id	sid	tid	token	lemma	pos
iajs-2704	1	1	68	68	NUM
iajs-2704	1	2	some	some	DET
iajs-2704	1	3	topological	topological	ADJ
iajs-2704	1	4	and	and	CCONJ
iajs-2704	1	5	polynomial	polynomial	ADJ
iajs-2704	1	6	indices	index	NOUN
iajs-2704	1	7	(	(	PUNCT
iajs-2704	1	8	hosoya	hosoya	NOUN
iajs-2704	1	9	and	and	CCONJ
iajs-2704	1	10	schultz	schultz	PROPN
iajs-2704	1	11	)	)	PUNCT
iajs-2704	1	12	for	for	ADP
iajs-2704	1	13	the	the	DET
iajs-2704	1	14	intersection	intersection	NOUN
iajs-2704	1	15	graph	graph	NOUN
iajs-2704	1	16	of	of	ADP
iajs-2704	1	17	the	the	DET
iajs-2704	1	18	subgroup	subgroup	NOUN
iajs-2704	1	19	of	of	ADP
iajs-2704	1	20	𝒁𝒓𝒏	𝒁𝒓𝒏	PROPN
iajs-2704	1	21	alaa	alaa	PROPN
iajs-2704	1	22	j.nawaf	j.nawaf	PROPN
iajs-2704	1	23	akram	akram	PROPN
iajs-2704	1	24	s.mohammad	s.mohammad	NOUN
iajs-2704	1	25	alaagamilnawaf@gmail.com	alaagamilnawaf@gmail.com	PROPN
iajs-2704	2	1	akr-tel@tu.edu.iq	akr-tel@tu.edu.iq	PROPN
iajs-2704	2	2	department	department	PROPN
iajs-2704	2	3	of	of	ADP
iajs-2704	2	4	mathematics	mathematics	PROPN
iajs-2704	2	5	,	,	PUNCT
iajs-2704	2	6	college	college	NOUN
iajs-2704	2	7	of	of	ADP
iajs-2704	2	8	computer	computer	NOUN
iajs-2704	2	9	and	and	CCONJ
iajs-2704	2	10	mathematics	mathematic	NOUN
iajs-2704	2	11	,	,	PUNCT
iajs-2704	2	12	tikrit	tikrit	NOUN
iajs-2704	2	13	university	university	NOUN
iajs-2704	2	14	,	,	PUNCT
iajs-2704	2	15	tikrit	tikrit	NOUN
iajs-2704	2	16	,	,	PUNCT
iajs-2704	2	17	iraq	iraq	PROPN
iajs-2704	2	18	.	.	PUNCT
iajs-2704	3	1	abstract	abstract	ADV
iajs-2704	3	2	let	let	VERB
iajs-2704	3	3	𝑍𝑟𝑛	𝑍𝑟𝑛	PROPN
iajs-2704	3	4	be	be	AUX
iajs-2704	3	5	any	any	DET
iajs-2704	3	6	group	group	NOUN
iajs-2704	3	7	with	with	ADP
iajs-2704	3	8	identity	identity	NOUN
iajs-2704	3	9	element	element	NOUN
iajs-2704	3	10	(	(	PUNCT
iajs-2704	3	11	e	e	NOUN
iajs-2704	3	12	)	)	PUNCT
iajs-2704	3	13	.	.	PUNCT
iajs-2704	4	1	a	a	DET
iajs-2704	4	2	subgroup	subgroup	NOUN
iajs-2704	4	3	intersection	intersection	NOUN
iajs-2704	4	4	graph	graph	NOUN
iajs-2704	4	5	of	of	ADP
iajs-2704	4	6	a	a	DET
iajs-2704	4	7	subset	subset	NOUN
iajs-2704	4	8	𝑍𝑟𝑛	𝑍𝑟𝑛	PROPN
iajs-2704	4	9	is	be	AUX
iajs-2704	4	10	the	the	DET
iajs-2704	4	11	graph	graph	NOUN
iajs-2704	4	12	with	with	ADP
iajs-2704	4	13	v	v	NOUN
iajs-2704	4	14	(	(	PUNCT
iajs-2704	4	15	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	4	16	)	)	PUNCT
iajs-2704	4	17	)	)	PUNCT
iajs-2704	5	1	=	=	PUNCT
iajs-2704	6	1	𝑍𝑟𝑛	𝑍𝑟𝑛	PROPN
iajs-2704	6	2	e	e	NOUN
iajs-2704	6	3	and	and	CCONJ
iajs-2704	6	4	two	two	NUM
iajs-2704	6	5	separate	separate	ADJ
iajs-2704	6	6	peaks	peak	NOUN
iajs-2704	6	7	c	c	NOUN
iajs-2704	6	8	and	and	CCONJ
iajs-2704	6	9	d	d	X
iajs-2704	6	10	contiguous	contiguous	ADJ
iajs-2704	6	11	for	for	ADP
iajs-2704	6	12	c	c	PROPN
iajs-2704	6	13	and	and	CCONJ
iajs-2704	6	14	d	d	NOUN
iajs-2704	6	15	if	if	SCONJ
iajs-2704	6	16	and	and	CCONJ
iajs-2704	6	17	only	only	ADV
iajs-2704	6	18	if	if	SCONJ
iajs-2704	6	19	|〈𝑐	|〈𝑐	PROPN
iajs-2704	6	20	〉	〉	NOUN
iajs-2704	6	21	∩	∩	NOUN
iajs-2704	6	22	〈	〈	NOUN
iajs-2704	6	23	𝑑〉|	𝑑〉|	PROPN
iajs-2704	6	24	>	>	X
iajs-2704	6	25	1	1	NUM
iajs-2704	6	26	,	,	PUNCT
iajs-2704	6	27	where	where	SCONJ
iajs-2704	6	28	〈	〈	PROPN
iajs-2704	6	29	𝑐	𝑐	NOUN
iajs-2704	6	30	〉	〉	NOUN
iajs-2704	6	31	is	be	AUX
iajs-2704	6	32	a	a	DET
iajs-2704	6	33	periodic	periodic	ADJ
iajs-2704	6	34	subset	subset	NOUN
iajs-2704	6	35	of	of	ADP
iajs-2704	6	36	𝑍𝑟𝑛	𝑍𝑟𝑛	PROPN
iajs-2704	6	37	resulting	result	VERB
iajs-2704	6	38	from	from	ADP
iajs-2704	6	39	𝑐	𝑐	PROPN
iajs-2704	6	40	∈	∈	PROPN
iajs-2704	6	41	𝑍𝑟𝑛.	𝑍𝑟𝑛.	PROPN
iajs-2704	7	1	we	we	PRON
iajs-2704	7	2	find	find	VERB
iajs-2704	7	3	some	some	DET
iajs-2704	7	4	topological	topological	ADJ
iajs-2704	7	5	indicators	indicator	NOUN
iajs-2704	7	6	in	in	ADP
iajs-2704	7	7	this	this	DET
iajs-2704	7	8	paper	paper	NOUN
iajs-2704	7	9	and	and	CCONJ
iajs-2704	7	10	multiborder	multiborder	NOUN
iajs-2704	7	11	(	(	PUNCT
iajs-2704	7	12	hosoya	hosoya	NOUN
iajs-2704	7	13	and	and	CCONJ
iajs-2704	7	14	schultz	schultz	PROPN
iajs-2704	7	15	)	)	PUNCT
iajs-2704	7	16	of	of	ADP
iajs-2704	7	17	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	7	18	)	)	PUNCT
iajs-2704	7	19	,	,	PUNCT
iajs-2704	7	20	where	where	SCONJ
iajs-2704	7	21	𝑟	𝑟	X
iajs-2704	7	22	≥	≥	NUM
iajs-2704	7	23	2	2	NUM
iajs-2704	7	24	,	,	PUNCT
iajs-2704	7	25	𝑛	𝑛	PROPN
iajs-2704	7	26	>	>	SYM
iajs-2704	7	27	1	1	NUM
iajs-2704	7	28	,	,	PUNCT
iajs-2704	7	29	𝑟	𝑟	PRON
iajs-2704	7	30	is	be	AUX
iajs-2704	7	31	aprime	aprime	ADJ
iajs-2704	7	32	number	number	NOUN
iajs-2704	7	33	.	.	PUNCT
iajs-2704	8	1	keyword	keyword	NOUN
iajs-2704	8	2	:	:	PUNCT
iajs-2704	8	3	hosoya	hosoya	PROPN
iajs-2704	8	4	polynomial	polynomial	ADJ
iajs-2704	8	5	,	,	PUNCT
iajs-2704	8	6	schultz	schultz	PROPN
iajs-2704	8	7	polynomial	polynomial	PROPN
iajs-2704	8	8	.	.	PUNCT
iajs-2704	9	1	,	,	PUNCT
iajs-2704	9	2	connectivity	connectivity	NOUN
iajs-2704	9	3	index	index	NOUN
iajs-2704	9	4	,	,	PUNCT
iajs-2704	9	5	sum	sum	NOUN
iajs-2704	9	6	connectivity	connectivity	NOUN
iajs-2704	9	7	index	index	NOUN
iajs-2704	9	8	,	,	PUNCT
iajs-2704	9	9	forgotten	forget	VERB
iajs-2704	9	10	index	index	NOUN
iajs-2704	9	11	,	,	PUNCT
iajs-2704	9	12	first	first	PROPN
iajs-2704	9	13	zagreb	zagreb	PROPN
iajs-2704	9	14	index	index	PROPN
iajs-2704	9	15	,	,	PUNCT
iajs-2704	9	16	harmonic	harmonic	ADJ
iajs-2704	9	17	index	index	NOUN
iajs-2704	9	18	.	.	PUNCT
iajs-2704	10	1	1.introduction	1.introduction	NUM
iajs-2704	10	2	a	a	DET
iajs-2704	10	3	topological	topological	ADJ
iajs-2704	10	4	index	index	NOUN
iajs-2704	10	5	is	be	AUX
iajs-2704	10	6	a	a	DET
iajs-2704	10	7	real	real	ADJ
iajs-2704	10	8	number	number	NOUN
iajs-2704	10	9	associated	associate	VERB
iajs-2704	10	10	with	with	ADP
iajs-2704	10	11	the	the	DET
iajs-2704	10	12	graph	graph	NOUN
iajs-2704	10	13	,	,	PUNCT
iajs-2704	10	14	which	which	PRON
iajs-2704	10	15	must	must	AUX
iajs-2704	10	16	be	be	AUX
iajs-2704	10	17	structurally	structurally	ADV
iajs-2704	10	18	constant	constant	ADJ
iajs-2704	10	19	.	.	PUNCT
iajs-2704	11	1	topological	topological	ADJ
iajs-2704	11	2	index	index	NOUN
iajs-2704	11	3	sometimes	sometimes	ADV
iajs-2704	11	4	called	call	VERB
iajs-2704	11	5	molecular	molecular	ADJ
iajs-2704	11	6	structure	structure	NOUN
iajs-2704	11	7	descriptor[1	descriptor[1	NOUN
iajs-2704	11	8	]	]	PUNCT
iajs-2704	11	9	.	.	PUNCT
iajs-2704	12	1	many	many	ADJ
iajs-2704	12	2	topological	topological	ADJ
iajs-2704	12	3	indicators	indicator	NOUN
iajs-2704	12	4	have	have	AUX
iajs-2704	12	5	been	be	AUX
iajs-2704	12	6	identified	identify	VERB
iajs-2704	12	7	and	and	CCONJ
iajs-2704	12	8	many	many	ADJ
iajs-2704	12	9	applications	application	NOUN
iajs-2704	12	10	have	have	AUX
iajs-2704	12	11	been	be	AUX
iajs-2704	12	12	found	find	VERB
iajs-2704	12	13	as	as	ADP
iajs-2704	12	14	a	a	DET
iajs-2704	12	15	means	means	NOUN
iajs-2704	12	16	of	of	ADP
iajs-2704	12	17	nemuls	nemuls	ADJ
iajs-2704	12	18	chemical	chemical	NOUN
iajs-2704	12	19	,	,	PUNCT
iajs-2704	12	20	pharmaceutical	pharmaceutical	NOUN
iajs-2704	12	21	and	and	CCONJ
iajs-2704	12	22	other	other	ADJ
iajs-2704	12	23	molecular	molecular	ADJ
iajs-2704	12	24	properties	property	NOUN
iajs-2704	12	25	.	.	PUNCT
iajs-2704	13	1	the	the	DET
iajs-2704	13	2	weiner	weiner	NOUN
iajs-2704	13	3	index	index	NOUN
iajs-2704	13	4	is	be	AUX
iajs-2704	13	5	the	the	DET
iajs-2704	13	6	first	first	ADJ
iajs-2704	13	7	topological	topological	ADJ
iajs-2704	13	8	indicator	indicator	NOUN
iajs-2704	13	9	used	use	VERB
iajs-2704	13	10	in	in	ADP
iajs-2704	13	11	chemistry	chemistry	NOUN
iajs-2704	13	12	.	.	PUNCT
iajs-2704	14	1	more	more	ADV
iajs-2704	14	2	precisely	precisely	ADV
iajs-2704	14	3	,	,	PUNCT
iajs-2704	14	4	in	in	ADP
iajs-2704	14	5	1947	1947	NUM
iajs-2704	14	6	,	,	PUNCT
iajs-2704	14	7	harold	harold	PROPN
iajs-2704	14	8	weiner	weiner	NOUN
iajs-2704	14	9	presented	present	VERB
iajs-2704	14	10	and	and	CCONJ
iajs-2704	14	11	developed	develop	VERB
iajs-2704	14	12	this	this	DET
iajs-2704	14	13	interesting	interesting	ADJ
iajs-2704	14	14	indicator	indicator	NOUN
iajs-2704	14	15	to	to	PART
iajs-2704	14	16	determine	determine	VERB
iajs-2704	14	17	the	the	DET
iajs-2704	14	18	physical	physical	ADJ
iajs-2704	14	19	properties	property	NOUN
iajs-2704	14	20	of	of	ADP
iajs-2704	14	21	the	the	DET
iajs-2704	14	22	hens	hen	NOUN
iajs-2704	14	23	known	know	VERB
iajs-2704	14	24	as	as	ADP
iajs-2704	14	25	paraffins	paraffin	NOUN
iajs-2704	14	26	.	.	PUNCT
iajs-2704	15	1	in	in	ADP
iajs-2704	15	2	this	this	DET
iajs-2704	15	3	paper	paper	NOUN
iajs-2704	15	4	we	we	PRON
iajs-2704	15	5	examine	examine	VERB
iajs-2704	15	6	some	some	DET
iajs-2704	15	7	topological	topological	ADJ
iajs-2704	15	8	indicators	indicator	NOUN
iajs-2704	15	9	that	that	PRON
iajs-2704	15	10	depend	depend	VERB
iajs-2704	15	11	on	on	ADP
iajs-2704	15	12	the	the	DET
iajs-2704	15	13	degree	degree	NOUN
iajs-2704	15	14	of	of	ADP
iajs-2704	15	15	examples	example	NOUN
iajs-2704	15	16	of	of	ADP
iajs-2704	15	17	eccentric	eccentric	ADJ
iajs-2704	15	18	connectivity	connectivity	NOUN
iajs-2704	15	19	index[2	index[2	NOUN
iajs-2704	15	20	]	]	PUNCT
iajs-2704	15	21	,	,	PUNCT
iajs-2704	15	22	connectivity	connectivity	NOUN
iajs-2704	15	23	index[3	index[3	PROPN
iajs-2704	15	24	]	]	PUNCT
iajs-2704	15	25	,	,	PUNCT
iajs-2704	15	26	sum	sum	NOUN
iajs-2704	15	27	connectivity	connectivity	NOUN
iajs-2704	15	28	index[4	index[4	PROPN
iajs-2704	15	29	]	]	X
iajs-2704	15	30	,	,	PUNCT
iajs-2704	15	31	zagreb	zagreb	PROPN
iajs-2704	15	32	index[5	index[5	PROPN
iajs-2704	15	33	]	]	PUNCT
iajs-2704	15	34	,	,	PUNCT
iajs-2704	15	35	forgotten	forget	VERB
iajs-2704	15	36	index[6	index[6	ADV
iajs-2704	15	37	]	]	PUNCT
iajs-2704	15	38	,	,	PUNCT
iajs-2704	15	39	the	the	DET
iajs-2704	15	40	index	index	NOUN
iajs-2704	15	41	of	of	ADP
iajs-2704	15	42	geometricarithmetic	geometricarithmetic	ADJ
iajs-2704	15	43	[	[	X
iajs-2704	15	44	3	3	NUM
iajs-2704	15	45	]	]	PUNCT
iajs-2704	15	46	,	,	PUNCT
iajs-2704	15	47	index	index	NOUN
iajs-2704	15	48	of	of	ADP
iajs-2704	15	49	atom	atom	NOUN
iajs-2704	15	50	-	-	PUNCT
iajs-2704	15	51	bond	bond	NOUN
iajs-2704	15	52	connectivity	connectivity	NOUN
iajs-2704	15	53	[	[	X
iajs-2704	15	54	3	3	NUM
iajs-2704	15	55	]	]	PUNCT
iajs-2704	15	56	and	and	CCONJ
iajs-2704	15	57	harmonic	harmonic	ADJ
iajs-2704	15	58	index[7	index[7	NOUN
iajs-2704	15	59	]	]	PUNCT
iajs-2704	15	60	.	.	PUNCT
iajs-2704	16	1	ibn	ibn	PROPN
iajs-2704	16	2	al	al	PROPN
iajs-2704	16	3	haitham	haitham	PROPN
iajs-2704	16	4	journal	journal	PROPN
iajs-2704	16	5	for	for	ADP
iajs-2704	16	6	pure	pure	ADJ
iajs-2704	16	7	and	and	CCONJ
iajs-2704	16	8	applied	apply	VERB
iajs-2704	16	9	science	science	NOUN
iajs-2704	16	10	journal	journal	PROPN
iajs-2704	16	11	homepage	homepage	NOUN
iajs-2704	16	12	:	:	PUNCT
iajs-2704	16	13	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2704	16	14	doi	doi	NOUN
iajs-2704	16	15	:	:	PUNCT
iajs-2704	16	16	10.30526/34.4.2704	10.30526/34.4.2704	NUM
iajs-2704	16	17	article	article	NOUN
iajs-2704	16	18	history	history	NOUN
iajs-2704	16	19	:	:	PUNCT
iajs-2704	16	20	received	receive	VERB
iajs-2704	16	21	26	26	NUM
iajs-2704	16	22	january	january	NOUN
iajs-2704	16	23	2021	2021	NUM
iajs-2704	16	24	,	,	PUNCT
iajs-2704	16	25	accepted	accept	VERB
iajs-2704	16	26	29	29	NUM
iajs-2704	16	27	march	march	NOUN
iajs-2704	16	28	20	20	NUM
iajs-2704	16	29	12	12	NUM
iajs-2704	16	30	,	,	PUNCT
iajs-2704	16	31	published	publish	VERB
iajs-2704	16	32	in	in	ADP
iajs-2704	16	33	october	october	PROPN
iajs-2704	16	34	2021	2021	NUM
iajs-2704	16	35	.	.	PUNCT
iajs-2704	17	1	mailto:nawaf@gmail.com	mailto:nawaf@gmail.com	X
iajs-2704	17	2	mailto:akr-tel@tu.edu.iq	mailto:akr-tel@tu.edu.iq	PROPN
iajs-2704	17	3	ibn	ibn	PROPN
iajs-2704	17	4	al	al	PROPN
iajs-2704	17	5	-	-	PUNCT
iajs-2704	17	6	haitham	haitham	PROPN
iajs-2704	17	7	jour	jour	X
iajs-2704	17	8	.	.	PROPN
iajs-2704	18	1	for	for	ADP
iajs-2704	18	2	pure	pure	ADJ
iajs-2704	18	3	&	&	CCONJ
iajs-2704	18	4	appl	appl	PROPN
iajs-2704	18	5	.	.	PUNCT
iajs-2704	19	1	sci	sci	PROPN
iajs-2704	19	2	.	.	PROPN
iajs-2704	20	1	34(4)2021	34(4)2021	NUM
iajs-2704	20	2	69	69	NUM
iajs-2704	20	3	in	in	ADP
iajs-2704	20	4	(	(	PUNCT
iajs-2704	20	5	2019),abdussakir	2019),abdussakir	NUM
iajs-2704	20	6	[	[	X
iajs-2704	20	7	8	8	NUM
iajs-2704	20	8	]	]	PUNCT
iajs-2704	20	9	introduced	introduce	VERB
iajs-2704	20	10	topological	topological	ADJ
iajs-2704	20	11	indices	index	NOUN
iajs-2704	20	12	about	about	ADP
iajs-2704	20	13	symmetric	symmetric	ADJ
iajs-2704	20	14	group	group	NOUN
iajs-2704	20	15	graph	graph	NOUN
iajs-2704	20	16	,	,	PUNCT
iajs-2704	20	17	also	also	ADV
iajs-2704	20	18	in	in	ADP
iajs-2704	20	19	(	(	PUNCT
iajs-2704	20	20	2020	2020	NUM
iajs-2704	20	21	)	)	PUNCT
iajs-2704	20	22	g.	g.	PROPN
iajs-2704	20	23	r.	r.	PROPN
iajs-2704	20	24	roshini	roshini	PROPN
iajs-2704	21	1	[	[	X
iajs-2704	21	2	9	9	NUM
iajs-2704	21	3	]	]	PUNCT
iajs-2704	21	4	studied	study	VERB
iajs-2704	21	5	topological	topological	ADJ
iajs-2704	21	6	indices	index	NOUN
iajs-2704	21	7	of	of	ADP
iajs-2704	21	8	transformation	transformation	NOUN
iajs-2704	21	9	graphs	graph	NOUN
iajs-2704	21	10	,	,	PUNCT
iajs-2704	21	11	and	and	CCONJ
iajs-2704	21	12	in	in	ADP
iajs-2704	21	13	(	(	PUNCT
iajs-2704	21	14	2021	2021	NUM
iajs-2704	21	15	)	)	PUNCT
iajs-2704	21	16	alaa	alaa	PROPN
iajs-2704	21	17	.j	.j	PROPN
iajs-2704	21	18	and	and	CCONJ
iajs-2704	21	19	akram.s	akram.s	PUNCT
iajs-2704	22	1	[	[	X
iajs-2704	22	2	10	10	NUM
iajs-2704	22	3	]	]	PUNCT
iajs-2704	22	4	studied	study	VERB
iajs-2704	22	5	topological	topological	ADJ
iajs-2704	22	6	indices	index	NOUN
iajs-2704	22	7	and	and	CCONJ
iajs-2704	22	8	(	(	PUNCT
iajs-2704	22	9	hosoya	hosoya	NOUN
iajs-2704	22	10	and	and	CCONJ
iajs-2704	22	11	schultz	schultz	PROPN
iajs-2704	22	12	)	)	PUNCT
iajs-2704	22	13	polynomial	polynomial	NOUN
iajs-2704	22	14	about	about	ADP
iajs-2704	22	15	subgroup	subgroup	NOUN
iajs-2704	22	16	intersection	intersection	NOUN
iajs-2704	22	17	graph	graph	NOUN
iajs-2704	22	18	of	of	ADP
iajs-2704	22	19	a	a	DET
iajs-2704	22	20	group	group	NOUN
iajs-2704	22	21	𝑍𝑟	𝑍𝑟	PROPN
iajs-2704	22	22	.	.	PUNCT
iajs-2704	23	1	one	one	NUM
iajs-2704	23	2	of	of	ADP
iajs-2704	23	3	the	the	DET
iajs-2704	23	4	graphic	graphic	ADJ
iajs-2704	23	5	concepts	concept	NOUN
iajs-2704	23	6	obtained	obtain	VERB
iajs-2704	23	7	from	from	ADP
iajs-2704	23	8	the	the	DET
iajs-2704	23	9	group	group	NOUN
iajs-2704	23	10	is	be	AUX
iajs-2704	23	11	the	the	DET
iajs-2704	23	12	concept	concept	NOUN
iajs-2704	23	13	of	of	ADP
iajs-2704	23	14	a	a	DET
iajs-2704	23	15	subset	subset	NOUN
iajs-2704	23	16	cross	cross	NOUN
iajs-2704	23	17	chart	chart	NOUN
iajs-2704	23	18	of	of	ADP
iajs-2704	23	19	a	a	DET
iajs-2704	23	20	group	group	NOUN
iajs-2704	23	21	introduced	introduce	VERB
iajs-2704	23	22	by	by	ADP
iajs-2704	23	23	[	[	X
iajs-2704	23	24	11	11	NUM
iajs-2704	23	25	]	]	PUNCT
iajs-2704	23	26	.	.	PUNCT
iajs-2704	24	1	in	in	ADP
iajs-2704	24	2	refere	refere	VERB
iajs-2704	24	3	to	to	ADP
iajs-2704	24	4	the	the	DET
iajs-2704	24	5	subgroup	subgroup	NOUN
iajs-2704	24	6	intersection	intersection	NOUN
iajs-2704	24	7	graph	graph	NOUN
iajs-2704	24	8	definition	definition	NOUN
iajs-2704	24	9	by	by	ADP
iajs-2704	24	10	[	[	X
iajs-2704	24	11	11	11	NUM
iajs-2704	24	12	]	]	PUNCT
iajs-2704	24	13	,	,	PUNCT
iajs-2704	24	14	let	let	VERB
iajs-2704	24	15	graph	graph	NOUN
iajs-2704	24	16	group	group	NOUN
iajs-2704	24	17	be	be	AUX
iajs-2704	24	18	the	the	DET
iajs-2704	24	19	intersection	intersection	NOUN
iajs-2704	24	20	(	(	PUNCT
iajs-2704	24	21	g	g	NOUN
iajs-2704	24	22	)	)	PUNCT
iajs-2704	24	23	where	where	SCONJ
iajs-2704	24	24	g	g	PROPN
iajs-2704	24	25	is	be	AUX
iajs-2704	24	26	a	a	DET
iajs-2704	24	27	graph	graph	NOUN
iajs-2704	24	28	with	with	ADP
iajs-2704	24	29	v	v	NOUN
iajs-2704	24	30	(	(	PUNCT
iajs-2704	24	31	ᴦ𝑆𝐼(𝐺))=	ᴦ𝑆𝐼(𝐺))=	NOUN
iajs-2704	24	32	g	g	NOUN
iajs-2704	24	33	-	-	PUNCT
iajs-2704	24	34	e	e	NOUN
iajs-2704	24	35	and	and	CCONJ
iajs-2704	24	36	two	two	NUM
iajs-2704	24	37	distinct	distinct	ADJ
iajs-2704	24	38	peaks	peak	NOUN
iajs-2704	24	39	a	a	PRON
iajs-2704	24	40	and	and	CCONJ
iajs-2704	24	41	b	b	NOUN
iajs-2704	24	42	are	be	AUX
iajs-2704	24	43	adjacent	adjacent	ADJ
iajs-2704	24	44	in	in	ADP
iajs-2704	24	45	the	the	DET
iajs-2704	24	46	ᴦ𝑆𝐼	ᴦ𝑆𝐼	PROPN
iajs-2704	24	47	(	(	PUNCT
iajs-2704	24	48	g	g	NOUN
iajs-2704	24	49	)	)	PUNCT
iajs-2704	24	50	if	if	SCONJ
iajs-2704	24	51	|〈a〉∩〈b〉|	|〈a〉∩〈b〉|	ADJ
iajs-2704	24	52	>	>	X
iajs-2704	24	53	1	1	NUM
iajs-2704	24	54	,	,	PUNCT
iajs-2704	24	55	where〈a〉is	where〈a〉is	PROPN
iajs-2704	24	56	a	a	DET
iajs-2704	24	57	periodic	periodic	ADJ
iajs-2704	24	58	subset	subset	NOUN
iajs-2704	24	59	of	of	ADP
iajs-2704	24	60	g	g	NOUN
iajs-2704	24	61	resulting	result	VERB
iajs-2704	24	62	from	from	ADP
iajs-2704	24	63	a	a	DET
iajs-2704	24	64	∈g	∈g	NOUN
iajs-2704	24	65	.	.	NOUN
iajs-2704	25	1	2	2	NUM
iajs-2704	25	2	.	.	NOUN
iajs-2704	25	3	method	method	NOUN
iajs-2704	25	4	and	and	CCONJ
iajs-2704	25	5	materials	material	NOUN
iajs-2704	25	6	in	in	ADP
iajs-2704	25	7	an	an	DET
iajs-2704	25	8	existing	exist	VERB
iajs-2704	25	9	article	article	NOUN
iajs-2704	25	10	,	,	PUNCT
iajs-2704	25	11	all	all	DET
iajs-2704	25	12	graphs	graph	NOUN
iajs-2704	25	13	are	be	AUX
iajs-2704	25	14	simple	simple	ADJ
iajs-2704	25	15	,	,	PUNCT
iajs-2704	25	16	limited	limited	ADJ
iajs-2704	25	17	,	,	PUNCT
iajs-2704	25	18	connected	connected	ADJ
iajs-2704	25	19	and	and	CCONJ
iajs-2704	25	20	:	:	PUNCT
iajs-2704	25	21	directed	direct	VERB
iajs-2704	25	22	.	.	PUNCT
iajs-2704	26	1	for	for	ADP
iajs-2704	26	2	𝐺	𝐺	PROPN
iajs-2704	26	3	=	=	SYM
iajs-2704	26	4	(	(	PUNCT
iajs-2704	26	5	𝑉(𝐺	𝑉(𝐺	NOUN
iajs-2704	26	6	)	)	PUNCT
iajs-2704	26	7	,	,	PUNCT
iajs-2704	26	8	𝐸(𝐺	𝐸(𝐺	NOUN
iajs-2704	26	9	)	)	PUNCT
iajs-2704	26	10	)	)	PUNCT
iajs-2704	26	11	graph	graph	NOUN
iajs-2704	26	12	,	,	PUNCT
iajs-2704	26	13	the	the	DET
iajs-2704	26	14	order	order	NOUN
iajs-2704	26	15	of	of	ADP
iajs-2704	26	16	𝐺	𝐺	PROPN
iajs-2704	26	17	is	be	AUX
iajs-2704	26	18	𝑝(𝐺	𝑝(𝐺	NOUN
iajs-2704	26	19	)	)	PUNCT
iajs-2704	27	1	=	=	SYM
iajs-2704	27	2	𝑉(𝐺	𝑉(𝐺	NOUN
iajs-2704	27	3	)	)	PUNCT
iajs-2704	27	4	and	and	CCONJ
iajs-2704	27	5	the	the	DET
iajs-2704	27	6	scale	scale	NOUN
iajs-2704	27	7	of	of	ADP
iajs-2704	27	8	𝐺	𝐺	PROPN
iajs-2704	27	9	is	be	AUX
iajs-2704	27	10	𝑞(𝐺	𝑞(𝐺	NOUN
iajs-2704	27	11	)	)	PUNCT
iajs-2704	27	12	=	=	SYM
iajs-2704	27	13	𝐸(𝐺	𝐸(𝐺	NOUN
iajs-2704	27	14	)	)	PUNCT
iajs-2704	27	15	.	.	PUNCT
iajs-2704	28	1	let	let	AUX
iajs-2704	28	2	𝑑𝑒𝑔(𝑢	𝑑𝑒𝑔(𝑢	PROPN
iajs-2704	28	3	)	)	PUNCT
iajs-2704	28	4	denote	denote	VERB
iajs-2704	28	5	the	the	DET
iajs-2704	28	6	degree	degree	NOUN
iajs-2704	28	7	of	of	ADP
iajs-2704	28	8	vertex	vertex	NOUN
iajs-2704	28	9	𝑢	𝑢	NOUN
iajs-2704	28	10	in	in	ADP
iajs-2704	28	11	𝐺.	𝐺.	PROPN
iajs-2704	28	12	if	if	SCONJ
iajs-2704	28	13	𝑑𝑒𝑔(𝑢	𝑑𝑒𝑔(𝑢	PROPN
iajs-2704	28	14	)	)	PUNCT
iajs-2704	28	15	=	=	SYM
iajs-2704	29	1	0	0	NUM
iajs-2704	29	2	,	,	PUNCT
iajs-2704	29	3	then	then	ADV
iajs-2704	29	4	u	u	NOUN
iajs-2704	29	5	is	be	AUX
iajs-2704	29	6	an	an	DET
iajs-2704	29	7	isolated	isolated	ADJ
iajs-2704	29	8	vertices	vertex	NOUN
iajs-2704	29	9	.	.	PUNCT
iajs-2704	30	1	let	let	VERB
iajs-2704	30	2	𝑑(𝑢	𝑑(𝑢	NOUN
iajs-2704	30	3	,	,	PUNCT
iajs-2704	30	4	𝑣)indicatex	𝑣)indicatex	PROPN
iajs-2704	30	5	the	the	DET
iajs-2704	30	6	distance	distance	NOUN
iajs-2704	30	7	between	between	ADP
iajs-2704	30	8	the	the	DET
iajs-2704	30	9	peaks	peak	NOUN
iajs-2704	30	10	𝑢	𝑢	NOUN
iajs-2704	30	11	and	and	CCONJ
iajs-2704	30	12	𝑣	𝑣	X
iajs-2704	30	13	in	in	ADP
iajs-2704	30	14	𝐺.	𝐺.	NOUN
iajs-2704	30	15	the	the	DET
iajs-2704	30	16	eccentricity	eccentricity	NOUN
iajs-2704	30	17	𝑒𝑐𝑐(𝑢	𝑒𝑐𝑐(𝑢	PROPN
iajs-2704	30	18	)	)	PUNCT
iajs-2704	30	19	of	of	ADP
iajs-2704	30	20	the	the	DET
iajs-2704	30	21	vertex	vertex	NOUN
iajs-2704	30	22	𝑢	𝑢	PROPN
iajs-2704	30	23	is	be	AUX
iajs-2704	30	24	𝑒𝑐𝑐(𝑢	𝑒𝑐𝑐(𝑢	PROPN
iajs-2704	30	25	)	)	PUNCT
iajs-2704	30	26	=	=	SYM
iajs-2704	31	1	𝑠𝑢𝑝{𝑑(𝑢	𝑠𝑢𝑝{𝑑(𝑢	PROPN
iajs-2704	31	2	,	,	PUNCT
iajs-2704	31	3	𝑣	𝑣	NOUN
iajs-2704	31	4	):	):	PUNCT
iajs-2704	31	5	𝑣	𝑣	PRON
iajs-2704	31	6	∈	∈	PROPN
iajs-2704	31	7	𝑉(𝐺	𝑉(𝐺	NOUN
iajs-2704	31	8	)	)	PUNCT
iajs-2704	31	9	}	}	PUNCT
iajs-2704	31	10	.	.	PUNCT
iajs-2704	32	1	the	the	DET
iajs-2704	32	2	following	follow	VERB
iajs-2704	32	3	definition	definition	NOUN
iajs-2704	32	4	refers	refer	VERB
iajs-2704	32	5	to	to	ADP
iajs-2704	32	6	a	a	DET
iajs-2704	32	7	graph	graph	NOUN
iajs-2704	32	8	𝐺	𝐺	NOUN
iajs-2704	32	9	=	=	PUNCT
iajs-2704	32	10	(	(	PUNCT
iajs-2704	32	11	𝑉(𝐺	𝑉(𝐺	NOUN
iajs-2704	32	12	)	)	PUNCT
iajs-2704	32	13	,	,	PUNCT
iajs-2704	32	14	𝐸(𝐺	𝐸(𝐺	PROPN
iajs-2704	32	15	)	)	PUNCT
iajs-2704	32	16	)	)	PUNCT
iajs-2704	32	17	.	.	PUNCT
iajs-2704	33	1	eccentric	eccentric	ADJ
iajs-2704	33	2	connectivity	connectivity	NOUN
iajs-2704	33	3	index	index	NOUN
iajs-2704	33	4	of	of	ADP
iajs-2704	33	5	𝐺	𝐺	PROPN
iajs-2704	33	6	is	be	AUX
iajs-2704	33	7	[	[	X
iajs-2704	33	8	2	2	NUM
iajs-2704	33	9	]	]	PUNCT
iajs-2704	33	10	𝜉𝐶(𝐺	𝜉𝐶(𝐺	NOUN
iajs-2704	33	11	)	)	PUNCT
iajs-2704	33	12	)	)	PUNCT
iajs-2704	33	13	)	)	PUNCT
iajs-2704	34	1	=	=	PUNCT
iajs-2704	34	2	∑	∑	PUNCT
iajs-2704	34	3	𝑑𝑒𝑔(𝑢	𝑑𝑒𝑔(𝑢	PROPN
iajs-2704	34	4	)	)	PUNCT
iajs-2704	34	5	.	.	PUNCT
iajs-2704	35	1	𝑒(𝑢)𝑢∈	𝑒(𝑢)𝑢∈	PRON
iajs-2704	35	2	𝑉(𝐺	𝑉(𝐺	NOUN
iajs-2704	35	3	)	)	PUNCT
iajs-2704	35	4	the	the	DET
iajs-2704	35	5	index	index	NOUN
iajs-2704	35	6	of	of	ADP
iajs-2704	35	7	connectivity	connectivity	NOUN
iajs-2704	35	8	of	of	ADP
iajs-2704	35	9	𝐺	𝐺	PROPN
iajs-2704	35	10	is[3	is[3	PROPN
iajs-2704	35	11	]	]	X
iajs-2704	35	12	𝑋(𝐺	𝑋(𝐺	ADJ
iajs-2704	35	13	)	)	PUNCT
iajs-2704	35	14	=	=	PUNCT
iajs-2704	35	15	∑	∑	PUNCT
iajs-2704	35	16	1	1	NUM
iajs-2704	35	17	√𝑑𝑒𝑔(𝑢	√𝑑𝑒𝑔(𝑢	NOUN
iajs-2704	35	18	)	)	PUNCT
iajs-2704	35	19	.	.	PUNCT
iajs-2704	36	1	𝑑𝑒𝑔(𝑣)𝑢𝑣∈	𝑑𝑒𝑔(𝑣)𝑢𝑣∈	DET
iajs-2704	36	2	𝐸(𝐺	𝐸(𝐺	NOUN
iajs-2704	36	3	)	)	PUNCT
iajs-2704	36	4	sum	sum	VERB
iajs-2704	36	5	the	the	DET
iajs-2704	36	6	index	index	NOUN
iajs-2704	36	7	of	of	ADP
iajs-2704	36	8	connectivity	connectivity	NOUN
iajs-2704	36	9	of	of	ADP
iajs-2704	36	10	𝐺	𝐺	PROPN
iajs-2704	36	11	is	be	AUX
iajs-2704	36	12	[	[	X
iajs-2704	36	13	4	4	NUM
iajs-2704	36	14	]	]	SYM
iajs-2704	36	15	𝑆(𝐺	𝑆(𝐺	NOUN
iajs-2704	36	16	)	)	PUNCT
iajs-2704	37	1	=	=	PUNCT
iajs-2704	37	2	∑	∑	PUNCT
iajs-2704	37	3	1	1	NUM
iajs-2704	37	4	√𝑑𝑒𝑔(𝑢)+𝑑𝑒𝑔(𝑣)𝑢𝑣∈	√𝑑𝑒𝑔(𝑢)+𝑑𝑒𝑔(𝑣)𝑢𝑣∈	PROPN
iajs-2704	37	5	𝐸(𝐺	𝐸(𝐺	NOUN
iajs-2704	37	6	)	)	PUNCT
iajs-2704	37	7	a	a	DET
iajs-2704	37	8	first	first	ADJ
iajs-2704	37	9	zagreb	zagreb	PROPN
iajs-2704	37	10	index	index	NOUN
iajs-2704	37	11	of	of	ADP
iajs-2704	37	12	g	g	PROPN
iajs-2704	37	13	is	be	AUX
iajs-2704	37	14	[	[	X
iajs-2704	37	15	5	5	NUM
iajs-2704	37	16	]	]	SYM
iajs-2704	37	17	𝑀1(𝐺	𝑀1(𝐺	NOUN
iajs-2704	37	18	)	)	PUNCT
iajs-2704	37	19	=	=	PUNCT
iajs-2704	37	20	∑	∑	PUNCT
iajs-2704	37	21	(	(	PUNCT
iajs-2704	37	22	𝑑𝑒𝑔(𝑢))2𝑢∈	𝑑𝑒𝑔(𝑢))2𝑢∈	PROPN
iajs-2704	37	23	𝑉(𝐺	𝑉(𝐺	NOUN
iajs-2704	37	24	)	)	PUNCT
iajs-2704	37	25	a	a	DET
iajs-2704	37	26	second	second	ADJ
iajs-2704	37	27	zagreb	zagreb	PROPN
iajs-2704	37	28	index	index	NOUN
iajs-2704	37	29	of	of	ADP
iajs-2704	37	30	𝐺	𝐺	PROPN
iajs-2704	37	31	is	be	AUX
iajs-2704	37	32	[	[	X
iajs-2704	37	33	5	5	NUM
iajs-2704	37	34	]	]	SYM
iajs-2704	37	35	𝑀2(𝐺	𝑀2(𝐺	NOUN
iajs-2704	37	36	)	)	PUNCT
iajs-2704	37	37	=	=	PUNCT
iajs-2704	37	38	∑	∑	PUNCT
iajs-2704	37	39	𝑑𝑒𝑔(𝑢	𝑑𝑒𝑔(𝑢	PROPN
iajs-2704	37	40	)	)	PUNCT
iajs-2704	37	41	.	.	PUNCT
iajs-2704	38	1	𝑑𝑒𝑔(𝑣)𝑢𝑣	𝑑𝑒𝑔(𝑣)𝑢𝑣	PUNCT
iajs-2704	38	2	𝐸𝐺	𝐸𝐺	ADJ
iajs-2704	38	3	)	)	PUNCT
iajs-2704	38	4	the	the	DET
iajs-2704	38	5	forgotten	forget	VERB
iajs-2704	38	6	index	index	NOUN
iajs-2704	38	7	of	of	ADP
iajs-2704	38	8	𝐺	𝐺	PROPN
iajs-2704	38	9	is	be	AUX
iajs-2704	38	10	[	[	X
iajs-2704	38	11	6	6	NUM
iajs-2704	38	12	]	]	SYM
iajs-2704	38	13	𝐹(𝐺	𝐹(𝐺	NUM
iajs-2704	38	14	)	)	PUNCT
iajs-2704	38	15	)	)	PUNCT
iajs-2704	39	1	=	=	PUNCT
iajs-2704	39	2	∑	∑	PUNCT
iajs-2704	39	3	(	(	PUNCT
iajs-2704	39	4	𝑑𝑒𝑔(𝑢))3	𝑑𝑒𝑔(𝑢))3	ADV
iajs-2704	39	5	𝑢∈𝑉(𝐺	𝑢∈𝑉(𝐺	ADJ
iajs-2704	39	6	)	)	PUNCT
iajs-2704	39	7	atom	atom	NOUN
iajs-2704	39	8	bond	bond	NOUN
iajs-2704	39	9	connectivity	connectivity	NOUN
iajs-2704	39	10	index	index	NOUN
iajs-2704	39	11	of	of	ADP
iajs-2704	39	12	g	g	PROPN
iajs-2704	39	13	is	be	AUX
iajs-2704	39	14	[	[	X
iajs-2704	39	15	3	3	NUM
iajs-2704	39	16	]	]	X
iajs-2704	39	17	ibn	ibn	PROPN
iajs-2704	39	18	al	al	PROPN
iajs-2704	39	19	-	-	PUNCT
iajs-2704	39	20	haitham	haitham	PROPN
iajs-2704	39	21	jour	jour	X
iajs-2704	39	22	.	.	PROPN
iajs-2704	40	1	for	for	ADP
iajs-2704	40	2	pure	pure	ADJ
iajs-2704	40	3	&	&	CCONJ
iajs-2704	40	4	appl	appl	PROPN
iajs-2704	40	5	.	.	PUNCT
iajs-2704	41	1	sci	sci	PROPN
iajs-2704	41	2	.	.	PROPN
iajs-2704	42	1	34(4)2021	34(4)2021	NUM
iajs-2704	42	2	70	70	NUM
iajs-2704	42	3	𝐴𝐵𝐶(𝐺	𝐴𝐵𝐶(𝐺	NOUN
iajs-2704	42	4	)	)	PUNCT
iajs-2704	42	5	)	)	PUNCT
iajs-2704	43	1	=	=	PUNCT
iajs-2704	43	2	∑	∑	PUNCT
iajs-2704	43	3	√	√	PROPN
iajs-2704	43	4	𝑑𝑒𝑔(𝑢)+𝑑𝑒𝑔(𝑣)−2	𝑑𝑒𝑔(𝑢)+𝑑𝑒𝑔(𝑣)−2	VERB
iajs-2704	43	5	𝑑𝑒𝑔(𝑢).𝑑𝑒𝑔(𝑣)𝑢𝑣∈	𝑑𝑒𝑔(𝑢).𝑑𝑒𝑔(𝑣)𝑢𝑣∈	PROPN
iajs-2704	43	6	𝐸(𝐺	𝐸(𝐺	NOUN
iajs-2704	43	7	)	)	PUNCT
iajs-2704	43	8	geometric	geometric	ADJ
iajs-2704	43	9	-	-	PUNCT
iajs-2704	43	10	arithmetic	arithmetic	ADJ
iajs-2704	43	11	index	index	NOUN
iajs-2704	43	12	of	of	ADP
iajs-2704	43	13	𝐺	𝐺	PROPN
iajs-2704	43	14	is	be	AUX
iajs-2704	43	15	[	[	X
iajs-2704	43	16	3	3	NUM
iajs-2704	43	17	]	]	PUNCT
iajs-2704	43	18	𝐺𝐴(𝐺	𝐺𝐴(𝐺	NOUN
iajs-2704	43	19	)	)	PUNCT
iajs-2704	43	20	=	=	SYM
iajs-2704	43	21	∑	∑	PUNCT
iajs-2704	43	22	2√𝑑𝑒𝑔(𝑢).𝑑𝑒𝑔(𝑣	2√𝑑𝑒𝑔(𝑢).𝑑𝑒𝑔(𝑣	NUM
iajs-2704	43	23	)	)	PUNCT
iajs-2704	43	24	𝑑𝑒𝑔(𝑢)+𝑑𝑒𝑔(𝑣)𝑢𝑣∈	𝑑𝑒𝑔(𝑢)+𝑑𝑒𝑔(𝑣)𝑢𝑣∈	PROPN
iajs-2704	43	25	𝐸(𝐺	𝐸(𝐺	NOUN
iajs-2704	43	26	)	)	PUNCT
iajs-2704	43	27	harmonic	harmonic	ADJ
iajs-2704	43	28	index	index	NOUN
iajs-2704	43	29	of	of	ADP
iajs-2704	43	30	𝐺	𝐺	PROPN
iajs-2704	43	31	is	be	AUX
iajs-2704	43	32	[	[	X
iajs-2704	43	33	7	7	NUM
iajs-2704	43	34	]	]	SYM
iajs-2704	43	35	𝐻(𝐺	𝐻(𝐺	NOUN
iajs-2704	43	36	)	)	PUNCT
iajs-2704	44	1	=	=	NOUN
iajs-2704	44	2	∑	∑	PROPN
iajs-2704	44	3	2	2	NUM
iajs-2704	44	4	𝑑𝑒𝑔(𝑢	𝑑𝑒𝑔(𝑢	PROPN
iajs-2704	44	5	)	)	PUNCT
iajs-2704	45	1	+	+	CCONJ
iajs-2704	45	2	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	45	3	(	(	PUNCT
iajs-2704	45	4	𝑣)𝑢𝑣∈	𝑣)𝑢𝑣∈	NOUN
iajs-2704	45	5	𝐸(𝐺	𝐸(𝐺	PROPN
iajs-2704	45	6	)	)	PUNCT
iajs-2704	45	7	3	3	NUM
iajs-2704	45	8	.	.	PUNCT
iajs-2704	46	1	the	the	DET
iajs-2704	46	2	main	main	ADJ
iajs-2704	46	3	result	result	NOUN
iajs-2704	46	4	to	to	PART
iajs-2704	46	5	get	get	VERB
iajs-2704	46	6	a	a	DET
iajs-2704	46	7	good	good	ADJ
iajs-2704	46	8	look	look	NOUN
iajs-2704	46	9	,	,	PUNCT
iajs-2704	46	10	:	:	PUNCT
iajs-2704	46	11	𝑟	𝑟	PRON
iajs-2704	46	12	≥	≥	NOUN
iajs-2704	46	13	2	2	NUM
iajs-2704	46	14	,	,	PUNCT
iajs-2704	46	15	𝑛	𝑛	PROPN
iajs-2704	46	16	>	>	X
iajs-2704	46	17	1	1	NUM
iajs-2704	46	18	,	,	PUNCT
iajs-2704	46	19	a	a	DET
iajs-2704	46	20	subgroup	subgroup	NOUN
iajs-2704	46	21	intersection	intersection	NOUN
iajs-2704	46	22	graph	graph	NOUN
iajs-2704	46	23	of	of	ADP
iajs-2704	46	24	a	a	DET
iajs-2704	46	25	group	group	NOUN
iajs-2704	46	26	𝑍𝑟𝑛	𝑍𝑟𝑛	PROPN
iajs-2704	46	27	is	be	AUX
iajs-2704	46	28	(	(	PUNCT
iajs-2704	46	29	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	46	30	)	)	PUNCT
iajs-2704	46	31	)	)	PUNCT
iajs-2704	47	1	a	a	DET
iajs-2704	47	2	graph	graph	NOUN
iajs-2704	47	3	with	with	ADP
iajs-2704	47	4	v	v	NOUN
iajs-2704	47	5	(	(	PUNCT
iajs-2704	47	6	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	47	7	)	)	PUNCT
iajs-2704	47	8	)	)	PUNCT
iajs-2704	48	1	=	=	PUNCT
iajs-2704	49	1	𝑍𝑟𝑛	𝑍𝑟𝑛	PROPN
iajs-2704	49	2	−	−	NOUN
iajs-2704	49	3	𝑒	𝑒	PROPN
iajs-2704	49	4	,	,	PUNCT
iajs-2704	49	5	any	any	DET
iajs-2704	49	6	two	two	NUM
iajs-2704	49	7	different	different	ADJ
iajs-2704	49	8	vertices	vertex	NOUN
iajs-2704	49	9	a	a	PRON
iajs-2704	49	10	and	and	CCONJ
iajs-2704	49	11	b	b	NOUN
iajs-2704	49	12	are	be	AUX
iajs-2704	49	13	adjacent:|〈a	adjacent:|〈a	PROPN
iajs-2704	49	14	〉	〉	NOUN
iajs-2704	49	15	∩	∩	ADJ
iajs-2704	49	16	〈	〈	NOUN
iajs-2704	49	17	b〉|	b〉|	NOUN
iajs-2704	49	18	>	>	X
iajs-2704	49	19	1	1	NUM
iajs-2704	49	20	,	,	PUNCT
iajs-2704	49	21	where	where	SCONJ
iajs-2704	49	22	〈	〈	PROPN
iajs-2704	49	23	a	a	DET
iajs-2704	49	24	〉	〉	NOUN
iajs-2704	49	25	is	be	AUX
iajs-2704	49	26	the	the	DET
iajs-2704	49	27	subset	subset	NOUN
iajs-2704	49	28	created	create	VERB
iajs-2704	49	29	by	by	ADP
iajs-2704	49	30	a	a	DET
iajs-2704	49	31	∈	∈	PROPN
iajs-2704	49	32	𝑍𝑟𝑛.	𝑍𝑟𝑛.	PROPN
iajs-2704	49	33	theorem	theorem	VERB
iajs-2704	49	34	3.1	3.1	NUM
iajs-2704	49	35	let	let	VERB
iajs-2704	49	36	𝑍𝑟𝑛	𝑍𝑟𝑛	PROPN
iajs-2704	49	37	be	be	AUX
iajs-2704	49	38	a	a	DET
iajs-2704	49	39	group	group	NOUN
iajs-2704	49	40	with	with	ADP
iajs-2704	49	41	𝑟	𝑟	PRON
iajs-2704	49	42	≥	≥	NUM
iajs-2704	49	43	2	2	NUM
iajs-2704	49	44	,	,	PUNCT
iajs-2704	49	45	𝑛	𝑛	PROPN
iajs-2704	49	46	>	>	X
iajs-2704	49	47	1,:then	1,:then	NUM
iajs-2704	49	48	the	the	DET
iajs-2704	49	49	eccentric	eccentric	ADJ
iajs-2704	49	50	connectivity	connectivity	NOUN
iajs-2704	49	51	index	index	NOUN
iajs-2704	49	52	of	of	ADP
iajs-2704	49	53	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	49	54	)	)	PUNCT
iajs-2704	49	55	is	be	AUX
iajs-2704	49	56	𝜉	𝜉	ADP
iajs-2704	49	57	𝑐(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝑐(ᴦ𝑆𝐼(𝑍𝑟𝑛	PROPN
iajs-2704	49	58	)	)	PUNCT
iajs-2704	49	59	)	)	PUNCT
iajs-2704	50	1	=	=	PUNCT
iajs-2704	50	2	(	(	PUNCT
iajs-2704	50	3	𝑟	𝑟	NOUN
iajs-2704	50	4	𝑛	𝑛	PRON
iajs-2704	50	5	−	−	PROPN
iajs-2704	50	6	1)(𝑟𝑛	1)(𝑟𝑛	NUM
iajs-2704	50	7	−	−	PROPN
iajs-2704	50	8	2	2	NUM
iajs-2704	50	9	)	)	PUNCT
iajs-2704	50	10	proof	proof	NOUN
iajs-2704	50	11	:	:	PUNCT
iajs-2704	50	12	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	NUM
iajs-2704	50	13	)	)	PUNCT
iajs-2704	50	14	=	=	PUNCT
iajs-2704	51	1	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	51	2	−	−	NOUN
iajs-2704	51	3	2	2	NUM
iajs-2704	51	4	,	,	PUNCT
iajs-2704	51	5	∀𝑣	∀𝑣	PROPN
iajs-2704	51	6	∈	∈	PROPN
iajs-2704	51	7	𝑉	𝑉	PROPN
iajs-2704	51	8	(	(	PUNCT
iajs-2704	51	9	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	51	10	)	)	PUNCT
iajs-2704	51	11	)	)	PUNCT
iajs-2704	51	12	,	,	PUNCT
iajs-2704	51	13	𝑣	𝑣	X
iajs-2704	51	14	=	=	SYM
iajs-2704	51	15	1,2	1,2	NUM
iajs-2704	51	16	,	,	PUNCT
iajs-2704	51	17	.	.	PUNCT
iajs-2704	51	18	.	.	PUNCT
iajs-2704	51	19	.	.	PUNCT
iajs-2704	52	1	,	,	PUNCT
iajs-2704	52	2	𝑟	𝑟	X
iajs-2704	52	3	𝑛	𝑛	PRON
iajs-2704	52	4	−	−	NUM
iajs-2704	52	5	1	1	NUM
iajs-2704	52	6	e	e	NOUN
iajs-2704	52	7	(	(	PUNCT
iajs-2704	52	8	𝑣	𝑣	NOUN
iajs-2704	52	9	)	)	PUNCT
iajs-2704	52	10	=	=	SYM
iajs-2704	52	11	1	1	NUM
iajs-2704	52	12	,	,	PUNCT
iajs-2704	52	13	∀𝑣	∀𝑣	PROPN
iajs-2704	52	14	∈	∈	PROPN
iajs-2704	52	15	v	v	PROPN
iajs-2704	52	16	(	(	PUNCT
iajs-2704	52	17	ᴦsi(z𝑟𝑛	ᴦsi(z𝑟𝑛	PROPN
iajs-2704	52	18	)	)	PUNCT
iajs-2704	52	19	)	)	PUNCT
iajs-2704	52	20	,	,	PUNCT
iajs-2704	52	21	𝑣	𝑣	X
iajs-2704	52	22	=	=	SYM
iajs-2704	52	23	1,2	1,2	NUM
iajs-2704	52	24	,	,	PUNCT
iajs-2704	52	25	.	.	PUNCT
iajs-2704	52	26	.	.	PUNCT
iajs-2704	52	27	.	.	PUNCT
iajs-2704	53	1	,	,	PUNCT
iajs-2704	53	2	𝑟	𝑟	X
iajs-2704	53	3	𝑛	𝑛	PRON
iajs-2704	53	4	−	−	PROPN
iajs-2704	53	5	1	1	NUM
iajs-2704	53	6	𝜉𝐶(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝜉𝐶(ᴦ𝑆𝐼(𝑍𝑟𝑛	NUM
iajs-2704	53	7	)	)	PUNCT
iajs-2704	53	8	)	)	PUNCT
iajs-2704	53	9	)	)	PUNCT
iajs-2704	54	1	=	=	X
iajs-2704	54	2	∑	∑	PUNCT
iajs-2704	54	3	𝑑𝑒𝑔(𝑢	𝑑𝑒𝑔(𝑢	PROPN
iajs-2704	54	4	)	)	PUNCT
iajs-2704	54	5	.	.	PUNCT
iajs-2704	55	1	𝑒(𝑢	𝑒(𝑢	PROPN
iajs-2704	55	2	)	)	PUNCT
iajs-2704	55	3	𝑢∈	𝑢∈	PROPN
iajs-2704	55	4	𝑉(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝑉(ᴦ𝑆𝐼(𝑍𝑟𝑛	PROPN
iajs-2704	55	5	)	)	PUNCT
iajs-2704	55	6	)	)	PUNCT
iajs-2704	56	1	=	=	SYM
iajs-2704	56	2	𝑑𝑒𝑔(1	𝑑𝑒𝑔(1	PROPN
iajs-2704	56	3	)	)	PUNCT
iajs-2704	56	4	.	.	PUNCT
iajs-2704	57	1	𝑒(1	𝑒(1	NOUN
iajs-2704	57	2	)	)	PUNCT
iajs-2704	57	3	+	+	NUM
iajs-2704	57	4	⋯+	⋯+	NOUN
iajs-2704	57	5	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	VERB
iajs-2704	57	6	−	−	PROPN
iajs-2704	57	7	1	1	NUM
iajs-2704	57	8	)	)	PUNCT
iajs-2704	57	9	.	.	PUNCT
iajs-2704	58	1	𝑒(𝑟𝑛	𝑒(𝑟𝑛	VERB
iajs-2704	58	2	−	−	PROPN
iajs-2704	58	3	1)⏟	1)⏟	NUM
iajs-2704	58	4	(	(	PUNCT
iajs-2704	58	5	𝑟𝑛−1)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−1)𝑡𝑖𝑚𝑒𝑠	ADJ
iajs-2704	58	6	=(	=(	NOUN
iajs-2704	58	7	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	58	8	−	−	PROPN
iajs-2704	58	9	1)(𝑟𝑛	1)(𝑟𝑛	NUM
iajs-2704	58	10	−	−	PROPN
iajs-2704	58	11	2	2	NUM
iajs-2704	58	12	)	)	PUNCT
iajs-2704	58	13	theorem	theorem	ADJ
iajs-2704	58	14	3.2	3.2	NUM
iajs-2704	58	15	let	let	VERB
iajs-2704	58	16	z𝑟𝑛	z𝑟𝑛	PROPN
iajs-2704	58	17	be	be	AUX
iajs-2704	58	18	a	a	DET
iajs-2704	58	19	group	group	NOUN
iajs-2704	58	20	with	with	ADP
iajs-2704	58	21	𝑟	𝑟	PRON
iajs-2704	58	22	≥	≥	NUM
iajs-2704	58	23	2	2	NUM
iajs-2704	58	24	,	,	PUNCT
iajs-2704	58	25	n	n	CCONJ
iajs-2704	58	26	>	>	ADP
iajs-2704	58	27	1	1	NUM
iajs-2704	58	28	then	then	ADV
iajs-2704	58	29	the	the	DET
iajs-2704	58	30	connectivity	connectivity	NOUN
iajs-2704	58	31	index	index	NOUN
iajs-2704	58	32	of	of	ADP
iajs-2704	58	33	ᴦsi(z𝑟𝑛	ᴦsi(z𝑟𝑛	PROPN
iajs-2704	58	34	)	)	PUNCT
iajs-2704	58	35	is	be	AUX
iajs-2704	58	36	𝑋(ᴦ𝑆𝐼	𝑋(ᴦ𝑆𝐼	NUM
iajs-2704	58	37	(	(	PUNCT
iajs-2704	58	38	(	(	PUNCT
iajs-2704	58	39	𝑍𝑟𝑛	𝑍𝑟𝑛	PROPN
iajs-2704	58	40	)	)	PUNCT
iajs-2704	58	41	)	)	PUNCT
iajs-2704	59	1	=	=	SYM
iajs-2704	59	2	1	1	NUM
iajs-2704	59	3	+	+	CCONJ
iajs-2704	59	4	∑	∑	PROPN
iajs-2704	59	5	(	(	PUNCT
iajs-2704	59	6	𝑟𝑛−𝑖)𝑟−1	𝑟𝑛−𝑖)𝑟−1	NUM
iajs-2704	59	7	𝑖=3	𝑖=3	X
iajs-2704	59	8	(	(	PUNCT
iajs-2704	59	9	𝑟𝑛−2	𝑟𝑛−2	PROPN
iajs-2704	59	10	)	)	PUNCT
iajs-2704	59	11	proof	proof	NOUN
iajs-2704	59	12	:	:	PUNCT
iajs-2704	59	13	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	NUM
iajs-2704	59	14	)	)	PUNCT
iajs-2704	59	15	=	=	PUNCT
iajs-2704	60	1	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	60	2	−	−	NOUN
iajs-2704	60	3	2	2	NUM
iajs-2704	60	4	,	,	PUNCT
iajs-2704	60	5	∀𝑣	∀𝑣	PROPN
iajs-2704	60	6	∈	∈	PROPN
iajs-2704	60	7	𝑉	𝑉	PROPN
iajs-2704	60	8	(	(	PUNCT
iajs-2704	60	9	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	60	10	)	)	PUNCT
iajs-2704	60	11	)	)	PUNCT
iajs-2704	60	12	,	,	PUNCT
iajs-2704	60	13	𝑣	𝑣	X
iajs-2704	60	14	=	=	SYM
iajs-2704	60	15	1,2	1,2	NUM
iajs-2704	60	16	,	,	PUNCT
iajs-2704	60	17	.	.	PUNCT
iajs-2704	60	18	.	.	PUNCT
iajs-2704	60	19	.	.	PUNCT
iajs-2704	61	1	,	,	PUNCT
iajs-2704	61	2	𝑟	𝑟	X
iajs-2704	61	3	𝑛	𝑛	PRON
iajs-2704	61	4	−	−	PROPN
iajs-2704	61	5	1	1	NUM
iajs-2704	61	6	ibn	ibn	PROPN
iajs-2704	61	7	al	al	PROPN
iajs-2704	61	8	-	-	PUNCT
iajs-2704	61	9	haitham	haitham	PROPN
iajs-2704	61	10	jour	jour	X
iajs-2704	61	11	.	.	PROPN
iajs-2704	62	1	for	for	ADP
iajs-2704	62	2	pure	pure	ADJ
iajs-2704	62	3	&	&	CCONJ
iajs-2704	62	4	appl	appl	PROPN
iajs-2704	62	5	.	.	PUNCT
iajs-2704	63	1	sci	sci	PROPN
iajs-2704	63	2	.	.	PROPN
iajs-2704	64	1	34(4)2021	34(4)2021	NUM
iajs-2704	64	2	71	71	NUM
iajs-2704	64	3	𝑋(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝑋(ᴦ𝑆𝐼(𝑍𝑟𝑛	NOUN
iajs-2704	64	4	)	)	PUNCT
iajs-2704	64	5	)	)	PUNCT
iajs-2704	65	1	=	=	PUNCT
iajs-2704	65	2	∑	∑	PUNCT
iajs-2704	65	3	1	1	NUM
iajs-2704	65	4	√𝑑𝑒𝑔(𝑢	√𝑑𝑒𝑔(𝑢	NOUN
iajs-2704	65	5	)	)	PUNCT
iajs-2704	65	6	.	.	PUNCT
iajs-2704	66	1	𝑑𝑒𝑔(𝑣)𝑢𝑣∈	𝑑𝑒𝑔(𝑣)𝑢𝑣∈	NOUN
iajs-2704	66	2	𝐸(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝐸(ᴦ𝑆𝐼(𝑍𝑟𝑛	NUM
iajs-2704	66	3	)	)	PUNCT
iajs-2704	66	4	)	)	PUNCT
iajs-2704	67	1	=	=	SYM
iajs-2704	67	2	1	1	NUM
iajs-2704	67	3	√𝑑𝑒𝑔(1	√𝑑𝑒𝑔(1	NOUN
iajs-2704	67	4	)	)	PUNCT
iajs-2704	67	5	.	.	PUNCT
iajs-2704	68	1	𝑑𝑒𝑔(2	𝑑𝑒𝑔(2	NOUN
iajs-2704	68	2	)	)	PUNCT
iajs-2704	69	1	+	+	CCONJ
iajs-2704	69	2	⋯+	⋯+	NUM
iajs-2704	69	3	1	1	NUM
iajs-2704	69	4	√𝑑𝑒𝑔(1	√𝑑𝑒𝑔(1	NOUN
iajs-2704	69	5	)	)	PUNCT
iajs-2704	69	6	.	.	PUNCT
iajs-2704	70	1	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	PROPN
iajs-2704	70	2	−	−	PROPN
iajs-2704	70	3	1)⏟	1)⏟	NUM
iajs-2704	70	4	(	(	PUNCT
iajs-2704	70	5	𝑟𝑛−2)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−2)𝑡𝑖𝑚𝑒𝑠	NUM
iajs-2704	70	6	+	+	ADJ
iajs-2704	70	7	1	1	NUM
iajs-2704	70	8	√𝑑𝑒𝑔(2	√𝑑𝑒𝑔(2	NOUN
iajs-2704	70	9	)	)	PUNCT
iajs-2704	70	10	.	.	PUNCT
iajs-2704	71	1	𝑑𝑒𝑔(3	𝑑𝑒𝑔(3	PROPN
iajs-2704	71	2	)	)	PUNCT
iajs-2704	72	1	+	+	ADJ
iajs-2704	72	2	⋯+	⋯+	NOUN
iajs-2704	72	3	1	1	NUM
iajs-2704	72	4	√𝑑𝑒𝑔(3	√𝑑𝑒𝑔(3	NOUN
iajs-2704	72	5	)	)	PUNCT
iajs-2704	72	6	.	.	PUNCT
iajs-2704	73	1	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	PROPN
iajs-2704	73	2	−	−	PROPN
iajs-2704	73	3	1)⏟	1)⏟	NUM
iajs-2704	73	4	(	(	PUNCT
iajs-2704	73	5	𝑟𝑛−3)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−3)𝑡𝑖𝑚𝑒𝑠	ADJ
iajs-2704	73	6	+	+	CCONJ
iajs-2704	73	7	1	1	NUM
iajs-2704	73	8	√𝑑𝑒𝑔(3	√𝑑𝑒𝑔(3	NOUN
iajs-2704	73	9	)	)	PUNCT
iajs-2704	73	10	.	.	PUNCT
iajs-2704	74	1	𝑑𝑒𝑔(4	𝑑𝑒𝑔(4	NOUN
iajs-2704	74	2	)	)	PUNCT
iajs-2704	75	1	+	+	CCONJ
iajs-2704	75	2	⋯+	⋯+	NOUN
iajs-2704	75	3	1	1	NUM
iajs-2704	75	4	√𝑑𝑒𝑔(3	√𝑑𝑒𝑔(3	NOUN
iajs-2704	75	5	)	)	PUNCT
iajs-2704	75	6	.	.	PUNCT
iajs-2704	76	1	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	PROPN
iajs-2704	76	2	−	−	PROPN
iajs-2704	76	3	1)⏟	1)⏟	NUM
iajs-2704	76	4	(	(	PUNCT
iajs-2704	76	5	𝑟𝑛−4)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−4)𝑡𝑖𝑚𝑒𝑠	PROPN
iajs-2704	77	1	+	+	PROPN
iajs-2704	77	2	⋯	⋯	PROPN
iajs-2704	77	3	.	.	PUNCT
iajs-2704	78	1	.+	.+	NOUN
iajs-2704	78	2	1	1	NUM
iajs-2704	78	3	√𝑑𝑒𝑔(𝑟𝑛	√𝑑𝑒𝑔(𝑟𝑛	NUM
iajs-2704	78	4	−	−	PROPN
iajs-2704	78	5	2	2	NUM
iajs-2704	78	6	)	)	PUNCT
iajs-2704	78	7	.	.	PUNCT
iajs-2704	79	1	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	79	2	−	−	PROPN
iajs-2704	79	3	1	1	NUM
iajs-2704	79	4	)	)	PUNCT
iajs-2704	79	5	=	=	SYM
iajs-2704	80	1	(	(	PUNCT
iajs-2704	80	2	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	80	3	−	−	PROPN
iajs-2704	80	4	2	2	NUM
iajs-2704	80	5	)	)	PUNCT
iajs-2704	80	6	(	(	PUNCT
iajs-2704	80	7	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	80	8	−	−	NUM
iajs-2704	80	9	2	2	NUM
iajs-2704	80	10	)	)	PUNCT
iajs-2704	80	11	+	+	CCONJ
iajs-2704	80	12	(	(	PUNCT
iajs-2704	80	13	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	80	14	−	−	NOUN
iajs-2704	80	15	3	3	NUM
iajs-2704	80	16	)	)	PUNCT
iajs-2704	80	17	(	(	PUNCT
iajs-2704	80	18	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	80	19	−	−	NUM
iajs-2704	80	20	2	2	NUM
iajs-2704	80	21	)	)	PUNCT
iajs-2704	80	22	+	+	CCONJ
iajs-2704	80	23	(	(	PUNCT
iajs-2704	80	24	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	80	25	−	−	NOUN
iajs-2704	80	26	4	4	NUM
iajs-2704	80	27	)	)	PUNCT
iajs-2704	80	28	(	(	PUNCT
iajs-2704	80	29	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	80	30	−	−	NUM
iajs-2704	80	31	2	2	X
iajs-2704	80	32	)	)	PUNCT
iajs-2704	80	33	+	+	NOUN
iajs-2704	80	34	⋯+	⋯+	NOUN
iajs-2704	80	35	1	1	NUM
iajs-2704	80	36	(	(	PUNCT
iajs-2704	80	37	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	80	38	−	−	NOUN
iajs-2704	80	39	2	2	NUM
iajs-2704	80	40	)	)	PUNCT
iajs-2704	80	41	=	=	SYM
iajs-2704	80	42	1	1	NUM
iajs-2704	80	43	+	+	CCONJ
iajs-2704	80	44	∑	∑	PUNCT
iajs-2704	80	45	(	(	PUNCT
iajs-2704	80	46	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	80	47	−	−	PROPN
iajs-2704	80	48	𝑖)𝑟𝑛−1	𝑖)𝑟𝑛−1	PROPN
iajs-2704	80	49	𝑖=3	𝑖=3	PROPN
iajs-2704	81	1	(	(	PUNCT
iajs-2704	81	2	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	81	3	−	−	PROPN
iajs-2704	81	4	2	2	NUM
iajs-2704	81	5	)	)	PUNCT
iajs-2704	81	6	theorem	theorem	VERB
iajs-2704	81	7	3.3	3.3	NUM
iajs-2704	81	8	let	let	VERB
iajs-2704	81	9	𝑍𝑟𝑛	𝑍𝑟𝑛	PROPN
iajs-2704	81	10	be	be	AUX
iajs-2704	81	11	a	a	DET
iajs-2704	81	12	group	group	NOUN
iajs-2704	81	13	with	with	ADP
iajs-2704	81	14	𝑟	𝑟	PRON
iajs-2704	81	15	≥	≥	NUM
iajs-2704	81	16	2	2	NUM
iajs-2704	81	17	,	,	PUNCT
iajs-2704	81	18	𝑛	𝑛	PROPN
iajs-2704	81	19	>	>	X
iajs-2704	81	20	1,:then	1,:then	NUM
iajs-2704	81	21	the	the	DET
iajs-2704	81	22	sum	sum	NOUN
iajs-2704	81	23	connectivity	connectivity	NOUN
iajs-2704	81	24	index	index	NOUN
iajs-2704	81	25	of	of	ADP
iajs-2704	81	26	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	81	27	)	)	PUNCT
iajs-2704	81	28	is	be	AUX
iajs-2704	81	29	s(ᴦ𝑆𝐼(𝑍𝑟𝑛	s(ᴦ𝑆𝐼(𝑍𝑟𝑛	PROPN
iajs-2704	81	30	)	)	PUNCT
iajs-2704	81	31	)	)	PUNCT
iajs-2704	82	1	=	=	PUNCT
iajs-2704	82	2	∑	∑	PUNCT
iajs-2704	82	3	(	(	PUNCT
iajs-2704	82	4	𝑟𝑛−𝑖)𝑟𝑛−1	𝑟𝑛−𝑖)𝑟𝑛−1	NOUN
iajs-2704	82	5	𝑖=2	𝑖=2	CCONJ
iajs-2704	82	6	√2𝑟𝑛−4	√2𝑟𝑛−4	PROPN
iajs-2704	82	7	proof	proof	NOUN
iajs-2704	82	8	:	:	PUNCT
iajs-2704	82	9	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	NUM
iajs-2704	82	10	)	)	PUNCT
iajs-2704	82	11	=	=	PUNCT
iajs-2704	83	1	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	83	2	−	−	NOUN
iajs-2704	83	3	2	2	NUM
iajs-2704	83	4	,	,	PUNCT
iajs-2704	83	5	∀𝑣	∀𝑣	PROPN
iajs-2704	83	6	∈	∈	PROPN
iajs-2704	83	7	𝑉	𝑉	PROPN
iajs-2704	83	8	(	(	PUNCT
iajs-2704	83	9	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	83	10	)	)	PUNCT
iajs-2704	83	11	)	)	PUNCT
iajs-2704	83	12	,	,	PUNCT
iajs-2704	83	13	𝑣	𝑣	X
iajs-2704	83	14	=	=	SYM
iajs-2704	83	15	1,2	1,2	NUM
iajs-2704	83	16	,	,	PUNCT
iajs-2704	83	17	.	.	PUNCT
iajs-2704	83	18	.	.	PUNCT
iajs-2704	83	19	.	.	PUNCT
iajs-2704	84	1	,	,	PUNCT
iajs-2704	84	2	𝑟	𝑟	X
iajs-2704	84	3	𝑛	𝑛	PRON
iajs-2704	84	4	−	−	PROPN
iajs-2704	84	5	1	1	NUM
iajs-2704	84	6	𝑆(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝑆(ᴦ𝑆𝐼(𝑍𝑟𝑛	PROPN
iajs-2704	84	7	)	)	PUNCT
iajs-2704	84	8	)	)	PUNCT
iajs-2704	85	1	=	=	PUNCT
iajs-2704	85	2	∑	∑	PUNCT
iajs-2704	85	3	1	1	NUM
iajs-2704	85	4	√𝑑𝑒𝑔(𝑢	√𝑑𝑒𝑔(𝑢	NOUN
iajs-2704	85	5	)	)	PUNCT
iajs-2704	86	1	+	+	CCONJ
iajs-2704	86	2	𝑑𝑒𝑔(𝑣)𝑢𝑣∈	𝑑𝑒𝑔(𝑣)𝑢𝑣∈	NOUN
iajs-2704	86	3	𝐸(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝐸(ᴦ𝑆𝐼(𝑍𝑟𝑛	NUM
iajs-2704	86	4	)	)	PUNCT
iajs-2704	86	5	)	)	PUNCT
iajs-2704	87	1	=	=	SYM
iajs-2704	87	2	1	1	NUM
iajs-2704	87	3	√𝑑𝑒𝑔(1	√𝑑𝑒𝑔(1	NOUN
iajs-2704	87	4	)	)	PUNCT
iajs-2704	87	5	+	+	CCONJ
iajs-2704	87	6	𝑑𝑒𝑔(2	𝑑𝑒𝑔(2	NOUN
iajs-2704	87	7	)	)	PUNCT
iajs-2704	88	1	+	+	NUM
iajs-2704	88	2	⋯+	⋯+	NUM
iajs-2704	88	3	1	1	NUM
iajs-2704	88	4	√𝑑𝑒𝑔(1	√𝑑𝑒𝑔(1	NOUN
iajs-2704	88	5	)	)	PUNCT
iajs-2704	89	1	+	+	ADJ
iajs-2704	89	2	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	89	3	−	−	PROPN
iajs-2704	89	4	1)⏟	1)⏟	NUM
iajs-2704	89	5	(	(	PUNCT
iajs-2704	89	6	𝑟𝑛−2)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−2)𝑡𝑖𝑚𝑒𝑠	NUM
iajs-2704	89	7	+	+	ADJ
iajs-2704	89	8	1	1	NUM
iajs-2704	89	9	√𝑑𝑒𝑔(2	√𝑑𝑒𝑔(2	NOUN
iajs-2704	89	10	)	)	PUNCT
iajs-2704	89	11	+	+	NUM
iajs-2704	89	12	𝑑𝑒𝑔(3	𝑑𝑒𝑔(3	NOUN
iajs-2704	89	13	)	)	PUNCT
iajs-2704	90	1	+	+	NUM
iajs-2704	90	2	⋯+	⋯+	NOUN
iajs-2704	90	3	1	1	NUM
iajs-2704	90	4	√𝑑𝑒𝑔(3	√𝑑𝑒𝑔(3	NOUN
iajs-2704	90	5	)	)	PUNCT
iajs-2704	90	6	+	+	NUM
iajs-2704	90	7	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	90	8	−	−	PROPN
iajs-2704	90	9	1)⏟	1)⏟	NUM
iajs-2704	90	10	(	(	PUNCT
iajs-2704	90	11	𝑟𝑛−3)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−3)𝑡𝑖𝑚𝑒𝑠	ADJ
iajs-2704	90	12	+	+	CCONJ
iajs-2704	90	13	1	1	NUM
iajs-2704	90	14	√𝑑𝑒𝑔(3	√𝑑𝑒𝑔(3	NOUN
iajs-2704	90	15	)	)	PUNCT
iajs-2704	90	16	+	+	NUM
iajs-2704	90	17	𝑑𝑒𝑔(4	𝑑𝑒𝑔(4	NOUN
iajs-2704	90	18	)	)	PUNCT
iajs-2704	91	1	+	+	CCONJ
iajs-2704	91	2	⋯+	⋯+	NOUN
iajs-2704	91	3	1	1	NUM
iajs-2704	91	4	√𝑑𝑒𝑔(3	√𝑑𝑒𝑔(3	NOUN
iajs-2704	91	5	)	)	PUNCT
iajs-2704	92	1	+	+	NUM
iajs-2704	92	2	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	92	3	−	−	PROPN
iajs-2704	92	4	1)⏟	1)⏟	NUM
iajs-2704	92	5	(	(	PUNCT
iajs-2704	92	6	𝑟𝑛−4)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−4)𝑡𝑖𝑚𝑒𝑠	PROPN
iajs-2704	93	1	+	+	PROPN
iajs-2704	93	2	⋯	⋯	PROPN
iajs-2704	93	3	.	.	PUNCT
iajs-2704	94	1	.+	.+	NOUN
iajs-2704	94	2	1	1	NUM
iajs-2704	94	3	√𝑑𝑒𝑔(𝑟𝑛	√𝑑𝑒𝑔(𝑟𝑛	NUM
iajs-2704	94	4	−	−	NOUN
iajs-2704	94	5	2	2	NUM
iajs-2704	94	6	)	)	PUNCT
iajs-2704	94	7	+	+	ADJ
iajs-2704	94	8	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	94	9	−	−	PROPN
iajs-2704	94	10	1	1	NUM
iajs-2704	94	11	)	)	PUNCT
iajs-2704	94	12	ibn	ibn	PROPN
iajs-2704	94	13	al	al	PROPN
iajs-2704	94	14	-	-	PUNCT
iajs-2704	94	15	haitham	haitham	PROPN
iajs-2704	94	16	jour	jour	X
iajs-2704	94	17	.	.	PROPN
iajs-2704	95	1	for	for	ADP
iajs-2704	95	2	pure	pure	ADJ
iajs-2704	95	3	&	&	CCONJ
iajs-2704	95	4	appl	appl	PROPN
iajs-2704	95	5	.	.	PUNCT
iajs-2704	96	1	sci	sci	PROPN
iajs-2704	96	2	.	.	PROPN
iajs-2704	97	1	34(4)2021	34(4)2021	NUM
iajs-2704	97	2	72	72	NUM
iajs-2704	97	3	=	=	SYM
iajs-2704	97	4	(	(	PUNCT
iajs-2704	97	5	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	97	6	−	−	NOUN
iajs-2704	97	7	2	2	X
iajs-2704	97	8	)	)	PUNCT
iajs-2704	97	9	√2𝑟𝑛	√2𝑟𝑛	NOUN
iajs-2704	97	10	−	−	PROPN
iajs-2704	97	11	4	4	NUM
iajs-2704	97	12	+	+	CCONJ
iajs-2704	97	13	(	(	PUNCT
iajs-2704	97	14	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	97	15	−	−	NOUN
iajs-2704	97	16	3	3	X
iajs-2704	97	17	)	)	PUNCT
iajs-2704	97	18	√2𝑟𝑛	√2𝑟𝑛	NOUN
iajs-2704	97	19	−	−	PROPN
iajs-2704	97	20	4	4	NUM
iajs-2704	97	21	+	+	CCONJ
iajs-2704	97	22	(	(	PUNCT
iajs-2704	97	23	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	97	24	−	−	NOUN
iajs-2704	97	25	4	4	X
iajs-2704	97	26	)	)	PUNCT
iajs-2704	97	27	√2𝑟𝑛	√2𝑟𝑛	NOUN
iajs-2704	97	28	−	−	PROPN
iajs-2704	97	29	4	4	NUM
iajs-2704	97	30	+	+	NOUN
iajs-2704	97	31	⋯+	⋯+	NOUN
iajs-2704	97	32	1	1	NUM
iajs-2704	97	33	√2𝑟𝑛	√2𝑟𝑛	NOUN
iajs-2704	97	34	−	−	PROPN
iajs-2704	97	35	4	4	NUM
iajs-2704	97	36	=	=	SYM
iajs-2704	97	37	∑	∑	PUNCT
iajs-2704	97	38	(	(	PUNCT
iajs-2704	97	39	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	97	40	−	−	PROPN
iajs-2704	97	41	𝑖)𝑟𝑛−1	𝑖)𝑟𝑛−1	NOUN
iajs-2704	97	42	𝑖=2	𝑖=2	PUNCT
iajs-2704	98	1	√2𝑟𝑛	√2𝑟𝑛	NOUN
iajs-2704	98	2	−	−	PROPN
iajs-2704	98	3	4	4	NUM
iajs-2704	98	4	theorem	theorem	VERB
iajs-2704	98	5	3.4	3.4	NUM
iajs-2704	98	6	let	let	VERB
iajs-2704	98	7	𝑍𝑟𝑛	𝑍𝑟𝑛	PROPN
iajs-2704	98	8	be	be	AUX
iajs-2704	98	9	a	a	DET
iajs-2704	98	10	group	group	NOUN
iajs-2704	98	11	with	with	ADP
iajs-2704	98	12	𝑟	𝑟	PRON
iajs-2704	98	13	≥	≥	NUM
iajs-2704	98	14	2	2	NUM
iajs-2704	98	15	,	,	PUNCT
iajs-2704	98	16	𝑛	𝑛	PROPN
iajs-2704	98	17	>	>	X
iajs-2704	98	18	1	1	NUM
iajs-2704	98	19	then	then	ADV
iajs-2704	98	20	the	the	DET
iajs-2704	98	21	first	first	ADJ
iajs-2704	98	22	zegrab	zegrab	NOUN
iajs-2704	98	23	index	index	NOUN
iajs-2704	98	24	of	of	ADP
iajs-2704	98	25	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	98	26	)	)	PUNCT
iajs-2704	98	27	is	be	AUX
iajs-2704	98	28	𝑀1(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝑀1(ᴦ𝑆𝐼(𝑍𝑟𝑛	NUM
iajs-2704	98	29	)	)	PUNCT
iajs-2704	98	30	)	)	PUNCT
iajs-2704	99	1	=(	=(	NOUN
iajs-2704	99	2	𝑟	𝑟	X
iajs-2704	99	3	𝑛	𝑛	PRON
iajs-2704	99	4	−	−	PROPN
iajs-2704	100	1	1)(𝑟𝑛	1)(𝑟𝑛	NUM
iajs-2704	100	2	−	−	PROPN
iajs-2704	100	3	2)2	2)2	NUM
iajs-2704	100	4	proof	proof	NOUN
iajs-2704	100	5	:	:	PUNCT
iajs-2704	100	6	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	NUM
iajs-2704	100	7	)	)	PUNCT
iajs-2704	100	8	=	=	PUNCT
iajs-2704	101	1	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	101	2	−	−	NOUN
iajs-2704	101	3	2	2	NUM
iajs-2704	101	4	,	,	PUNCT
iajs-2704	101	5	∀𝑣	∀𝑣	PROPN
iajs-2704	101	6	∈	∈	PROPN
iajs-2704	101	7	𝑉	𝑉	PROPN
iajs-2704	101	8	(	(	PUNCT
iajs-2704	101	9	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	101	10	)	)	PUNCT
iajs-2704	101	11	)	)	PUNCT
iajs-2704	101	12	,	,	PUNCT
iajs-2704	101	13	𝑣	𝑣	X
iajs-2704	101	14	=	=	SYM
iajs-2704	101	15	1,2	1,2	NUM
iajs-2704	101	16	,	,	PUNCT
iajs-2704	101	17	.	.	PUNCT
iajs-2704	101	18	.	.	PUNCT
iajs-2704	101	19	.	.	PUNCT
iajs-2704	102	1	,	,	PUNCT
iajs-2704	102	2	𝑟	𝑟	X
iajs-2704	102	3	𝑛	𝑛	PRON
iajs-2704	102	4	−	−	PROPN
iajs-2704	102	5	1	1	NUM
iajs-2704	102	6	𝑀1(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝑀1(ᴦ𝑆𝐼(𝑍𝑟𝑛	NUM
iajs-2704	102	7	)	)	PUNCT
iajs-2704	102	8	)	)	PUNCT
iajs-2704	103	1	=	=	PUNCT
iajs-2704	103	2	∑	∑	PUNCT
iajs-2704	103	3	(	(	PUNCT
iajs-2704	103	4	𝑑𝑒𝑔(𝑢))2𝑢∈	𝑑𝑒𝑔(𝑢))2𝑢∈	PROPN
iajs-2704	103	5	𝑉(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝑉(ᴦ𝑆𝐼(𝑍𝑟𝑛	PROPN
iajs-2704	103	6	)	)	PUNCT
iajs-2704	103	7	)	)	PUNCT
iajs-2704	103	8	(	(	PUNCT
iajs-2704	103	9	𝑑𝑒𝑔(1))2	𝑑𝑒𝑔(1))2	NOUN
iajs-2704	103	10	+	+	NOUN
iajs-2704	103	11	⋯+	⋯+	NOUN
iajs-2704	103	12	(	(	PUNCT
iajs-2704	103	13	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	103	14	−	−	PROPN
iajs-2704	103	15	1))2⏟	1))2⏟	NUM
iajs-2704	103	16	(	(	PUNCT
iajs-2704	103	17	𝑟𝑛−1)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−1)𝑡𝑖𝑚𝑒𝑠	NOUN
iajs-2704	103	18	=	=	SYM
iajs-2704	103	19	=	=	SYM
iajs-2704	103	20	(	(	PUNCT
iajs-2704	103	21	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	103	22	−	−	PROPN
iajs-2704	103	23	1)(𝑟𝑛	1)(𝑟𝑛	NUM
iajs-2704	103	24	−	−	PROPN
iajs-2704	103	25	2)2	2)2	NUM
iajs-2704	103	26	theorem	theorem	VERB
iajs-2704	103	27	3.5	3.5	NUM
iajs-2704	103	28	let	let	VERB
iajs-2704	103	29	𝑍𝑟𝑛	𝑍𝑟𝑛	PROPN
iajs-2704	103	30	be	be	AUX
iajs-2704	103	31	a	a	DET
iajs-2704	103	32	group	group	NOUN
iajs-2704	103	33	with	with	ADP
iajs-2704	103	34	𝑟	𝑟	PRON
iajs-2704	103	35	≥	≥	NUM
iajs-2704	103	36	2	2	NUM
iajs-2704	103	37	,	,	PUNCT
iajs-2704	103	38	𝑛	𝑛	PROPN
iajs-2704	103	39	>	>	X
iajs-2704	103	40	1	1	NUM
iajs-2704	103	41	then	then	ADV
iajs-2704	103	42	the	the	DET
iajs-2704	103	43	second	second	ADJ
iajs-2704	103	44	zegrab	zegrab	NOUN
iajs-2704	103	45	index	index	NOUN
iajs-2704	103	46	of	of	ADP
iajs-2704	103	47	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	103	48	)	)	PUNCT
iajs-2704	103	49	is	be	AUX
iajs-2704	103	50	𝑀2(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝑀2(ᴦ𝑆𝐼(𝑍𝑟𝑛	NUM
iajs-2704	103	51	)	)	PUNCT
iajs-2704	103	52	)	)	PUNCT
iajs-2704	104	1	=	=	PUNCT
iajs-2704	104	2	(	(	PUNCT
iajs-2704	104	3	𝑟	𝑟	NOUN
iajs-2704	104	4	𝑛	𝑛	PRON
iajs-2704	104	5	−	−	PROPN
iajs-2704	104	6	2)3	2)3	NUM
iajs-2704	104	7	+	+	CCONJ
iajs-2704	104	8	(	(	PUNCT
iajs-2704	104	9	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	104	10	−	−	PROPN
iajs-2704	104	11	2)2∑	2)2∑	NUM
iajs-2704	104	12	(	(	PUNCT
iajs-2704	104	13	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	104	14	−	−	PROPN
iajs-2704	104	15	𝑖)𝑟𝑛−1	𝑖)𝑟𝑛−1	NOUN
iajs-2704	105	1	𝑖=3	𝑖=3	PROPN
iajs-2704	105	2	proof	proof	NOUN
iajs-2704	105	3	:	:	PUNCT
iajs-2704	105	4	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	NUM
iajs-2704	105	5	)	)	PUNCT
iajs-2704	105	6	=	=	PUNCT
iajs-2704	106	1	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	106	2	−	−	NOUN
iajs-2704	106	3	2	2	NUM
iajs-2704	106	4	,	,	PUNCT
iajs-2704	106	5	∀𝑣	∀𝑣	PROPN
iajs-2704	106	6	∈	∈	PROPN
iajs-2704	106	7	𝑉	𝑉	PROPN
iajs-2704	106	8	(	(	PUNCT
iajs-2704	106	9	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	106	10	)	)	PUNCT
iajs-2704	106	11	)	)	PUNCT
iajs-2704	106	12	,	,	PUNCT
iajs-2704	106	13	𝑣	𝑣	X
iajs-2704	106	14	=	=	SYM
iajs-2704	106	15	1,2	1,2	NUM
iajs-2704	106	16	,	,	PUNCT
iajs-2704	106	17	.	.	PUNCT
iajs-2704	106	18	.	.	PUNCT
iajs-2704	106	19	.	.	PUNCT
iajs-2704	107	1	,	,	PUNCT
iajs-2704	107	2	𝑟	𝑟	X
iajs-2704	107	3	𝑛	𝑛	PRON
iajs-2704	107	4	−	−	PROPN
iajs-2704	107	5	1	1	NUM
iajs-2704	107	6	𝑀2(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝑀2(ᴦ𝑆𝐼(𝑍𝑟𝑛	NUM
iajs-2704	107	7	)	)	PUNCT
iajs-2704	107	8	)	)	PUNCT
iajs-2704	108	1	=	=	PUNCT
iajs-2704	108	2	∑	∑	PUNCT
iajs-2704	108	3	𝑑𝑒𝑔(𝑢	𝑑𝑒𝑔(𝑢	PROPN
iajs-2704	108	4	)	)	PUNCT
iajs-2704	108	5	.	.	PUNCT
iajs-2704	109	1	𝑑𝑒𝑔(𝑣)𝑢𝑣	𝑑𝑒𝑔(𝑣)𝑢𝑣	PROPN
iajs-2704	109	2	𝐸(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝐸(ᴦ𝑆𝐼(𝑍𝑟𝑛	NUM
iajs-2704	109	3	)	)	PUNCT
iajs-2704	109	4	)	)	PUNCT
iajs-2704	110	1	=	=	SYM
iajs-2704	110	2	𝑑𝑒𝑔(1	𝑑𝑒𝑔(1	PROPN
iajs-2704	110	3	)	)	PUNCT
iajs-2704	110	4	.	.	PUNCT
iajs-2704	111	1	𝑑𝑒𝑔(2	𝑑𝑒𝑔(2	NOUN
iajs-2704	111	2	)	)	PUNCT
iajs-2704	112	1	+	+	NUM
iajs-2704	112	2	⋯+𝑑𝑒𝑔(1	⋯+𝑑𝑒𝑔(1	NOUN
iajs-2704	112	3	)	)	PUNCT
iajs-2704	112	4	.	.	PUNCT
iajs-2704	113	1	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	PROPN
iajs-2704	113	2	−	−	PROPN
iajs-2704	113	3	1)⏟	1)⏟	NUM
iajs-2704	113	4	(	(	PUNCT
iajs-2704	113	5	𝑟𝑛−2)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−2)𝑡𝑖𝑚𝑒𝑠	ADJ
iajs-2704	113	6	+	+	CCONJ
iajs-2704	113	7	𝑑𝑒𝑔(2	𝑑𝑒𝑔(2	NOUN
iajs-2704	113	8	)	)	PUNCT
iajs-2704	113	9	.	.	PUNCT
iajs-2704	114	1	𝑑𝑒𝑔(3	𝑑𝑒𝑔(3	PUNCT
iajs-2704	114	2	)	)	PUNCT
iajs-2704	115	1	+	+	PUNCT
iajs-2704	115	2	⋯+𝑑𝑒𝑔(2	⋯+𝑑𝑒𝑔(2	PROPN
iajs-2704	115	3	)	)	PUNCT
iajs-2704	115	4	.	.	PUNCT
iajs-2704	116	1	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	PROPN
iajs-2704	116	2	−	−	PROPN
iajs-2704	116	3	1)⏟	1)⏟	NUM
iajs-2704	116	4	(	(	PUNCT
iajs-2704	116	5	𝑟𝑛−3)times	𝑟𝑛−3)time	NOUN
iajs-2704	116	6	+	+	PUNCT
iajs-2704	116	7	𝑑𝑒𝑔(3	𝑑𝑒𝑔(3	NOUN
iajs-2704	116	8	)	)	PUNCT
iajs-2704	116	9	.	.	PUNCT
iajs-2704	117	1	𝑑𝑒𝑔(4	𝑑𝑒𝑔(4	NOUN
iajs-2704	117	2	)	)	PUNCT
iajs-2704	118	1	+	+	CCONJ
iajs-2704	119	1	⋯+𝑑𝑒𝑔(3	⋯+𝑑𝑒𝑔(3	NOUN
iajs-2704	119	2	)	)	PUNCT
iajs-2704	119	3	.	.	PUNCT
iajs-2704	120	1	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	PROPN
iajs-2704	120	2	−	−	PROPN
iajs-2704	120	3	1)⏟	1)⏟	NUM
iajs-2704	120	4	(	(	PUNCT
iajs-2704	120	5	𝑟𝑛−4)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−4)𝑡𝑖𝑚𝑒𝑠	NOUN
iajs-2704	120	6	+	+	NOUN
iajs-2704	120	7	⋯+	⋯+	NOUN
iajs-2704	120	8	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	120	9	−	−	PROPN
iajs-2704	120	10	2	2	NUM
iajs-2704	120	11	)	)	PUNCT
iajs-2704	120	12	.	.	PUNCT
iajs-2704	121	1	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	121	2	−	−	PROPN
iajs-2704	121	3	1	1	NUM
iajs-2704	121	4	)	)	PUNCT
iajs-2704	121	5	=	=	SYM
iajs-2704	122	1	(	(	PUNCT
iajs-2704	122	2	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	122	3	−	−	PROPN
iajs-2704	122	4	2)3	2)3	NUM
iajs-2704	123	1	+	+	CCONJ
iajs-2704	123	2	(	(	PUNCT
iajs-2704	123	3	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	123	4	−	−	PROPN
iajs-2704	123	5	3)(𝑟𝑛	3)(𝑟𝑛	NUM
iajs-2704	123	6	−	−	PROPN
iajs-2704	123	7	2)2	2)2	NUM
iajs-2704	123	8	+	+	CCONJ
iajs-2704	123	9	(	(	PUNCT
iajs-2704	123	10	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	123	11	−	−	PROPN
iajs-2704	123	12	4)(𝑟𝑛	4)(𝑟𝑛	NUM
iajs-2704	123	13	−	−	PROPN
iajs-2704	123	14	2)2	2)2	NUM
iajs-2704	123	15	+	+	NOUN
iajs-2704	123	16	⋯+	⋯+	NOUN
iajs-2704	123	17	(	(	PUNCT
iajs-2704	123	18	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	123	19	−	−	PROPN
iajs-2704	123	20	2)2	2)2	NUM
iajs-2704	123	21	=	=	SYM
iajs-2704	123	22	(	(	PUNCT
iajs-2704	123	23	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	123	24	−	−	PROPN
iajs-2704	123	25	2)3	2)3	NUM
iajs-2704	123	26	+	+	CCONJ
iajs-2704	123	27	(	(	PUNCT
iajs-2704	123	28	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	123	29	−	−	PROPN
iajs-2704	123	30	2)2	2)2	NUM
iajs-2704	123	31	∑(𝑟𝑛	∑(𝑟𝑛	ADP
iajs-2704	123	32	−	−	PROPN
iajs-2704	123	33	𝑖	𝑖	SYM
iajs-2704	123	34	)	)	PUNCT
iajs-2704	123	35	𝑟𝑛−1	𝑟𝑛−1	NOUN
iajs-2704	123	36	𝑖=3	𝑖=3	PROPN
iajs-2704	123	37	ibn	ibn	PROPN
iajs-2704	123	38	al	al	PROPN
iajs-2704	123	39	-	-	PUNCT
iajs-2704	123	40	haitham	haitham	PROPN
iajs-2704	123	41	jour	jour	X
iajs-2704	123	42	.	.	PROPN
iajs-2704	124	1	for	for	ADP
iajs-2704	124	2	pure	pure	ADJ
iajs-2704	124	3	&	&	CCONJ
iajs-2704	124	4	appl	appl	PROPN
iajs-2704	124	5	.	.	PUNCT
iajs-2704	125	1	sci	sci	PROPN
iajs-2704	125	2	.	.	PROPN
iajs-2704	126	1	34(4)2021	34(4)2021	NUM
iajs-2704	126	2	73	73	NUM
iajs-2704	126	3	theorem	theorem	VERB
iajs-2704	126	4	3.6	3.6	NUM
iajs-2704	126	5	let	let	VERB
iajs-2704	126	6	𝑍𝑟𝑛	𝑍𝑟𝑛	PROPN
iajs-2704	126	7	be	be	AUX
iajs-2704	126	8	a	a	DET
iajs-2704	126	9	group	group	NOUN
iajs-2704	126	10	with	with	ADP
iajs-2704	126	11	r	r	PROPN
iajs-2704	126	12	≥	≥	NUM
iajs-2704	126	13	2	2	NUM
iajs-2704	126	14	,	,	PUNCT
iajs-2704	126	15	𝑛	𝑛	PROPN
iajs-2704	126	16	>	>	X
iajs-2704	126	17	1	1	NUM
iajs-2704	126	18	then	then	ADV
iajs-2704	126	19	the	the	DET
iajs-2704	126	20	forgotten	forget	VERB
iajs-2704	126	21	index	index	NOUN
iajs-2704	126	22	of	of	ADP
iajs-2704	126	23	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	126	24	)	)	PUNCT
iajs-2704	126	25	is	be	AUX
iajs-2704	126	26	f(ᴦ𝑆𝐼(𝑍𝑟𝑛	f(ᴦ𝑆𝐼(𝑍𝑟𝑛	PROPN
iajs-2704	126	27	)	)	PUNCT
iajs-2704	126	28	)	)	PUNCT
iajs-2704	127	1	=	=	PUNCT
iajs-2704	127	2	(	(	PUNCT
iajs-2704	127	3	𝑟	𝑟	NOUN
iajs-2704	127	4	𝑛	𝑛	PRON
iajs-2704	127	5	−	−	PROPN
iajs-2704	127	6	1)(𝑟𝑛	1)(𝑟𝑛	NUM
iajs-2704	127	7	−	−	PROPN
iajs-2704	127	8	2)3	2)3	NUM
iajs-2704	127	9	proof	proof	NOUN
iajs-2704	127	10	:	:	PUNCT
iajs-2704	127	11	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	NUM
iajs-2704	127	12	)	)	PUNCT
iajs-2704	127	13	=	=	PUNCT
iajs-2704	128	1	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	128	2	−	−	NOUN
iajs-2704	128	3	2	2	NUM
iajs-2704	128	4	,	,	PUNCT
iajs-2704	128	5	∀𝑣	∀𝑣	PROPN
iajs-2704	128	6	∈	∈	PROPN
iajs-2704	128	7	𝑉	𝑉	PROPN
iajs-2704	128	8	(	(	PUNCT
iajs-2704	128	9	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	128	10	)	)	PUNCT
iajs-2704	128	11	)	)	PUNCT
iajs-2704	128	12	,	,	PUNCT
iajs-2704	128	13	𝑣	𝑣	X
iajs-2704	128	14	=	=	SYM
iajs-2704	128	15	1,2	1,2	NUM
iajs-2704	128	16	,	,	PUNCT
iajs-2704	128	17	.	.	PUNCT
iajs-2704	128	18	.	.	PUNCT
iajs-2704	128	19	.	.	PUNCT
iajs-2704	129	1	,	,	PUNCT
iajs-2704	129	2	𝑟	𝑟	X
iajs-2704	129	3	𝑛	𝑛	PRON
iajs-2704	129	4	−	−	PROPN
iajs-2704	129	5	1	1	NUM
iajs-2704	129	6	f(ᴦ𝑆𝐼(𝑍𝑟𝑛	f(ᴦ𝑆𝐼(𝑍𝑟𝑛	PROPN
iajs-2704	129	7	)	)	PUNCT
iajs-2704	129	8	)	)	PUNCT
iajs-2704	130	1	=	=	PUNCT
iajs-2704	130	2	∑	∑	PUNCT
iajs-2704	130	3	(	(	PUNCT
iajs-2704	130	4	𝑑𝑒𝑔(𝑢))3𝑢∈𝑉(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝑑𝑒𝑔(𝑢))3𝑢∈𝑉(ᴦ𝑆𝐼(𝑍𝑟𝑛	NOUN
iajs-2704	130	5	)	)	PUNCT
iajs-2704	130	6	)	)	PUNCT
iajs-2704	131	1	=	=	PRON
iajs-2704	131	2	(	(	PUNCT
iajs-2704	131	3	𝑑𝑒𝑔(1))3	𝑑𝑒𝑔(1))3	X
iajs-2704	131	4	+	+	NOUN
iajs-2704	131	5	⋯+	⋯+	NOUN
iajs-2704	131	6	(	(	PUNCT
iajs-2704	131	7	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	131	8	−	−	PROPN
iajs-2704	131	9	1))3⏟	1))3⏟	NUM
iajs-2704	131	10	(	(	PUNCT
iajs-2704	131	11	𝑟𝑛−1	𝑟𝑛−1	NOUN
iajs-2704	131	12	)	)	PUNCT
iajs-2704	131	13	𝑡𝑖𝑚𝑒𝑠	𝑡𝑖𝑚𝑒𝑠	NOUN
iajs-2704	131	14	=(	=(	PROPN
iajs-2704	131	15	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	132	1	−	−	PROPN
iajs-2704	132	2	1)(𝑟𝑛	1)(𝑟𝑛	NUM
iajs-2704	132	3	−	−	PROPN
iajs-2704	132	4	2)3	2)3	NUM
iajs-2704	132	5	theorem	theorem	VERB
iajs-2704	132	6	3.7	3.7	NUM
iajs-2704	132	7	let	let	VERB
iajs-2704	132	8	z𝑟𝑛	z𝑟𝑛	PROPN
iajs-2704	132	9	be	be	AUX
iajs-2704	132	10	a	a	DET
iajs-2704	132	11	group	group	NOUN
iajs-2704	132	12	with	with	ADP
iajs-2704	132	13	𝑟	𝑟	PRON
iajs-2704	132	14	≥	≥	NUM
iajs-2704	132	15	2	2	NUM
iajs-2704	132	16	,	,	PUNCT
iajs-2704	132	17	𝑛	𝑛	PROPN
iajs-2704	132	18	>	>	X
iajs-2704	132	19	1,:then	1,:then	NUM
iajs-2704	132	20	the	the	DET
iajs-2704	132	21	atom	atom	NOUN
iajs-2704	132	22	bond	bond	NOUN
iajs-2704	132	23	connectivity	connectivity	NOUN
iajs-2704	132	24	index	index	NOUN
iajs-2704	132	25	of	of	ADP
iajs-2704	132	26	ᴦsi(z𝑟𝑛	ᴦsi(z𝑟𝑛	PROPN
iajs-2704	132	27	)	)	PUNCT
iajs-2704	132	28	is	be	AUX
iajs-2704	132	29	abc(ᴦsi(z𝑟𝑛	abc(ᴦsi(z𝑟𝑛	ADV
iajs-2704	132	30	)	)	PUNCT
iajs-2704	132	31	)	)	PUNCT
iajs-2704	132	32	)	)	PUNCT
iajs-2704	133	1	=	=	PUNCT
iajs-2704	133	2	√2𝑟𝑛	√2𝑟𝑛	NOUN
iajs-2704	133	3	−	−	PROPN
iajs-2704	133	4	6	6	NUM
iajs-2704	133	5	+	+	CCONJ
iajs-2704	133	6	√2𝑟𝑛	√2𝑟𝑛	NUM
iajs-2704	133	7	−	−	PROPN
iajs-2704	133	8	6∑	6∑	NOUN
iajs-2704	133	9	(	(	PUNCT
iajs-2704	133	10	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	133	11	−	−	PUNCT
iajs-2704	133	12	i)𝑟𝑛−1	i)𝑟𝑛−1	PROPN
iajs-2704	133	13	i=3	i=3	X
iajs-2704	134	1	(	(	PUNCT
iajs-2704	135	1	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	135	2	−	−	NOUN
iajs-2704	135	3	2	2	X
iajs-2704	135	4	)	)	PUNCT
iajs-2704	135	5	proof	proof	NOUN
iajs-2704	135	6	:	:	PUNCT
iajs-2704	135	7	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	NUM
iajs-2704	135	8	)	)	PUNCT
iajs-2704	135	9	=	=	PUNCT
iajs-2704	136	1	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	136	2	−	−	NOUN
iajs-2704	136	3	2	2	NUM
iajs-2704	136	4	,	,	PUNCT
iajs-2704	136	5	∀𝑣	∀𝑣	PROPN
iajs-2704	136	6	∈	∈	PROPN
iajs-2704	136	7	𝑉	𝑉	PROPN
iajs-2704	136	8	(	(	PUNCT
iajs-2704	136	9	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	136	10	)	)	PUNCT
iajs-2704	136	11	)	)	PUNCT
iajs-2704	136	12	,	,	PUNCT
iajs-2704	136	13	𝑣	𝑣	X
iajs-2704	136	14	=	=	SYM
iajs-2704	136	15	1,2	1,2	NUM
iajs-2704	136	16	,	,	PUNCT
iajs-2704	136	17	.	.	PUNCT
iajs-2704	136	18	.	.	PUNCT
iajs-2704	136	19	.	.	PUNCT
iajs-2704	137	1	,	,	PUNCT
iajs-2704	137	2	𝑟	𝑟	X
iajs-2704	137	3	𝑛	𝑛	PRON
iajs-2704	137	4	−	−	PROPN
iajs-2704	137	5	1	1	NUM
iajs-2704	137	6	𝐴𝐵𝐶(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝐴𝐵𝐶(ᴦ𝑆𝐼(𝑍𝑟𝑛	NUM
iajs-2704	137	7	)	)	PUNCT
iajs-2704	137	8	)	)	PUNCT
iajs-2704	138	1	=	=	NOUN
iajs-2704	138	2	∑	∑	PROPN
iajs-2704	138	3	√	√	NUM
iajs-2704	138	4	𝑑𝑒𝑔(𝑢	𝑑𝑒𝑔(𝑢	PROPN
iajs-2704	138	5	)	)	PUNCT
iajs-2704	138	6	+	+	CCONJ
iajs-2704	138	7	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	NOUN
iajs-2704	138	8	)	)	PUNCT
iajs-2704	138	9	−	−	PROPN
iajs-2704	138	10	2	2	NUM
iajs-2704	138	11	𝑑𝑒𝑔(𝑢	𝑑𝑒𝑔(𝑢	PROPN
iajs-2704	138	12	)	)	PUNCT
iajs-2704	138	13	.	.	PUNCT
iajs-2704	139	1	𝑑𝑒𝑔(𝑣)𝑢𝑣∈	𝑑𝑒𝑔(𝑣)𝑢𝑣∈	NOUN
iajs-2704	139	2	𝐸(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝐸(ᴦ𝑆𝐼(𝑍𝑟𝑛	NUM
iajs-2704	139	3	)	)	PUNCT
iajs-2704	139	4	)	)	PUNCT
iajs-2704	140	1	=	=	SYM
iajs-2704	140	2	√	√	PROPN
iajs-2704	140	3	𝑑𝑒𝑔(1	𝑑𝑒𝑔(1	NOUN
iajs-2704	140	4	)	)	PUNCT
iajs-2704	141	1	+	+	CCONJ
iajs-2704	141	2	𝑑𝑒𝑔(2	𝑑𝑒𝑔(2	NOUN
iajs-2704	141	3	)	)	PUNCT
iajs-2704	141	4	−	−	PROPN
iajs-2704	141	5	2	2	NUM
iajs-2704	141	6	𝑑𝑒𝑔(1	𝑑𝑒𝑔(1	NOUN
iajs-2704	141	7	)	)	PUNCT
iajs-2704	141	8	.	.	PUNCT
iajs-2704	142	1	𝑑𝑒𝑔(2	𝑑𝑒𝑔(2	NOUN
iajs-2704	142	2	)	)	PUNCT
iajs-2704	143	1	+	+	NUM
iajs-2704	143	2	⋯+√	⋯+√	NOUN
iajs-2704	143	3	𝑑𝑒𝑔(1	𝑑𝑒𝑔(1	NOUN
iajs-2704	143	4	)	)	PUNCT
iajs-2704	144	1	+	+	CCONJ
iajs-2704	144	2	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	144	3	−	−	PROPN
iajs-2704	144	4	1	1	NUM
iajs-2704	144	5	)	)	PUNCT
iajs-2704	144	6	−	−	PROPN
iajs-2704	144	7	2	2	NUM
iajs-2704	144	8	𝑑𝑒𝑔(1	𝑑𝑒𝑔(1	NOUN
iajs-2704	144	9	)	)	PUNCT
iajs-2704	144	10	.	.	PUNCT
iajs-2704	145	1	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	145	2	−	−	PROPN
iajs-2704	145	3	1	1	NUM
iajs-2704	145	4	)	)	PUNCT
iajs-2704	145	5	⏟	⏟	NOUN
iajs-2704	145	6	(	(	PUNCT
iajs-2704	145	7	𝑟𝑛−2)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−2)𝑡𝑖𝑚𝑒𝑠	NUM
iajs-2704	145	8	+	+	NOUN
iajs-2704	145	9	√	√	NOUN
iajs-2704	145	10	𝑑𝑒𝑔(2	𝑑𝑒𝑔(2	NOUN
iajs-2704	145	11	)	)	PUNCT
iajs-2704	145	12	+	+	SYM
iajs-2704	145	13	𝑑𝑒𝑔(3	𝑑𝑒𝑔(3	NOUN
iajs-2704	145	14	)	)	PUNCT
iajs-2704	145	15	−	−	PROPN
iajs-2704	145	16	2	2	NUM
iajs-2704	145	17	𝑑𝑒𝑔(2	𝑑𝑒𝑔(2	NOUN
iajs-2704	145	18	)	)	PUNCT
iajs-2704	145	19	.	.	PUNCT
iajs-2704	146	1	𝑑𝑒𝑔(3	𝑑𝑒𝑔(3	VERB
iajs-2704	146	2	)	)	PUNCT
iajs-2704	147	1	+	+	NUM
iajs-2704	147	2	⋯+√	⋯+√	NOUN
iajs-2704	147	3	𝑑𝑒𝑔(2	𝑑𝑒𝑔(2	NOUN
iajs-2704	147	4	)	)	PUNCT
iajs-2704	148	1	+	+	CCONJ
iajs-2704	148	2	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	148	3	−	−	PROPN
iajs-2704	148	4	1	1	NUM
iajs-2704	148	5	)	)	PUNCT
iajs-2704	148	6	−	−	PROPN
iajs-2704	148	7	2	2	NUM
iajs-2704	148	8	𝑑𝑒𝑔(2	𝑑𝑒𝑔(2	NOUN
iajs-2704	148	9	)	)	PUNCT
iajs-2704	148	10	.	.	PUNCT
iajs-2704	149	1	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	149	2	−	−	PROPN
iajs-2704	149	3	1	1	NUM
iajs-2704	149	4	)	)	PUNCT
iajs-2704	149	5	⏟	⏟	NOUN
iajs-2704	149	6	(	(	PUNCT
iajs-2704	149	7	𝑟𝑛−3)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−3)𝑡𝑖𝑚𝑒𝑠	ADJ
iajs-2704	149	8	+	+	NOUN
iajs-2704	149	9	√	√	NOUN
iajs-2704	149	10	𝑑𝑒𝑔(3	𝑑𝑒𝑔(3	NUM
iajs-2704	149	11	)	)	PUNCT
iajs-2704	150	1	+	+	CCONJ
iajs-2704	150	2	𝑑𝑒𝑔(4	𝑑𝑒𝑔(4	NOUN
iajs-2704	150	3	)	)	PUNCT
iajs-2704	150	4	−	−	PROPN
iajs-2704	150	5	2	2	NUM
iajs-2704	150	6	𝑑𝑒𝑔(3	𝑑𝑒𝑔(3	NUM
iajs-2704	150	7	)	)	PUNCT
iajs-2704	150	8	.	.	PUNCT
iajs-2704	151	1	𝑑𝑒𝑔(4	𝑑𝑒𝑔(4	NOUN
iajs-2704	151	2	)	)	PUNCT
iajs-2704	152	1	+	+	NUM
iajs-2704	152	2	⋯+√	⋯+√	NOUN
iajs-2704	152	3	𝑑𝑒𝑔(3	𝑑𝑒𝑔(3	NOUN
iajs-2704	152	4	)	)	PUNCT
iajs-2704	153	1	+	+	CCONJ
iajs-2704	153	2	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	153	3	−	−	PROPN
iajs-2704	153	4	1	1	NUM
iajs-2704	153	5	)	)	PUNCT
iajs-2704	153	6	−	−	PROPN
iajs-2704	153	7	2	2	NUM
iajs-2704	153	8	𝑑𝑒𝑔(3	𝑑𝑒𝑔(3	NUM
iajs-2704	153	9	)	)	PUNCT
iajs-2704	153	10	.	.	PUNCT
iajs-2704	154	1	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	154	2	−	−	PROPN
iajs-2704	154	3	1	1	NUM
iajs-2704	154	4	)	)	PUNCT
iajs-2704	154	5	⏟	⏟	NOUN
iajs-2704	154	6	(	(	PUNCT
iajs-2704	154	7	𝑟𝑛−4)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−4)𝑡𝑖𝑚𝑒𝑠	NOUN
iajs-2704	154	8	+	+	NOUN
iajs-2704	154	9	⋯	⋯	NOUN
iajs-2704	154	10	+	+	NOUN
iajs-2704	154	11	√	√	NOUN
iajs-2704	154	12	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	154	13	−	−	PROPN
iajs-2704	154	14	2	2	NUM
iajs-2704	154	15	)	)	PUNCT
iajs-2704	154	16	+	+	ADJ
iajs-2704	154	17	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	154	18	−	−	PROPN
iajs-2704	154	19	1	1	NUM
iajs-2704	154	20	)	)	PUNCT
iajs-2704	154	21	−	−	PROPN
iajs-2704	154	22	2	2	NUM
iajs-2704	154	23	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	154	24	−	−	PROPN
iajs-2704	154	25	2	2	NUM
iajs-2704	154	26	)	)	PUNCT
iajs-2704	154	27	.	.	PUNCT
iajs-2704	155	1	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	155	2	−	−	PROPN
iajs-2704	155	3	1	1	NUM
iajs-2704	155	4	)	)	PUNCT
iajs-2704	155	5	ibn	ibn	PROPN
iajs-2704	155	6	al	al	PROPN
iajs-2704	155	7	-	-	PUNCT
iajs-2704	155	8	haitham	haitham	PROPN
iajs-2704	155	9	jour	jour	X
iajs-2704	155	10	.	.	PROPN
iajs-2704	156	1	for	for	ADP
iajs-2704	156	2	pure	pure	ADJ
iajs-2704	156	3	&	&	CCONJ
iajs-2704	156	4	appl	appl	PROPN
iajs-2704	156	5	.	.	PUNCT
iajs-2704	157	1	sci	sci	PROPN
iajs-2704	157	2	.	.	PROPN
iajs-2704	158	1	34(4)2021	34(4)2021	NUM
iajs-2704	158	2	74	74	NUM
iajs-2704	158	3	=	=	SYM
iajs-2704	158	4	√2𝑟𝑛	√2𝑟𝑛	NOUN
iajs-2704	158	5	−	−	PROPN
iajs-2704	158	6	6	6	NUM
iajs-2704	158	7	+	+	CCONJ
iajs-2704	158	8	(	(	PUNCT
iajs-2704	158	9	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	158	10	−	−	PROPN
iajs-2704	158	11	3)√2𝑟𝑛	3)√2𝑟𝑛	NUM
iajs-2704	158	12	−	−	PROPN
iajs-2704	158	13	6	6	NUM
iajs-2704	158	14	(	(	PUNCT
iajs-2704	158	15	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	158	16	−	−	NOUN
iajs-2704	158	17	2	2	NUM
iajs-2704	158	18	)	)	PUNCT
iajs-2704	158	19	+	+	CCONJ
iajs-2704	158	20	(	(	PUNCT
iajs-2704	158	21	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	158	22	−	−	NOUN
iajs-2704	158	23	4)√2𝑟𝑛	4)√2𝑟𝑛	NUM
iajs-2704	158	24	−	−	PROPN
iajs-2704	158	25	6	6	NUM
iajs-2704	158	26	(	(	PUNCT
iajs-2704	158	27	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	158	28	−	−	NOUN
iajs-2704	158	29	2	2	X
iajs-2704	158	30	)	)	PUNCT
iajs-2704	159	1	+	+	NOUN
iajs-2704	159	2	⋯+	⋯+	NOUN
iajs-2704	159	3	√2𝑟𝑛	√2𝑟𝑛	VERB
iajs-2704	159	4	−	−	PROPN
iajs-2704	159	5	6	6	NUM
iajs-2704	159	6	(	(	PUNCT
iajs-2704	159	7	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	159	8	−	−	NOUN
iajs-2704	159	9	2	2	NUM
iajs-2704	159	10	)	)	PUNCT
iajs-2704	159	11	=	=	PUNCT
iajs-2704	159	12	√2𝑟𝑛	√2𝑟𝑛	NOUN
iajs-2704	159	13	−	−	PROPN
iajs-2704	159	14	6	6	NUM
iajs-2704	159	15	+	+	CCONJ
iajs-2704	159	16	√2𝑟𝑛	√2𝑟𝑛	NUM
iajs-2704	159	17	−	−	PROPN
iajs-2704	159	18	6∑	6∑	NOUN
iajs-2704	159	19	(	(	PUNCT
iajs-2704	159	20	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	159	21	−	−	PROPN
iajs-2704	159	22	𝑖)𝑟𝑛−1	𝑖)𝑟𝑛−1	PROPN
iajs-2704	159	23	𝑖=3	𝑖=3	PROPN
iajs-2704	160	1	(	(	PUNCT
iajs-2704	160	2	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	160	3	−	−	PROPN
iajs-2704	160	4	2	2	NUM
iajs-2704	160	5	)	)	PUNCT
iajs-2704	160	6	theorem	theorem	NOUN
iajs-2704	160	7	3.8	3.8	NUM
iajs-2704	160	8	let	let	VERB
iajs-2704	160	9	𝑍𝑟𝑛	𝑍𝑟𝑛	PROPN
iajs-2704	160	10	be	be	AUX
iajs-2704	160	11	a	a	DET
iajs-2704	160	12	group	group	NOUN
iajs-2704	160	13	with	with	ADP
iajs-2704	160	14	𝑟	𝑟	PRON
iajs-2704	160	15	≥	≥	NUM
iajs-2704	160	16	2	2	NUM
iajs-2704	160	17	,	,	PUNCT
iajs-2704	160	18	𝑛	𝑛	PROPN
iajs-2704	160	19	>	>	X
iajs-2704	160	20	1	1	NUM
iajs-2704	160	21	then	then	ADV
iajs-2704	160	22	the	the	DET
iajs-2704	160	23	geometric	geometric	ADJ
iajs-2704	160	24	–	–	PUNCT
iajs-2704	160	25	arithmetic	arithmetic	ADJ
iajs-2704	160	26	index	index	NOUN
iajs-2704	160	27	of	of	ADP
iajs-2704	160	28	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	160	29	)	)	PUNCT
iajs-2704	160	30	is	be	AUX
iajs-2704	160	31	𝐺𝐴(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝐺𝐴(ᴦ𝑆𝐼(𝑍𝑟𝑛	ADJ
iajs-2704	160	32	)	)	PUNCT
iajs-2704	160	33	)	)	PUNCT
iajs-2704	161	1	=	=	PUNCT
iajs-2704	161	2	(	(	PUNCT
iajs-2704	161	3	𝑟	𝑟	NOUN
iajs-2704	161	4	𝑛	𝑛	PRON
iajs-2704	161	5	−	−	NOUN
iajs-2704	161	6	2	2	NUM
iajs-2704	161	7	)	)	PUNCT
iajs-2704	161	8	+	+	CCONJ
iajs-2704	161	9	∑	∑	PUNCT
iajs-2704	161	10	(	(	PUNCT
iajs-2704	161	11	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	161	12	−	−	PROPN
iajs-2704	161	13	𝑖)𝑟𝑛−1	𝑖)𝑟𝑛−1	NOUN
iajs-2704	162	1	𝑖=3	𝑖=3	PROPN
iajs-2704	162	2	proof	proof	NOUN
iajs-2704	162	3	:	:	PUNCT
iajs-2704	162	4	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	NUM
iajs-2704	162	5	)	)	PUNCT
iajs-2704	162	6	=	=	PUNCT
iajs-2704	163	1	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	163	2	−	−	NOUN
iajs-2704	163	3	2	2	NUM
iajs-2704	163	4	,	,	PUNCT
iajs-2704	163	5	∀𝑣	∀𝑣	PROPN
iajs-2704	163	6	∈	∈	PROPN
iajs-2704	163	7	𝑉	𝑉	PROPN
iajs-2704	163	8	(	(	PUNCT
iajs-2704	163	9	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	163	10	)	)	PUNCT
iajs-2704	163	11	)	)	PUNCT
iajs-2704	163	12	,	,	PUNCT
iajs-2704	163	13	𝑣	𝑣	X
iajs-2704	163	14	=	=	SYM
iajs-2704	163	15	1,2	1,2	NUM
iajs-2704	163	16	,	,	PUNCT
iajs-2704	163	17	.	.	PUNCT
iajs-2704	163	18	.	.	PUNCT
iajs-2704	163	19	.	.	PUNCT
iajs-2704	164	1	,	,	PUNCT
iajs-2704	164	2	𝑟	𝑟	X
iajs-2704	164	3	𝑛	𝑛	PRON
iajs-2704	164	4	−	−	PROPN
iajs-2704	164	5	1	1	NUM
iajs-2704	164	6	𝐺𝐴(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝐺𝐴(ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	164	7	)	)	PUNCT
iajs-2704	164	8	)	)	PUNCT
iajs-2704	164	9	)	)	PUNCT
iajs-2704	165	1	=	=	X
iajs-2704	165	2	∑	∑	PROPN
iajs-2704	165	3	2√𝑑𝑒𝑔(𝑢	2√𝑑𝑒𝑔(𝑢	NUM
iajs-2704	165	4	)	)	PUNCT
iajs-2704	165	5	.	.	PUNCT
iajs-2704	166	1	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	PROPN
iajs-2704	166	2	)	)	PUNCT
iajs-2704	166	3	𝑑𝑒𝑔(𝑢	𝑑𝑒𝑔(𝑢	PROPN
iajs-2704	166	4	)	)	PUNCT
iajs-2704	167	1	+	+	CCONJ
iajs-2704	167	2	𝑑𝑒𝑔(𝑣)𝑢𝑣∈	𝑑𝑒𝑔(𝑣)𝑢𝑣∈	NOUN
iajs-2704	167	3	𝐸(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝐸(ᴦ𝑆𝐼(𝑍𝑟𝑛	NUM
iajs-2704	167	4	)	)	PUNCT
iajs-2704	167	5	)	)	PUNCT
iajs-2704	168	1	=	=	SYM
iajs-2704	168	2	2√𝑑𝑒𝑔(1	2√𝑑𝑒𝑔(1	NUM
iajs-2704	168	3	)	)	PUNCT
iajs-2704	168	4	.	.	PUNCT
iajs-2704	169	1	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	169	2	(	(	PUNCT
iajs-2704	169	3	2	2	NUM
iajs-2704	169	4	)	)	PUNCT
iajs-2704	169	5	𝑑𝑒𝑔(1	𝑑𝑒𝑔(1	NOUN
iajs-2704	169	6	)	)	PUNCT
iajs-2704	170	1	+	+	CCONJ
iajs-2704	170	2	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	170	3	(	(	PUNCT
iajs-2704	170	4	2	2	NUM
iajs-2704	170	5	)	)	PUNCT
iajs-2704	170	6	+	+	NUM
iajs-2704	170	7	⋯+	⋯+	NUM
iajs-2704	170	8	2√𝑑𝑒𝑔(1	2√𝑑𝑒𝑔(1	NUM
iajs-2704	170	9	)	)	PUNCT
iajs-2704	170	10	.	.	PUNCT
iajs-2704	171	1	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	171	2	(	(	PUNCT
iajs-2704	171	3	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	171	4	−	−	NUM
iajs-2704	171	5	1	1	NUM
iajs-2704	171	6	)	)	PUNCT
iajs-2704	171	7	𝑑𝑒𝑔(1	𝑑𝑒𝑔(1	NOUN
iajs-2704	171	8	)	)	PUNCT
iajs-2704	172	1	+	+	CCONJ
iajs-2704	172	2	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	172	3	(	(	PUNCT
iajs-2704	172	4	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	172	5	−	−	PROPN
iajs-2704	172	6	1)⏟	1)⏟	NUM
iajs-2704	172	7	(	(	PUNCT
iajs-2704	172	8	𝑟𝑛−2)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−2)𝑡𝑖𝑚𝑒𝑠	PROPN
iajs-2704	172	9	+	+	NOUN
iajs-2704	172	10	2√𝑑𝑒𝑔(2	2√𝑑𝑒𝑔(2	NUM
iajs-2704	172	11	)	)	PUNCT
iajs-2704	172	12	.	.	PUNCT
iajs-2704	173	1	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	173	2	(	(	PUNCT
iajs-2704	173	3	3	3	NUM
iajs-2704	173	4	)	)	PUNCT
iajs-2704	173	5	𝑑𝑒𝑔(2	𝑑𝑒𝑔(2	NOUN
iajs-2704	173	6	)	)	PUNCT
iajs-2704	174	1	+	+	CCONJ
iajs-2704	174	2	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	174	3	(	(	PUNCT
iajs-2704	174	4	3	3	NUM
iajs-2704	174	5	)	)	PUNCT
iajs-2704	174	6	+	+	NUM
iajs-2704	174	7	⋯+	⋯+	NOUN
iajs-2704	174	8	2√𝑑𝑒𝑔(2	2√𝑑𝑒𝑔(2	NUM
iajs-2704	174	9	)	)	PUNCT
iajs-2704	174	10	.	.	PUNCT
iajs-2704	175	1	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	175	2	(	(	PUNCT
iajs-2704	175	3	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	175	4	−	−	NUM
iajs-2704	175	5	1	1	NUM
iajs-2704	175	6	)	)	PUNCT
iajs-2704	175	7	𝑑𝑒𝑔(2	𝑑𝑒𝑔(2	NOUN
iajs-2704	175	8	)	)	PUNCT
iajs-2704	176	1	+	+	CCONJ
iajs-2704	176	2	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	176	3	(	(	PUNCT
iajs-2704	176	4	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	176	5	−	−	PROPN
iajs-2704	176	6	1)⏟	1)⏟	NUM
iajs-2704	176	7	(	(	PUNCT
iajs-2704	176	8	𝑟𝑛−3)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−3)𝑡𝑖𝑚𝑒𝑠	NOUN
iajs-2704	176	9	+	+	NOUN
iajs-2704	176	10	2√𝑑𝑒𝑔(3	2√𝑑𝑒𝑔(3	NUM
iajs-2704	176	11	)	)	PUNCT
iajs-2704	176	12	.	.	PUNCT
iajs-2704	177	1	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	177	2	(	(	PUNCT
iajs-2704	177	3	4	4	NUM
iajs-2704	177	4	)	)	PUNCT
iajs-2704	177	5	𝑑𝑒𝑔(3	𝑑𝑒𝑔(3	PUNCT
iajs-2704	177	6	)	)	PUNCT
iajs-2704	178	1	+	+	CCONJ
iajs-2704	178	2	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	178	3	(	(	PUNCT
iajs-2704	178	4	4	4	NUM
iajs-2704	178	5	)	)	PUNCT
iajs-2704	178	6	+	+	NUM
iajs-2704	178	7	⋯+	⋯+	NOUN
iajs-2704	178	8	2√𝑑𝑒𝑔(3	2√𝑑𝑒𝑔(3	NUM
iajs-2704	178	9	)	)	PUNCT
iajs-2704	178	10	.	.	PUNCT
iajs-2704	179	1	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	179	2	(	(	PUNCT
iajs-2704	179	3	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	179	4	−	−	NUM
iajs-2704	179	5	1	1	NUM
iajs-2704	179	6	)	)	PUNCT
iajs-2704	179	7	𝑑𝑒𝑔(3	𝑑𝑒𝑔(3	PUNCT
iajs-2704	179	8	)	)	PUNCT
iajs-2704	180	1	+	+	CCONJ
iajs-2704	180	2	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	180	3	(	(	PUNCT
iajs-2704	180	4	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	180	5	−	−	PROPN
iajs-2704	180	6	1)⏟	1)⏟	NUM
iajs-2704	180	7	(	(	PUNCT
iajs-2704	180	8	𝑟𝑛−4)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−4)𝑡𝑖𝑚𝑒𝑠	PROPN
iajs-2704	180	9	+	+	PROPN
iajs-2704	180	10	⋯	⋯	VERB
iajs-2704	180	11	.+	.+	NOUN
iajs-2704	180	12	2√𝑑𝑒𝑔(𝑟𝑛	2√𝑑𝑒𝑔(𝑟𝑛	PRON
iajs-2704	181	1	−	−	NUM
iajs-2704	181	2	2	2	NUM
iajs-2704	181	3	)	)	PUNCT
iajs-2704	181	4	.	.	PUNCT
iajs-2704	182	1	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	182	2	(	(	PUNCT
iajs-2704	182	3	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	182	4	−	−	NUM
iajs-2704	182	5	1	1	NUM
iajs-2704	182	6	)	)	PUNCT
iajs-2704	182	7	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	182	8	−	−	PROPN
iajs-2704	182	9	2	2	NUM
iajs-2704	182	10	)	)	PUNCT
iajs-2704	182	11	+	+	CCONJ
iajs-2704	182	12	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	182	13	(	(	PUNCT
iajs-2704	182	14	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	182	15	−	−	NUM
iajs-2704	182	16	1	1	NUM
iajs-2704	182	17	)	)	PUNCT
iajs-2704	182	18	=	=	NOUN
iajs-2704	183	1	2(𝑟𝑛	2(𝑟𝑛	NUM
iajs-2704	183	2	−	−	NUM
iajs-2704	183	3	2)2	2)2	NUM
iajs-2704	183	4	2𝑟𝑛	2𝑟𝑛	ADJ
iajs-2704	183	5	−	−	ADP
iajs-2704	183	6	4	4	NUM
iajs-2704	183	7	+	+	NOUN
iajs-2704	183	8	2(𝑟𝑛	2(𝑟𝑛	NUM
iajs-2704	183	9	−	−	NOUN
iajs-2704	183	10	3)(𝑟𝑛	3)(𝑟𝑛	NUM
iajs-2704	183	11	−	−	NOUN
iajs-2704	183	12	2	2	NUM
iajs-2704	183	13	)	)	PUNCT
iajs-2704	183	14	2𝑟𝑛	2𝑟𝑛	ADJ
iajs-2704	183	15	−	−	PROPN
iajs-2704	183	16	4	4	NUM
iajs-2704	183	17	+	+	NOUN
iajs-2704	183	18	2(𝑟𝑛	2(𝑟𝑛	NUM
iajs-2704	183	19	−	−	NOUN
iajs-2704	183	20	4)(𝑟𝑛	4)(𝑟𝑛	NUM
iajs-2704	183	21	−	−	NOUN
iajs-2704	183	22	2	2	NUM
iajs-2704	183	23	)	)	PUNCT
iajs-2704	183	24	2𝑟𝑛	2𝑟𝑛	NOUN
iajs-2704	183	25	−	−	PROPN
iajs-2704	183	26	4	4	NUM
iajs-2704	183	27	+	+	NOUN
iajs-2704	183	28	⋯+	⋯+	NOUN
iajs-2704	183	29	2(𝑟𝑛	2(𝑟𝑛	NUM
iajs-2704	183	30	−	−	NOUN
iajs-2704	183	31	2	2	NUM
iajs-2704	183	32	)	)	PUNCT
iajs-2704	183	33	2𝑟𝑛	2𝑟𝑛	NOUN
iajs-2704	183	34	−	−	PROPN
iajs-2704	183	35	4	4	NUM
iajs-2704	183	36	=	=	SYM
iajs-2704	183	37	(	(	PUNCT
iajs-2704	183	38	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	183	39	−	−	NOUN
iajs-2704	183	40	2	2	NUM
iajs-2704	183	41	)	)	PUNCT
iajs-2704	183	42	+	+	CCONJ
iajs-2704	183	43	∑	∑	PUNCT
iajs-2704	183	44	(	(	PUNCT
iajs-2704	183	45	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	183	46	−	−	PROPN
iajs-2704	183	47	𝑖	𝑖	SYM
iajs-2704	183	48	)	)	PUNCT
iajs-2704	183	49	𝑟𝑛−1	𝑟𝑛−1	PROPN
iajs-2704	183	50	𝑖=3	𝑖=3	PROPN
iajs-2704	183	51	theorem	theorem	VERB
iajs-2704	183	52	3.9	3.9	NUM
iajs-2704	183	53	let	let	VERB
iajs-2704	183	54	𝑍𝑟𝑛	𝑍𝑟𝑛	PROPN
iajs-2704	183	55	be	be	AUX
iajs-2704	183	56	a	a	DET
iajs-2704	183	57	group	group	NOUN
iajs-2704	183	58	with	with	ADP
iajs-2704	183	59	𝑟	𝑟	PRON
iajs-2704	183	60	≥	≥	NUM
iajs-2704	183	61	2	2	NUM
iajs-2704	183	62	,	,	PUNCT
iajs-2704	183	63	𝑛	𝑛	PROPN
iajs-2704	183	64	>	>	X
iajs-2704	183	65	1	1	NUM
iajs-2704	183	66	then	then	ADV
iajs-2704	183	67	the	the	DET
iajs-2704	183	68	harmonic	harmonic	ADJ
iajs-2704	183	69	index	index	NOUN
iajs-2704	183	70	of	of	ADP
iajs-2704	183	71	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	183	72	)	)	PUNCT
iajs-2704	183	73	is	be	AUX
iajs-2704	183	74	1	1	NUM
iajs-2704	183	75	+	+	SYM
iajs-2704	183	76	2	2	NUM
iajs-2704	183	77	2𝑟𝑛−4	2𝑟𝑛−4	NUM
iajs-2704	183	78	∑	∑	PUNCT
iajs-2704	183	79	(	(	PUNCT
iajs-2704	183	80	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	183	81	−	−	PROPN
iajs-2704	183	82	𝑖)𝑟𝑛−1	𝑖)𝑟𝑛−1	PROPN
iajs-2704	183	83	𝑖=3	𝑖=3	PROPN
iajs-2704	183	84	𝐻(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝐻(ᴦ𝑆𝐼(𝑍𝑟𝑛	PROPN
iajs-2704	183	85	)	)	PUNCT
iajs-2704	183	86	)	)	PUNCT
iajs-2704	183	87	)	)	PUNCT
iajs-2704	184	1	=	=	NOUN
iajs-2704	184	2	proof	proof	NOUN
iajs-2704	184	3	:	:	PUNCT
iajs-2704	184	4	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	NUM
iajs-2704	184	5	)	)	PUNCT
iajs-2704	184	6	=	=	PUNCT
iajs-2704	185	1	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	185	2	−	−	NOUN
iajs-2704	185	3	2	2	NUM
iajs-2704	185	4	,	,	PUNCT
iajs-2704	185	5	∀𝑣	∀𝑣	PROPN
iajs-2704	185	6	∈	∈	PROPN
iajs-2704	185	7	𝑉	𝑉	PROPN
iajs-2704	185	8	(	(	PUNCT
iajs-2704	185	9	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	185	10	)	)	PUNCT
iajs-2704	185	11	)	)	PUNCT
iajs-2704	185	12	,	,	PUNCT
iajs-2704	185	13	𝑣	𝑣	X
iajs-2704	185	14	=	=	SYM
iajs-2704	185	15	1,2	1,2	NUM
iajs-2704	185	16	,	,	PUNCT
iajs-2704	185	17	.	.	PUNCT
iajs-2704	185	18	.	.	PUNCT
iajs-2704	185	19	.	.	PUNCT
iajs-2704	186	1	,	,	PUNCT
iajs-2704	186	2	𝑟	𝑟	X
iajs-2704	186	3	𝑛	𝑛	PRON
iajs-2704	186	4	−	−	PROPN
iajs-2704	186	5	1	1	NUM
iajs-2704	186	6	ibn	ibn	PROPN
iajs-2704	186	7	al	al	PROPN
iajs-2704	186	8	-	-	PUNCT
iajs-2704	186	9	haitham	haitham	PROPN
iajs-2704	186	10	jour	jour	X
iajs-2704	186	11	.	.	PROPN
iajs-2704	187	1	for	for	ADP
iajs-2704	187	2	pure	pure	ADJ
iajs-2704	187	3	&	&	CCONJ
iajs-2704	187	4	appl	appl	PROPN
iajs-2704	187	5	.	.	PUNCT
iajs-2704	188	1	sci	sci	PROPN
iajs-2704	188	2	.	.	PROPN
iajs-2704	189	1	34(4)2021	34(4)2021	NUM
iajs-2704	189	2	75	75	NUM
iajs-2704	189	3	𝐻(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝐻(ᴦ𝑆𝐼(𝑍𝑟𝑛	NOUN
iajs-2704	189	4	)	)	PUNCT
iajs-2704	189	5	)	)	PUNCT
iajs-2704	189	6	)	)	PUNCT
iajs-2704	190	1	=	=	SYM
iajs-2704	190	2	∑	∑	PROPN
iajs-2704	190	3	2	2	NUM
iajs-2704	190	4	𝑑𝑒𝑔(𝑢	𝑑𝑒𝑔(𝑢	PROPN
iajs-2704	190	5	)	)	PUNCT
iajs-2704	190	6	+	+	CCONJ
iajs-2704	190	7	𝑑𝑒𝑔(𝑣)𝑢𝑣∈	𝑑𝑒𝑔(𝑣)𝑢𝑣∈	NOUN
iajs-2704	190	8	𝐸(ᴦ𝑆𝐼(𝑍𝑟𝑛	𝐸(ᴦ𝑆𝐼(𝑍𝑟𝑛	NUM
iajs-2704	190	9	)	)	PUNCT
iajs-2704	190	10	)	)	PUNCT
iajs-2704	190	11	=	=	SYM
iajs-2704	190	12	2	2	NUM
iajs-2704	190	13	𝑑𝑒𝑔(1	𝑑𝑒𝑔(1	NOUN
iajs-2704	190	14	)	)	PUNCT
iajs-2704	191	1	+	+	CCONJ
iajs-2704	191	2	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	191	3	(	(	PUNCT
iajs-2704	191	4	2	2	NUM
iajs-2704	191	5	)	)	PUNCT
iajs-2704	191	6	+	+	NUM
iajs-2704	191	7	⋯+	⋯+	NUM
iajs-2704	191	8	2	2	NUM
iajs-2704	191	9	𝑑𝑒𝑔(1	𝑑𝑒𝑔(1	NOUN
iajs-2704	191	10	)	)	PUNCT
iajs-2704	192	1	+	+	CCONJ
iajs-2704	192	2	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	192	3	(	(	PUNCT
iajs-2704	192	4	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	192	5	−	−	PROPN
iajs-2704	192	6	1)⏟	1)⏟	NUM
iajs-2704	192	7	(	(	PUNCT
iajs-2704	192	8	𝑟𝑛−2)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−2)𝑡𝑖𝑚𝑒𝑠	PROPN
iajs-2704	192	9	+	+	ADJ
iajs-2704	192	10	2	2	NUM
iajs-2704	192	11	𝑑𝑒𝑔(2	𝑑𝑒𝑔(2	NOUN
iajs-2704	192	12	)	)	PUNCT
iajs-2704	193	1	+	+	CCONJ
iajs-2704	193	2	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	193	3	(	(	PUNCT
iajs-2704	193	4	3	3	NUM
iajs-2704	193	5	)	)	PUNCT
iajs-2704	193	6	+	+	NUM
iajs-2704	193	7	⋯+	⋯+	NUM
iajs-2704	193	8	2	2	NUM
iajs-2704	193	9	𝑑𝑒𝑔(2	𝑑𝑒𝑔(2	NOUN
iajs-2704	193	10	)	)	PUNCT
iajs-2704	194	1	+	+	CCONJ
iajs-2704	194	2	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	194	3	(	(	PUNCT
iajs-2704	194	4	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	194	5	−	−	PROPN
iajs-2704	194	6	1)⏟	1)⏟	NUM
iajs-2704	194	7	(	(	PUNCT
iajs-2704	194	8	𝑟𝑛−3)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−3)𝑡𝑖𝑚𝑒𝑠	ADJ
iajs-2704	194	9	+	+	CCONJ
iajs-2704	194	10	2	2	NUM
iajs-2704	194	11	𝑑𝑒𝑔(3	𝑑𝑒𝑔(3	NUM
iajs-2704	194	12	)	)	PUNCT
iajs-2704	195	1	+	+	CCONJ
iajs-2704	195	2	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	195	3	(	(	PUNCT
iajs-2704	195	4	4	4	NUM
iajs-2704	195	5	)	)	PUNCT
iajs-2704	195	6	+	+	NUM
iajs-2704	195	7	⋯+	⋯+	NUM
iajs-2704	195	8	2	2	NUM
iajs-2704	195	9	𝑑𝑒𝑔(3	𝑑𝑒𝑔(3	NUM
iajs-2704	195	10	)	)	PUNCT
iajs-2704	196	1	+	+	CCONJ
iajs-2704	196	2	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	196	3	(	(	PUNCT
iajs-2704	196	4	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	196	5	−	−	PROPN
iajs-2704	196	6	1)⏟	1)⏟	NUM
iajs-2704	196	7	(	(	PUNCT
iajs-2704	196	8	𝑟𝑛−4)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−4)𝑡𝑖𝑚𝑒𝑠	PROPN
iajs-2704	196	9	+	+	NOUN
iajs-2704	196	10	⋯	⋯	VERB
iajs-2704	196	11	.+	.+	NOUN
iajs-2704	196	12	2	2	NUM
iajs-2704	196	13	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	196	14	−	−	PROPN
iajs-2704	196	15	2	2	NUM
iajs-2704	196	16	)	)	PUNCT
iajs-2704	196	17	+	+	CCONJ
iajs-2704	196	18	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	196	19	(	(	PUNCT
iajs-2704	196	20	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	196	21	−	−	NUM
iajs-2704	196	22	1	1	NUM
iajs-2704	196	23	)	)	PUNCT
iajs-2704	196	24	=	=	NOUN
iajs-2704	196	25	2(𝑟𝑛	2(𝑟𝑛	NUM
iajs-2704	196	26	−	−	NUM
iajs-2704	196	27	2	2	NUM
iajs-2704	196	28	)	)	PUNCT
iajs-2704	196	29	2𝑟𝑛	2𝑟𝑛	ADJ
iajs-2704	196	30	−	−	PROPN
iajs-2704	196	31	4	4	NUM
iajs-2704	196	32	+	+	NOUN
iajs-2704	196	33	2(𝑟𝑛	2(𝑟𝑛	NUM
iajs-2704	196	34	−	−	NOUN
iajs-2704	196	35	3	3	NUM
iajs-2704	196	36	)	)	PUNCT
iajs-2704	196	37	2𝑟𝑛	2𝑟𝑛	ADJ
iajs-2704	196	38	−	−	PROPN
iajs-2704	196	39	4	4	NUM
iajs-2704	196	40	+	+	NOUN
iajs-2704	196	41	2(𝑟𝑛	2(𝑟𝑛	NUM
iajs-2704	196	42	−	−	NOUN
iajs-2704	196	43	4	4	NUM
iajs-2704	196	44	)	)	PUNCT
iajs-2704	196	45	2𝑟𝑛	2𝑟𝑛	NOUN
iajs-2704	196	46	−	−	PROPN
iajs-2704	196	47	4	4	NUM
iajs-2704	196	48	+	+	NOUN
iajs-2704	196	49	⋯+	⋯+	NOUN
iajs-2704	196	50	2	2	NUM
iajs-2704	196	51	2𝑟𝑛	2𝑟𝑛	NOUN
iajs-2704	196	52	−	−	PROPN
iajs-2704	196	53	4	4	NUM
iajs-2704	196	54	=	=	SYM
iajs-2704	196	55	1	1	NUM
iajs-2704	196	56	+	+	NUM
iajs-2704	196	57	2	2	NUM
iajs-2704	196	58	2𝑟𝑛	2𝑟𝑛	NOUN
iajs-2704	196	59	−	−	PROPN
iajs-2704	196	60	4	4	NUM
iajs-2704	196	61	∑	∑	PUNCT
iajs-2704	196	62	(	(	PUNCT
iajs-2704	196	63	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	196	64	−	−	PROPN
iajs-2704	196	65	𝑖	𝑖	SYM
iajs-2704	196	66	)	)	PUNCT
iajs-2704	196	67	𝑟𝑛−1	𝑟𝑛−1	NOUN
iajs-2704	196	68	𝑖=3	𝑖=3	PROPN
iajs-2704	196	69	4	4	NUM
iajs-2704	196	70	.	.	PUNCT
iajs-2704	196	71	(	(	PUNCT
iajs-2704	196	72	hosoya	hosoya	PROPN
iajs-2704	196	73	and	and	CCONJ
iajs-2704	196	74	schultz	schultz	PROPN
iajs-2704	196	75	)	)	PUNCT
iajs-2704	196	76	polynomial	polynomial	NOUN
iajs-2704	196	77	of	of	ADP
iajs-2704	196	78	ᴦ𝑺𝑰(𝒁𝒓𝒏	ᴦ𝑺𝑰(𝒁𝒓𝒏	NOUN
iajs-2704	196	79	)	)	PUNCT
iajs-2704	196	80	in	in	ADP
iajs-2704	196	81	this	this	DET
iajs-2704	196	82	section	section	NOUN
iajs-2704	196	83	,	,	PUNCT
iajs-2704	196	84	we	we	PRON
iajs-2704	196	85	find	find	VERB
iajs-2704	196	86	the	the	DET
iajs-2704	196	87	(	(	PUNCT
iajs-2704	196	88	hosoya	hosoya	PROPN
iajs-2704	196	89	and	and	CCONJ
iajs-2704	196	90	schultz	schultz	PROPN
iajs-2704	196	91	)	)	PUNCT
iajs-2704	196	92	polynomial	polynomial	NOUN
iajs-2704	196	93	of	of	ADP
iajs-2704	196	94	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	196	95	)	)	PUNCT
iajs-2704	196	96	.	.	PUNCT
iajs-2704	197	1	definition	definition	NOUN
iajs-2704	197	2	4.1(12	4.1(12	NUM
iajs-2704	197	3	):	):	PUNCT
iajs-2704	197	4	let	let	VERB
iajs-2704	197	5	g	g	PRON
iajs-2704	197	6	be	be	AUX
iajs-2704	197	7	a	a	DET
iajs-2704	197	8	connected	connected	ADJ
iajs-2704	197	9	graph	graph	NOUN
iajs-2704	197	10	,	,	PUNCT
iajs-2704	197	11	then	then	ADV
iajs-2704	197	12	a	a	DET
iajs-2704	197	13	hosoya	hosoya	ADJ
iajs-2704	197	14	polynomial	polynomial	NOUN
iajs-2704	197	15	of	of	ADP
iajs-2704	197	16	graph	graph	NOUN
iajs-2704	197	17	g	g	PROPN
iajs-2704	197	18	is	be	AUX
iajs-2704	197	19	defined	define	VERB
iajs-2704	197	20	by	by	ADP
iajs-2704	197	21	h(g	h(g	NOUN
iajs-2704	197	22	;	;	PUNCT
iajs-2704	197	23	x	x	X
iajs-2704	197	24	)	)	PUNCT
iajs-2704	197	25	=	=	SYM
iajs-2704	197	26	∑	∑	PUNCT
iajs-2704	197	27	𝑑(𝐺	𝑑(𝐺	PROPN
iajs-2704	197	28	,	,	PUNCT
iajs-2704	197	29	𝑘	𝑘	NOUN
iajs-2704	197	30	)	)	PUNCT
iajs-2704	197	31	xk	xk	PROPN
iajs-2704	197	32	𝑑𝑖𝑎𝑚(𝐺	𝑑𝑖𝑎𝑚(𝐺	PROPN
iajs-2704	197	33	)	)	PUNCT
iajs-2704	197	34	k=0	k=0	PROPN
iajs-2704	197	35	,	,	PUNCT
iajs-2704	197	36	where	where	SCONJ
iajs-2704	197	37	𝑑(𝐺	𝑑(𝐺	NUM
iajs-2704	197	38	,	,	PUNCT
iajs-2704	197	39	𝑘	𝑘	NOUN
iajs-2704	197	40	)	)	PUNCT
iajs-2704	197	41	is	be	AUX
iajs-2704	197	42	the	the	DET
iajs-2704	197	43	number	number	NOUN
iajs-2704	197	44	of	of	ADP
iajs-2704	197	45	pairs	pair	NOUN
iajs-2704	197	46	of	of	ADP
iajs-2704	197	47	vertices	vertex	NOUN
iajs-2704	197	48	of	of	ADP
iajs-2704	197	49	a	a	DET
iajs-2704	197	50	graph	graph	NOUN
iajs-2704	197	51	g	g	NOUN
iajs-2704	197	52	that	that	PRON
iajs-2704	197	53	are	be	AUX
iajs-2704	197	54	at	at	ADP
iajs-2704	197	55	distance	distance	NOUN
iajs-2704	197	56	k	k	PROPN
iajs-2704	197	57	apart	apart	ADV
iajs-2704	197	58	,	,	PUNCT
iajs-2704	197	59	for	for	ADP
iajs-2704	197	60	𝑘	𝑘	NOUN
iajs-2704	197	61	=	=	NOUN
iajs-2704	197	62	0,1,2	0,1,2	NUM
iajs-2704	197	63	,	,	PUNCT
iajs-2704	197	64	…	…	PUNCT
iajs-2704	197	65	,	,	PUNCT
iajs-2704	197	66	𝑑𝑖𝑎𝑚(𝐺),where	𝑑𝑖𝑎𝑚(𝐺),where	ADJ
iajs-2704	197	67	𝑑𝑖𝑎𝑚(𝐺	𝑑𝑖𝑎𝑚(𝐺	PRON
iajs-2704	197	68	)	)	PUNCT
iajs-2704	197	69	=	=	SYM
iajs-2704	197	70	maxu	maxu	NOUN
iajs-2704	197	71	,	,	PUNCT
iajs-2704	197	72	v∈v(g)d(u	v∈v(g)d(u	X
iajs-2704	197	73	,	,	PUNCT
iajs-2704	197	74	v	v	NOUN
iajs-2704	197	75	)	)	PUNCT
iajs-2704	197	76	.	.	PUNCT
iajs-2704	198	1	𝑑(𝐺	𝑑(𝐺	PROPN
iajs-2704	198	2	,	,	PUNCT
iajs-2704	198	3	0	0	NUM
iajs-2704	198	4	)	)	PUNCT
iajs-2704	198	5	=	=	SYM
iajs-2704	198	6	𝑝(𝐺	𝑝(𝐺	NOUN
iajs-2704	198	7	)	)	PUNCT
iajs-2704	198	8	-1	-1	PUNCT
iajs-2704	198	9	:	:	PUNCT
iajs-2704	198	10	note	note	VERB
iajs-2704	198	11	4.2(13	4.2(13	NOUN
iajs-2704	198	12	)	)	PUNCT
iajs-2704	198	13	2𝑑(𝐺	2𝑑(𝐺	NUM
iajs-2704	198	14	,	,	PUNCT
iajs-2704	198	15	1	1	NUM
iajs-2704	198	16	)	)	PUNCT
iajs-2704	198	17	=	=	SYM
iajs-2704	198	18	𝑞(𝐺	𝑞(𝐺	NOUN
iajs-2704	198	19	)	)	PUNCT
iajs-2704	198	20	definition	definition	NOUN
iajs-2704	198	21	4.3(14	4.3(14	NOUN
iajs-2704	198	22	):	):	PUNCT
iajs-2704	198	23	let	let	VERB
iajs-2704	198	24	g	g	PRON
iajs-2704	198	25	be	be	AUX
iajs-2704	198	26	a	a	DET
iajs-2704	198	27	connected	connected	ADJ
iajs-2704	198	28	graph	graph	NOUN
iajs-2704	198	29	,	,	PUNCT
iajs-2704	198	30	then	then	ADV
iajs-2704	198	31	a	a	DET
iajs-2704	198	32	schultz	schultz	NOUN
iajs-2704	198	33	polynomial	polynomial	NOUN
iajs-2704	198	34	of	of	ADP
iajs-2704	198	35	a	a	DET
iajs-2704	198	36	graph	graph	NOUN
iajs-2704	198	37	g	g	NOUN
iajs-2704	198	38	is	be	AUX
iajs-2704	198	39	defined	define	VERB
iajs-2704	198	40	by	by	ADP
iajs-2704	198	41	sc(g	sc(g	NOUN
iajs-2704	198	42	;	;	PUNCT
iajs-2704	198	43	x	x	X
iajs-2704	198	44	)	)	PUNCT
iajs-2704	198	45	=	=	SYM
iajs-2704	198	46	∑	∑	PUNCT
iajs-2704	198	47	(	(	PUNCT
iajs-2704	198	48	𝑑𝑒𝑔(𝑢	𝑑𝑒𝑔(𝑢	PROPN
iajs-2704	198	49	)	)	PUNCT
iajs-2704	198	50	+	+	CCONJ
iajs-2704	199	1	𝑑𝑒𝑔(𝑣))xd(u	𝑑𝑒𝑔(𝑣))xd(u	NOUN
iajs-2704	199	2	,	,	PUNCT
iajs-2704	199	3	v)u	v)u	ADV
iajs-2704	199	4	,	,	PUNCT
iajs-2704	199	5	v∈v(g	v∈v(g	NOUN
iajs-2704	199	6	)	)	PUNCT
iajs-2704	199	7	u≠v	u≠v	PUNCT
iajs-2704	199	8	,	,	PUNCT
iajs-2704	199	9	where	where	SCONJ
iajs-2704	199	10	𝑑𝑒𝑔(𝑢	𝑑𝑒𝑔(𝑢	PROPN
iajs-2704	199	11	)	)	PUNCT
iajs-2704	199	12	is	be	AUX
iajs-2704	199	13	the	the	DET
iajs-2704	199	14	degree	degree	NOUN
iajs-2704	199	15	of	of	ADP
iajs-2704	199	16	the	the	DET
iajs-2704	199	17	vertices	vertex	NOUN
iajs-2704	199	18	u	u	NOUN
iajs-2704	199	19	and	and	CCONJ
iajs-2704	199	20	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	NOUN
iajs-2704	199	21	)	)	PUNCT
iajs-2704	199	22	is	be	AUX
iajs-2704	199	23	the	the	DET
iajs-2704	199	24	degree	degree	NOUN
iajs-2704	199	25	of	of	ADP
iajs-2704	199	26	vertices	vertex	NOUN
iajs-2704	199	27	𝑣	𝑣	ADP
iajs-2704	199	28	,	,	PUNCT
iajs-2704	199	29	𝑑(𝑢	𝑑(𝑢	NOUN
iajs-2704	199	30	,	,	PUNCT
iajs-2704	199	31	𝑣	𝑣	NOUN
iajs-2704	199	32	)	)	PUNCT
iajs-2704	199	33	is	be	AUX
iajs-2704	199	34	the	the	DET
iajs-2704	199	35	distance	distance	NOUN
iajs-2704	199	36	between	between	ADP
iajs-2704	199	37	𝑢	𝑢	NOUN
iajs-2704	199	38	and	and	CCONJ
iajs-2704	199	39	𝑣.	𝑣.	PROPN
iajs-2704	199	40	theorem	theorem	VERB
iajs-2704	199	41	4.4	4.4	NUM
iajs-2704	199	42	:	:	PUNCT
iajs-2704	199	43	h	h	NUM
iajs-2704	199	44	(	(	PUNCT
iajs-2704	199	45	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	199	46	)	)	PUNCT
iajs-2704	199	47	;	;	PUNCT
iajs-2704	199	48	𝑥	𝑥	X
iajs-2704	199	49	)	)	PUNCT
iajs-2704	199	50	=	=	SYM
iajs-2704	199	51	𝑐0	𝑐0	NOUN
iajs-2704	199	52	+	+	CCONJ
iajs-2704	199	53	𝑐1𝑥	𝑐1𝑥	NOUN
iajs-2704	199	54	,	,	PUNCT
iajs-2704	199	55	where	where	SCONJ
iajs-2704	199	56	𝑟	𝑟	X
iajs-2704	199	57	≥	≥	NUM
iajs-2704	199	58	2	2	NUM
iajs-2704	199	59	,	,	PUNCT
iajs-2704	199	60	𝑛	𝑛	PROPN
iajs-2704	199	61	>	>	SYM
iajs-2704	199	62	1	1	NUM
iajs-2704	199	63	,	,	PUNCT
iajs-2704	199	64	𝑐0	𝑐0	NOUN
iajs-2704	199	65	=	=	PUNCT
iajs-2704	199	66	𝑟	𝑟	X
iajs-2704	199	67	𝑛	𝑛	PRON
iajs-2704	199	68	−	−	PROPN
iajs-2704	199	69	1	1	NUM
iajs-2704	199	70	,	,	PUNCT
iajs-2704	199	71	𝑐1	𝑐1	NOUN
iajs-2704	199	72	=	=	PUNCT
iajs-2704	199	73	∑	∑	PUNCT
iajs-2704	199	74	(	(	PUNCT
iajs-2704	199	75	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	199	76	−	−	PROPN
iajs-2704	199	77	𝑖)𝑟𝑛−1	𝑖)𝑟𝑛−1	PUNCT
iajs-2704	199	78	𝑖=2	𝑖=2	PROPN
iajs-2704	199	79	ibn	ibn	PROPN
iajs-2704	199	80	al	al	PROPN
iajs-2704	199	81	-	-	PUNCT
iajs-2704	199	82	haitham	haitham	PROPN
iajs-2704	199	83	jour	jour	X
iajs-2704	199	84	.	.	PROPN
iajs-2704	200	1	for	for	ADP
iajs-2704	200	2	pure	pure	ADJ
iajs-2704	200	3	&	&	CCONJ
iajs-2704	200	4	appl	appl	PROPN
iajs-2704	200	5	.	.	PUNCT
iajs-2704	201	1	sci	sci	PROPN
iajs-2704	201	2	.	.	PROPN
iajs-2704	202	1	34(4)2021	34(4)2021	NUM
iajs-2704	202	2	76	76	NUM
iajs-2704	202	3	proof	proof	NOUN
iajs-2704	202	4	:	:	PUNCT
iajs-2704	202	5	for	for	ADP
iajs-2704	202	6	every	every	DET
iajs-2704	202	7	𝑟	𝑟	NOUN
iajs-2704	202	8	≥	≥	NUM
iajs-2704	202	9	2	2	NUM
iajs-2704	202	10	,	,	PUNCT
iajs-2704	202	11	𝑛	𝑛	PROPN
iajs-2704	202	12	>	>	SYM
iajs-2704	202	13	1	1	NUM
iajs-2704	202	14	,	,	PUNCT
iajs-2704	202	15	we	we	PRON
iajs-2704	202	16	note	note	VERB
iajs-2704	202	17	that	that	SCONJ
iajs-2704	202	18	every	every	DET
iajs-2704	202	19	vertices	vertex	NOUN
iajs-2704	202	20	of	of	ADP
iajs-2704	202	21	graph	graph	NOUN
iajs-2704	202	22	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	202	23	)	)	PUNCT
iajs-2704	202	24	is	be	AUX
iajs-2704	202	25	adjacent	adjacent	ADJ
iajs-2704	202	26	of	of	ADP
iajs-2704	202	27	all	all	DET
iajs-2704	202	28	vertices	vertex	NOUN
iajs-2704	202	29	of	of	ADP
iajs-2704	202	30	graph	graph	NOUN
iajs-2704	202	31	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	202	32	)	)	PUNCT
iajs-2704	202	33	,	,	PUNCT
iajs-2704	202	34	then	then	ADV
iajs-2704	202	35	diam	diam	PROPN
iajs-2704	202	36	(	(	PUNCT
iajs-2704	202	37	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	202	38	)	)	PUNCT
iajs-2704	202	39	)	)	PUNCT
iajs-2704	203	1	=	=	SYM
iajs-2704	203	2	1	1	NUM
iajs-2704	203	3	,	,	PUNCT
iajs-2704	203	4	its	its	PRON
iajs-2704	203	5	mean	mean	NOUN
iajs-2704	203	6	is	be	AUX
iajs-2704	203	7	h	h	NOUN
iajs-2704	203	8	(	(	PUNCT
iajs-2704	203	9	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	203	10	)	)	PUNCT
iajs-2704	203	11	,	,	PUNCT
iajs-2704	203	12	𝑥	𝑥	X
iajs-2704	203	13	)	)	PUNCT
iajs-2704	203	14	=	=	SYM
iajs-2704	203	15	𝑐0	𝑐0	NOUN
iajs-2704	203	16	+	+	CCONJ
iajs-2704	203	17	𝑐1𝑥	𝑐1𝑥	NOUN
iajs-2704	203	18	where	where	SCONJ
iajs-2704	203	19	𝑐𝑖	𝑐𝑖	NOUN
iajs-2704	203	20	=	=	SYM
iajs-2704	203	21	𝑑	𝑑	PROPN
iajs-2704	203	22	(	(	PUNCT
iajs-2704	203	23	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	203	24	)	)	PUNCT
iajs-2704	203	25	,	,	PUNCT
iajs-2704	203	26	𝑖	𝑖	X
iajs-2704	203	27	)	)	PUNCT
iajs-2704	203	28	,	,	PUNCT
iajs-2704	203	29	∀	∀	NOUN
iajs-2704	203	30	𝑖	𝑖	NOUN
iajs-2704	204	1	=	=	SYM
iajs-2704	204	2	0,1	0,1	NUM
iajs-2704	204	3	it	it	PRON
iajs-2704	204	4	is	be	AUX
iajs-2704	204	5	clear	clear	ADJ
iajs-2704	204	6	that	that	SCONJ
iajs-2704	204	7	𝑐0	𝑐0	AUX
iajs-2704	204	8	=	=	SYM
iajs-2704	204	9	𝑑	𝑑	NOUN
iajs-2704	204	10	(	(	PUNCT
iajs-2704	204	11	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	204	12	)	)	PUNCT
iajs-2704	204	13	,	,	PUNCT
iajs-2704	204	14	0	0	X
iajs-2704	204	15	)	)	PUNCT
iajs-2704	204	16	=	=	PUNCT
iajs-2704	205	1	|	|	ADV
iajs-2704	205	2	ᴦ𝑆𝐼(𝑍𝑟𝑛)|	ᴦ𝑆𝐼(𝑍𝑟𝑛)|	ADV
iajs-2704	205	3	=	=	NOUN
iajs-2704	205	4	𝑟	𝑟	X
iajs-2704	205	5	𝑛	𝑛	PRON
iajs-2704	205	6	−	−	NOUN
iajs-2704	205	7	1	1	NUM
iajs-2704	205	8	now	now	ADV
iajs-2704	205	9	we	we	PRON
iajs-2704	205	10	find	find	VERB
iajs-2704	205	11	the	the	DET
iajs-2704	205	12	size	size	NOUN
iajs-2704	205	13	of	of	ADP
iajs-2704	205	14	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	205	15	)	)	PUNCT
iajs-2704	205	16	,	,	PUNCT
iajs-2704	205	17	we	we	PRON
iajs-2704	205	18	note	note	VERB
iajs-2704	205	19	that	that	SCONJ
iajs-2704	205	20	there	there	PRON
iajs-2704	205	21	is	be	VERB
iajs-2704	205	22	𝑚𝑟𝑛−1	𝑚𝑟𝑛−1	PROPN
iajs-2704	205	23	of	of	ADP
iajs-2704	205	24	edges	edge	NOUN
iajs-2704	205	25	s.t	s.t	PROPN
iajs-2704	205	26	𝑚1	𝑚1	NOUN
iajs-2704	205	27	=	=	PUNCT
iajs-2704	205	28	𝑟	𝑟	X
iajs-2704	205	29	𝑛	𝑛	PRON
iajs-2704	205	30	−	−	PROPN
iajs-2704	205	31	2	2	NUM
iajs-2704	205	32	,	,	PUNCT
iajs-2704	205	33	𝑚2	𝑚2	NOUN
iajs-2704	205	34	=	=	PUNCT
iajs-2704	206	1	𝑟	𝑟	X
iajs-2704	206	2	𝑛	𝑛	PRON
iajs-2704	206	3	−	−	PROPN
iajs-2704	206	4	3	3	NUM
iajs-2704	206	5	,	,	PUNCT
iajs-2704	206	6	…	…	PUNCT
iajs-2704	206	7	.	.	PUNCT
iajs-2704	207	1	,	,	PUNCT
iajs-2704	207	2	𝑚𝑟𝑛−1	𝑚𝑟𝑛−1	PROPN
iajs-2704	207	3	=	=	NOUN
iajs-2704	207	4	1	1	NUM
iajs-2704	207	5	then	then	ADV
iajs-2704	207	6	,	,	PUNCT
iajs-2704	207	7	:	:	PUNCT
iajs-2704	207	8	𝑐1	𝑐1	NOUN
iajs-2704	207	9	=	=	SYM
iajs-2704	207	10	𝑚1	𝑚1	NOUN
iajs-2704	207	11	+	+	NOUN
iajs-2704	207	12	𝑚2	𝑚2	NOUN
iajs-2704	207	13	+	+	NOUN
iajs-2704	207	14	⋯+𝑚𝑟𝑛−1	⋯+𝑚𝑟𝑛−1	PROPN
iajs-2704	207	15	we	we	PRON
iajs-2704	207	16	can	can	AUX
iajs-2704	207	17	write	write	VERB
iajs-2704	207	18	:	:	PUNCT
iajs-2704	207	19	𝑐1	𝑐1	NOUN
iajs-2704	207	20	=	=	PUNCT
iajs-2704	207	21	∑	∑	PUNCT
iajs-2704	207	22	(	(	PUNCT
iajs-2704	207	23	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	207	24	−	−	PROPN
iajs-2704	207	25	𝑖	𝑖	SYM
iajs-2704	207	26	𝑟𝑛−1	𝑟𝑛−1	PROPN
iajs-2704	207	27	𝑖=2	𝑖=2	PRON
iajs-2704	207	28	)	)	PUNCT
iajs-2704	207	29	theorem	theorem	VERB
iajs-2704	207	30	4.5	4.5	NUM
iajs-2704	207	31	:	:	PUNCT
iajs-2704	207	32	𝑆𝑐	𝑆𝑐	PROPN
iajs-2704	207	33	(	(	PUNCT
iajs-2704	207	34	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	207	35	)	)	PUNCT
iajs-2704	207	36	;	;	PUNCT
iajs-2704	207	37	𝑥	𝑥	X
iajs-2704	207	38	)	)	PUNCT
iajs-2704	208	1	=	=	SYM
iajs-2704	208	2	∑	∑	PUNCT
iajs-2704	208	3	(	(	PUNCT
iajs-2704	208	4	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	208	5	−	−	PROPN
iajs-2704	208	6	𝑖)(2𝑟𝑛	𝑖)(2𝑟𝑛	PUNCT
iajs-2704	209	1	−	−	NOUN
iajs-2704	209	2	4)𝑥𝑟𝑛−1	4)𝑥𝑟𝑛−1	NOUN
iajs-2704	210	1	𝑖=2	𝑖=2	PUNCT
iajs-2704	210	2	,	,	PUNCT
iajs-2704	210	3	where	where	SCONJ
iajs-2704	210	4	𝑟	𝑟	X
iajs-2704	210	5	≥	≥	NUM
iajs-2704	210	6	2	2	NUM
iajs-2704	210	7	,	,	PUNCT
iajs-2704	210	8	𝑛	𝑛	PROPN
iajs-2704	210	9	>	>	X
iajs-2704	210	10	1	1	X
iajs-2704	210	11	.	.	PUNCT
iajs-2704	211	1	proof	proof	NOUN
iajs-2704	211	2	:	:	PUNCT
iajs-2704	211	3	𝑑𝑒𝑔(𝑣	𝑑𝑒𝑔(𝑣	NUM
iajs-2704	211	4	)	)	PUNCT
iajs-2704	211	5	=	=	PUNCT
iajs-2704	212	1	𝑟𝑛	𝑟𝑛	ADP
iajs-2704	212	2	−	−	NOUN
iajs-2704	212	3	2	2	NUM
iajs-2704	212	4	,	,	PUNCT
iajs-2704	212	5	∀𝑣	∀𝑣	PROPN
iajs-2704	212	6	∈	∈	PROPN
iajs-2704	212	7	𝑉	𝑉	PROPN
iajs-2704	212	8	(	(	PUNCT
iajs-2704	212	9	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	212	10	)	)	PUNCT
iajs-2704	212	11	)	)	PUNCT
iajs-2704	212	12	,	,	PUNCT
iajs-2704	212	13	𝑣	𝑣	X
iajs-2704	212	14	=	=	SYM
iajs-2704	212	15	1,2	1,2	NUM
iajs-2704	212	16	,	,	PUNCT
iajs-2704	212	17	.	.	PUNCT
iajs-2704	212	18	.	.	PUNCT
iajs-2704	212	19	.	.	PUNCT
iajs-2704	213	1	,	,	PUNCT
iajs-2704	213	2	𝑟	𝑟	X
iajs-2704	213	3	𝑛	𝑛	PRON
iajs-2704	213	4	−	−	PROPN
iajs-2704	213	5	1	1	NUM
iajs-2704	213	6	𝑑(𝑢	𝑑(𝑢	X
iajs-2704	213	7	,	,	PUNCT
iajs-2704	213	8	𝑣	𝑣	NOUN
iajs-2704	213	9	)	)	PUNCT
iajs-2704	213	10	=	=	SYM
iajs-2704	213	11	1	1	NUM
iajs-2704	213	12	,	,	PUNCT
iajs-2704	213	13	∀𝑢	∀𝑢	NOUN
iajs-2704	213	14	,	,	PUNCT
iajs-2704	213	15	𝑣	𝑣	PROPN
iajs-2704	213	16	∈	∈	PROPN
iajs-2704	213	17	𝑉	𝑉	PROPN
iajs-2704	213	18	(	(	PUNCT
iajs-2704	213	19	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	213	20	)	)	PUNCT
iajs-2704	213	21	𝑆𝑐	𝑆𝑐	PROPN
iajs-2704	213	22	(	(	PUNCT
iajs-2704	213	23	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	213	24	)	)	PUNCT
iajs-2704	213	25	;	;	PUNCT
iajs-2704	213	26	𝑥	𝑥	X
iajs-2704	213	27	)	)	PUNCT
iajs-2704	213	28	=	=	SYM
iajs-2704	213	29	∑	∑	PROPN
iajs-2704	213	30	(	(	PUNCT
iajs-2704	213	31	𝑑𝑒𝑔(𝑢	𝑑𝑒𝑔(𝑢	PROPN
iajs-2704	213	32	)	)	PUNCT
iajs-2704	214	1	+	+	CCONJ
iajs-2704	214	2	𝑑𝑒𝑔(𝑣))𝑥𝑑(𝑢,𝑣)𝑢,𝑣∈𝑉	𝑑𝑒𝑔(𝑣))𝑥𝑑(𝑢,𝑣)𝑢,𝑣∈𝑉	ADJ
iajs-2704	214	3	(	(	PUNCT
iajs-2704	214	4	ᴦ𝑆𝐼(𝑍𝑟𝑛	ᴦ𝑆𝐼(𝑍𝑟𝑛	ADV
iajs-2704	214	5	)	)	PUNCT
iajs-2704	214	6	)	)	PUNCT
iajs-2704	215	1	=	=	SYM
iajs-2704	215	2	(	(	PUNCT
iajs-2704	215	3	𝑑𝑒𝑔(1	𝑑𝑒𝑔(1	PROPN
iajs-2704	215	4	)	)	PUNCT
iajs-2704	216	1	+	+	CCONJ
iajs-2704	216	2	𝑑𝑒	𝑑𝑒	PROPN
iajs-2704	216	3	𝑔(2	𝑔(2	NOUN
iajs-2704	216	4	)	)	PUNCT
iajs-2704	216	5	)	)	PUNCT
iajs-2704	217	1	𝑥	𝑥	PROPN
iajs-2704	218	1	+	+	NUM
iajs-2704	218	2	⋯+(𝑑𝑒𝑔(1	⋯+(𝑑𝑒𝑔(1	NOUN
iajs-2704	218	3	)	)	PUNCT
iajs-2704	219	1	+	+	CCONJ
iajs-2704	219	2	𝑑𝑒𝑔	𝑑𝑒𝑔	PROPN
iajs-2704	219	3	(	(	PUNCT
iajs-2704	219	4	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	219	5	−	−	PROPN
iajs-2704	219	6	1))𝑥⏟	1))𝑥⏟	NUM
iajs-2704	219	7	(	(	PUNCT
iajs-2704	219	8	𝑟𝑛−2)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−2)𝑡𝑖𝑚𝑒𝑠	PROPN
iajs-2704	219	9	+	+	CCONJ
iajs-2704	219	10	(	(	PUNCT
iajs-2704	219	11	𝑑𝑒𝑔(2	𝑑𝑒𝑔(2	NOUN
iajs-2704	219	12	)	)	PUNCT
iajs-2704	220	1	+	+	CCONJ
iajs-2704	220	2	𝑑𝑒	𝑑𝑒	X
iajs-2704	220	3	𝑔(3))𝑥	𝑔(3))𝑥	PRON
iajs-2704	220	4	+	+	NUM
iajs-2704	220	5	⋯+	⋯+	NOUN
iajs-2704	220	6	(	(	PUNCT
iajs-2704	220	7	𝑑𝑒𝑔(2	𝑑𝑒𝑔(2	NOUN
iajs-2704	220	8	)	)	PUNCT
iajs-2704	221	1	+	+	CCONJ
iajs-2704	221	2	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	221	3	(	(	PUNCT
iajs-2704	221	4	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	221	5	−	−	NUM
iajs-2704	221	6	1))𝑥⏟	1))𝑥⏟	NUM
iajs-2704	221	7	(	(	PUNCT
iajs-2704	221	8	𝑟𝑛−3)𝑡𝑖𝑚𝑒𝑠	𝑟𝑛−3)𝑡𝑖𝑚𝑒𝑠	NOUN
iajs-2704	221	9	+	+	PROPN
iajs-2704	221	10	⋯	⋯	PROPN
iajs-2704	221	11	+	+	CCONJ
iajs-2704	221	12	(	(	PUNCT
iajs-2704	221	13	𝑑𝑒𝑔(𝑟𝑛	𝑑𝑒𝑔(𝑟𝑛	NOUN
iajs-2704	221	14	−	−	PROPN
iajs-2704	221	15	1	1	NUM
iajs-2704	221	16	)	)	PUNCT
iajs-2704	221	17	+	+	CCONJ
iajs-2704	221	18	𝑑𝑒𝑔	𝑑𝑒𝑔	X
iajs-2704	221	19	(	(	PUNCT
iajs-2704	221	20	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	221	21	−	−	NUM
iajs-2704	221	22	2))𝑥	2))𝑥	NUM
iajs-2704	221	23	=	=	SYM
iajs-2704	221	24	∑	∑	PUNCT
iajs-2704	221	25	(	(	PUNCT
iajs-2704	221	26	𝑟𝑛	𝑟𝑛	INTJ
iajs-2704	221	27	−	−	PROPN
iajs-2704	221	28	𝑖)(2𝑟𝑛	𝑖)(2𝑟𝑛	PUNCT
iajs-2704	221	29	−	−	PROPN
iajs-2704	221	30	4)𝑥	4)𝑥	PROPN
iajs-2704	221	31	𝑟𝑛−1	𝑟𝑛−1	PROPN
iajs-2704	221	32	𝑖=2	𝑖=2	ADP
iajs-2704	221	33	5	5	X
iajs-2704	221	34	.	.	PUNCT
iajs-2704	221	35	conclusions	conclusion	NOUN
iajs-2704	221	36	this	this	DET
iajs-2704	221	37	article	article	NOUN
iajs-2704	221	38	has	have	AUX
iajs-2704	221	39	presented	present	VERB
iajs-2704	221	40	the	the	DET
iajs-2704	221	41	formulae	formulae	NOUN
iajs-2704	221	42	of	of	ADP
iajs-2704	221	43	some	some	DET
iajs-2704	221	44	degree	degree	NOUN
iajs-2704	221	45	-	-	PUNCT
iajs-2704	221	46	based	base	VERB
iajs-2704	221	47	and	and	CCONJ
iajs-2704	221	48	eccentric	eccentric	NOUN
iajs-2704	221	49	-	-	PUNCT
iajs-2704	221	50	based	base	VERB
iajs-2704	221	51	topological	topological	ADJ
iajs-2704	221	52	indices	index	NOUN
iajs-2704	221	53	of	of	ADP
iajs-2704	221	54	subgroup	subgroup	NOUN
iajs-2704	221	55	intersection	intersection	NOUN
iajs-2704	221	56	graph	graph	NOUN
iajs-2704	221	57	of	of	ADP
iajs-2704	221	58	a	a	DET
iajs-2704	221	59	group	group	NOUN
iajs-2704	221	60	𝑍𝑟𝑛	𝑍𝑟𝑛	PROPN
iajs-2704	221	61	,	,	PUNCT
iajs-2704	221	62	where	where	SCONJ
iajs-2704	221	63	𝑟	𝑟	X
iajs-2704	221	64	≥	≥	NUM
iajs-2704	221	65	2	2	NUM
iajs-2704	221	66	,	,	PUNCT
iajs-2704	221	67	𝑛	𝑛	PROPN
iajs-2704	221	68	>	>	X
iajs-2704	221	69	1	1	X
iajs-2704	221	70	.	.	PUNCT
iajs-2704	221	71	for	for	ADP
iajs-2704	221	72	further	further	ADJ
iajs-2704	221	73	research	research	NOUN
iajs-2704	221	74	,	,	PUNCT
iajs-2704	221	75	revise	revise	VERB
iajs-2704	221	76	on	on	ADP
iajs-2704	221	77	subgroup	subgroup	NOUN
iajs-2704	221	78	intersection	intersection	NOUN
iajs-2704	221	79	graph	graph	NOUN
iajs-2704	221	80	of	of	ADP
iajs-2704	221	81	a	a	DET
iajs-2704	221	82	group	group	NOUN
iajs-2704	221	83	𝑍𝑟𝑛	𝑍𝑟𝑛	PROPN
iajs-2704	221	84	,	,	PUNCT
iajs-2704	221	85	where	where	SCONJ
iajs-2704	221	86	𝑟	𝑟	X
iajs-2704	221	87	≥	≥	NUM
iajs-2704	221	88	2	2	NUM
iajs-2704	221	89	,	,	PUNCT
iajs-2704	221	90	𝑛	𝑛	PROPN
iajs-2704	221	91	>	>	X
iajs-2704	221	92	1	1	NUM
iajs-2704	221	93	,	,	PUNCT
iajs-2704	221	94	𝑟	𝑟	PRON
iajs-2704	221	95	is	be	AUX
iajs-2704	221	96	a	a	DET
iajs-2704	221	97	prime	prime	ADJ
iajs-2704	221	98	number	number	NOUN
iajs-2704	221	99	.	.	PUNCT
iajs-2704	222	1	ibn	ibn	PROPN
iajs-2704	222	2	al	al	PROPN
iajs-2704	222	3	-	-	PUNCT
iajs-2704	222	4	haitham	haitham	PROPN
iajs-2704	222	5	jour	jour	X
iajs-2704	222	6	.	.	PROPN
iajs-2704	222	7	for	for	ADP
iajs-2704	222	8	pure	pure	ADJ
iajs-2704	222	9	&	&	CCONJ
iajs-2704	222	10	appl	appl	PROPN
iajs-2704	222	11	.	.	PUNCT
iajs-2704	223	1	sci	sci	PROPN
iajs-2704	223	2	.	.	PROPN
iajs-2704	224	1	34(4)2021	34(4)2021	NUM
iajs-2704	224	2	77	77	NUM
iajs-2704	224	3	references	reference	NOUN
iajs-2704	224	4	1	1	NUM
iajs-2704	224	5	.	.	PUNCT
iajs-2704	225	1	h.q	h.q	DET
iajs-2704	225	2	u	u	PROPN
iajs-2704	225	3	;	;	PUNCT
iajs-2704	225	4	s.	s.	PROPN
iajs-2704	225	5	cao	cao	PROPN
iajs-2704	225	6	.	.	PUNCT
iajs-2704	226	1	on	on	ADP
iajs-2704	226	2	the	the	DET
iajs-2704	226	3	adjacent	adjacent	ADJ
iajs-2704	226	4	eccentric	eccentric	ADJ
iajs-2704	226	5	distance	distance	NOUN
iajs-2704	226	6	sum	sum	NOUN
iajs-2704	226	7	index	index	NOUN
iajs-2704	226	8	of	of	ADP
iajs-2704	226	9	graphs	graph	NOUN
iajs-2704	226	10	.	.	PUNCT
iajs-2704	227	1	plos	plos	PROPN
iajs-2704	227	2	one	one	NUM
iajs-2704	227	3	,	,	PUNCT
iajs-2704	227	4	1	1	NUM
iajs-2704	227	5	-	-	SYM
iajs-2704	227	6	12	12	NUM
iajs-2704	227	7	2015	2015	NUM
iajs-2704	227	8	2	2	NUM
iajs-2704	227	9	.	.	PUNCT
iajs-2704	227	10	morgan	morgan	PROPN
iajs-2704	227	11	,	,	PUNCT
iajs-2704	227	12	m	m	VERB
iajs-2704	227	13	.j	.j	ADJ
iajs-2704	227	14	.	.	PUNCT
iajs-2704	227	15	,	,	PUNCT
iajs-2704	227	16	mukwembi	mukwembi	PROPN
iajs-2704	227	17	s.	s.	PROPN
iajs-2704	227	18	and	and	CCONJ
iajs-2704	227	19	swart	swart	PROPN
iajs-2704	227	20	h.c	h.c	PROPN
iajs-2704	227	21	.	.	PROPN
iajs-2704	228	1	on	on	ADP
iajs-2704	228	2	the	the	DET
iajs-2704	228	3	eccentric	eccentric	ADJ
iajs-2704	228	4	connectivity	connectivity	NOUN
iajs-2704	228	5	index	index	NOUN
iajs-2704	228	6	of	of	ADP
iajs-2704	228	7	graph	graph	NOUN
iajs-2704	228	8	,	,	PUNCT
iajs-2704	228	9	discrete	discrete	ADJ
iajs-2704	228	10	mathematics	mathematic	NOUN
iajs-2704	228	11	.	.	PUNCT
iajs-2704	228	12	2011	2011	NUM
iajs-2704	228	13	,	,	PUNCT
iajs-2704	228	14	311	311	NUM
iajs-2704	228	15	.	.	NOUN
iajs-2704	228	16	2009	2009	NUM
iajs-2704	228	17	,	,	PUNCT
iajs-2704	228	18	1229	1229	NUM
iajs-2704	228	19	-	-	SYM
iajs-2704	228	20	1234	1234	NUM
iajs-2704	228	21	.	.	PUNCT
iajs-2704	229	1	3	3	X
iajs-2704	229	2	.	.	X
iajs-2704	229	3	abdelgader	abdelgader	PROPN
iajs-2704	229	4	,	,	PUNCT
iajs-2704	229	5	m.s	m.s	PROPN
iajs-2704	229	6	.	.	PROPN
iajs-2704	229	7	;	;	PUNCT
iajs-2704	230	1	wang	wang	PROPN
iajs-2704	230	2	,	,	PUNCT
iajs-2704	230	3	c.	c.	PROPN
iajs-2704	230	4	;	;	PUNCT
iajs-2704	230	5	mohamed	mohamed	PROPN
iajs-2704	230	6	,	,	PUNCT
iajs-2704	230	7	s.a	s.a	PROPN
iajs-2704	230	8	.	.	PROPN
iajs-2704	230	9	computation	computation	NOUN
iajs-2704	230	10	of	of	ADP
iajs-2704	230	11	topological	topological	ADJ
iajs-2704	230	12	indices	index	NOUN
iajs-2704	230	13	of	of	ADP
iajs-2704	230	14	some	some	DET
iajs-2704	230	15	special	special	ADJ
iajs-2704	230	16	graphs	graph	NOUN
iajs-2704	230	17	,	,	PUNCT
iajs-2704	230	18	mathematics	mathematic	NOUN
iajs-2704	230	19	.	.	PUNCT
iajs-2704	231	1	2018,6(33	2018,6(33	NUM
iajs-2704	231	2	)	)	PUNCT
iajs-2704	231	3	.	.	PUNCT
iajs-2704	232	1	4	4	X
iajs-2704	232	2	.	.	X
iajs-2704	232	3	kinkar	kinkar	PROPN
iajs-2704	232	4	,	,	PUNCT
iajs-2704	232	5	ch.d	ch.d	PROPN
iajs-2704	232	6	;	;	PUNCT
iajs-2704	232	7	das	das	PROPN
iajs-2704	232	8	,	,	PUNCT
iajs-2704	232	9	s.	s.	PROPN
iajs-2704	232	10	;	;	PUNCT
iajs-2704	232	11	zkou	zkou	PROPN
iajs-2704	232	12	,	,	PUNCT
iajs-2704	232	13	b.	b.	PROPN
iajs-2704	232	14	sum	sum	NOUN
iajs-2704	232	15	-	-	PUNCT
iajs-2704	232	16	connectivity	connectivity	NOUN
iajs-2704	232	17	index	index	NOUN
iajs-2704	232	18	of	of	ADP
iajs-2704	232	19	graph	graph	NOUN
iajs-2704	232	20	,	,	PUNCT
iajs-2704	232	21	frontiers	frontier	NOUN
iajs-2704	232	22	of	of	ADP
iajs-2704	232	23	mathematics	mathematic	NOUN
iajs-2704	232	24	in	in	ADP
iajs-2704	232	25	china	china	PROPN
iajs-2704	232	26	.	.	PUNCT
iajs-2704	233	1	2016	2016	NUM
iajs-2704	233	2	,	,	PUNCT
iajs-2704	233	3	11(1),47	11(1),47	NUM
iajs-2704	233	4	-	-	SYM
iajs-2704	233	5	54	54	NUM
iajs-2704	233	6	.	.	PUNCT
iajs-2704	234	1	5	5	NUM
iajs-2704	234	2	.	.	X
iajs-2704	234	3	khalifeh	khalifeh	PROPN
iajs-2704	234	4	,	,	PUNCT
iajs-2704	234	5	m.h	m.h	PROPN
iajs-2704	234	6	.	.	PROPN
iajs-2704	234	7	;	;	PUNCT
iajs-2704	234	8	yousefiazari	yousefiazari	PROPN
iajs-2704	234	9	,	,	PUNCT
iajs-2704	234	10	h.	h.	PROPN
iajs-2704	234	11	;	;	PUNCT
iajs-2704	235	1	ashrafi	ashrafi	PROPN
iajs-2704	235	2	,	,	PUNCT
iajs-2704	235	3	a.r	a.r	PROPN
iajs-2704	235	4	.	.	PUNCT
iajs-2704	236	1	the	the	DET
iajs-2704	236	2	first	first	ADJ
iajs-2704	236	3	and	and	CCONJ
iajs-2704	236	4	second	second	ADJ
iajs-2704	236	5	zagreb	zagreb	PROPN
iajs-2704	236	6	indices	index	NOUN
iajs-2704	236	7	of	of	ADP
iajs-2704	236	8	some	some	DET
iajs-2704	236	9	graph	graph	NOUN
iajs-2704	236	10	operations	operation	NOUN
iajs-2704	236	11	,	,	PUNCT
iajs-2704	236	12	discrete	discrete	ADJ
iajs-2704	236	13	applied	apply	VERB
iajs-2704	236	14	mathematics	mathematic	NOUN
iajs-2704	236	15	.2009	.2009	PROPN
iajs-2704	236	16	,	,	PUNCT
iajs-2704	236	17	157	157	NUM
iajs-2704	236	18	,	,	PUNCT
iajs-2704	236	19	2008	2008	NUM
iajs-2704	236	20	,	,	PUNCT
iajs-2704	236	21	804	804	NUM
iajs-2704	236	22	-	-	SYM
iajs-2704	236	23	811	811	NUM
iajs-2704	236	24	.	.	PUNCT
iajs-2704	237	1	6	6	NUM
iajs-2704	237	2	.	.	X
iajs-2704	237	3	khaksari	khaksari	PROPN
iajs-2704	237	4	,	,	PUNCT
iajs-2704	237	5	a.	a.	NOUN
iajs-2704	237	6	;	;	PUNCT
iajs-2704	237	7	ghorbain	ghorbain	NOUN
iajs-2704	237	8	,	,	PUNCT
iajs-2704	237	9	m.	m.	NOUN
iajs-2704	237	10	the	the	DET
iajs-2704	237	11	forgotten	forget	VERB
iajs-2704	237	12	topological	topological	PROPN
iajs-2704	237	13	index	index	NOUN
iajs-2704	237	14	,	,	PUNCT
iajs-2704	237	15	iranian	iranian	ADJ
iajs-2704	237	16	journal	journal	PROPN
iajs-2704	237	17	of	of	ADP
iajs-2704	237	18	mathematical	mathematical	ADJ
iajs-2704	237	19	chemistry	chemistry	NOUN
iajs-2704	237	20	.	.	PUNCT
iajs-2704	238	1	2017	2017	NUM
iajs-2704	238	2	,	,	PUNCT
iajs-2704	238	3	8(3	8(3	NUM
iajs-2704	238	4	)	)	PUNCT
iajs-2704	238	5	,	,	PUNCT
iajs-2704	238	6	327	327	NUM
iajs-2704	238	7	-	-	SYM
iajs-2704	238	8	338	338	NUM
iajs-2704	238	9	.	.	PUNCT
iajs-2704	239	1	7	7	X
iajs-2704	239	2	.	.	X
iajs-2704	239	3	zhong	zhong	PROPN
iajs-2704	239	4	,	,	PUNCT
iajs-2704	239	5	l.	l.	PROPN
iajs-2704	239	6	the	the	DET
iajs-2704	239	7	harmonic	harmonic	ADJ
iajs-2704	239	8	index	index	NOUN
iajs-2704	239	9	for	for	ADP
iajs-2704	239	10	graphs	graph	NOUN
iajs-2704	239	11	,	,	PUNCT
iajs-2704	239	12	applied	apply	VERB
iajs-2704	239	13	mathematics	mathematics	NOUN
iajs-2704	239	14	letters	letter	NOUN
iajs-2704	239	15	,	,	PUNCT
iajs-2704	239	16	2012,25(3),561566	2012,25(3),561566	NUM
iajs-2704	239	17	.	.	NOUN
iajs-2704	239	18	8	8	NUM
iajs-2704	239	19	.	.	PUNCT
iajs-2704	240	1	abdussakir	abdussakir	NOUN
iajs-2704	240	2	,	,	PUNCT
iajs-2704	240	3	some	some	DET
iajs-2704	240	4	topological	topological	ADJ
iajs-2704	240	5	indices	index	NOUN
iajs-2704	240	6	of	of	ADP
iajs-2704	240	7	subgroup	subgroup	NOUN
iajs-2704	240	8	graph	graph	NOUN
iajs-2704	240	9	of	of	ADP
iajs-2704	240	10	symmetric	symmetric	ADJ
iajs-2704	240	11	group	group	NOUN
iajs-2704	240	12	,	,	PUNCT
iajs-2704	240	13	mathematics	mathematic	NOUN
iajs-2704	240	14	and	and	CCONJ
iajs-2704	240	15	statistics,2019,7(4),98	statistics,2019,7(4),98	NOUN
iajs-2704	240	16	-	-	PUNCT
iajs-2704	240	17	105	105	NUM
iajs-2704	240	18	.	.	PUNCT
iajs-2704	241	1	9	9	NUM
iajs-2704	241	2	.	.	X
iajs-2704	241	3	roshini	roshini	PROPN
iajs-2704	241	4	,	,	PUNCT
iajs-2704	241	5	g.	g.	PROPN
iajs-2704	241	6	r.	r.	PROPN
iajs-2704	241	7	some	some	DET
iajs-2704	241	8	degree	degree	NOUN
iajs-2704	241	9	based	base	VERB
iajs-2704	241	10	topological	topological	ADJ
iajs-2704	241	11	indices	index	NOUN
iajs-2704	241	12	of	of	ADP
iajs-2704	241	13	transformation	transformation	NOUN
iajs-2704	241	14	graphs	graph	NOUN
iajs-2704	241	15	,	,	PUNCT
iajs-2704	241	16	bull	bull	NOUN
iajs-2704	241	17	.	.	PUNCT
iajs-2704	242	1	int	int	NOUN
iajs-2704	242	2	.	.	PUNCT
iajs-2704	243	1	math	math	NOUN
iajs-2704	243	2	.virtual	.virtual	PROPN
iajs-2704	243	3	inst	inst	PROPN
iajs-2704	243	4	.	.	PROPN
iajs-2704	244	1	2020	2020	NUM
iajs-2704	244	2	,	,	PUNCT
iajs-2704	244	3	10(2	10(2	NUM
iajs-2704	244	4	)	)	PUNCT
iajs-2704	244	5	,	,	PUNCT
iajs-2704	244	6	225	225	NUM
iajs-2704	244	7	-	-	SYM
iajs-2704	244	8	237	237	NUM
iajs-2704	244	9	.	.	PUNCT
iajs-2704	245	1	10	10	NUM
iajs-2704	245	2	.	.	PUNCT
iajs-2704	246	1	alaa	alaa	PROPN
iajs-2704	246	2	,	,	PUNCT
iajs-2704	246	3	j.	j.	PROPN
iajs-2704	246	4	nawaf	nawaf	PROPN
iajs-2704	246	5	;	;	PUNCT
iajs-2704	246	6	akram	akram	PROPN
iajs-2704	246	7	,	,	PUNCT
iajs-2704	246	8	s.	s.	PROPN
iajs-2704	246	9	mohammad	mohammad	PROPN
iajs-2704	246	10	,	,	PUNCT
iajs-2704	246	11	some	some	DET
iajs-2704	246	12	topological	topological	ADJ
iajs-2704	246	13	indices	index	NOUN
iajs-2704	246	14	and	and	CCONJ
iajs-2704	246	15	(	(	PUNCT
iajs-2704	246	16	hosoya	hosoya	NOUN
iajs-2704	246	17	and	and	CCONJ
iajs-2704	246	18	schultz	schultz	PROPN
iajs-2704	246	19	)	)	PUNCT
iajs-2704	246	20	polynomial	polynomial	NOUN
iajs-2704	246	21	of	of	ADP
iajs-2704	246	22	subgroup	subgroup	NOUN
iajs-2704	246	23	intersection	intersection	NOUN
iajs-2704	246	24	graph	graph	NOUN
iajs-2704	246	25	of	of	ADP
iajs-2704	246	26	a	a	DET
iajs-2704	246	27	group	group	NOUN
iajs-2704	246	28	𝑍𝑟	𝑍𝑟	PROPN
iajs-2704	246	29	,	,	PUNCT
iajs-2704	246	30	journal	journal	NOUN
iajs-2704	246	31	of	of	ADP
iajs-2704	246	32	al	al	PROPN
iajs-2704	246	33	-	-	PUNCT
iajs-2704	246	34	qadisiyah	qadisiyah	NOUN
iajs-2704	246	35	for	for	ADP
iajs-2704	246	36	computer	computer	NOUN
iajs-2704	246	37	and	and	CCONJ
iajs-2704	246	38	mathematics	mathematic	NOUN
iajs-2704	246	39	.2021	.2021	PROPN
iajs-2704	246	40	,	,	PUNCT
iajs-2704	246	41	13(1),120	13(1),120	NUM
iajs-2704	246	42	-	-	SYM
iajs-2704	246	43	130	130	NUM
iajs-2704	246	44	.	.	PUNCT
iajs-2704	246	45	11	11	NUM
iajs-2704	246	46	.	.	PUNCT
iajs-2704	247	1	tamizh	tamizh	PROPN
iajs-2704	247	2	chelvam	chelvam	PROPN
iajs-2704	247	3	,	,	PUNCT
iajs-2704	247	4	t.	t.	PROPN
iajs-2704	247	5	;	;	PUNCT
iajs-2704	247	6	sattanathan	sattanathan	INTJ
iajs-2704	247	7	,	,	PUNCT
iajs-2704	247	8	m.	m.	NOUN
iajs-2704	247	9	subgroup	subgroup	NOUN
iajs-2704	247	10	intersection	intersection	NOUN
iajs-2704	247	11	graph	graph	NOUN
iajs-2704	247	12	of	of	ADP
iajs-2704	247	13	a	a	DET
iajs-2704	247	14	group	group	NOUN
iajs-2704	247	15	.j	.j	NOUN
iajs-2704	247	16	.	.	PUNCT
iajs-2704	248	1	adv	adv	PROPN
iajs-2704	248	2	.	.	PUNCT
iajs-2704	249	1	research	research	NOUN
iajs-2704	249	2	in	in	ADP
iajs-2704	249	3	pure	pure	ADJ
iajs-2704	249	4	math	math	NOUN
iajs-2704	249	5	(	(	PUNCT
iajs-2704	249	6	doi	doi	NOUN
iajs-2704	249	7	:	:	PUNCT
iajs-2704	249	8	10.5373/	10.5373/	NUM
iajs-2704	249	9	jarpm	jarpm	NOUN
iajs-2704	249	10	.	.	PUNCT
iajs-2704	250	1	2011	2011	NUM
iajs-2704	250	2	,	,	PUNCT
iajs-2704	250	3	3(4),44	3(4),44	NUM
iajs-2704	250	4	-	-	SYM
iajs-2704	250	5	49	49	NUM
iajs-2704	250	6	.	.	PUNCT
iajs-2704	251	1	594.100910	594.100910	NUM
iajs-2704	251	2	,	,	PUNCT
iajs-2704	251	3	issn:19432380	issn:19432380	NOUN
iajs-2704	251	4	)	)	PUNCT
iajs-2704	251	5	.	.	PUNCT
iajs-2704	252	1	12	12	NUM
iajs-2704	252	2	.	.	PUNCT
iajs-2704	252	3	hosoya	hosoya	PROPN
iajs-2704	252	4	,	,	PUNCT
iajs-2704	252	5	h.	h.	PROPN
iajs-2704	252	6	on	on	ADP
iajs-2704	252	7	some	some	DET
iajs-2704	252	8	counting	counting	NOUN
iajs-2704	252	9	polynomials	polynomial	NOUN
iajs-2704	252	10	in	in	ADP
iajs-2704	252	11	chemistry	chemistry	NOUN
iajs-2704	252	12	,	,	PUNCT
iajs-2704	252	13	𝟏𝟗𝟖𝟓.	𝟏𝟗𝟖𝟓.	NOUN
iajs-2704	252	14	13	13	NUM
iajs-2704	252	15	.	.	PUNCT
iajs-2704	253	1	chartrand	chartrand	PROPN
iajs-2704	253	2	,	,	PUNCT
iajs-2704	253	3	g.	g.	PROPN
iajs-2704	253	4	;	;	PUNCT
iajs-2704	253	5	lesniak	lesniak	PROPN
iajs-2704	253	6	.	.	PUNCT
iajs-2704	253	7	,	,	PUNCT
iajs-2704	253	8	graph	graph	NOUN
iajs-2704	253	9	and	and	CCONJ
iajs-2704	253	10	diagraphs	diagraph	NOUN
iajs-2704	253	11	,	,	PUNCT
iajs-2704	253	12	6th	6th	ADJ
iajs-2704	253	13	ed	ed	NOUN
iajs-2704	253	14	.	.	PUNCT
iajs-2704	253	15	,	,	PUNCT
iajs-2704	253	16	wadsworth	wadsworth	PROPN
iajs-2704	253	17	and	and	CCONJ
iajs-2704	253	18	brooks	brooks	PROPN
iajs-2704	253	19	/	/	SYM
iajs-2704	253	20	cole	cole	PROPN
iajs-2704	253	21	.	.	PUNCT
iajs-2704	254	1	california	california	PROPN
iajs-2704	254	2	.	.	PUNCT
iajs-2704	255	1	2016	2016	NUM
iajs-2704	255	2	.	.	PUNCT
iajs-2704	256	1	14	14	NUM
iajs-2704	256	2	.	.	PUNCT
iajs-2704	257	1	gutman	gutman	NOUN
iajs-2704	257	2	.	.	PUNCT
iajs-2704	257	3	selected	select	VERB
iajs-2704	257	4	properties	property	NOUN
iajs-2704	257	5	of	of	ADP
iajs-2704	257	6	the	the	DET
iajs-2704	257	7	schultz	schultz	PROPN
iajs-2704	257	8	molecular	molecular	PROPN
iajs-2704	257	9	topological	topological	PROPN
iajs-2704	257	10	index	index	PROPN
iajs-2704	257	11	,	,	PUNCT
iajs-2704	257	12	.j.chem	.j.chem	PROPN
iajs-2704	257	13	.	.	PUNCT
iajs-2704	258	1	inf	inf	PROPN
iajs-2704	258	2	.	.	PUNCT
iajs-2704	258	3	comput	comput	PROPN
iajs-2704	258	4	.	.	PUNCT
iajs-2704	259	1	sci	sci	PROPN
iajs-2704	259	2	.	.	PUNCT
iajs-2704	259	3	𝟏𝟗𝟗𝟒,34	𝟏𝟗𝟗𝟒,34	PROPN
iajs-2704	259	4	,	,	PUNCT
iajs-2704	259	5	1087	1087	NUM
iajs-2704	259	6	-	-	SYM
iajs-2704	259	7	1089	1089	NUM
iajs-2704	259	8	.	.	PUNCT