
ejpam-524	534	3	4	4	X
ejpam-524	534	4	.	.	NOUN
ejpam-524	534	5	subcase	subcase	PROPN
ejpam-524	534	6	1	1	NUM
ejpam-524	534	7	:	:	PUNCT
ejpam-524	534	8	let	let	VERB
ejpam-524	534	9	m	m	VERB
ejpam-524	534	10	=	=	PUNCT
ejpam-524	534	11	{	{	PUNCT
ejpam-524	534	12	v1	v1	PROPN
ejpam-524	534	13	,	,	PUNCT
ejpam-524	534	14	v2	v2	PROPN
ejpam-524	534	15	,	,	PUNCT
ejpam-524	534	16	v3	v3	PROPN
ejpam-524	534	17	,	,	PUNCT
ejpam-524	534	18	v4	v4	NOUN
ejpam-524	534	19	}	}	PUNCT
ejpam-524	534	20	d∗mg	d∗mg	NOUN
ejpam-524	534	21	=	=	SYM
ejpam-524	534	22			PROPN
ejpam-524	534	23			NOUN
ejpam-524	534	24			NOUN
ejpam-524	534	25			NOUN
ejpam-524	534	26			NOUN
ejpam-524	534	27			NOUN
ejpam-524	534	28			NOUN
ejpam-524	534	29			NOUN
ejpam-524	534	30			NOUN
ejpam-524	534	31	1	1	NUM
ejpam-524	534	32	1	1	NUM
ejpam-524	534	33	1	1	NUM
ejpam-524	534	34	1	1	NUM
ejpam-524	534	35	1	1	NUM
ejpam-524	534	36	1	1	NUM
ejpam-524	534	37	1	1	NUM
ejpam-524	534	38	0	0	NUM
ejpam-524	534	39	1	1	NUM
ejpam-524	534	40	1	1	NUM
ejpam-524	534	41	1	1	NUM
ejpam-524	534	42	0	0	NUM
ejpam-524	534	43	1	1	NUM
ejpam-524	534	44	1	1	NUM
ejpam-524	534	45	1	1	NUM
ejpam-524	534	46	1	1	NUM
ejpam-524	534	47	0	0	NUM
ejpam-524	534	48	1	1	NUM
ejpam-524	534	49	1	1	NUM
ejpam-524	534	50	1	1	NUM
ejpam-524	534	51	0	0	NUM
ejpam-524	534	52	1	1	NUM
ejpam-524	534	53	1	1	NUM
ejpam-524	534	54	1	1	NUM
ejpam-524	534	55			NOUN
ejpam-524	534	56			NOUN
ejpam-524	534	57			VERB
ejpam-524	534	58			NOUN
ejpam-524	534	59			NOUN
ejpam-524	534	60			NOUN
ejpam-524	534	61			NOUN
ejpam-524	534	62			NOUN
ejpam-524	534	63			PUNCT
ejpam-524	535	1	in	in	ADP
ejpam-524	535	2	which	which	PRON
ejpam-524	535	3	there	there	PRON
ejpam-524	535	4	are	be	VERB
ejpam-524	535	5	identical	identical	ADJ
ejpam-524	535	6	rows	row	NOUN
ejpam-524	535	7	and	and	CCONJ
ejpam-524	535	8	hence	hence	ADV
ejpam-524	535	9	,	,	PUNCT
ejpam-524	535	10	m	m	VERB
ejpam-524	535	11	is	be	AUX
ejpam-524	535	12	not	not	PART
ejpam-524	535	13	a	a	DET
ejpam-524	535	14	dpd	dpd	NOUN
ejpam-524	535	15	-	-	PUNCT
ejpam-524	535	16	set	set	NOUN
ejpam-524	535	17	.	.	PUNCT
ejpam-524	536	1	subcase	subcase	PROPN
ejpam-524	536	2	2	2	NUM
ejpam-524	536	3	:	:	PUNCT
ejpam-524	536	4	m	m	PROPN
ejpam-524	536	5	=	=	SYM
ejpam-524	536	6	{	{	PUNCT
ejpam-524	536	7	v1	v1	PROPN
ejpam-524	536	8	,	,	PUNCT
ejpam-524	536	9	v3	v3	PROPN
ejpam-524	536	10	,	,	PUNCT
ejpam-524	536	11	v4	v4	PROPN
ejpam-524	536	12	,	,	PUNCT
ejpam-524	536	13	v5	v5	NOUN
ejpam-524	536	14	}	}	PUNCT
ejpam-524	536	15	d∗mg	d∗mg	NOUN
ejpam-524	536	16	=	=	SYM
ejpam-524	536	17			PROPN
ejpam-524	536	18			NOUN
ejpam-524	536	19			NOUN
ejpam-524	536	20			NOUN
ejpam-524	536	21			NOUN
ejpam-524	536	22			NOUN
ejpam-524	536	23			NOUN
ejpam-524	536	24			NOUN
ejpam-524	536	25			NOUN
ejpam-524	536	26	1	1	NUM
ejpam-524	536	27	0	0	NUM
ejpam-524	536	28	1	1	NUM
ejpam-524	536	29	1	1	NUM
ejpam-524	536	30	0	0	NUM
ejpam-524	536	31	1	1	NUM
ejpam-524	536	32	1	1	NUM
ejpam-524	536	33	1	1	NUM
ejpam-524	536	34	1	1	NUM
ejpam-524	536	35	1	1	NUM
ejpam-524	536	36	1	1	NUM
ejpam-524	536	37	0	0	NUM
ejpam-524	536	38	1	1	NUM
ejpam-524	536	39	1	1	NUM
ejpam-524	536	40	0	0	NUM
ejpam-524	536	41	1	1	NUM
ejpam-524	536	42	1	1	NUM
ejpam-524	536	43	1	1	NUM
ejpam-524	536	44	1	1	NUM
ejpam-524	536	45	0	0	NUM
ejpam-524	536	46	0	0	NUM
ejpam-524	536	47	1	1	NUM
ejpam-524	536	48	1	1	NUM
ejpam-524	536	49	1	1	NUM
ejpam-524	536	50			NOUN
ejpam-524	536	51			NOUN
ejpam-524	536	52			VERB
ejpam-524	536	53			NOUN
ejpam-524	536	54			NOUN
ejpam-524	536	55			NOUN
ejpam-524	536	56			NOUN
ejpam-524	536	57			NOUN
ejpam-524	536	58			PUNCT
ejpam-524	537	1	in	in	ADP
ejpam-524	537	2	which	which	PRON
ejpam-524	537	3	there	there	PRON
ejpam-524	537	4	are	be	VERB
ejpam-524	537	5	identical	identical	ADJ
ejpam-524	537	6	rows	row	NOUN
ejpam-524	537	7	and	and	CCONJ
ejpam-524	537	8	hence	hence	ADV
ejpam-524	537	9	,	,	PUNCT
ejpam-524	537	10	m	m	VERB
ejpam-524	537	11	is	be	AUX
ejpam-524	537	12	not	not	PART
ejpam-524	537	13	a	a	DET
ejpam-524	537	14	dpd	dpd	NOUN
ejpam-524	537	15	-	-	PUNCT
ejpam-524	537	16	set	set	NOUN
ejpam-524	537	17	.	.	PUNCT
ejpam-524	538	1	subcase	subcase	PROPN
ejpam-524	538	2	3	3	NUM
ejpam-524	538	3	:	:	PUNCT
ejpam-524	538	4	m	m	PROPN
ejpam-524	538	5	=	=	SYM
ejpam-524	538	6	{	{	PUNCT
ejpam-524	538	7	v1	v1	PROPN
ejpam-524	538	8	,	,	PUNCT
ejpam-524	538	9	v3	v3	PROPN
ejpam-524	538	10	,	,	PUNCT
ejpam-524	538	11	v4	v4	PROPN
ejpam-524	538	12	,	,	PUNCT
ejpam-524	538	13	v6	v6	NOUN
ejpam-524	538	14	}	}	PUNCT
ejpam-524	538	15	d∗mg	d∗mg	PROPN
ejpam-524	538	16	=	=	SYM
ejpam-524	538	17			PROPN
ejpam-524	538	18			NOUN
ejpam-524	538	19			NOUN
ejpam-524	538	20			NOUN
ejpam-524	538	21			NOUN
ejpam-524	538	22			NOUN
ejpam-524	538	23			NOUN
ejpam-524	538	24			NOUN
ejpam-524	538	25			NOUN
ejpam-524	538	26	1	1	NUM
ejpam-524	538	27	1	1	NUM
ejpam-524	538	28	1	1	NUM
ejpam-524	538	29	1	1	NUM
ejpam-524	538	30	0	0	NUM
ejpam-524	538	31	1	1	NUM
ejpam-524	538	32	1	1	NUM
ejpam-524	538	33	0	0	NUM
ejpam-524	538	34	1	1	NUM
ejpam-524	538	35	1	1	NUM
ejpam-524	538	36	1	1	NUM
ejpam-524	538	37	1	1	NUM
ejpam-524	538	38	1	1	NUM
ejpam-524	538	39	1	1	NUM
ejpam-524	538	40	1	1	NUM
ejpam-524	538	41	1	1	NUM
ejpam-524	538	42	0	0	NUM
ejpam-524	538	43	1	1	NUM
ejpam-524	538	44	1	1	NUM
ejpam-524	538	45	0	0	NUM
ejpam-524	538	46	1	1	NUM
ejpam-524	538	47	1	1	NUM
ejpam-524	538	48	1	1	NUM
ejpam-524	538	49	1	1	NUM
ejpam-524	538	50			NOUN
ejpam-524	538	51			NOUN
ejpam-524	538	52			VERB
ejpam-524	538	53			NOUN
ejpam-524	538	54			NOUN
ejpam-524	538	55			NOUN
ejpam-524	538	56			NOUN
ejpam-524	538	57			NOUN
ejpam-524	538	58			PUNCT
ejpam-524	539	1	in	in	ADP
ejpam-524	539	2	which	which	PRON
ejpam-524	539	3	there	there	PRON
ejpam-524	539	4	are	be	VERB
ejpam-524	539	5	identical	identical	ADJ
ejpam-524	539	6	rows	row	NOUN
ejpam-524	539	7	and	and	CCONJ
ejpam-524	539	8	hence	hence	ADV
ejpam-524	539	9	,	,	PUNCT
ejpam-524	539	10	m	m	VERB
ejpam-524	539	11	is	be	AUX
ejpam-524	539	12	not	not	PART
ejpam-524	539	13	a	a	DET
ejpam-524	539	14	dpd	dpd	NOUN
ejpam-524	539	15	-	-	PUNCT
ejpam-524	539	16	set	set	NOUN
ejpam-524	539	17	.	.	PUNCT
ejpam-524	540	1	by	by	ADP
ejpam-524	540	2	symmetry	symmetry	NOUN
ejpam-524	540	3	,	,	PUNCT
ejpam-524	540	4	similar	similar	ADJ
ejpam-524	540	5	argument	argument	NOUN
ejpam-524	540	6	follows	follow	VERB
ejpam-524	540	7	for	for	ADP
ejpam-524	540	8	the	the	DET
ejpam-524	540	9	other	other	ADJ
ejpam-524	540	10	choices	choice	NOUN
ejpam-524	540	11	of	of	ADP
ejpam-524	540	12	four	four	NUM
ejpam-524	540	13	vertices	vertex	NOUN
ejpam-524	540	14	in	in	ADP
ejpam-524	540	15	m	m	PROPN
ejpam-524	540	16	and	and	CCONJ
ejpam-524	540	17	hence	hence	ADV
ejpam-524	540	18	,	,	PUNCT
ejpam-524	540	19	c6	c6	PROPN
ejpam-524	540	20	does	do	AUX
ejpam-524	540	21	n’t	not	PART
ejpam-524	540	22	have	have	VERB
ejpam-524	540	23	a	a	DET
ejpam-524	540	24	dpd	dpd	NOUN
ejpam-524	540	25	-	-	PUNCT
ejpam-524	540	26	set	set	NOUN
ejpam-524	540	27	with	with	ADP
ejpam-524	540	28	|m	|m	NOUN
ejpam-524	540	29	|	|	ADV
ejpam-524	540	30	=	=	NOUN
ejpam-524	540	31	4	4	X
ejpam-524	540	32	.	.	PUNCT
ejpam-524	540	33	g.	g.	PROPN
ejpam-524	540	34	augustine	augustine	PROPN
ejpam-524	540	35	,	,	PUNCT
ejpam-524	540	36	a.	a.	PROPN
ejpam-524	540	37	joseph	joseph	PROPN
ejpam-524	540	38	,	,	PUNCT
ejpam-524	540	39	s.	s.	PROPN
ejpam-524	540	40	jose	jose	PROPN
ejpam-524	540	41	/	/	SYM
ejpam-524	540	42	eur	eur	PROPN
ejpam-524	540	43	.	.	PUNCT
ejpam-524	541	1	j.	j.	PROPN
ejpam-524	541	2	pure	pure	PROPN
ejpam-524	541	3	appl	appl	PROPN
ejpam-524	541	4	.	.	PROPN
ejpam-524	541	5	math	math	PROPN
ejpam-524	541	6	,	,	PUNCT
ejpam-524	541	7	3	3	NUM
ejpam-524	541	8	(	(	PUNCT
ejpam-524	541	9	2010	2010	NUM
ejpam-524	541	10	)	)	PUNCT
ejpam-524	541	11	,	,	PUNCT
ejpam-524	541	12	748	748	NUM
ejpam-524	541	13	-	-	SYM
ejpam-524	541	14	764	764	NUM
ejpam-524	541	15	761	761	NUM
ejpam-524	541	16	now	now	ADV
ejpam-524	541	17	,	,	PUNCT
ejpam-524	541	18	let	let	VERB
ejpam-524	541	19	c6	c6	PROPN
ejpam-524	541	20	has	have	VERB
ejpam-524	541	21	a	a	DET
ejpam-524	541	22	dpd	dpd	NOUN
ejpam-524	541	23	-	-	PUNCT
ejpam-524	541	24	set	set	VERB
ejpam-524	541	25	m	m	NOUN
ejpam-524	541	26	of	of	ADP
ejpam-524	541	27	|m	|m	NOUN
ejpam-524	542	1	|	|	ADV
ejpam-524	542	2	=	=	SYM
ejpam-524	542	3	5	5	X
ejpam-524	542	4	.	.	PUNCT
ejpam-524	543	1	then	then	ADV
ejpam-524	543	2	,	,	PUNCT
ejpam-524	543	3	d∗mg	d∗mg	NOUN
ejpam-524	543	4	=	=	SYM
ejpam-524	543	5			PROPN
ejpam-524	543	6			NOUN
ejpam-524	543	7			NOUN
ejpam-524	543	8			NOUN
ejpam-524	543	9			NOUN
ejpam-524	543	10			NOUN
ejpam-524	543	11			NOUN
ejpam-524	543	12			NOUN
ejpam-524	543	13			NOUN
ejpam-524	543	14	1	1	NUM
ejpam-524	543	15	1	1	NUM
ejpam-524	543	16	1	1	NUM
ejpam-524	543	17	1	1	NUM
ejpam-524	543	18	1	1	NUM
ejpam-524	543	19	1	1	NUM
ejpam-524	543	20	1	1	NUM
ejpam-524	543	21	1	1	NUM
ejpam-524	543	22	1	1	NUM
ejpam-524	543	23	1	1	NUM
ejpam-524	543	24	1	1	NUM
ejpam-524	543	25	1	1	NUM
ejpam-524	543	26	1	1	NUM
ejpam-524	543	27	1	1	NUM
ejpam-524	543	28	1	1	NUM
ejpam-524	543	29	1	1	NUM
ejpam-524	543	30	1	1	NUM
ejpam-524	543	31	1	1	NUM
ejpam-524	543	32	1	1	NUM
ejpam-524	543	33	1	1	NUM
ejpam-524	543	34	0	0	NUM
ejpam-524	543	35	1	1	NUM
ejpam-524	543	36	1	1	NUM
ejpam-524	543	37	1	1	NUM
ejpam-524	543	38			NOUN
ejpam-524	543	39			NOUN
ejpam-524	543	40			VERB
ejpam-524	543	41			NOUN
ejpam-524	543	42			NOUN
ejpam-524	543	43			NOUN
ejpam-524	543	44			NOUN
ejpam-524	543	45			NOUN
ejpam-524	543	46			PUNCT
ejpam-524	544	1	in	in	ADP
ejpam-524	544	2	which	which	PRON
ejpam-524	544	3	there	there	PRON
ejpam-524	544	4	are	be	VERB
ejpam-524	544	5	identical	identical	ADJ
ejpam-524	544	6	rows	row	NOUN
ejpam-524	544	7	and	and	CCONJ
ejpam-524	544	8	hence	hence	ADV
ejpam-524	544	9	,	,	PUNCT
ejpam-524	544	10	m	m	VERB
ejpam-524	544	11	is	be	AUX
ejpam-524	544	12	not	not	PART
ejpam-524	544	13	a	a	DET
ejpam-524	544	14	dpd	dpd	NOUN
ejpam-524	544	15	-	-	PUNCT
ejpam-524	544	16	set	set	NOUN
ejpam-524	544	17	.	.	PUNCT
ejpam-524	545	1	thus	thus	ADV
ejpam-524	545	2	,	,	PUNCT
ejpam-524	545	3	for	for	ADP
ejpam-524	545	4	c6	c6	PROPN
ejpam-524	545	5	,	,	PUNCT
ejpam-524	545	6	a	a	DET
ejpam-524	545	7	dpd	dpd	NOUN
ejpam-524	545	8	-	-	PUNCT
ejpam-524	545	9	set	set	VERB
ejpam-524	545	10	m	m	NOUN
ejpam-524	545	11	with	with	ADP
ejpam-524	545	12	|m	|m	NOUN
ejpam-524	545	13	|	|	ADV
ejpam-524	545	14	=	=	SYM
ejpam-524	545	15	5	5	NUM
ejpam-524	545	16	is	be	AUX
ejpam-524	545	17	not	not	PART
ejpam-524	545	18	possible	possible	ADJ
ejpam-524	545	19	.	.	PUNCT
ejpam-524	546	1	by	by	ADP
ejpam-524	546	2	theorem	theorem	NOUN
ejpam-524	546	3	14	14	NUM
ejpam-524	546	4	,	,	PUNCT
ejpam-524	546	5	c6	c6	PROPN
ejpam-524	546	6	can	can	AUX
ejpam-524	546	7	not	not	PART
ejpam-524	546	8	possess	possess	VERB
ejpam-524	546	9	a	a	DET
ejpam-524	546	10	dpd	dpd	NOUN
ejpam-524	546	11	-	-	PUNCT
ejpam-524	546	12	set	set	VERB
ejpam-524	546	13	m	m	NOUN
ejpam-524	546	14	with	with	ADP
ejpam-524	546	15	|m	|m	NOUN
ejpam-524	546	16	|	|	ADV
ejpam-524	546	17	=	=	SYM
ejpam-524	546	18	6	6	NUM
ejpam-524	546	19	.	.	PUNCT
ejpam-524	547	1	thus	thus	ADV
ejpam-524	547	2	c6	c6	PROPN
ejpam-524	547	3	is	be	AUX
ejpam-524	547	4	not	not	PART
ejpam-524	547	5	a	a	DET
ejpam-524	547	6	dpd	dpd	NOUN
ejpam-524	547	7	-	-	PUNCT
ejpam-524	547	8	graph	graph	NOUN
ejpam-524	547	9	.	.	PUNCT
ejpam-524	548	1	theorem	theorem	NOUN
ejpam-524	548	2	19	19	NUM
ejpam-524	548	3	.	.	PUNCT
ejpam-524	549	1	the	the	DET
ejpam-524	549	2	set	set	NOUN
ejpam-524	549	3	of	of	ADP
ejpam-524	549	4	all	all	DET
ejpam-524	549	5	vertices	vertex	NOUN
ejpam-524	549	6	in	in	ADP
ejpam-524	549	7	a	a	DET
ejpam-524	549	8	diametrical	diametrical	ADJ
ejpam-524	549	9	path	path	NOUN
ejpam-524	549	10	of	of	ADP
ejpam-524	549	11	a	a	DET
ejpam-524	549	12	graph	graph	NOUN
ejpam-524	549	13	g	g	NOUN
ejpam-524	549	14	can	can	AUX
ejpam-524	549	15	not	not	PART
ejpam-524	549	16	form	form	VERB
ejpam-524	549	17	a	a	DET
ejpam-524	549	18	dpd	dpd	NOUN
ejpam-524	549	19	-	-	PUNCT
ejpam-524	549	20	set	set	NOUN
ejpam-524	549	21	.	.	PUNCT
ejpam-524	550	1	proof	proof	NOUN
ejpam-524	550	2	.	.	PUNCT
ejpam-524	551	1	let	let	VERB
ejpam-524	551	2	pn	pn	NOUN
ejpam-524	551	3	=	=	PUNCT
ejpam-524	551	4	v1	v1	PROPN
ejpam-524	551	5	,	,	PUNCT
ejpam-524	551	6	v2	v2	NOUN
ejpam-524	551	7	,	,	PUNCT
ejpam-524	551	8	.	.	PUNCT
ejpam-524	551	9	.	.	PUNCT
ejpam-524	552	1	.	.	PUNCT
ejpam-524	553	1	,	,	PUNCT
ejpam-524	553	2	vn	vn	INTJ
ejpam-524	553	3	be	be	AUX
ejpam-524	553	4	an	an	DET
ejpam-524	553	5	arbitrary	arbitrary	ADJ
ejpam-524	553	6	diametrical	diametrical	ADJ
ejpam-524	553	7	path	path	NOUN
ejpam-524	553	8	of	of	ADP
ejpam-524	553	9	g	g	NOUN
ejpam-524	553	10	,	,	PUNCT
ejpam-524	553	11	where	where	SCONJ
ejpam-524	553	12	m	m	VERB
ejpam-524	553	13	=	=	SYM
ejpam-524	553	14	{	{	PUNCT
ejpam-524	553	15	v1	v1	PROPN
ejpam-524	553	16	,	,	PUNCT
ejpam-524	553	17	v2	v2	PROPN
ejpam-524	553	18	,	,	PUNCT
ejpam-524	553	19	.	.	PUNCT
ejpam-524	553	20	.	.	PUNCT
ejpam-524	554	1	.	.	PUNCT
ejpam-524	555	1	,	,	PUNCT
ejpam-524	555	2	vn	vn	AUX
ejpam-524	555	3	}	}	PUNCT
ejpam-524	555	4	be	be	AUX
ejpam-524	555	5	a	a	DET
ejpam-524	555	6	dpd	dpd	NOUN
ejpam-524	555	7	-	-	PUNCT
ejpam-524	555	8	set	set	NOUN
ejpam-524	555	9	of	of	ADP
ejpam-524	555	10	g.	g.	PROPN
ejpam-524	555	11	then	then	ADV
ejpam-524	555	12	,	,	PUNCT
ejpam-524	555	13	the	the	DET
ejpam-524	555	14	rows	row	NOUN
ejpam-524	555	15	representing	represent	VERB
ejpam-524	555	16	the	the	DET
ejpam-524	555	17	m	m	PROPN
ejpam-524	555	18	-	-	PUNCT
ejpam-524	555	19	dnp	dnp	PROPN
ejpam-524	555	20	of	of	ADP
ejpam-524	555	21	the	the	DET
ejpam-524	555	22	antipodal	antipodal	PROPN
ejpam-524	555	23	vertices	vertice	VERB
ejpam-524	555	24	v1	v1	VERB
ejpam-524	555	25	and	and	CCONJ
ejpam-524	555	26	vn	vn	X
ejpam-524	555	27	in	in	ADP
ejpam-524	555	28	d∗mg	d∗mg	PROPN
ejpam-524	555	29	forms	form	VERB
ejpam-524	555	30	a	a	DET
ejpam-524	555	31	2×	2×	NUM
ejpam-524	555	32	(	(	PUNCT
ejpam-524	555	33	dg	dg	X
ejpam-524	555	34	+	+	NOUN
ejpam-524	555	35	1	1	X
ejpam-524	555	36	)	)	PUNCT
ejpam-524	555	37	sub	sub	NOUN
ejpam-524	555	38	matrix	matrix	NOUN
ejpam-524	555	39	as	as	ADP
ejpam-524	555	40	�	�	PROPN
ejpam-524	555	41	1	1	NUM
ejpam-524	555	42	1	1	NUM
ejpam-524	555	43	.	.	PUNCT
ejpam-524	555	44	.	.	PUNCT
ejpam-524	556	1	.	.	PUNCT
ejpam-524	557	1	1	1	NUM
ejpam-524	557	2	1	1	NUM
ejpam-524	557	3	1	1	NUM
ejpam-524	557	4	1	1	NUM
ejpam-524	557	5	.	.	PUNCT
ejpam-524	557	6	.	.	PUNCT
ejpam-524	557	7	.	.	PUNCT
ejpam-524	558	1	1	1	NUM
ejpam-524	558	2	1	1	NUM
ejpam-524	558	3	�	�	NOUN
ejpam-524	558	4	hence	hence	ADV
ejpam-524	558	5	,	,	PUNCT
ejpam-524	558	6	m	m	VERB
ejpam-524	558	7	is	be	AUX
ejpam-524	558	8	not	not	PART
ejpam-524	558	9	a	a	DET
ejpam-524	558	10	dpd	dpd	NOUN
ejpam-524	558	11	-	-	PUNCT
ejpam-524	558	12	set	set	NOUN
ejpam-524	558	13	.	.	PUNCT
ejpam-524	559	1	theorem	theorem	ADJ
ejpam-524	559	2	20	20	NUM
ejpam-524	559	3	.	.	PUNCT
ejpam-524	560	1	for	for	ADP
ejpam-524	560	2	all	all	DET
ejpam-524	560	3	non	non	ADJ
ejpam-524	560	4	-	-	ADJ
ejpam-524	560	5	trivial	trivial	ADJ
ejpam-524	560	6	dpd	dpd	NOUN
ejpam-524	560	7	-	-	PUNCT
ejpam-524	560	8	graphs	graphs	NOUN
ejpam-524	560	9	g	g	NOUN
ejpam-524	560	10	,	,	PUNCT
ejpam-524	560	11	the	the	DET
ejpam-524	560	12	number	number	NOUN
ejpam-524	560	13	of	of	ADP
ejpam-524	560	14	nonzero	nonzero	PROPN
ejpam-524	560	15	entries	entry	NOUN
ejpam-524	560	16	in	in	ADP
ejpam-524	560	17	the	the	DET
ejpam-524	560	18	first	first	ADJ
ejpam-524	560	19	column	column	NOUN
ejpam-524	560	20	of	of	ADP
ejpam-524	560	21	dm	dm	PROPN
ejpam-524	560	22	g	g	PROPN
ejpam-524	560	23	is	be	AUX
ejpam-524	560	24	less	less	ADJ
ejpam-524	560	25	than	than	ADP
ejpam-524	560	26	the	the	DET
ejpam-524	560	27	number	number	NOUN
ejpam-524	560	28	of	of	ADP
ejpam-524	560	29	rows	row	NOUN
ejpam-524	560	30	.	.	PUNCT
ejpam-524	561	1	in	in	ADP
ejpam-524	561	2	particular	particular	ADJ
ejpam-524	561	3	,	,	PUNCT
ejpam-524	561	4	all	all	DET
ejpam-524	561	5	the	the	DET
ejpam-524	561	6	nonzero	nonzero	ADJ
ejpam-524	561	7	entries	entry	NOUN
ejpam-524	561	8	in	in	ADP
ejpam-524	561	9	the	the	DET
ejpam-524	561	10	first	first	ADJ
ejpam-524	561	11	column	column	NOUN
ejpam-524	561	12	of	of	ADP
ejpam-524	561	13	dm	dm	PROPN
ejpam-524	561	14	g	g	PROPN
ejpam-524	561	15	are	be	AUX
ejpam-524	561	16	unity	unity	NOUN
ejpam-524	561	17	.	.	PUNCT
ejpam-524	562	1	proof	proof	NOUN
ejpam-524	562	2	.	.	PUNCT
ejpam-524	563	1	by	by	ADP
ejpam-524	563	2	proposition	proposition	NOUN
ejpam-524	563	3	2	2	NUM
ejpam-524	563	4	,	,	PUNCT
ejpam-524	563	5	all	all	DET
ejpam-524	563	6	the	the	DET
ejpam-524	563	7	nonzero	nonzero	ADJ
ejpam-524	563	8	entries	entry	NOUN
ejpam-524	563	9	in	in	ADP
ejpam-524	563	10	the	the	DET
ejpam-524	563	11	first	first	ADJ
ejpam-524	563	12	column	column	NOUN
ejpam-524	563	13	are	be	AUX
ejpam-524	563	14	unity	unity	NOUN
ejpam-524	563	15	.	.	PUNCT
ejpam-524	564	1	if	if	SCONJ
ejpam-524	564	2	possible	possible	ADJ
ejpam-524	564	3	,	,	PUNCT
ejpam-524	564	4	let	let	VERB
ejpam-524	564	5	the	the	DET
ejpam-524	564	6	number	number	NOUN
ejpam-524	564	7	of	of	ADP
ejpam-524	564	8	entries	entry	NOUN
ejpam-524	564	9	in	in	ADP
ejpam-524	564	10	the	the	DET
ejpam-524	564	11	first	first	ADJ
ejpam-524	564	12	column	column	NOUN
ejpam-524	564	13	of	of	ADP
ejpam-524	564	14	dm	dm	PROPN
ejpam-524	564	15	g	g	PROPN
ejpam-524	564	16	is	be	AUX
ejpam-524	564	17	equal	equal	ADJ
ejpam-524	564	18	to	to	ADP
ejpam-524	564	19	the	the	DET
ejpam-524	564	20	number	number	NOUN
ejpam-524	564	21	of	of	ADP
ejpam-524	564	22	rows	row	NOUN
ejpam-524	564	23	.	.	PUNCT
ejpam-524	565	1	since	since	ADV
ejpam-524	565	2	,	,	PUNCT
ejpam-524	565	3	all	all	DET
ejpam-524	565	4	the	the	DET
ejpam-524	565	5	nonzero	nonzero	ADJ
ejpam-524	565	6	entries	entry	NOUN
ejpam-524	565	7	in	in	ADP
ejpam-524	565	8	the	the	DET
ejpam-524	565	9	first	first	ADJ
ejpam-524	565	10	column	column	NOUN
ejpam-524	565	11	are	be	AUX
ejpam-524	565	12	unity	unity	NOUN
ejpam-524	565	13	,	,	PUNCT
ejpam-524	565	14	|n	|n	NOUN
ejpam-524	565	15	m	m	PROPN
ejpam-524	565	16	0	0	NUM
ejpam-524	566	1	(	(	PUNCT
ejpam-524	566	2	ui)|	ui)|	PROPN
ejpam-524	566	3	=	=	SYM
ejpam-524	566	4	1	1	NUM
ejpam-524	566	5	∀ui	∀ui	PROPN
ejpam-524	566	6	∈	∈	PROPN
ejpam-524	566	7	v	v	ADP
ejpam-524	566	8	(	(	PUNCT
ejpam-524	566	9	g	g	NOUN
ejpam-524	566	10	)	)	PUNCT
ejpam-524	566	11	,	,	PUNCT
ejpam-524	566	12	which	which	PRON
ejpam-524	566	13	implies	imply	VERB
ejpam-524	566	14	,	,	PUNCT
ejpam-524	566	15	n	n	ADV
ejpam-524	566	16	m	m	VERB
ejpam-524	566	17	0	0	NUM
ejpam-524	566	18	(	(	PUNCT
ejpam-524	566	19	ui	ui	NOUN
ejpam-524	566	20	)	)	PUNCT
ejpam-524	566	21	=	=	PRON
ejpam-524	566	22	{	{	PUNCT
ejpam-524	566	23	ui	ui	PROPN
ejpam-524	566	24	}	}	PUNCT
ejpam-524	566	25	∀ui	∀ui	PROPN
ejpam-524	566	26	∈	∈	PROPN
ejpam-524	566	27	v	v	ADP
ejpam-524	566	28	(	(	PUNCT
ejpam-524	566	29	g	g	NOUN
ejpam-524	566	30	)	)	PUNCT
ejpam-524	566	31	.	.	PUNCT
ejpam-524	567	1	hence	hence	ADV
ejpam-524	567	2	,	,	PUNCT
ejpam-524	567	3	ui	ui	PROPN
ejpam-524	567	4	∈	∈	PROPN
ejpam-524	567	5	m	m	VERB
ejpam-524	567	6	∀ui	∀ui	PROPN
ejpam-524	567	7	∈	∈	PROPN
ejpam-524	567	8	v	v	ADP
ejpam-524	567	9	(	(	PUNCT
ejpam-524	567	10	g	g	NOUN
ejpam-524	567	11	)	)	PUNCT
ejpam-524	567	12	.	.	PUNCT
ejpam-524	568	1	therefore	therefore	ADV
ejpam-524	568	2	,	,	PUNCT
ejpam-524	568	3	by	by	ADP
ejpam-524	568	4	theorem	theorem	NOUN
ejpam-524	568	5	14	14	NUM
ejpam-524	568	6	,	,	PUNCT
ejpam-524	568	7	g	g	PROPN
ejpam-524	568	8	≅	≅	PROPN
ejpam-524	568	9	k1	k1	PROPN
ejpam-524	568	10	.	.	PUNCT
ejpam-524	569	1	corollary	corollary	ADJ
ejpam-524	569	2	6	6	NUM
ejpam-524	569	3	.	.	PUNCT
ejpam-524	570	1	let	let	VERB
ejpam-524	570	2	g	g	PRON
ejpam-524	570	3	be	be	AUX
ejpam-524	570	4	a	a	DET
ejpam-524	570	5	nontrivial	nontrivial	ADJ
ejpam-524	570	6	graph	graph	NOUN
ejpam-524	570	7	with	with	ADP
ejpam-524	570	8	dpd	dpd	NOUN
ejpam-524	570	9	-	-	PUNCT
ejpam-524	570	10	set	set	VERB
ejpam-524	570	11	m	m	NOUN
ejpam-524	570	12	and	and	CCONJ
ejpam-524	570	13	m	m	PROPN
ejpam-524	570	14	-	-	PROPN
ejpam-524	570	15	dnp	dnp	PROPN
ejpam-524	570	16	matrix	matrix	NOUN
ejpam-524	570	17	dm	dm	VERB
ejpam-524	570	18	g	g	NOUN
ejpam-524	570	19	as	as	ADP
ejpam-524	570	20	an	an	DET
ejpam-524	570	21	n×	n×	PRON
ejpam-524	570	22	n	n	CCONJ
ejpam-524	570	23	square	square	ADJ
ejpam-524	570	24	matrix	matrix	NOUN
ejpam-524	570	25	.	.	PUNCT
ejpam-524	571	1	then	then	ADV
ejpam-524	571	2	,	,	PUNCT
ejpam-524	571	3	the	the	DET
ejpam-524	571	4	number	number	NOUN
ejpam-524	571	5	of	of	ADP
ejpam-524	571	6	nonzero	nonzero	PROPN
ejpam-524	571	7	entries	entry	NOUN
ejpam-524	571	8	in	in	ADP
ejpam-524	571	9	the	the	DET
ejpam-524	571	10	first	first	ADJ
ejpam-524	571	11	column	column	NOUN
ejpam-524	571	12	≦	≦	VERB
ejpam-524	571	13	n−	n−	NOUN
ejpam-524	571	14	1	1	NUM
ejpam-524	571	15	.	.	PUNCT
ejpam-524	572	1	theorem	theorem	NOUN
ejpam-524	572	2	21	21	NUM
ejpam-524	572	3	.	.	PUNCT
ejpam-524	573	1	let	let	VERB
ejpam-524	573	2	g	g	PRON
ejpam-524	573	3	be	be	AUX
ejpam-524	573	4	a	a	DET
ejpam-524	573	5	graph	graph	NOUN
ejpam-524	573	6	with	with	ADP
ejpam-524	573	7	a	a	DET
ejpam-524	573	8	dpd	dpd	NOUN
ejpam-524	573	9	-	-	PUNCT
ejpam-524	573	10	set	set	VERB
ejpam-524	573	11	m.	m.	NOUN
ejpam-524	573	12	then	then	ADV
ejpam-524	573	13	,	,	PUNCT
ejpam-524	573	14	the	the	DET
ejpam-524	573	15	m	m	PROPN
ejpam-524	573	16	-	-	PUNCT
ejpam-524	573	17	dnp	dnp	PROPN
ejpam-524	573	18	matrix	matrix	NOUN
ejpam-524	573	19	dm	dm	X
ejpam-524	573	20	g	g	PROPN
ejpam-524	573	21	is	be	AUX
ejpam-524	573	22	a	a	DET
ejpam-524	573	23	square	square	ADJ
ejpam-524	573	24	matrix	matrix	NOUN
ejpam-524	573	25	of	of	ADP
ejpam-524	573	26	order	order	NOUN
ejpam-524	573	27	n	n	NOUN
ejpam-524	573	28	if	if	SCONJ
ejpam-524	574	1	and	and	CCONJ
ejpam-524	574	2	only	only	ADV
ejpam-524	574	3	if	if	SCONJ
ejpam-524	574	4	g	g	PROPN
ejpam-524	574	5	≅	≅	PROPN
ejpam-524	574	6	pn	pn	PROPN
ejpam-524	574	7	,	,	PUNCT
ejpam-524	574	8	path	path	NOUN
ejpam-524	574	9	on	on	ADP
ejpam-524	574	10	n	n	DET
ejpam-524	574	11	vertices	vertex	NOUN
ejpam-524	574	12	.	.	PUNCT
ejpam-524	575	1	proof	proof	NOUN
ejpam-524	575	2	.	.	PUNCT
ejpam-524	576	1	assume	assume	VERB
ejpam-524	576	2	that	that	SCONJ
ejpam-524	576	3	the	the	DET
ejpam-524	576	4	m	m	PROPN
ejpam-524	576	5	-dnp	-dnp	NOUN
ejpam-524	576	6	matrix	matrix	NOUN
ejpam-524	576	7	dm	dm	X
ejpam-524	576	8	g	g	NOUN
ejpam-524	576	9	of	of	ADP
ejpam-524	576	10	dpd	dpd	NOUN
ejpam-524	576	11	-	-	PUNCT
ejpam-524	576	12	graph	graph	NOUN
ejpam-524	576	13	g	g	NOUN
ejpam-524	576	14	is	be	AUX
ejpam-524	576	15	a	a	DET
ejpam-524	576	16	square	square	ADJ
ejpam-524	576	17	matrix	matrix	NOUN
ejpam-524	576	18	of	of	ADP
ejpam-524	576	19	order	order	NOUN
ejpam-524	576	20	n.	n.	NOUN
ejpam-524	576	21	then	then	ADV
ejpam-524	576	22	o(g	o(g	ADV
ejpam-524	576	23	)	)	PUNCT
ejpam-524	576	24	=	=	SYM
ejpam-524	577	1	n	n	PROPN
ejpam-524	577	2	and	and	CCONJ
ejpam-524	577	3	dg	dg	X
ejpam-524	577	4	=	=	SYM
ejpam-524	577	5	n	n	CCONJ
ejpam-524	577	6	−	−	PROPN
ejpam-524	577	7	1	1	NUM
ejpam-524	577	8	.	.	PUNCT
ejpam-524	578	1	since	since	SCONJ
ejpam-524	578	2	dg	dg	PROPN
ejpam-524	578	3	=	=	SYM
ejpam-524	578	4	n	n	CCONJ
ejpam-524	578	5	−	−	PROPN
ejpam-524	578	6	1	1	NUM
ejpam-524	578	7	,	,	PUNCT
ejpam-524	578	8	g	g	PROPN
ejpam-524	578	9	contains	contain	VERB
ejpam-524	578	10	a	a	DET
ejpam-524	578	11	path	path	NOUN
ejpam-524	578	12	p	p	NOUN
ejpam-524	578	13	of	of	ADP
ejpam-524	578	14	length	length	NOUN
ejpam-524	578	15	n	n	CCONJ
ejpam-524	578	16	−	−	PROPN
ejpam-524	578	17	1	1	NUM
ejpam-524	578	18	.	.	PUNCT
ejpam-524	578	19	since	since	SCONJ
ejpam-524	578	20	o(g	o(g	NOUN
ejpam-524	578	21	)	)	PUNCT
ejpam-524	578	22	=	=	SYM
ejpam-524	578	23	o(p	o(p	PROPN
ejpam-524	578	24	)	)	PUNCT
ejpam-524	578	25	=	=	SYM
ejpam-524	578	26	n	n	CCONJ
ejpam-524	578	27	,	,	PUNCT
ejpam-524	578	28	the	the	DET
ejpam-524	578	29	number	number	NOUN
ejpam-524	578	30	of	of	ADP
ejpam-524	578	31	vertices	vertex	NOUN
ejpam-524	578	32	of	of	ADP
ejpam-524	578	33	g	g	PROPN
ejpam-524	578	34	and	and	CCONJ
ejpam-524	578	35	p	p	NOUN
ejpam-524	578	36	are	be	AUX
ejpam-524	578	37	same	same	ADJ
ejpam-524	578	38	.	.	PUNCT
ejpam-524	579	1	therefore	therefore	ADV
ejpam-524	579	2	,	,	PUNCT
ejpam-524	579	3	if	if	SCONJ
ejpam-524	579	4	g	g	PROPN
ejpam-524	579	5	�	�	PROPN
ejpam-524	579	6	p	p	X
ejpam-524	579	7	,	,	PUNCT
ejpam-524	579	8	g	g	PROPN
ejpam-524	579	9	contains	contain	VERB
ejpam-524	579	10	at	at	ADV
ejpam-524	579	11	least	least	ADV
ejpam-524	579	12	one	one	NUM
ejpam-524	579	13	edge	edge	NOUN
ejpam-524	579	14	connecting	connect	VERB
ejpam-524	579	15	the	the	DET
ejpam-524	579	16	nonadjacent	nonadjacent	ADJ
ejpam-524	579	17	vertices	vertex	NOUN
ejpam-524	579	18	of	of	ADP
ejpam-524	579	19	p	p	X
ejpam-524	579	20	,	,	PUNCT
ejpam-524	579	21	which	which	PRON
ejpam-524	579	22	is	be	AUX
ejpam-524	579	23	not	not	PART
ejpam-524	579	24	possible	possible	ADJ
ejpam-524	579	25	since	since	SCONJ
ejpam-524	579	26	,	,	PUNCT
ejpam-524	579	27	in	in	ADP
ejpam-524	579	28	this	this	DET
ejpam-524	579	29	case	case	NOUN
ejpam-524	579	30	dg	dg	VERB
ejpam-524	579	31	<	<	X
ejpam-524	579	32	n−	n−	PROPN
ejpam-524	579	33	1	1	NUM
ejpam-524	579	34	,	,	PUNCT
ejpam-524	579	35	a	a	DET
ejpam-524	579	36	contradiction	contradiction	NOUN
ejpam-524	579	37	.	.	PUNCT
ejpam-524	580	1	hence	hence	ADV
ejpam-524	580	2	,	,	PUNCT
ejpam-524	580	3	g	g	PROPN
ejpam-524	580	4	≅	≅	PROPN
ejpam-524	580	5	pn	pn	PROPN
ejpam-524	580	6	.	.	PUNCT
ejpam-524	581	1	conversely	conversely	ADV
ejpam-524	581	2	,	,	PUNCT
ejpam-524	581	3	let	let	VERB
ejpam-524	581	4	g	g	PRON
ejpam-524	581	5	be	be	AUX
ejpam-524	581	6	a	a	DET
ejpam-524	581	7	path	path	NOUN
ejpam-524	581	8	on	on	ADP
ejpam-524	581	9	n	n	NOUN
ejpam-524	581	10	vertices	vertex	NOUN
ejpam-524	581	11	with	with	ADP
ejpam-524	581	12	dpd	dpd	NOUN
ejpam-524	581	13	-	-	PUNCT
ejpam-524	581	14	set	set	VERB
ejpam-524	581	15	m	m	NOUN
ejpam-524	581	16	and	and	CCONJ
ejpam-524	581	17	m	m	PROPN
ejpam-524	581	18	-dnp	-dnp	NOUN
ejpam-524	581	19	matrix	matrix	NOUN
ejpam-524	581	20	dm	dm	VERB
ejpam-524	581	21	g	g	NOUN
ejpam-524	581	22	.	.	PUNCT
ejpam-524	582	1	then	then	ADV
ejpam-524	582	2	,	,	PUNCT
ejpam-524	582	3	dm	dm	PROPN
ejpam-524	582	4	g	g	PROPN
ejpam-524	582	5	is	be	AUX
ejpam-524	582	6	a	a	DET
ejpam-524	582	7	square	square	ADJ
ejpam-524	582	8	matrix	matrix	NOUN
ejpam-524	582	9	of	of	ADP
ejpam-524	582	10	order	order	NOUN
ejpam-524	582	11	n	n	CCONJ
ejpam-524	582	12	,	,	PUNCT
ejpam-524	582	13	since	since	SCONJ
ejpam-524	582	14	the	the	DET
ejpam-524	582	15	number	number	NOUN
ejpam-524	582	16	of	of	ADP
ejpam-524	582	17	vertices	vertex	NOUN
ejpam-524	582	18	of	of	ADP
ejpam-524	582	19	g	g	PROPN
ejpam-524	582	20	is	be	AUX
ejpam-524	582	21	n	n	ADJ
ejpam-524	582	22	and	and	CCONJ
ejpam-524	582	23	dg	dg	PROPN
ejpam-524	583	1	=	=	VERB
ejpam-524	583	2	n−	n−	NOUN
ejpam-524	583	3	1	1	NUM
ejpam-524	583	4	.	.	PUNCT
ejpam-524	584	1	g.	g.	PROPN
ejpam-524	584	2	augustine	augustine	PROPN
ejpam-524	584	3	,	,	PUNCT
ejpam-524	584	4	a.	a.	PROPN
ejpam-524	584	5	joseph	joseph	PROPN
ejpam-524	584	6	,	,	PUNCT
ejpam-524	584	7	s.	s.	PROPN
ejpam-524	584	8	jose	jose	PROPN
ejpam-524	584	9	/	/	SYM
ejpam-524	584	10	eur	eur	PROPN
ejpam-524	584	11	.	.	PUNCT
ejpam-524	585	1	j.	j.	PROPN
ejpam-524	585	2	pure	pure	PROPN
ejpam-524	585	3	appl	appl	PROPN
ejpam-524	585	4	.	.	PROPN
ejpam-524	585	5	math	math	PROPN
ejpam-524	585	6	,	,	PUNCT
ejpam-524	585	7	3	3	NUM
ejpam-524	585	8	(	(	PUNCT
ejpam-524	585	9	2010	2010	NUM
ejpam-524	585	10	)	)	PUNCT
ejpam-524	585	11	,	,	PUNCT
ejpam-524	585	12	748	748	NUM
ejpam-524	585	13	-	-	SYM
ejpam-524	585	14	764	764	NUM
ejpam-524	585	15	762	762	NUM
ejpam-524	585	16	corollary	corollary	NOUN
ejpam-524	585	17	7	7	NUM
ejpam-524	585	18	.	.	PUNCT
ejpam-524	586	1	let	let	VERB
ejpam-524	586	2	g	g	PRON
ejpam-524	586	3	be	be	AUX
ejpam-524	586	4	a	a	DET
ejpam-524	586	5	graph	graph	NOUN
ejpam-524	586	6	with	with	ADP
ejpam-524	586	7	dpd	dpd	NOUN
ejpam-524	586	8	-	-	PUNCT
ejpam-524	586	9	set	set	VERB
ejpam-524	586	10	m	m	NOUN
ejpam-524	586	11	and	and	CCONJ
ejpam-524	586	12	the	the	DET
ejpam-524	586	13	m	m	PROPN
ejpam-524	586	14	-	-	PROPN
ejpam-524	586	15	dnp	dnp	PROPN
ejpam-524	586	16	matrix	matrix	NOUN
ejpam-524	586	17	dm	dm	VERB
ejpam-524	586	18	g	g	NOUN
ejpam-524	586	19	as	as	ADP
ejpam-524	586	20	an	an	DET
ejpam-524	586	21	invertible	invertible	ADJ
ejpam-524	586	22	matrix	matrix	NOUN
ejpam-524	586	23	.	.	PUNCT
ejpam-524	587	1	then	then	ADV
ejpam-524	587	2	g	g	PROPN
ejpam-524	587	3	≅	≅	PROPN
ejpam-524	587	4	pn	pn	PROPN
ejpam-524	587	5	,	,	PUNCT
ejpam-524	587	6	a	a	DET
ejpam-524	587	7	path	path	NOUN
ejpam-524	587	8	on	on	ADP
ejpam-524	587	9	n	n	DET
ejpam-524	587	10	vertices	vertex	NOUN
ejpam-524	587	11	.	.	PUNCT
ejpam-524	588	1	theorem	theorem	VERB
ejpam-524	588	2	22	22	NUM
ejpam-524	588	3	.	.	PUNCT
ejpam-524	589	1	let	let	VERB
ejpam-524	589	2	g	g	PRON
ejpam-524	589	3	be	be	AUX
ejpam-524	589	4	a	a	DET
ejpam-524	589	5	graph	graph	NOUN
ejpam-524	589	6	with	with	ADP
ejpam-524	589	7	dpd	dpd	NOUN
ejpam-524	589	8	-	-	PUNCT
ejpam-524	589	9	set	set	VERB
ejpam-524	589	10	m	m	NOUN
ejpam-524	589	11	and	and	CCONJ
ejpam-524	589	12	the	the	DET
ejpam-524	589	13	m	m	PROPN
ejpam-524	589	14	-	-	PROPN
ejpam-524	589	15	dnp	dnp	PROPN
ejpam-524	589	16	matrix	matrix	NOUN
ejpam-524	589	17	dm	dm	X
ejpam-524	589	18	g	g	PROPN
ejpam-524	589	19	is	be	AUX
ejpam-524	589	20	such	such	ADJ
ejpam-524	589	21	that	that	SCONJ
ejpam-524	589	22	the	the	DET
ejpam-524	589	23	rows	row	NOUN
ejpam-524	589	24	of	of	ADP
ejpam-524	589	25	dm	dm	PROPN
ejpam-524	589	26	g	g	PROPN
ejpam-524	589	27	are	be	AUX
ejpam-524	589	28	the	the	DET
ejpam-524	589	29	elements	element	NOUN
ejpam-524	589	30	of	of	ADP
ejpam-524	589	31	a	a	DET
ejpam-524	589	32	basis	basis	NOUN
ejpam-524	589	33	of	of	ADP
ejpam-524	589	34	the	the	DET
ejpam-524	589	35	euclidean	euclidean	ADJ
ejpam-524	589	36	space	space	NOUN
ejpam-524	589	37	rn	rn	PROPN
ejpam-524	589	38	.	.	PROPN
ejpam-524	590	1	then	then	ADV
ejpam-524	590	2	g	g	PROPN
ejpam-524	590	3	≅	≅	PROPN
ejpam-524	590	4	pn	pn	PROPN
ejpam-524	590	5	,	,	PUNCT
ejpam-524	590	6	a	a	DET
ejpam-524	590	7	path	path	NOUN
ejpam-524	590	8	on	on	ADP
ejpam-524	590	9	n	n	DET
ejpam-524	590	10	vertices	vertex	NOUN
ejpam-524	590	11	.	.	PUNCT
ejpam-524	591	1	proof	proof	NOUN
ejpam-524	591	2	.	.	PUNCT
ejpam-524	592	1	since	since	SCONJ
ejpam-524	592	2	the	the	DET
ejpam-524	592	3	rows	row	NOUN
ejpam-524	592	4	of	of	ADP
ejpam-524	592	5	dm	dm	PROPN
ejpam-524	592	6	g	g	PROPN
ejpam-524	592	7	are	be	AUX
ejpam-524	592	8	the	the	DET
ejpam-524	592	9	elements	element	NOUN
ejpam-524	592	10	of	of	ADP
ejpam-524	592	11	a	a	DET
ejpam-524	592	12	basis	basis	NOUN
ejpam-524	592	13	of	of	ADP
ejpam-524	592	14	rn	rn	PROPN
ejpam-524	592	15	,	,	PUNCT
ejpam-524	592	16	dm	dm	PROPN
ejpam-524	592	17	g	g	PROPN
ejpam-524	592	18	is	be	AUX
ejpam-524	592	19	a	a	DET
ejpam-524	592	20	square	square	ADJ
ejpam-524	592	21	matrix	matrix	NOUN
ejpam-524	592	22	of	of	ADP
ejpam-524	592	23	order	order	NOUN
ejpam-524	592	24	n.	n.	PROPN
ejpam-524	592	25	therefore	therefore	ADV
ejpam-524	592	26	,	,	PUNCT
ejpam-524	592	27	g	g	PROPN
ejpam-524	592	28	≅	≅	PROPN
ejpam-524	592	29	pn	pn	PROPN
ejpam-524	592	30	,	,	PUNCT
ejpam-524	592	31	a	a	DET
ejpam-524	592	32	path	path	NOUN
ejpam-524	592	33	on	on	ADP
ejpam-524	592	34	n	n	DET
ejpam-524	592	35	vertices	vertex	NOUN
ejpam-524	592	36	.	.	PUNCT
ejpam-524	593	1	remark	remark	NOUN
ejpam-524	593	2	3	3	NUM
ejpam-524	593	3	.	.	PUNCT
ejpam-524	594	1	in	in	ADP
ejpam-524	594	2	proposition	proposition	NOUN
ejpam-524	594	3	3	3	NUM
ejpam-524	594	4	,	,	PUNCT
ejpam-524	594	5	we	we	PRON
ejpam-524	594	6	proved	prove	VERB
ejpam-524	594	7	that	that	SCONJ
ejpam-524	594	8	if	if	SCONJ
ejpam-524	594	9	the	the	DET
ejpam-524	594	10	rows	row	NOUN
ejpam-524	594	11	of	of	ADP
ejpam-524	594	12	d∗mg	d∗mg	NOUN
ejpam-524	594	13	are	be	AUX
ejpam-524	594	14	the	the	DET
ejpam-524	594	15	elements	element	NOUN
ejpam-524	594	16	of	of	ADP
ejpam-524	594	17	the	the	DET
ejpam-524	594	18	standard	standard	ADJ
ejpam-524	594	19	basis	basis	NOUN
ejpam-524	594	20	of	of	ADP
ejpam-524	594	21	the	the	DET
ejpam-524	594	22	euclidean	euclidean	ADJ
ejpam-524	594	23	space	space	PROPN
ejpam-524	594	24	rn	rn	PROPN
ejpam-524	594	25	,	,	PUNCT
ejpam-524	594	26	then	then	ADV
ejpam-524	594	27	g	g	PROPN
ejpam-524	594	28	is	be	AUX
ejpam-524	594	29	a	a	DET
ejpam-524	594	30	path	path	NOUN
ejpam-524	594	31	pn	pn	NOUN
ejpam-524	594	32	on	on	ADP
ejpam-524	594	33	n	n	PRON
ejpam-524	594	34	vertices	vertex	NOUN
ejpam-524	594	35	with	with	ADP
ejpam-524	594	36	the	the	DET
ejpam-524	594	37	dpd	dpd	NOUN
ejpam-524	594	38	-	-	PUNCT
ejpam-524	594	39	set	set	VERB
ejpam-524	594	40	m	m	NOUN
ejpam-524	594	41	as	as	ADP
ejpam-524	594	42	one	one	NUM
ejpam-524	594	43	of	of	ADP
ejpam-524	594	44	its	its	PRON
ejpam-524	594	45	pendent	pendent	ADJ
ejpam-524	594	46	vertices	vertex	NOUN
ejpam-524	594	47	.	.	PUNCT
ejpam-524	595	1	remark	remark	NOUN
ejpam-524	595	2	4	4	NUM
ejpam-524	595	3	.	.	PUNCT
ejpam-524	596	1	the	the	DET
ejpam-524	596	2	converse	converse	NOUN
ejpam-524	596	3	of	of	ADP
ejpam-524	596	4	theorem	theorem	ADJ
ejpam-524	596	5	22	22	NUM
ejpam-524	596	6	and	and	CCONJ
ejpam-524	596	7	corollary	corollary	ADJ
ejpam-524	596	8	7	7	NUM
ejpam-524	596	9	need	need	NOUN
ejpam-524	596	10	not	not	PART
ejpam-524	596	11	be	be	AUX
ejpam-524	596	12	true	true	ADJ
ejpam-524	596	13	.	.	PUNCT
ejpam-524	597	1	consider	consider	VERB
ejpam-524	597	2	the	the	DET
ejpam-524	597	3	path	path	NOUN
ejpam-524	597	4	p7	p7	NOUN
ejpam-524	597	5	=	=	PUNCT
ejpam-524	597	6	v1v2v3	v1v2v3	NOUN
ejpam-524	597	7	.	.	PUNCT
ejpam-524	597	8	.	.	PUNCT
ejpam-524	597	9	.	.	PUNCT
ejpam-524	598	1	v7	v7	VERB
ejpam-524	598	2	.	.	PUNCT
ejpam-524	599	1	let	let	VERB
ejpam-524	599	2	m	m	VERB
ejpam-524	599	3	=	=	PUNCT
ejpam-524	599	4	{	{	PUNCT
ejpam-524	599	5	v1	v1	PROPN
ejpam-524	599	6	,	,	PUNCT
ejpam-524	599	7	v2	v2	PROPN
ejpam-524	599	8	,	,	PUNCT
ejpam-524	599	9	v3	v3	PROPN
ejpam-524	599	10	,	,	PUNCT
ejpam-524	599	11	v4	v4	PROPN
ejpam-524	599	12	,	,	PUNCT
ejpam-524	599	13	v5	v5	NOUN
ejpam-524	599	14	,	,	PUNCT
ejpam-524	599	15	v7	v7	NOUN
ejpam-524	599	16	}	}	PUNCT
ejpam-524	599	17	.	.	PUNCT
ejpam-524	600	1	then	then	ADV
ejpam-524	600	2	,	,	PUNCT
ejpam-524	600	3	m	m	PROPN
ejpam-524	600	4	is	be	AUX
ejpam-524	600	5	a	a	DET
ejpam-524	600	6	dpd	dpd	NOUN
ejpam-524	600	7	-	-	PUNCT
ejpam-524	600	8	set	set	NOUN
ejpam-524	600	9	.	.	PUNCT
ejpam-524	601	1	now	now	ADV
ejpam-524	601	2	dm	dm	X
ejpam-524	601	3	g	g	PROPN
ejpam-524	601	4	is	be	AUX
ejpam-524	601	5	a	a	DET
ejpam-524	601	6	square	square	ADJ
ejpam-524	601	7	matrix	matrix	NOUN
ejpam-524	601	8	,	,	PUNCT
ejpam-524	601	9	but	but	CCONJ
ejpam-524	601	10	the	the	DET
ejpam-524	601	11	rows	row	NOUN
ejpam-524	601	12	of	of	ADP
ejpam-524	601	13	dm	dm	PROPN
ejpam-524	601	14	g	g	NOUN
ejpam-524	601	15	are	be	AUX
ejpam-524	601	16	not	not	PART
ejpam-524	601	17	linearly	linearly	ADV
ejpam-524	601	18	independent	independent	ADJ
ejpam-524	601	19	.	.	PUNCT
ejpam-524	602	1	therefore	therefore	ADV
ejpam-524	602	2	,	,	PUNCT
ejpam-524	602	3	the	the	DET
ejpam-524	602	4	rows	row	NOUN
ejpam-524	602	5	can	can	AUX
ejpam-524	602	6	not	not	PART
ejpam-524	602	7	form	form	VERB
ejpam-524	602	8	the	the	DET
ejpam-524	602	9	basis	basis	NOUN
ejpam-524	602	10	elements	element	NOUN
ejpam-524	602	11	of	of	ADP
ejpam-524	602	12	r7	r7	NOUN
ejpam-524	602	13	.	.	PUNCT
ejpam-524	603	1	also	also	ADV
ejpam-524	603	2	note	note	VERB
ejpam-524	603	3	that	that	SCONJ
ejpam-524	603	4	dm	dm	PROPN
ejpam-524	603	5	g	g	PROPN
ejpam-524	603	6	is	be	AUX
ejpam-524	603	7	not	not	PART
ejpam-524	603	8	invertible	invertible	ADJ
ejpam-524	603	9	.	.	PUNCT
ejpam-524	604	1	remark	remark	NOUN
ejpam-524	604	2	5	5	NUM
ejpam-524	604	3	.	.	PUNCT
ejpam-524	605	1	all	all	DET
ejpam-524	605	2	invertible	invertible	ADJ
ejpam-524	605	3	matrices	matrix	NOUN
ejpam-524	605	4	need	need	AUX
ejpam-524	605	5	not	not	PART
ejpam-524	605	6	be	be	AUX
ejpam-524	605	7	a	a	DET
ejpam-524	605	8	m	m	PROPN
ejpam-524	605	9	-	-	PUNCT
ejpam-524	605	10	dnp	dnp	PROPN
ejpam-524	605	11	matrix	matrix	NOUN
ejpam-524	605	12	dm	dm	X
ejpam-524	605	13	g	g	NOUN
ejpam-524	605	14	of	of	ADP
ejpam-524	605	15	a	a	DET
ejpam-524	605	16	graph	graph	NOUN
ejpam-524	605	17	g.	g.	NOUN
ejpam-524	606	1	for	for	ADP
ejpam-524	606	2	example	example	NOUN
ejpam-524	606	3	a=	a=	PROPN
ejpam-524	606	4			NOUN
ejpam-524	606	5			NOUN
ejpam-524	606	6			NOUN
ejpam-524	606	7	1	1	NUM
ejpam-524	606	8	2	2	NUM
ejpam-524	606	9	3	3	NUM
ejpam-524	606	10	3	3	NUM
ejpam-524	606	11	2	2	NUM
ejpam-524	606	12	1	1	NUM
ejpam-524	606	13	0	0	NUM
ejpam-524	606	14	0	0	NUM
ejpam-524	606	15	1	1	NUM
ejpam-524	606	16			NOUN
ejpam-524	606	17			NOUN
ejpam-524	606	18			X
ejpam-524	606	19	is	be	AUX
ejpam-524	606	20	invertible	invertible	ADJ
ejpam-524	606	21	but	but	CCONJ
ejpam-524	606	22	not	not	PART
ejpam-524	606	23	a	a	DET
ejpam-524	606	24	m	m	NOUN
ejpam-524	606	25	-	-	PROPN
ejpam-524	606	26	dnp	dnp	PROPN
ejpam-524	606	27	,	,	PUNCT
ejpam-524	606	28	since	since	SCONJ
ejpam-524	606	29	the	the	DET
ejpam-524	606	30	row	row	NOUN
ejpam-524	606	31	sums	sum	NOUN
ejpam-524	606	32	are	be	AUX
ejpam-524	606	33	not	not	PART
ejpam-524	606	34	equal	equal	ADJ
ejpam-524	606	35	.	.	PUNCT
ejpam-524	607	1	from	from	ADP
ejpam-524	607	2	above	above	ADP
ejpam-524	607	3	discussion	discussion	NOUN
ejpam-524	607	4	,	,	PUNCT
ejpam-524	607	5	it	it	PRON
ejpam-524	607	6	is	be	AUX
ejpam-524	607	7	interesting	interesting	ADJ
ejpam-524	607	8	to	to	PART
ejpam-524	607	9	investigate	investigate	VERB
ejpam-524	607	10	those	those	DET
ejpam-524	607	11	m−dnp	m−dnp	ADJ
ejpam-524	607	12	matrices	matrix	NOUN
ejpam-524	608	1	dm	dm	PRON
ejpam-524	608	2	g	g	NOUN
ejpam-524	608	3	that	that	PRON
ejpam-524	608	4	are	be	AUX
ejpam-524	608	5	invertible	invertible	ADJ
ejpam-524	608	6	.	.	PUNCT
ejpam-524	609	1	also	also	ADV
ejpam-524	609	2	,	,	PUNCT
ejpam-524	609	3	distinguishing	distinguish	VERB
ejpam-524	609	4	those	those	DET
ejpam-524	609	5	invertible	invertible	ADJ
ejpam-524	609	6	matrices	matrix	NOUN
ejpam-524	609	7	which	which	PRON
ejpam-524	609	8	are	be	AUX
ejpam-524	609	9	m	m	PROPN
ejpam-524	609	10	-dnp	-dnp	NOUN
ejpam-524	609	11	matrix	matrix	NOUN
ejpam-524	609	12	of	of	ADP
ejpam-524	609	13	a	a	DET
ejpam-524	609	14	graph	graph	NOUN
ejpam-524	609	15	is	be	AUX
ejpam-524	609	16	an	an	DET
ejpam-524	609	17	open	open	ADJ
ejpam-524	609	18	problem	problem	NOUN
ejpam-524	609	19	.	.	PUNCT
ejpam-524	610	1	problem	problem	NOUN
ejpam-524	610	2	23	23	NUM
ejpam-524	610	3	.	.	PUNCT
ejpam-524	611	1	characterize	characterize	VERB
ejpam-524	611	2	those	those	DET
ejpam-524	611	3	invertible	invertible	ADJ
ejpam-524	611	4	matrices	matrix	NOUN
ejpam-524	611	5	,	,	PUNCT
ejpam-524	611	6	which	which	PRON
ejpam-524	611	7	are	be	AUX
ejpam-524	611	8	the	the	DET
ejpam-524	611	9	m	m	PROPN
ejpam-524	611	10	-	-	PUNCT
ejpam-524	611	11	dnp	dnp	PROPN
ejpam-524	611	12	of	of	ADP
ejpam-524	611	13	some	some	DET
ejpam-524	611	14	graph	graph	NOUN
ejpam-524	611	15	g.	g.	NOUN
ejpam-524	611	16	5	5	NUM
ejpam-524	611	17	.	.	PUNCT
ejpam-524	611	18	conclusion	conclusion	NOUN
ejpam-524	611	19	and	and	CCONJ
ejpam-524	611	20	scope	scope	NOUN
ejpam-524	611	21	as	as	ADV
ejpam-524	611	22	well	well	ADV
ejpam-524	611	23	known	know	VERB
ejpam-524	611	24	,	,	PUNCT
ejpam-524	611	25	apart	apart	ADV
ejpam-524	611	26	from	from	ADP
ejpam-524	611	27	theoretical	theoretical	ADJ
ejpam-524	611	28	interest	interest	NOUN
ejpam-524	611	29	in	in	ADP
ejpam-524	611	30	the	the	DET
ejpam-524	611	31	study	study	NOUN
ejpam-524	611	32	of	of	ADP
ejpam-524	611	33	the	the	DET
ejpam-524	611	34	distance	distance	NOUN
ejpam-524	611	35	matrix	matrix	NOUN
ejpam-524	611	36	,	,	PUNCT
ejpam-524	611	37	such	such	ADJ
ejpam-524	611	38	as	as	ADP
ejpam-524	611	39	the	the	DET
ejpam-524	611	40	realization	realization	NOUN
ejpam-524	611	41	of	of	ADP
ejpam-524	611	42	a	a	DET
ejpam-524	611	43	given	give	VERB
ejpam-524	611	44	matrix	matrix	NOUN
ejpam-524	611	45	as	as	ADP
ejpam-524	611	46	the	the	DET
ejpam-524	611	47	distance	distance	NOUN
ejpam-524	611	48	matrix	matrix	NOUN
ejpam-524	611	49	of	of	ADP
ejpam-524	611	50	a	a	DET
ejpam-524	611	51	graph	graph	NOUN
ejpam-524	611	52	[	[	X
ejpam-524	611	53	12	12	NUM
ejpam-524	611	54	]	]	PUNCT
ejpam-524	611	55	,	,	PUNCT
ejpam-524	611	56	it	it	PRON
ejpam-524	611	57	has	have	AUX
ejpam-524	611	58	found	find	VERB
ejpam-524	611	59	applications	application	NOUN
ejpam-524	611	60	in	in	ADP
ejpam-524	611	61	many	many	ADJ
ejpam-524	611	62	practically	practically	ADV
ejpam-524	611	63	interesting	interesting	ADJ
ejpam-524	611	64	areas	area	NOUN
ejpam-524	611	65	such	such	ADJ
ejpam-524	611	66	as	as	ADP
ejpam-524	611	67	quantitative	quantitative	ADJ
ejpam-524	611	68	structure	structure	NOUN
ejpam-524	611	69	-	-	PUNCT
ejpam-524	611	70	activity	activity	NOUN
ejpam-524	611	71	relation	relation	NOUN
ejpam-524	611	72	(	(	PUNCT
ejpam-524	611	73	qsar	qsar	NOUN
ejpam-524	611	74	)	)	PUNCT
ejpam-524	611	75	in	in	ADP
ejpam-524	611	76	discrete	discrete	ADJ
ejpam-524	611	77	mathematical	mathematical	ADJ
ejpam-524	611	78	chemistry	chemistry	NOUN
ejpam-524	612	1	[	[	X
ejpam-524	612	2	3	3	NUM
ejpam-524	612	3	]	]	PUNCT
ejpam-524	612	4	and	and	CCONJ
ejpam-524	612	5	studies	study	NOUN
ejpam-524	612	6	on	on	ADP
ejpam-524	612	7	the	the	DET
ejpam-524	612	8	effect	effect	NOUN
ejpam-524	612	9	of	of	ADP
ejpam-524	612	10	indirect	indirect	ADJ
ejpam-524	612	11	qualitative	qualitative	ADJ
ejpam-524	612	12	relationships	relationship	NOUN
ejpam-524	612	13	between	between	ADP
ejpam-524	612	14	individuals	individual	NOUN
ejpam-524	612	15	in	in	ADP
ejpam-524	612	16	a	a	DET
ejpam-524	612	17	social	social	ADJ
ejpam-524	612	18	network	network	NOUN
ejpam-524	612	19	[	[	X
ejpam-524	612	20	7	7	NUM
ejpam-524	612	21	,	,	PUNCT
ejpam-524	612	22	11	11	NUM
ejpam-524	612	23	]	]	PUNCT
ejpam-524	612	24	.	.	PUNCT
ejpam-524	613	1	also	also	ADV
ejpam-524	613	2	,	,	PUNCT
ejpam-524	613	3	the	the	DET
ejpam-524	613	4	m	m	NOUN
ejpam-524	613	5	-	-	PUNCT
ejpam-524	613	6	weiner	weiner	NOUN
ejpam-524	613	7	index	index	NOUN
ejpam-524	613	8	wm	wm	PROPN
ejpam-524	613	9	(	(	PUNCT
ejpam-524	613	10	g	g	NOUN
ejpam-524	613	11	)	)	PUNCT
ejpam-524	613	12	may	may	AUX
ejpam-524	613	13	be	be	AUX
ejpam-524	613	14	defined	define	VERB
ejpam-524	613	15	as	as	ADP
ejpam-524	613	16	the	the	DET
ejpam-524	613	17	sum	sum	NOUN
ejpam-524	613	18	of	of	ADP
ejpam-524	613	19	the	the	DET
ejpam-524	613	20	entries	entry	NOUN
ejpam-524	613	21	in	in	ADP
ejpam-524	613	22	the	the	DET
ejpam-524	613	23	upper	upper	ADJ
ejpam-524	613	24	triangular	triangular	NOUN
ejpam-524	613	25	half	half	NOUN
ejpam-524	613	26	of	of	ADP
ejpam-524	613	27	the	the	DET
ejpam-524	613	28	m	m	NOUN
ejpam-524	613	29	-distance	-distance	NOUN
ejpam-524	613	30	matrix	matrix	NOUN
ejpam-524	613	31	dm	dm	X
ejpam-524	613	32	g	g	NOUN
ejpam-524	613	33	;	;	PUNCT
ejpam-524	613	34	by	by	ADP
ejpam-524	613	35	a	a	DET
ejpam-524	613	36	partial	partial	ADJ
ejpam-524	613	37	weiner	weiner	NOUN
ejpam-524	613	38	index	index	NOUN
ejpam-524	613	39	w	w	PROPN
ejpam-524	613	40	′(g	′(g	PROPN
ejpam-524	613	41	)	)	PUNCT
ejpam-524	613	42	,	,	PUNCT
ejpam-524	613	43	we	we	PRON
ejpam-524	613	44	mean	mean	VERB
ejpam-524	613	45	the	the	DET
ejpam-524	613	46	m	m	PROPN
ejpam-524	613	47	-weiner	-weiner	PROPN
ejpam-524	613	48	index	index	NOUN
ejpam-524	613	49	of	of	ADP
ejpam-524	613	50	g	g	NOUN
ejpam-524	613	51	for	for	ADP
ejpam-524	613	52	some	some	DET
ejpam-524	613	53	nonempty	nonempty	ADJ
ejpam-524	613	54	proper	proper	ADJ
ejpam-524	613	55	subset	subset	NOUN
ejpam-524	613	56	m	m	NOUN
ejpam-524	613	57	of	of	ADP
ejpam-524	613	58	v	v	NOUN
ejpam-524	613	59	(	(	PUNCT
ejpam-524	613	60	g	g	NOUN
ejpam-524	613	61	)	)	PUNCT
ejpam-524	613	62	and	and	CCONJ
ejpam-524	613	63	the	the	DET
ejpam-524	613	64	well	well	ADV
ejpam-524	613	65	known	know	VERB
ejpam-524	613	66	weiner	weiner	NOUN
ejpam-524	613	67	index	index	NOUN
ejpam-524	613	68	w	w	PROPN
ejpam-524	613	69	(	(	PUNCT
ejpam-524	613	70	g	g	NOUN
ejpam-524	613	71	)	)	PUNCT
ejpam-524	614	1	[	[	X
ejpam-524	614	2	11	11	NUM
ejpam-524	614	3	]	]	PUNCT
ejpam-524	614	4	is	be	AUX
ejpam-524	614	5	then	then	ADV
ejpam-524	614	6	seen	see	VERB
ejpam-524	614	7	as	as	ADP
ejpam-524	614	8	the	the	DET
ejpam-524	614	9	m	m	PROPN
ejpam-524	614	10	-weiner	-weiner	PROPN
ejpam-524	614	11	index	index	NOUN
ejpam-524	614	12	with	with	ADP
ejpam-524	614	13	m	m	PROPN
ejpam-524	614	14	=	=	SYM
ejpam-524	614	15	v	v	ADJ
ejpam-524	614	16	(	(	PUNCT
ejpam-524	614	17	g	g	NOUN
ejpam-524	614	18	)	)	PUNCT
ejpam-524	614	19	.	.	PUNCT
ejpam-524	615	1	an	an	DET
ejpam-524	615	2	interesting	interesting	ADJ
ejpam-524	615	3	question	question	NOUN
ejpam-524	615	4	for	for	ADP
ejpam-524	615	5	chemists	chemist	NOUN
ejpam-524	615	6	would	would	AUX
ejpam-524	615	7	be	be	AUX
ejpam-524	615	8	the	the	DET
ejpam-524	615	9	following	following	NOUN
ejpam-524	615	10	.	.	PUNCT
ejpam-524	616	1	references	reference	NOUN
ejpam-524	616	2	763	763	NUM
ejpam-524	616	3	problem	problem	NOUN
ejpam-524	616	4	24	24	NUM
ejpam-524	616	5	.	.	PUNCT
ejpam-524	616	6	consider	consider	VERB
ejpam-524	616	7	any	any	DET
ejpam-524	616	8	structure	structure	NOUN
ejpam-524	616	9	-	-	PUNCT
ejpam-524	616	10	activity	activity	NOUN
ejpam-524	616	11	relationship	relationship	NOUN
ejpam-524	616	12	r	r	NOUN
ejpam-524	616	13	of	of	ADP
ejpam-524	616	14	a	a	DET
ejpam-524	616	15	molecular	molecular	ADJ
ejpam-524	616	16	graph	graph	NOUN
ejpam-524	616	17	that	that	PRON
ejpam-524	616	18	has	have	AUX
ejpam-524	616	19	been	be	AUX
ejpam-524	616	20	identified	identify	VERB
ejpam-524	616	21	to	to	PART
ejpam-524	616	22	be	be	AUX
ejpam-524	616	23	well	well	ADV
ejpam-524	616	24	correlated	correlate	VERB
ejpam-524	616	25	with	with	ADP
ejpam-524	616	26	the	the	DET
ejpam-524	616	27	weiner	weiner	NOUN
ejpam-524	616	28	index	index	NOUN
ejpam-524	616	29	.	.	PUNCT
ejpam-524	617	1	is	be	AUX
ejpam-524	617	2	it	it	PRON
ejpam-524	617	3	possible	possible	ADJ
ejpam-524	617	4	to	to	PART
ejpam-524	617	5	achieve	achieve	VERB
ejpam-524	617	6	such	such	DET
ejpam-524	617	7	a	a	DET
ejpam-524	617	8	correlation	correlation	NOUN
ejpam-524	617	9	using	use	VERB
ejpam-524	617	10	m	m	NOUN
ejpam-524	617	11	-	-	PUNCT
ejpam-524	617	12	weiner	weiner	NOUN
ejpam-524	617	13	index	index	NOUN
ejpam-524	617	14	for	for	ADP
ejpam-524	617	15	as	as	ADP
ejpam-524	617	16	low	low	ADJ
ejpam-524	617	17	cardinality	cardinality	NOUN
ejpam-524	617	18	(	(	PUNCT
ejpam-524	617	19	dpd-)sets	dpd-)set	NOUN
ejpam-524	617	20	m	m	NOUN
ejpam-524	617	21	as	as	ADP
ejpam-524	617	22	possible	possible	ADJ
ejpam-524	617	23	?	?	PUNCT
ejpam-524	618	1	[	[	X
ejpam-524	618	2	choice	choice	NOUN
ejpam-524	618	3	of	of	ADP
ejpam-524	618	4	marker	marker	NOUN
ejpam-524	618	5	sets	set	NOUN
ejpam-524	618	6	m	m	VERB
ejpam-524	618	7	in	in	ADP
ejpam-524	618	8	the	the	DET
ejpam-524	618	9	molecular	molecular	ADJ
ejpam-524	618	10	graph	graph	NOUN
ejpam-524	618	11	might	might	AUX
ejpam-524	618	12	be	be	AUX
ejpam-524	618	13	very	very	ADV
ejpam-524	618	14	crucial	crucial	ADJ
ejpam-524	618	15	and	and	CCONJ
ejpam-524	618	16	hence	hence	ADV
ejpam-524	618	17	might	might	AUX
ejpam-524	618	18	involve	involve	VERB
ejpam-524	618	19	deeper	deep	ADJ
ejpam-524	618	20	insights	insight	NOUN
ejpam-524	618	21	into	into	ADP
ejpam-524	618	22	the	the	DET
ejpam-524	618	23	molecular	molecular	ADJ
ejpam-524	618	24	characteristics	characteristic	NOUN
ejpam-524	618	25	.	.	PUNCT
ejpam-524	618	26	]	]	PUNCT
ejpam-524	619	1	acknowledgements	acknowledgement	NOUN
ejpam-524	619	2	authors	author	NOUN
ejpam-524	619	3	deeply	deeply	ADV
ejpam-524	619	4	indebted	indebted	ADJ
ejpam-524	619	5	to	to	ADP
ejpam-524	619	6	b.d	b.d	PROPN
ejpam-524	619	7	.	.	PROPN
ejpam-524	619	8	acharya	acharya	PROPN
ejpam-524	619	9	for	for	ADP
ejpam-524	619	10	suggesting	suggest	VERB
ejpam-524	619	11	the	the	DET
ejpam-524	619	12	concept	concept	NOUN
ejpam-524	619	13	of	of	ADP
ejpam-524	619	14	dnp	dnp	PROPN
ejpam-524	619	15	-	-	PUNCT
ejpam-524	619	16	matrices	matrix	NOUN
ejpam-524	619	17	of	of	ADP
ejpam-524	619	18	a	a	DET
ejpam-524	619	19	dpd	dpd	NOUN
ejpam-524	619	20	-	-	PUNCT
ejpam-524	619	21	graph	graph	NOUN
ejpam-524	619	22	and	and	CCONJ
ejpam-524	619	23	sparing	spare	VERB
ejpam-524	619	24	his	his	PRON
ejpam-524	619	25	valuable	valuable	ADJ
ejpam-524	619	26	time	time	NOUN
ejpam-524	619	27	in	in	ADP
ejpam-524	619	28	sharing	share	VERB
ejpam-524	619	29	his	his	PRON
ejpam-524	619	30	many	many	ADJ
ejpam-524	619	31	incisive	incisive	ADJ
ejpam-524	619	32	thoughts	thought	NOUN
ejpam-524	619	33	to	to	PART
ejpam-524	619	34	propel	propel	VERB
ejpam-524	619	35	our	our	PRON
ejpam-524	619	36	vigorous	vigorous	ADJ
ejpam-524	619	37	discussion	discussion	NOUN
ejpam-524	619	38	on	on	ADP
ejpam-524	619	39	the	the	DET
ejpam-524	619	40	content	content	NOUN
ejpam-524	619	41	of	of	ADP
ejpam-524	619	42	this	this	DET
ejpam-524	619	43	paper	paper	NOUN
ejpam-524	619	44	.	.	PUNCT
ejpam-524	620	1	the	the	DET
ejpam-524	620	2	work	work	NOUN
ejpam-524	620	3	reported	report	VERB
ejpam-524	620	4	in	in	ADP
ejpam-524	620	5	this	this	DET
ejpam-524	620	6	note	note	NOUN
ejpam-524	620	7	is	be	AUX
ejpam-524	620	8	a	a	DET
ejpam-524	620	9	part	part	NOUN
ejpam-524	620	10	of	of	ADP
ejpam-524	620	11	the	the	DET
ejpam-524	620	12	research	research	NOUN
ejpam-524	620	13	work	work	NOUN
ejpam-524	620	14	done	do	VERB
ejpam-524	620	15	under	under	ADP
ejpam-524	620	16	the	the	DET
ejpam-524	620	17	project	project	NOUN
ejpam-524	620	18	no.sr/s4/ms:287/05	no.sr/s4/ms:287/05	NUM
ejpam-524	620	19	funded	fund	VERB
ejpam-524	620	20	by	by	ADP
ejpam-524	620	21	the	the	DET
ejpam-524	620	22	department	department	PROPN
ejpam-524	620	23	of	of	ADP
ejpam-524	620	24	science	science	PROPN
ejpam-524	620	25	&	&	CCONJ
ejpam-524	620	26	technology	technology	PROPN
ejpam-524	620	27	(	(	PUNCT
ejpam-524	620	28	dst	dst	PROPN
ejpam-524	620	29	)	)	PUNCT
ejpam-524	620	30	,	,	PUNCT
ejpam-524	620	31	govt	govt	PROPN
ejpam-524	620	32	.	.	PUNCT
ejpam-524	621	1	of	of	ADP
ejpam-524	621	2	india	india	PROPN
ejpam-524	621	3	,	,	PUNCT
ejpam-524	621	4	new	new	PROPN
ejpam-524	621	5	delhi	delhi	PROPN
ejpam-524	621	6	.	.	PUNCT
ejpam-524	622	1	the	the	DET
ejpam-524	622	2	first	first	ADJ
ejpam-524	622	3	author	author	NOUN
ejpam-524	622	4	is	be	AUX
ejpam-524	622	5	thankful	thankful	ADJ
ejpam-524	622	6	to	to	ADP
ejpam-524	622	7	the	the	DET
ejpam-524	622	8	department	department	PROPN
ejpam-524	622	9	of	of	ADP
ejpam-524	622	10	science	science	PROPN
ejpam-524	622	11	&	&	CCONJ
ejpam-524	622	12	technology	technology	NOUN
ejpam-524	622	13	,	,	PUNCT
ejpam-524	622	14	government	government	NOUN
ejpam-524	622	15	of	of	ADP
ejpam-524	622	16	india	india	PROPN
ejpam-524	622	17	for	for	ADP
ejpam-524	622	18	supporting	support	VERB
ejpam-524	622	19	this	this	DET
ejpam-524	622	20	research	research	NOUN
ejpam-524	622	21	under	under	ADP
ejpam-524	622	22	the	the	DET
ejpam-524	622	23	project	project	NOUN
ejpam-524	622	24	no	no	INTJ
ejpam-524	622	25	.	.	PUNCT
ejpam-524	623	1	sr	sr	PROPN
ejpam-524	623	2	/	/	SYM
ejpam-524	623	3	s4	s4	PROPN
ejpam-524	623	4	/	/	SYM
ejpam-524	623	5	ms:277/06	ms:277/06	PROPN
ejpam-524	623	6	,	,	PUNCT
ejpam-524	623	7	govt	govt	PROPN
ejpam-524	623	8	.	.	PUNCT
ejpam-524	624	1	of	of	ADP
ejpam-524	624	2	india	india	PROPN
ejpam-524	624	3	,	,	PUNCT
ejpam-524	624	4	new	new	PROPN
ejpam-524	624	5	delhi	delhi	PROPN
ejpam-524	624	6	.	.	PUNCT
ejpam-524	625	1	references	reference	NOUN
ejpam-524	625	2	[	[	X
ejpam-524	625	3	1	1	NUM
ejpam-524	625	4	]	]	X
ejpam-524	625	5	b.d	b.d	PROPN
ejpam-524	625	6	.	.	PROPN
ejpam-524	625	7	acharya	acharya	PROPN
ejpam-524	625	8	.	.	PUNCT
ejpam-524	626	1	contributions	contribution	NOUN
ejpam-524	626	2	to	to	ADP
ejpam-524	626	3	the	the	DET
ejpam-524	626	4	theories	theory	NOUN
ejpam-524	626	5	of	of	ADP
ejpam-524	626	6	graphs	graph	NOUN
ejpam-524	626	7	,	,	PUNCT
ejpam-524	626	8	graphoids	graphoid	NOUN
ejpam-524	626	9	and	and	CCONJ
ejpam-524	626	10	hypergraphs	hypergraph	NOUN
ejpam-524	626	11	.	.	PUNCT
ejpam-524	627	1	phd	phd	NOUN
ejpam-524	627	2	thesis	thesis	PROPN
ejpam-524	627	3	,	,	PUNCT
ejpam-524	627	4	the	the	DET
ejpam-524	627	5	indian	indian	PROPN
ejpam-524	627	6	institute	institute	PROPN
ejpam-524	627	7	of	of	ADP
ejpam-524	627	8	technology	technology	PROPN
ejpam-524	627	9	,	,	PUNCT
ejpam-524	627	10	bombay	bombay	PROPN
ejpam-524	627	11	,	,	PUNCT
ejpam-524	627	12	1975	1975	NUM
ejpam-524	627	13	.	.	PUNCT
ejpam-524	628	1	[	[	X
ejpam-524	628	2	2	2	NUM
ejpam-524	628	3	]	]	X
ejpam-524	628	4	b.d	b.d	PROPN
ejpam-524	628	5	.	.	PROPN
ejpam-524	628	6	acharya	acharya	PROPN
ejpam-524	628	7	.	.	PUNCT
ejpam-524	629	1	personal	personal	ADJ
ejpam-524	629	2	communication	communication	NOUN
ejpam-524	629	3	,	,	PUNCT
ejpam-524	629	4	november	november	PROPN
ejpam-524	629	5	,	,	PUNCT
ejpam-524	629	6	2006	2006	NUM
ejpam-524	629	7	.	.	PUNCT
ejpam-524	630	1	[	[	X
ejpam-524	630	2	3	3	X
ejpam-524	630	3	]	]	X
ejpam-524	630	4	s.c	s.c	PROPN
ejpam-524	630	5	.	.	PROPN
ejpam-524	630	6	basak	basak	PROPN
ejpam-524	630	7	,	,	PUNCT
ejpam-524	630	8	d.	d.	PROPN
ejpam-524	630	9	mills	mills	PROPN
ejpam-524	630	10	and	and	CCONJ
ejpam-524	630	11	b.d	b.d	PROPN
ejpam-524	630	12	.	.	PROPN
ejpam-524	630	13	gute	gute	PROPN
ejpam-524	630	14	.	.	PUNCT
ejpam-524	631	1	predicting	predict	VERB
ejpam-524	631	2	bioactivity	bioactivity	NOUN
ejpam-524	631	3	and	and	CCONJ
ejpam-524	631	4	toxicity	toxicity	NOUN
ejpam-524	631	5	of	of	ADP
ejpam-524	631	6	chemicals	chemical	NOUN
ejpam-524	631	7	from	from	ADP
ejpam-524	631	8	mathematical	mathematical	ADJ
ejpam-524	631	9	descriptors	descriptor	NOUN
ejpam-524	631	10	:	:	PUNCT
ejpam-524	631	11	a	a	DET
ejpam-524	631	12	chemical	chemical	ADJ
ejpam-524	631	13	-	-	PUNCT
ejpam-524	631	14	cum	cum	NOUN
ejpam-524	631	15	-	-	PUNCT
ejpam-524	631	16	biochemical	biochemical	ADJ
ejpam-524	631	17	approach	approach	NOUN
ejpam-524	631	18	.	.	PUNCT
ejpam-524	632	1	in	in	ADP
ejpam-524	632	2	d.j	d.j	PROPN
ejpam-524	632	3	.	.	PROPN
ejpam-524	632	4	klein	klein	PROPN
ejpam-524	632	5	and	and	CCONJ
ejpam-524	632	6	d.	d.	PROPN
ejpam-524	632	7	brandas	brandas	PROPN
ejpam-524	632	8	,	,	PUNCT
ejpam-524	632	9	editors	editor	NOUN
ejpam-524	632	10	,	,	PUNCT
ejpam-524	632	11	advances	advance	NOUN
ejpam-524	632	12	in	in	ADP
ejpam-524	632	13	quantum	quantum	ADJ
ejpam-524	632	14	chemistry	chemistry	NOUN
ejpam-524	632	15	:	:	PUNCT
ejpam-524	632	16	chemical	chemical	NOUN
ejpam-524	632	17	graph	graph	NOUN
ejpam-524	632	18	theory	theory	NOUN
ejpam-524	632	19	:	:	PUNCT
ejpam-524	632	20	wherefrom	wherefrom	NOUN
ejpam-524	632	21	,	,	PUNCT
ejpam-524	632	22	wherefor	wherefor	ADV
ejpam-524	632	23	and	and	CCONJ
ejpam-524	632	24	whereto	whereto	VERB
ejpam-524	632	25	?	?	PUNCT
ejpam-524	632	26	,	,	PUNCT
ejpam-524	632	27	elsevier	elsevier	NOUN
ejpam-524	632	28	-	-	PUNCT
ejpam-524	632	29	academic	academic	ADJ
ejpam-524	632	30	press	press	NOUN
ejpam-524	632	31	,	,	PUNCT
ejpam-524	632	32	1	1	NUM
ejpam-524	632	33	-	-	SYM
ejpam-524	632	34	91	91	NUM
ejpam-524	632	35	,	,	PUNCT
ejpam-524	632	36	2007	2007	NUM
ejpam-524	632	37	.	.	PUNCT
ejpam-524	633	1	[	[	X
ejpam-524	633	2	4	4	NUM
ejpam-524	633	3	]	]	X
ejpam-524	633	4	f.	f.	PROPN
ejpam-524	633	5	buckley	buckley	PROPN
ejpam-524	633	6	and	and	CCONJ
ejpam-524	633	7	f.	f.	PROPN
ejpam-524	633	8	harary	harary	PROPN
ejpam-524	633	9	.	.	PUNCT
ejpam-524	634	1	distance	distance	NOUN
ejpam-524	634	2	in	in	ADP
ejpam-524	634	3	graphs	graph	NOUN
ejpam-524	634	4	.	.	PUNCT
ejpam-524	635	1	addison	addison	PROPN
ejpam-524	635	2	wesley	wesley	PROPN
ejpam-524	635	3	publishing	publishing	PROPN
ejpam-524	635	4	company	company	NOUN
ejpam-524	635	5	,	,	PUNCT
ejpam-524	635	6	advanced	advanced	ADJ
ejpam-524	635	7	book	book	NOUN
ejpam-524	635	8	programme	programme	NOUN
ejpam-524	635	9	,	,	PUNCT
ejpam-524	635	10	redwood	redwood	NOUN
ejpam-524	635	11	city	city	NOUN
ejpam-524	635	12	,	,	PUNCT
ejpam-524	635	13	ca	ca	NOUN
ejpam-524	635	14	,	,	PUNCT
ejpam-524	635	15	1990	1990	NUM
ejpam-524	635	16	.	.	PUNCT
ejpam-524	636	1	[	[	X
ejpam-524	636	2	5	5	X
ejpam-524	636	3	]	]	PUNCT
ejpam-524	636	4	f.	f.	PROPN
ejpam-524	636	5	harary	harary	PROPN
ejpam-524	636	6	and	and	CCONJ
ejpam-524	636	7	melter	melter	NOUN
ejpam-524	636	8	.	.	PUNCT
ejpam-524	637	1	on	on	ADP
ejpam-524	637	2	the	the	DET
ejpam-524	637	3	metric	metric	ADJ
ejpam-524	637	4	dimension	dimension	NOUN
ejpam-524	637	5	of	of	ADP
ejpam-524	637	6	a	a	DET
ejpam-524	637	7	graph	graph	NOUN
ejpam-524	637	8	,	,	PUNCT
ejpam-524	637	9	ars	ar	VERB
ejpam-524	637	10	combin	combin	NOUN
ejpam-524	637	11	.	.	PUNCT
ejpam-524	637	12	,	,	PUNCT
ejpam-524	637	13	2	2	NUM
ejpam-524	637	14	,	,	PUNCT
ejpam-524	637	15	191	191	NUM
ejpam-524	637	16	-	-	SYM
ejpam-524	637	17	195	195	NUM
ejpam-524	637	18	,	,	PUNCT
ejpam-524	637	19	1976	1976	NUM
ejpam-524	637	20	.	.	PUNCT
ejpam-524	638	1	[	[	X
ejpam-524	638	2	6	6	NUM
ejpam-524	638	3	]	]	PUNCT
ejpam-524	638	4	f.	f.	PROPN
ejpam-524	638	5	harary	harary	PROPN
ejpam-524	638	6	.	.	PUNCT
ejpam-524	639	1	graph	graph	NOUN
ejpam-524	639	2	theory	theory	NOUN
ejpam-524	639	3	,	,	PUNCT
ejpam-524	639	4	addison	addison	PROPN
ejpam-524	639	5	wesley	wesley	PROPN
ejpam-524	639	6	publ	publ	PROPN
ejpam-524	639	7	.	.	PUNCT
ejpam-524	640	1	comp	comp	PROPN
ejpam-524	640	2	.	.	PUNCT
ejpam-524	640	3	,	,	PUNCT
ejpam-524	640	4	reading	reading	NOUN
ejpam-524	640	5	,	,	PUNCT
ejpam-524	640	6	massachusetts	massachusetts	PROPN
ejpam-524	640	7	,	,	PUNCT
ejpam-524	640	8	1969	1969	NUM
ejpam-524	640	9	.	.	PUNCT
ejpam-524	641	1	[	[	X
ejpam-524	641	2	7	7	X
ejpam-524	641	3	]	]	X
ejpam-524	641	4	j.	j.	PROPN
ejpam-524	641	5	fiksel	fiksel	PROPN
ejpam-524	641	6	.	.	PUNCT
ejpam-524	642	1	dynamic	dynamic	ADJ
ejpam-524	642	2	evolution	evolution	NOUN
ejpam-524	642	3	of	of	ADP
ejpam-524	642	4	societal	societal	ADJ
ejpam-524	642	5	networks	network	NOUN
ejpam-524	642	6	,	,	PUNCT
ejpam-524	642	7	j.	j.	PROPN
ejpam-524	642	8	math	math	PROPN
ejpam-524	642	9	.	.	PUNCT
ejpam-524	643	1	sociology	sociology	NOUN
ejpam-524	643	2	,	,	PUNCT
ejpam-524	643	3	7	7	NUM
ejpam-524	643	4	,	,	PUNCT
ejpam-524	643	5	27	27	NUM
ejpam-524	643	6	-	-	SYM
ejpam-524	643	7	46	46	NUM
ejpam-524	643	8	,	,	PUNCT
ejpam-524	643	9	1980	1980	NUM
ejpam-524	643	10	.	.	PUNCT
ejpam-524	644	1	[	[	X
ejpam-524	644	2	8	8	NUM
ejpam-524	644	3	]	]	X
ejpam-524	644	4	h.j	h.j	PROPN
ejpam-524	644	5	.	.	PROPN
ejpam-524	644	6	ryser.(0,1)-matrices	ryser.(0,1)-matrice	NOUN
ejpam-524	644	7	,	,	PUNCT
ejpam-524	644	8	carus	carus	PROPN
ejpam-524	644	9	mathematical	mathematical	PROPN
ejpam-524	644	10	monographs	monographs	PROPN
ejpam-524	644	11	no.14	no.14	PROPN
ejpam-524	644	12	,	,	PUNCT
ejpam-524	644	13	new	new	PROPN
ejpam-524	644	14	york	york	PROPN
ejpam-524	644	15	,	,	PUNCT
ejpam-524	644	16	1968	1968	NUM
ejpam-524	644	17	.	.	PUNCT
ejpam-524	645	1	[	[	X
ejpam-524	645	2	9	9	NUM
ejpam-524	645	3	]	]	SYM
ejpam-524	645	4	k.a	k.a	PROPN
ejpam-524	645	5	.	.	PROPN
ejpam-524	645	6	germina	germina	PROPN
ejpam-524	645	7	,	,	PUNCT
ejpam-524	645	8	set	set	VERB
ejpam-524	645	9	valuations	valuation	NOUN
ejpam-524	645	10	of	of	ADP
ejpam-524	645	11	graphs	graph	NOUN
ejpam-524	645	12	and	and	CCONJ
ejpam-524	645	13	their	their	PRON
ejpam-524	645	14	applications	application	NOUN
ejpam-524	645	15	,	,	PUNCT
ejpam-524	645	16	technical	technical	ADJ
ejpam-524	645	17	report	report	NOUN
ejpam-524	645	18	,	,	PUNCT
ejpam-524	645	19	grantin	grantin	NOUN
ejpam-524	645	20	-	-	PUNCT
ejpam-524	645	21	aid	aid	NOUN
ejpam-524	645	22	project	project	NOUN
ejpam-524	645	23	no.sr/s4/277/06	no.sr/s4/277/06	NOUN
ejpam-524	645	24	,	,	PUNCT
ejpam-524	645	25	department	department	NOUN
ejpam-524	645	26	of	of	ADP
ejpam-524	645	27	science	science	PROPN
ejpam-524	645	28	&	&	CCONJ
ejpam-524	645	29	technology	technology	PROPN
ejpam-524	645	30	(	(	PUNCT
ejpam-524	645	31	dst),govt	dst),govt	PROPN
ejpam-524	645	32	.	.	PUNCT
ejpam-524	646	1	of	of	ADP
ejpam-524	646	2	india	india	PROPN
ejpam-524	646	3	,	,	PUNCT
ejpam-524	646	4	april	april	PROPN
ejpam-524	646	5	2009	2009	NUM
ejpam-524	646	6	.	.	PUNCT
ejpam-524	647	1	[	[	X
ejpam-524	647	2	10	10	NUM
ejpam-524	647	3	]	]	X
ejpam-524	647	4	d.h	d.h	PROPN
ejpam-524	647	5	.	.	PROPN
ejpam-524	647	6	rouvrey	rouvrey	PROPN
ejpam-524	647	7	.	.	PUNCT
ejpam-524	648	1	predicting	predict	VERB
ejpam-524	648	2	chemistry	chemistry	NOUN
ejpam-524	648	3	from	from	ADP
ejpam-524	648	4	topology	topology	NOUN
ejpam-524	648	5	.	.	PUNCT
ejpam-524	649	1	scientific	scientific	ADJ
ejpam-524	649	2	american	american	PROPN
ejpam-524	649	3	,	,	PUNCT
ejpam-524	649	4	254	254	NUM
ejpam-524	649	5	,	,	PUNCT
ejpam-524	649	6	9	9	NUM
ejpam-524	649	7	,	,	PUNCT
ejpam-524	649	8	40	40	NUM
ejpam-524	649	9	-	-	SYM
ejpam-524	649	10	47	47	NUM
ejpam-524	649	11	,	,	PUNCT
ejpam-524	649	12	1986	1986	NUM
ejpam-524	649	13	.	.	PUNCT
ejpam-524	650	1	[	[	X
ejpam-524	650	2	11	11	NUM
ejpam-524	650	3	]	]	X
ejpam-524	650	4	n.	n.	NOUN
ejpam-524	650	5	trinajstic	trinajstic	NOUN
ejpam-524	650	6	,	,	PUNCT
ejpam-524	650	7	chemical	chemical	NOUN
ejpam-524	650	8	graph	graph	NOUN
ejpam-524	650	9	theory	theory	NOUN
ejpam-524	650	10	,	,	PUNCT
ejpam-524	650	11	boca	boca	PROPN
ejpam-524	650	12	raton	raton	PROPN
ejpam-524	650	13	,	,	PUNCT
ejpam-524	650	14	1983	1983	NUM
ejpam-524	650	15	.	.	PUNCT
ejpam-524	651	1	references	reference	NOUN
ejpam-524	651	2	764	764	NUM
ejpam-524	652	1	[	[	X
ejpam-524	652	2	12	12	NUM
ejpam-524	652	3	]	]	X
ejpam-524	652	4	wai	wai	PROPN
ejpam-524	652	5	-	-	PUNCT
ejpam-524	652	6	kai	kai	PROPN
ejpam-524	652	7	chen	chen	PROPN
ejpam-524	652	8	.	.	PUNCT
ejpam-524	653	1	the	the	DET
ejpam-524	653	2	metric	metric	ADJ
ejpam-524	653	3	structure	structure	NOUN
ejpam-524	653	4	of	of	ADP
ejpam-524	653	5	graphs	graph	NOUN
ejpam-524	653	6	:	:	PUNCT
ejpam-524	653	7	theory	theory	NOUN
ejpam-524	653	8	and	and	CCONJ
ejpam-524	653	9	applications	application	NOUN
ejpam-524	653	10	.	.	PUNCT
ejpam-524	654	1	london	london	PROPN
ejpam-524	654	2	math	math	PROPN
ejpam-524	654	3	.	.	PUNCT
ejpam-524	655	1	soc	soc	PROPN
ejpam-524	655	2	.	.	PUNCT
ejpam-524	655	3	,	,	PUNCT
ejpam-524	655	4	123	123	NUM
ejpam-524	655	5	,	,	PUNCT
ejpam-524	655	6	197	197	NUM
ejpam-524	655	7	-	-	SYM
ejpam-524	655	8	221	221	NUM
ejpam-524	655	9	,	,	PUNCT
ejpam-524	655	10	1987	1987	NUM
ejpam-524	655	11	.	.	PUNCT