id	sid	tid	token	lemma	pos
easat-3258	1	1	edelweiss	edelweiss	PROPN
easat-3258	1	2	applied	apply	VERB
easat-3258	1	3	science	science	NOUN
easat-3258	1	4	and	and	CCONJ
easat-3258	1	5	technology	technology	NOUN
easat-3258	1	6	issn	issn	PROPN
easat-3258	1	7	:	:	PUNCT
easat-3258	1	8	2576	2576	NUM
easat-3258	1	9	-	-	SYM
easat-3258	1	10	8484	8484	NUM
easat-3258	1	11	vol	vol	NOUN
easat-3258	1	12	.	.	PROPN
easat-3258	1	13	8	8	NUM
easat-3258	1	14	,	,	PUNCT
easat-3258	1	15	no	no	INTJ
easat-3258	1	16	.	.	NOUN
easat-3258	1	17	6	6	NUM
easat-3258	1	18	,	,	PUNCT
easat-3258	1	19	5789	5789	NUM
easat-3258	1	20	-	-	SYM
easat-3258	1	21	5799	5799	NUM
easat-3258	1	22	2024	2024	NUM
easat-3258	1	23	publisher	publisher	NOUN
easat-3258	1	24	:	:	PUNCT
easat-3258	1	25	learning	learn	VERB
easat-3258	1	26	gate	gate	NOUN
easat-3258	1	27	doi	doi	PROPN
easat-3258	1	28	:	:	PUNCT
easat-3258	1	29	10.55214/25768484.v8i6.3258	10.55214/25768484.v8i6.3258	NUM
easat-3258	1	30	©	©	PROPN
easat-3258	1	31	2024	2024	NUM
easat-3258	1	32	by	by	ADP
easat-3258	1	33	the	the	DET
easat-3258	1	34	authors	author	NOUN
easat-3258	1	35	;	;	PUNCT
easat-3258	1	36	licensee	licensee	PROPN
easat-3258	1	37	learning	learning	NOUN
easat-3258	1	38	gate	gate	NOUN
easat-3258	1	39	©	©	PROPN
easat-3258	1	40	2024	2024	NUM
easat-3258	1	41	by	by	ADP
easat-3258	1	42	the	the	DET
easat-3258	1	43	authors	author	NOUN
easat-3258	1	44	;	;	PUNCT
easat-3258	1	45	licensee	licensee	PROPN
easat-3258	1	46	learning	learn	VERB
easat-3258	1	47	gate	gate	NOUN
easat-3258	1	48	*	*	PUNCT
easat-3258	1	49	correspondence	correspondence	NOUN
easat-3258	1	50	:	:	PUNCT
easat-3258	2	1	fuzzysansrmvcas@gmail.com	fuzzysansrmvcas@gmail.com	X
easat-3258	2	2	s	s	PART
easat-3258	2	3	total	total	ADJ
easat-3258	2	4	degree	degree	NOUN
easat-3258	2	5	of	of	ADP
easat-3258	2	6	maximal	maximal	ADJ
easat-3258	2	7	product	product	NOUN
easat-3258	2	8	of	of	ADP
easat-3258	2	9	two	two	NUM
easat-3258	2	10	constant	constant	ADJ
easat-3258	2	11	intuitionistic	intuitionistic	ADJ
easat-3258	2	12	fuzzy	fuzzy	ADJ
easat-3258	2	13	graphs	graph	NOUN
easat-3258	2	14	p.	p.	NOUN
easat-3258	2	15	indumathi1	indumathi1	PROPN
easat-3258	2	16	*	*	PART
easat-3258	2	17	,	,	PUNCT
easat-3258	2	18	s.	s.	PROPN
easat-3258	2	19	santhosh	santhosh	PROPN
easat-3258	2	20	kumar2	kumar2	PROPN
easat-3258	2	21	,	,	PUNCT
easat-3258	2	22	r.	r.	PROPN
easat-3258	2	23	,	,	PUNCT
easat-3258	2	24	buvaneswari3	buvaneswari3	PROPN
easat-3258	2	25	,	,	PUNCT
easat-3258	2	26	s.	s.	PROPN
easat-3258	2	27	k.	k.	PROPN
easat-3258	2	28	mala4	mala4	PROPN
easat-3258	3	1	1department	1department	NUM
easat-3258	3	2	of	of	ADP
easat-3258	3	3	science	science	NOUN
easat-3258	3	4	and	and	CCONJ
easat-3258	3	5	humanities	humanity	NOUN
easat-3258	3	6	,	,	PUNCT
easat-3258	3	7	karpagam	karpagam	PROPN
easat-3258	3	8	college	college	PROPN
easat-3258	3	9	of	of	ADP
easat-3258	3	10	engineering	engineering	PROPN
easat-3258	3	11	,	,	PUNCT
easat-3258	3	12	coimbatore	coimbatore	PROPN
easat-3258	3	13	,	,	PUNCT
easat-3258	3	14	fuzzysansrmvcas@gmail.com	fuzzysansrmvcas@gmail.com	PROPN
easat-3258	3	15	(	(	PUNCT
easat-3258	3	16	p.i	p.i	PROPN
easat-3258	3	17	.	.	PUNCT
easat-3258	3	18	)	)	PUNCT
easat-3258	3	19	.	.	PUNCT
easat-3258	4	1	2department	2department	NUM
easat-3258	4	2	of	of	ADP
easat-3258	4	3	mathematics	mathematic	NOUN
easat-3258	4	4	,	,	PUNCT
easat-3258	4	5	sri	sri	PROPN
easat-3258	4	6	ramakrishna	ramakrishna	PROPN
easat-3258	4	7	mission	mission	PROPN
easat-3258	4	8	vidyalaya	vidyalaya	PROPN
easat-3258	4	9	college	college	PROPN
easat-3258	4	10	of	of	ADP
easat-3258	4	11	arts	art	NOUN
easat-3258	4	12	and	and	CCONJ
easat-3258	4	13	science	science	NOUN
easat-3258	4	14	,	,	PUNCT
easat-3258	4	15	coimbatore	coimbatore	PROPN
easat-3258	4	16	.	.	PUNCT
easat-3258	5	1	3department	3department	NUM
easat-3258	5	2	of	of	ADP
easat-3258	5	3	mathematics	mathematic	NOUN
easat-3258	5	4	,	,	PUNCT
easat-3258	5	5	sri	sri	PROPN
easat-3258	5	6	krishna	krishna	PROPN
easat-3258	5	7	arts	arts	PROPN
easat-3258	5	8	and	and	CCONJ
easat-3258	5	9	science	science	PROPN
easat-3258	5	10	college	college	PROPN
easat-3258	5	11	,	,	PUNCT
easat-3258	5	12	coimbatore	coimbatore	PROPN
easat-3258	5	13	.	.	PUNCT
easat-3258	6	1	4department	4department	NUM
easat-3258	6	2	of	of	ADP
easat-3258	6	3	mathematics	mathematic	NOUN
easat-3258	6	4	,	,	PUNCT
easat-3258	6	5	psgr	psgr	ADJ
easat-3258	6	6	krishnammal	krishnammal	PROPN
easat-3258	6	7	college	college	NOUN
easat-3258	6	8	for	for	ADP
easat-3258	6	9	women	woman	NOUN
easat-3258	6	10	,	,	PUNCT
easat-3258	6	11	coimbatore	coimbatore	PROPN
easat-3258	6	12	.	.	PUNCT
easat-3258	7	1	abstract	abstract	PROPN
easat-3258	7	2	:	:	PUNCT
easat-3258	7	3	this	this	DET
easat-3258	7	4	paper	paper	NOUN
easat-3258	7	5	explains	explain	VERB
easat-3258	7	6	about	about	ADP
easat-3258	7	7	the	the	DET
easat-3258	7	8	total	total	ADJ
easat-3258	7	9	degree	degree	NOUN
easat-3258	7	10	of	of	ADP
easat-3258	7	11	maximal	maximal	ADJ
easat-3258	7	12	product	product	NOUN
easat-3258	7	13	of	of	ADP
easat-3258	7	14	two	two	NUM
easat-3258	7	15	constant	constant	ADJ
easat-3258	7	16	if	if	SCONJ
easat-3258	7	17	graphs	graph	NOUN
easat-3258	7	18	.	.	PUNCT
easat-3258	8	1	fuzzy	fuzzy	ADJ
easat-3258	8	2	graphs	graph	NOUN
easat-3258	8	3	are	be	AUX
easat-3258	8	4	derived	derive	VERB
easat-3258	8	5	from	from	ADP
easat-3258	8	6	crisp	crisp	ADJ
easat-3258	8	7	graphs	graph	NOUN
easat-3258	8	8	.	.	PUNCT
easat-3258	9	1	various	various	ADJ
easat-3258	9	2	properties	property	NOUN
easat-3258	9	3	of	of	ADP
easat-3258	9	4	if	if	SCONJ
easat-3258	9	5	graphs	graph	NOUN
easat-3258	9	6	are	be	AUX
easat-3258	9	7	extended	extend	VERB
easat-3258	9	8	from	from	ADP
easat-3258	9	9	fuzzy	fuzzy	ADJ
easat-3258	9	10	graphs	graph	NOUN
easat-3258	9	11	.	.	PUNCT
easat-3258	10	1	maximal	maximal	ADJ
easat-3258	10	2	product	product	NOUN
easat-3258	10	3	of	of	ADP
easat-3258	10	4	fuzzy	fuzzy	ADJ
easat-3258	10	5	graph	graph	NOUN
easat-3258	10	6	structures	structure	NOUN
easat-3258	10	7	with	with	ADP
easat-3258	10	8	applications	application	NOUN
easat-3258	10	9	have	have	AUX
easat-3258	10	10	been	be	AUX
easat-3258	10	11	discussed	discuss	VERB
easat-3258	10	12	in	in	ADP
easat-3258	10	13	different	different	ADJ
easat-3258	10	14	papers	paper	NOUN
easat-3258	10	15	and	and	CCONJ
easat-3258	10	16	extended	extend	VERB
easat-3258	10	17	to	to	ADP
easat-3258	10	18	if	if	SCONJ
easat-3258	10	19	graphs	graph	NOUN
easat-3258	10	20	.	.	PUNCT
easat-3258	11	1	constant	constant	ADJ
easat-3258	11	2	if	if	SCONJ
easat-3258	11	3	graphs	graph	NOUN
easat-3258	11	4	are	be	AUX
easat-3258	11	5	special	special	ADJ
easat-3258	11	6	type	type	NOUN
easat-3258	11	7	of	of	ADP
easat-3258	11	8	if	if	SCONJ
easat-3258	11	9	graphs	graph	NOUN
easat-3258	11	10	which	which	PRON
easat-3258	11	11	have	have	VERB
easat-3258	11	12	same	same	ADJ
easat-3258	11	13	degree	degree	NOUN
easat-3258	11	14	for	for	ADP
easat-3258	11	15	all	all	DET
easat-3258	11	16	its	its	PRON
easat-3258	11	17	vertices	vertex	NOUN
easat-3258	11	18	.	.	PUNCT
easat-3258	12	1	if	if	SCONJ
easat-3258	12	2	graphs	graph	NOUN
easat-3258	12	3	have	have	VERB
easat-3258	12	4	many	many	ADJ
easat-3258	12	5	applications	application	NOUN
easat-3258	12	6	including	include	VERB
easat-3258	12	7	the	the	DET
easat-3258	12	8	investigation	investigation	NOUN
easat-3258	12	9	of	of	ADP
easat-3258	12	10	images	image	NOUN
easat-3258	12	11	by	by	ADP
easat-3258	12	12	image	image	NOUN
easat-3258	12	13	segmentation	segmentation	NOUN
easat-3258	12	14	,	,	PUNCT
easat-3258	12	15	brain	brain	NOUN
easat-3258	12	16	mapping	mapping	NOUN
easat-3258	12	17	etc	etc	NOUN
easat-3258	12	18	,	,	PUNCT
easat-3258	12	19	maximal	maximal	ADJ
easat-3258	12	20	product	product	NOUN
easat-3258	12	21	of	of	ADP
easat-3258	12	22	fuzzy	fuzzy	ADJ
easat-3258	12	23	graphs	graph	NOUN
easat-3258	12	24	is	be	AUX
easat-3258	12	25	applied	apply	VERB
easat-3258	12	26	in	in	ADP
easat-3258	12	27	various	various	ADJ
easat-3258	12	28	fields	field	NOUN
easat-3258	12	29	like	like	ADP
easat-3258	12	30	effective	effective	ADJ
easat-3258	12	31	logistic	logistic	ADJ
easat-3258	12	32	management	management	NOUN
easat-3258	12	33	,	,	PUNCT
easat-3258	12	34	agricultural	agricultural	ADJ
easat-3258	12	35	product	product	NOUN
easat-3258	12	36	mapping	mapping	NOUN
easat-3258	12	37	etc	etc	X
easat-3258	12	38	.	.	X
easat-3258	13	1	here	here	ADV
easat-3258	13	2	in	in	ADP
easat-3258	13	3	this	this	DET
easat-3258	13	4	paper	paper	NOUN
easat-3258	13	5	,	,	PUNCT
easat-3258	13	6	the	the	DET
easat-3258	13	7	total	total	ADJ
easat-3258	13	8	degree	degree	NOUN
easat-3258	13	9	of	of	ADP
easat-3258	13	10	the	the	DET
easat-3258	13	11	vertices	vertex	NOUN
easat-3258	13	12	in	in	ADP
easat-3258	13	13	maximal	maximal	ADJ
easat-3258	13	14	product	product	NOUN
easat-3258	13	15	of	of	ADP
easat-3258	13	16	constant	constant	ADJ
easat-3258	13	17	if	if	SCONJ
easat-3258	13	18	graphs	graph	NOUN
easat-3258	13	19	are	be	AUX
easat-3258	13	20	studied	study	VERB
easat-3258	13	21	in	in	ADP
easat-3258	13	22	detail	detail	NOUN
easat-3258	13	23	with	with	ADP
easat-3258	13	24	definition	definition	NOUN
easat-3258	13	25	and	and	CCONJ
easat-3258	13	26	various	various	ADJ
easat-3258	13	27	examples	example	NOUN
easat-3258	13	28	and	and	CCONJ
easat-3258	13	29	theorems	theorem	NOUN
easat-3258	13	30	.	.	PUNCT
easat-3258	14	1	keywords	keyword	NOUN
easat-3258	14	2	:	:	PUNCT
easat-3258	14	3	fuzzy	fuzzy	ADJ
easat-3258	14	4	graph	graph	NOUN
easat-3258	14	5	,	,	PUNCT
easat-3258	14	6	ifgraphs	ifgraph	NOUN
easat-3258	14	7	,	,	PUNCT
easat-3258	14	8	investigation	investigation	NOUN
easat-3258	14	9	of	of	ADP
easat-3258	14	10	images	image	NOUN
easat-3258	14	11	,	,	PUNCT
easat-3258	14	12	maximal	maximal	ADJ
easat-3258	14	13	product	product	NOUN
easat-3258	14	14	,	,	PUNCT
easat-3258	14	15	theorems	theorem	NOUN
easat-3258	14	16	.	.	PROPN
easat-3258	14	17	1	1	X
easat-3258	14	18	.	.	X
easat-3258	14	19	overview	overview	NOUN
easat-3258	14	20	zadeh	zadeh	PROPN
easat-3258	14	21	introduced	introduce	VERB
easat-3258	14	22	the	the	DET
easat-3258	14	23	principle	principle	NOUN
easat-3258	14	24	of	of	ADP
easat-3258	14	25	fuzzy	fuzzy	ADJ
easat-3258	14	26	sets	set	NOUN
easat-3258	14	27	in	in	ADP
easat-3258	14	28	the	the	DET
easat-3258	14	29	year	year	NOUN
easat-3258	14	30	1965	1965	NUM
easat-3258	14	31	.	.	PUNCT
easat-3258	15	1	after	after	SCONJ
easat-3258	15	2	his	his	PRON
easat-3258	15	3	,	,	PUNCT
easat-3258	15	4	introduction	introduction	NOUN
easat-3258	15	5	,	,	PUNCT
easat-3258	15	6	many	many	ADJ
easat-3258	15	7	generalisations	generalisation	NOUN
easat-3258	15	8	of	of	ADP
easat-3258	15	9	this	this	DET
easat-3258	15	10	fundamental	fundamental	ADJ
easat-3258	15	11	concepts	concept	NOUN
easat-3258	15	12	have	have	AUX
easat-3258	15	13	been	be	AUX
easat-3258	15	14	developed.by	developed.by	VERB
easat-3258	15	15	many	many	ADJ
easat-3258	15	16	mathematicians	mathematician	NOUN
easat-3258	15	17	in	in	ADP
easat-3258	15	18	different	different	ADJ
easat-3258	15	19	field	field	NOUN
easat-3258	15	20	related	relate	VERB
easat-3258	15	21	to	to	ADP
easat-3258	15	22	the	the	DET
easat-3258	15	23	fuzzy	fuzzy	NOUN
easat-3258	15	24	.	.	PUNCT
easat-3258	16	1	in	in	ADP
easat-3258	16	2	1999	1999	NUM
easat-3258	16	3	atanassov	atanassov	NOUN
easat-3258	16	4	introduced	introduce	VERB
easat-3258	16	5	the	the	DET
easat-3258	16	6	notion	notion	NOUN
easat-3258	16	7	of	of	ADP
easat-3258	16	8	an	an	DET
easat-3258	16	9	if	if	NOUN
easat-3258	16	10	set	set	VERB
easat-3258	16	11	.	.	PUNCT
easat-3258	17	1	in	in	ADP
easat-3258	17	2	2002	2002	NUM
easat-3258	17	3	atanassov	atanassov	NOUN
easat-3258	17	4	along	along	ADP
easat-3258	17	5	with	with	ADP
easat-3258	17	6	shannon	shannon	PROPN
easat-3258	17	7	further	far	ADV
easat-3258	17	8	explained	explain	VERB
easat-3258	17	9	about	about	ADP
easat-3258	17	10	generalisation	generalisation	NOUN
easat-3258	17	11	of	of	ADP
easat-3258	17	12	an	an	DET
easat-3258	17	13	if	if	SCONJ
easat-3258	17	14	fuzzy	fuzzy	ADJ
easat-3258	17	15	graphs	graph	NOUN
easat-3258	17	16	.	.	PUNCT
easat-3258	18	1	subsequently	subsequently	ADV
easat-3258	18	2	,	,	PUNCT
easat-3258	18	3	in	in	ADP
easat-3258	18	4	2006	2006	NUM
easat-3258	18	5	&	&	CCONJ
easat-3258	18	6	2009	2009	NUM
easat-3258	18	7	,	,	PUNCT
easat-3258	18	8	various	various	ADJ
easat-3258	18	9	properties	property	NOUN
easat-3258	18	10	of	of	ADP
easat-3258	18	11	if	if	SCONJ
easat-3258	18	12	graph	graph	NOUN
easat-3258	18	13	have	have	AUX
easat-3258	18	14	been	be	AUX
easat-3258	18	15	discussed	discuss	VERB
easat-3258	18	16	by	by	ADP
easat-3258	18	17	parvathy	parvathy	NOUN
easat-3258	18	18	&	&	CCONJ
easat-3258	18	19	karunambigai	karunambigai	PROPN
easat-3258	18	20	on	on	ADP
easat-3258	18	21	identical	identical	ADJ
easat-3258	18	22	fields	field	NOUN
easat-3258	18	23	.	.	PUNCT
easat-3258	19	1	in	in	ADP
easat-3258	19	2	2012	2012	NUM
easat-3258	19	3	karunambigai	karunambigai	PROPN
easat-3258	19	4	,	,	PUNCT
easat-3258	19	5	parvathy	parvathy	PROPN
easat-3258	19	6	&	&	CCONJ
easat-3258	19	7	bhuvaneswari	bhuvaneswari	PROPN
easat-3258	19	8	explained	explain	VERB
easat-3258	19	9	in	in	ADP
easat-3258	19	10	details	detail	NOUN
easat-3258	19	11	,	,	PUNCT
easat-3258	19	12	the	the	DET
easat-3258	19	13	structure	structure	NOUN
easat-3258	19	14	of	of	ADP
easat-3258	19	15	an	an	DET
easat-3258	19	16	if	if	SCONJ
easat-3258	19	17	graph	graph	NOUN
easat-3258	19	18	on	on	ADP
easat-3258	19	19	its	its	PRON
easat-3258	19	20	arcs	arc	NOUN
easat-3258	19	21	and	and	CCONJ
easat-3258	19	22	the	the	DET
easat-3258	19	23	properties	property	NOUN
easat-3258	19	24	of	of	ADP
easat-3258	19	25	complete	complete	ADJ
easat-3258	19	26	if	if	SCONJ
easat-3258	19	27	graph	graph	NOUN
easat-3258	19	28	and	and	CCONJ
easat-3258	19	29	constant	constant	ADJ
easat-3258	19	30	if	if	SCONJ
easat-3258	19	31	graph	graph	NOUN
easat-3258	19	32	.	.	PUNCT
easat-3258	20	1	in	in	ADP
easat-3258	20	2	2019	2019	NUM
easat-3258	20	3	,	,	PUNCT
easat-3258	20	4	sitara	sitara	PROPN
easat-3258	20	5	,	,	PUNCT
easat-3258	20	6	muhannad	muhannad	PROPN
easat-3258	20	7	akram	akram	PROPN
easat-3258	20	8	and	and	CCONJ
easat-3258	20	9	muhammad	muhammad	PROPN
easat-3258	20	10	yusaf	yusaf	PROPN
easat-3258	20	11	introduced	introduce	VERB
easat-3258	20	12	maximal	maximal	ADJ
easat-3258	20	13	products	product	NOUN
easat-3258	20	14	of	of	ADP
easat-3258	20	15	fuzzy	fuzzy	ADJ
easat-3258	20	16	graph	graph	NOUN
easat-3258	20	17	structure	structure	NOUN
easat-3258	20	18	and	and	CCONJ
easat-3258	20	19	analysed	analyse	VERB
easat-3258	20	20	the	the	DET
easat-3258	20	21	properties	property	NOUN
easat-3258	20	22	with	with	ADP
easat-3258	20	23	examples	example	NOUN
easat-3258	20	24	.	.	PUNCT
easat-3258	21	1	in	in	ADP
easat-3258	21	2	2021	2021	NUM
easat-3258	21	3	,	,	PUNCT
easat-3258	21	4	mala	mala	PROPN
easat-3258	21	5	,	,	PUNCT
easat-3258	21	6	shanmugapriya	shanmugapriya	PROPN
easat-3258	21	7	&	&	CCONJ
easat-3258	21	8	santhosh	santhosh	PROPN
easat-3258	21	9	kumar	kumar	PROPN
easat-3258	21	10	explained	explain	VERB
easat-3258	21	11	the	the	DET
easat-3258	21	12	degrees	degree	NOUN
easat-3258	21	13	of	of	ADP
easat-3258	21	14	vertices	vertex	NOUN
easat-3258	21	15	and	and	CCONJ
easat-3258	21	16	edges	edge	NOUN
easat-3258	21	17	for	for	ADP
easat-3258	21	18	the	the	DET
easat-3258	21	19	maximal	maximal	ADJ
easat-3258	21	20	product	product	NOUN
easat-3258	21	21	of	of	ADP
easat-3258	21	22	an	an	PRON
easat-3258	21	23	if	if	SCONJ
easat-3258	21	24	ideals	ideal	NOUN
easat-3258	21	25	of	of	ADP
easat-3258	21	26	m𝛤groups	m𝛤groups	PROPN
easat-3258	21	27	in	in	ADP
easat-3258	21	28	near	near	ADP
easat-3258	21	29	rings	ring	NOUN
easat-3258	21	30	.	.	PUNCT
easat-3258	22	1	2	2	X
easat-3258	22	2	.	.	X
easat-3258	22	3	preliminaries	preliminary	NOUN
easat-3258	22	4	in	in	ADP
easat-3258	22	5	this	this	DET
easat-3258	22	6	part	part	NOUN
easat-3258	22	7	of	of	ADP
easat-3258	22	8	the	the	DET
easat-3258	22	9	article	article	NOUN
easat-3258	22	10	,	,	PUNCT
easat-3258	22	11	few	few	ADJ
easat-3258	22	12	descriptions	description	NOUN
easat-3258	22	13	of	of	ADP
easat-3258	22	14	an	an	PRON
easat-3258	23	1	if	if	SCONJ
easat-3258	23	2	graphs	graph	NOUN
easat-3258	23	3	,	,	PUNCT
easat-3258	23	4	constant	constant	ADJ
easat-3258	23	5	if	if	SCONJ
easat-3258	23	6	graphs	graph	NOUN
easat-3258	23	7	and	and	CCONJ
easat-3258	23	8	maximal	maximal	ADJ
easat-3258	23	9	product	product	NOUN
easat-3258	23	10	of	of	ADP
easat-3258	23	11	an	an	PRON
easat-3258	23	12	if	if	SCONJ
easat-3258	23	13	graphs	graph	NOUN
easat-3258	23	14	are	be	AUX
easat-3258	23	15	presented	present	VERB
easat-3258	23	16	.	.	PUNCT
easat-3258	24	1	definition	definition	NOUN
easat-3258	24	2	:	:	PUNCT
easat-3258	24	3	2.1	2.1	NUM
easat-3258	24	4	[	[	SYM
easat-3258	24	5	1	1	NUM
easat-3258	24	6	]	]	PUNCT
easat-3258	24	7	let	let	VERB
easat-3258	24	8	the	the	DET
easat-3258	24	9	set	set	NOUN
easat-3258	24	10	e	e	PRON
easat-3258	24	11	be	be	AUX
easat-3258	24	12	fixed	fix	VERB
easat-3258	24	13	.	.	PUNCT
easat-3258	25	1	an	an	PRON
easat-3258	25	2	if	if	SCONJ
easat-3258	25	3	set	set	VERB
easat-3258	25	4	a	a	PRON
easat-3258	25	5	in	in	ADP
easat-3258	25	6	e	e	NOUN
easat-3258	25	7	takes	take	VERB
easat-3258	25	8	the	the	DET
easat-3258	25	9	form	form	NOUN
easat-3258	25	10	a	a	DET
easat-3258	25	11	=	=	X
easat-3258	25	12	{	{	PUNCT
easat-3258	25	13	𝛼,μa(α	𝛼,μa(α	NOUN
easat-3258	25	14	)	)	PUNCT
easat-3258	25	15	,	,	PUNCT
easat-3258	25	16	γa(α)/αϵe	γa(α)/αϵe	NOUN
easat-3258	25	17	}	}	PUNCT
easat-3258	25	18	where	where	SCONJ
easat-3258	25	19	the	the	DET
easat-3258	25	20	degrees	degree	NOUN
easat-3258	25	21	of	of	ADP
easat-3258	25	22	membership	membership	NOUN
easat-3258	25	23	and	and	CCONJ
easat-3258	25	24	non	non	ADJ
easat-3258	25	25	–	–	PUNCT
easat-3258	25	26	membership	membership	NOUN
easat-3258	25	27	of	of	ADP
easat-3258	25	28	the	the	DET
easat-3258	25	29	element	element	NOUN
easat-3258	25	30	α∈	α∈	PROPN
easat-3258	25	31	e	e	NOUN
easat-3258	25	32	are	be	AUX
easat-3258	25	33	indicated	indicate	VERB
easat-3258	25	34	by	by	ADP
easat-3258	25	35	the	the	DET
easat-3258	25	36	functions	function	NOUN
easat-3258	25	37	μa	μa	NOUN
easat-3258	25	38	:	:	PUNCT
easat-3258	25	39	e	e	X
easat-3258	25	40	→	→	SYM
easat-3258	25	41	[	[	X
easat-3258	25	42	0,1	0,1	NUM
easat-3258	25	43	]	]	PUNCT
easat-3258	25	44	and	and	CCONJ
easat-3258	25	45	γa	γa	NOUN
easat-3258	25	46	:	:	PUNCT
easat-3258	25	47	e	e	X
easat-3258	25	48	→	→	PUNCT
easat-3258	25	49	[	[	X
easat-3258	25	50	0,1	0,1	NUM
easat-3258	25	51	]	]	PUNCT
easat-3258	25	52	where	where	SCONJ
easat-3258	25	53	0	0	NUM
easat-3258	25	54	≤	≤	NOUN
easat-3258	25	55	μa(α	μa(α	PUNCT
easat-3258	25	56	)	)	PUNCT
easat-3258	25	57	+	+	NUM
easat-3258	25	58	γa(α	γa(α	NOUN
easat-3258	25	59	)	)	PUNCT
easat-3258	25	60	≤	≤	NOUN
easat-3258	25	61	1	1	NUM
easat-3258	25	62	definition	definition	NOUN
easat-3258	25	63	:	:	PUNCT
easat-3258	25	64	2.2	2.2	NUM
easat-3258	26	1	[	[	X
easat-3258	26	2	2	2	X
easat-3258	26	3	]	]	PUNCT
easat-3258	26	4	the	the	DET
easat-3258	26	5	set	set	NOUN
easat-3258	26	6	g	g	PROPN
easat-3258	26	7	=	=	SYM
easat-3258	26	8	{	{	PUNCT
easat-3258	26	9	<	<	X
easat-3258	26	10	α	α	PROPN
easat-3258	26	11	,	,	PUNCT
easat-3258	26	12	β	β	X
easat-3258	26	13	>	>	X
easat-3258	26	14	,	,	PUNCT
easat-3258	26	15	μg(α	μg(α	NUM
easat-3258	26	16	,	,	PUNCT
easat-3258	26	17	β	β	NOUN
easat-3258	26	18	)	)	PUNCT
easat-3258	26	19	,	,	PUNCT
easat-3258	26	20	γg(α	γg(α	NOUN
easat-3258	26	21	,	,	PUNCT
easat-3258	26	22	β)/	β)/	PROPN
easat-3258	26	23	<	<	X
easat-3258	26	24	α	α	PROPN
easat-3258	26	25	,	,	PUNCT
easat-3258	26	26	β	β	X
easat-3258	26	27	>	>	X
easat-3258	26	28	ϵ	ϵ	X
easat-3258	26	29	vxv	vxv	NOUN
easat-3258	26	30	}	}	PUNCT
easat-3258	26	31	is	be	AUX
easat-3258	26	32	said	say	VERB
easat-3258	26	33	to	to	PART
easat-3258	26	34	be	be	AUX
easat-3258	26	35	an	an	DET
easat-3258	26	36	if	if	SCONJ
easat-3258	26	37	graph	graph	NOUN
easat-3258	26	38	if	if	SCONJ
easat-3258	26	39	these	these	DET
easat-3258	26	40	functions	function	NOUN
easat-3258	26	41	μg	μg	NOUN
easat-3258	26	42	:	:	PUNCT
easat-3258	26	43	vxv	vxv	X
easat-3258	26	44	→	→	SYM
easat-3258	26	45	[	[	X
easat-3258	26	46	0,1	0,1	NUM
easat-3258	26	47	]	]	PUNCT
easat-3258	26	48	and	and	CCONJ
easat-3258	26	49	γg	γg	ADV
easat-3258	26	50	:	:	PUNCT
easat-3258	26	51	vxv	vxv	NOUN
easat-3258	26	52	→	→	SYM
easat-3258	26	53	[	[	X
easat-3258	26	54	0,1	0,1	NUM
easat-3258	26	55	]	]	PUNCT
easat-3258	26	56	define	define	VERB
easat-3258	26	57	the	the	DET
easat-3258	26	58	corresponding	correspond	VERB
easat-3258	26	59	degrees	degree	NOUN
easat-3258	26	60	of	of	ADP
easat-3258	26	61	membership	membership	NOUN
easat-3258	26	62	and	and	CCONJ
easat-3258	26	63	https://orcid.org/0009-0007-5195-8744	https://orcid.org/0009-0007-5195-8744	PROPN
easat-3258	26	64	https://orcid.org/0000-0003-2276-3706	https://orcid.org/0000-0003-2276-3706	PROPN
easat-3258	26	65	https://orcid.org/0009-0009-0822-6761	https://orcid.org/0009-0009-0822-6761	VERB
easat-3258	26	66	5790	5790	NUM
easat-3258	26	67	edelweiss	edelweiss	PROPN
easat-3258	26	68	applied	apply	VERB
easat-3258	26	69	science	science	NOUN
easat-3258	26	70	and	and	CCONJ
easat-3258	26	71	technology	technology	NOUN
easat-3258	26	72	issn	issn	PROPN
easat-3258	26	73	:	:	PUNCT
easat-3258	26	74	2576	2576	NUM
easat-3258	26	75	-	-	SYM
easat-3258	26	76	8484	8484	NUM
easat-3258	26	77	vol	vol	NOUN
easat-3258	26	78	.	.	PROPN
easat-3258	26	79	8	8	NUM
easat-3258	26	80	,	,	PUNCT
easat-3258	26	81	no	no	INTJ
easat-3258	26	82	.	.	NOUN
easat-3258	27	1	6	6	NUM
easat-3258	27	2	:	:	PUNCT
easat-3258	27	3	5789	5789	NUM
easat-3258	27	4	-	-	SYM
easat-3258	27	5	5799	5799	NUM
easat-3258	27	6	,	,	PUNCT
easat-3258	27	7	2024	2024	NUM
easat-3258	27	8	doi	doi	NOUN
easat-3258	27	9	:	:	PUNCT
easat-3258	27	10	10.55214/25768484.v8i6.3258	10.55214/25768484.v8i6.3258	NUM
easat-3258	27	11	©	©	PROPN
easat-3258	27	12	2024	2024	NUM
easat-3258	27	13	by	by	ADP
easat-3258	27	14	the	the	DET
easat-3258	27	15	authors	author	NOUN
easat-3258	27	16	;	;	PUNCT
easat-3258	27	17	licensee	licensee	PROPN
easat-3258	27	18	learning	learn	VERB
easat-3258	27	19	gate	gate	NOUN
easat-3258	27	20	non	non	X
easat-3258	27	21	–	–	PUNCT
easat-3258	27	22	membership	membership	NOUN
easat-3258	27	23	of	of	ADP
easat-3258	27	24	the	the	DET
easat-3258	27	25	elements	element	NOUN
easat-3258	27	26	(	(	PUNCT
easat-3258	27	27	α	α	X
easat-3258	27	28	,	,	PUNCT
easat-3258	27	29	β	β	NOUN
easat-3258	27	30	)	)	PUNCT
easat-3258	27	31	∈	∈	PROPN
easat-3258	27	32	vxv	vxv	NOUN
easat-3258	27	33	over	over	ADP
easat-3258	27	34	ifss	ifss	NOUN
easat-3258	27	35	for	for	ADP
easat-3258	27	36	all	all	DET
easat-3258	27	37	(	(	PUNCT
easat-3258	27	38	α	α	NOUN
easat-3258	27	39	,	,	PUNCT
easat-3258	27	40	β	β	NOUN
easat-3258	27	41	)	)	PUNCT
easat-3258	27	42	∈	∈	NOUN
easat-3258	27	43	vxv	vxv	NOUN
easat-3258	28	1	such	such	ADJ
easat-3258	28	2	that	that	SCONJ
easat-3258	28	3	0	0	NUM
easat-3258	28	4	≤	≤	NUM
easat-3258	28	5	μg(α	μg(α	NUM
easat-3258	28	6	,	,	PUNCT
easat-3258	28	7	β	β	X
easat-3258	28	8	)	)	PUNCT
easat-3258	28	9	+	+	NUM
easat-3258	28	10	γg(α	γg(α	NOUN
easat-3258	28	11	,	,	PUNCT
easat-3258	28	12	β	β	NOUN
easat-3258	28	13	)	)	PUNCT
easat-3258	28	14	≤	≤	NUM
easat-3258	28	15	1	1	NUM
easat-3258	28	16	.	.	PUNCT
easat-3258	28	17	using	use	VERB
easat-3258	28	18	one	one	NUM
easat-3258	28	19	of	of	ADP
easat-3258	28	20	this	this	DET
easat-3258	28	21	cartesian	cartesian	ADJ
easat-3258	28	22	product	product	NOUN
easat-3258	28	23	the	the	DET
easat-3258	28	24	following	follow	VERB
easat-3258	28	25	definition	definition	NOUN
easat-3258	28	26	is	be	AUX
easat-3258	28	27	obtained	obtain	VERB
easat-3258	28	28	.	.	PUNCT
easat-3258	29	1	definition	definition	NOUN
easat-3258	29	2	:	:	PUNCT
easat-3258	29	3	2.3	2.3	NUM
easat-3258	30	1	[	[	SYM
easat-3258	30	2	4	4	X
easat-3258	30	3	]	]	X
easat-3258	30	4	maximum	maximum	NOUN
easat-3258	30	5	if	if	SCONJ
easat-3258	30	6	graph	graph	NOUN
easat-3258	30	7	takes	take	VERB
easat-3258	30	8	the	the	DET
easat-3258	30	9	form	form	NOUN
easat-3258	30	10	g	g	NOUN
easat-3258	30	11	=	=	SYM
easat-3258	30	12	(	(	PUNCT
easat-3258	30	13	v	v	NOUN
easat-3258	30	14	,	,	PUNCT
easat-3258	30	15	e	e	NOUN
easat-3258	30	16	)	)	PUNCT
easat-3258	30	17	where	where	SCONJ
easat-3258	30	18	v	v	NOUN
easat-3258	30	19	=	=	SYM
easat-3258	30	20	{	{	PUNCT
easat-3258	30	21	v1	v1	PROPN
easat-3258	30	22	,	,	PUNCT
easat-3258	30	23	v2	v2	PROPN
easat-3258	30	24	,	,	PUNCT
easat-3258	30	25	…	…	PUNCT
easat-3258	30	26	.	.	PUNCT
easat-3258	31	1	vn	vn	X
easat-3258	31	2	}	}	PUNCT
easat-3258	31	3	such	such	ADJ
easat-3258	31	4	that	that	SCONJ
easat-3258	31	5	μ	μ	NOUN
easat-3258	31	6	:	:	PUNCT
easat-3258	31	7	v	v	NOUN
easat-3258	31	8	→	→	SYM
easat-3258	31	9	[	[	X
easat-3258	31	10	0,1	0,1	NUM
easat-3258	31	11	]	]	PUNCT
easat-3258	31	12	and	and	CCONJ
easat-3258	31	13	γ	γ	X
easat-3258	31	14	:	:	PUNCT
easat-3258	31	15	v	v	NOUN
easat-3258	31	16	→	→	SYM
easat-3258	31	17	[	[	X
easat-3258	31	18	0,1	0,1	NUM
easat-3258	31	19	]	]	PUNCT
easat-3258	31	20	represent	represent	VERB
easat-3258	31	21	the	the	DET
easat-3258	31	22	degrees	degree	NOUN
easat-3258	31	23	of	of	ADP
easat-3258	31	24	membership	membership	NOUN
easat-3258	31	25	and	and	CCONJ
easat-3258	31	26	non	non	ADJ
easat-3258	31	27	–	–	PUNCT
easat-3258	31	28	membership	membership	NOUN
easat-3258	31	29	of	of	ADP
easat-3258	31	30	the	the	DET
easat-3258	31	31	element	element	NOUN
easat-3258	31	32	v1	v1	PROPN
easat-3258	31	33	∈	∈	PROPN
easat-3258	31	34	v	v	NOUN
easat-3258	31	35	respectively	respectively	ADV
easat-3258	31	36	with	with	ADP
easat-3258	31	37	0	0	NUM
easat-3258	31	38	≤	≤	NUM
easat-3258	31	39	μ(vi	μ(vi	NOUN
easat-3258	31	40	)	)	PUNCT
easat-3258	31	41	+	+	NUM
easat-3258	31	42	γ(vi	γ(vi	NOUN
easat-3258	31	43	)	)	PUNCT
easat-3258	31	44	≤	≤	NUM
easat-3258	31	45	1	1	NUM
easat-3258	31	46	for	for	ADP
easat-3258	31	47	i	i	PRON
easat-3258	31	48	=	=	SYM
easat-3258	31	49	1,2	1,2	NUM
easat-3258	31	50	,	,	PUNCT
easat-3258	31	51	…	…	PUNCT
easat-3258	31	52	…	…	PUNCT
easat-3258	31	53	.	.	PUNCT
easat-3258	32	1	n.	n.	NOUN
easat-3258	32	2	if	if	SCONJ
easat-3258	32	3	e	e	PROPN
easat-3258	32	4	<	<	X
easat-3258	32	5	vxv	vxv	X
easat-3258	32	6	where	where	SCONJ
easat-3258	32	7	μ	μ	NOUN
easat-3258	32	8	:	:	PUNCT
easat-3258	32	9	vxv	vxv	NOUN
easat-3258	32	10	→	→	SYM
easat-3258	32	11	[	[	X
easat-3258	32	12	0,1	0,1	NUM
easat-3258	32	13	]	]	PUNCT
easat-3258	32	14	and	and	CCONJ
easat-3258	32	15	γ	γ	PROPN
easat-3258	32	16	:	:	PUNCT
easat-3258	32	17	vxv	vxv	NOUN
easat-3258	32	18	→	→	SYM
easat-3258	32	19	[	[	X
easat-3258	32	20	0,1	0,1	NUM
easat-3258	32	21	]	]	PUNCT
easat-3258	32	22	such	such	ADJ
easat-3258	32	23	that	that	SCONJ
easat-3258	32	24	μ(vi	μ(vi	NOUN
easat-3258	32	25	,	,	PUNCT
easat-3258	32	26	vj	vj	NOUN
easat-3258	32	27	)	)	PUNCT
easat-3258	32	28	≤	≤	NOUN
easat-3258	32	29	max[μ(vi	max[μ(vi	PROPN
easat-3258	32	30	)	)	PUNCT
easat-3258	32	31	,	,	PUNCT
easat-3258	32	32	μ(vj	μ(vj	PROPN
easat-3258	32	33	)	)	PUNCT
easat-3258	32	34	]	]	PUNCT
easat-3258	32	35	and	and	CCONJ
easat-3258	32	36	γ(vi	γ(vi	NOUN
easat-3258	32	37	,	,	PUNCT
easat-3258	32	38	vj	vj	NOUN
easat-3258	32	39	)	)	PUNCT
easat-3258	32	40	≤	≤	NOUN
easat-3258	32	41	min[γ(vi	min[γ(vi	PROPN
easat-3258	32	42	)	)	PUNCT
easat-3258	32	43	,	,	PUNCT
easat-3258	32	44	γ(vj	γ(vj	PROPN
easat-3258	32	45	)	)	PUNCT
easat-3258	32	46	]	]	PUNCT
easat-3258	32	47	with	with	ADP
easat-3258	32	48	0	0	NUM
easat-3258	32	49	≤	≤	NUM
easat-3258	32	50	μ(vi	μ(vi	NOUN
easat-3258	32	51	,	,	PUNCT
easat-3258	32	52	vj	vj	INTJ
easat-3258	32	53	)	)	PUNCT
easat-3258	32	54	+	+	CCONJ
easat-3258	32	55	γ(vi	γ(vi	NOUN
easat-3258	32	56	,	,	PUNCT
easat-3258	32	57	vj	vj	NOUN
easat-3258	32	58	)	)	PUNCT
easat-3258	32	59	≤	≤	NOUN
easat-3258	32	60	1	1	NUM
easat-3258	32	61	for	for	ADP
easat-3258	32	62	every	every	DET
easat-3258	32	63	vi	vi	NOUN
easat-3258	32	64	,	,	PUNCT
easat-3258	32	65	vj	vj	X
easat-3258	32	66	∈	∈	PROPN
easat-3258	32	67	e	e	PROPN
easat-3258	32	68	for	for	ADP
easat-3258	32	69	i	i	PROPN
easat-3258	32	70	,	,	PUNCT
easat-3258	32	71	j	j	PROPN
easat-3258	32	72	=	=	SYM
easat-3258	32	73	1,2	1,2	NUM
easat-3258	32	74	,	,	PUNCT
easat-3258	32	75	.	.	PUNCT
easat-3258	32	76	.	.	PUNCT
easat-3258	32	77	.	.	PUNCT
easat-3258	32	78	.	.	PUNCT
easat-3258	32	79	.	.	PUNCT
easat-3258	33	1	n.	n.	PROPN
easat-3258	33	2	definition	definition	NOUN
easat-3258	33	3	:	:	PUNCT
easat-3258	33	4	2.4	2.4	NUM
easat-3258	33	5	[	[	SYM
easat-3258	33	6	7	7	X
easat-3258	33	7	]	]	X
easat-3258	33	8	let	let	AUX
easat-3258	33	9	g(μ	g(μ	NOUN
easat-3258	33	10	,	,	PUNCT
easat-3258	33	11	γ	γ	PROPN
easat-3258	33	12	)	)	PUNCT
easat-3258	33	13	be	be	VERB
easat-3258	33	14	an	an	DET
easat-3258	33	15	if	if	SCONJ
easat-3258	33	16	graph	graph	NOUN
easat-3258	33	17	,	,	PUNCT
easat-3258	33	18	the	the	DET
easat-3258	33	19	μ	μ	NOUN
easat-3258	33	20	−	−	NOUN
easat-3258	33	21	degree	degree	NOUN
easat-3258	33	22	of	of	ADP
easat-3258	33	23	a	a	DET
easat-3258	33	24	vertex	vertex	NOUN
easat-3258	33	25	viis	viis	NOUN
easat-3258	33	26	𝑑𝜇(vi	𝑑𝜇(vi	PROPN
easat-3258	33	27	)	)	PUNCT
easat-3258	33	28	=	=	SYM
easat-3258	33	29	∑	∑	PUNCT
easat-3258	33	30	μ(vi	μ(vi	PROPN
easat-3258	33	31	,	,	PUNCT
easat-3258	33	32	(	(	PUNCT
easat-3258	33	33	vi	vi	NOUN
easat-3258	33	34	,	,	PUNCT
easat-3258	33	35	vj)∈e	vj)∈e	NOUN
easat-3258	33	36	vj	vj	NOUN
easat-3258	33	37	)	)	PUNCT
easat-3258	33	38	and	and	CCONJ
easat-3258	33	39	the	the	DET
easat-3258	33	40	γ	γ	NOUN
easat-3258	33	41	−	−	NOUN
easat-3258	33	42	degree	degree	NOUN
easat-3258	33	43	of	of	ADP
easat-3258	33	44	the	the	DET
easat-3258	33	45	vertex	vertex	NOUN
easat-3258	33	46	vi	vi	PROPN
easat-3258	33	47	is	be	AUX
easat-3258	33	48	𝑑𝛾(vi	𝑑𝛾(vi	PROPN
easat-3258	33	49	)	)	PUNCT
easat-3258	33	50	=	=	PUNCT
easat-3258	33	51	∑	∑	PUNCT
easat-3258	33	52	γ(vi	γ(vi	NOUN
easat-3258	33	53	,	,	PUNCT
easat-3258	33	54	(	(	PUNCT
easat-3258	33	55	vi	vi	NOUN
easat-3258	33	56	,	,	PUNCT
easat-3258	33	57	vj)∈e	vj)∈e	NOUN
easat-3258	33	58	vj	vj	NOUN
easat-3258	33	59	)	)	PUNCT
easat-3258	33	60	the	the	DET
easat-3258	33	61	degree	degree	NOUN
easat-3258	33	62	of	of	ADP
easat-3258	33	63	the	the	DET
easat-3258	33	64	vertex	vertex	NOUN
easat-3258	33	65	is	be	AUX
easat-3258	33	66	d(vi	d(vi	PROPN
easat-3258	33	67	)	)	PUNCT
easat-3258	34	1	=	=	PRON
easat-3258	34	2	{	{	PUNCT
easat-3258	34	3	∑	∑	PROPN
easat-3258	34	4	μ(vi	μ(vi	NOUN
easat-3258	34	5	,	,	PUNCT
easat-3258	34	6	(	(	PUNCT
easat-3258	34	7	vi	vi	NOUN
easat-3258	34	8	,	,	PUNCT
easat-3258	34	9	vj)∈e	vj)∈e	NOUN
easat-3258	34	10	vj	vj	NOUN
easat-3258	34	11	)	)	PUNCT
easat-3258	34	12	,	,	PUNCT
easat-3258	34	13	∑	∑	ADP
easat-3258	34	14	γ(vi	γ(vi	NOUN
easat-3258	34	15	,	,	PUNCT
easat-3258	34	16	(	(	PUNCT
easat-3258	34	17	vi	vi	NOUN
easat-3258	34	18	,	,	PUNCT
easat-3258	34	19	vj)∈e	vj)∈e	NOUN
easat-3258	34	20	vj	vj	NOUN
easat-3258	34	21	)	)	PUNCT
easat-3258	34	22	}	}	PUNCT
easat-3258	34	23	and	and	CCONJ
easat-3258	34	24	μ(vi	μ(vi	PROPN
easat-3258	34	25	,	,	PUNCT
easat-3258	34	26	vj	vj	INTJ
easat-3258	34	27	)	)	PUNCT
easat-3258	34	28	=	=	NOUN
easat-3258	34	29	γ(vi	γ(vi	NOUN
easat-3258	34	30	,	,	PUNCT
easat-3258	34	31	vj	vj	INTJ
easat-3258	34	32	)	)	PUNCT
easat-3258	34	33	=	=	SYM
easat-3258	34	34	0	0	PUNCT
easat-3258	35	1	if	if	SCONJ
easat-3258	35	2	(	(	PUNCT
easat-3258	35	3	vi	vi	NOUN
easat-3258	35	4	,	,	PUNCT
easat-3258	35	5	vj	vj	ADJ
easat-3258	35	6	)	)	PUNCT
easat-3258	35	7	∉	∉	PROPN
easat-3258	35	8	e.	e.	PROPN
easat-3258	35	9	definition	definition	PROPN
easat-3258	35	10	:	:	PUNCT
easat-3258	35	11	2.5	2.5	NUM
easat-3258	35	12	.	.	PUNCT
easat-3258	36	1	[	[	X
easat-3258	36	2	5	5	X
easat-3258	36	3	]	]	PUNCT
easat-3258	36	4	let	let	AUX
easat-3258	36	5	g(μ	g(μ	NOUN
easat-3258	36	6	,	,	PUNCT
easat-3258	36	7	γ	γ	PROPN
easat-3258	36	8	)	)	PUNCT
easat-3258	36	9	be	be	VERB
easat-3258	36	10	an	an	DET
easat-3258	36	11	if	if	SCONJ
easat-3258	36	12	graph	graph	NOUN
easat-3258	36	13	with	with	ADP
easat-3258	36	14	dμ(vi	dμ(vi	PROPN
easat-3258	36	15	)	)	PUNCT
easat-3258	37	1	=	=	SYM
easat-3258	37	2	ki	ki	PROPN
easat-3258	37	3	and	and	CCONJ
easat-3258	37	4	dγ(vj	dγ(vj	PROPN
easat-3258	37	5	)	)	PUNCT
easat-3258	38	1	=	=	SYM
easat-3258	38	2	kj	kj	PROPN
easat-3258	38	3	for	for	ADP
easat-3258	38	4	all	all	DET
easat-3258	38	5	vi	vi	PROPN
easat-3258	38	6	,	,	PUNCT
easat-3258	38	7	vj	vj	X
easat-3258	38	8	∈	∈	PROPN
easat-3258	38	9	v	v	NOUN
easat-3258	38	10	of	of	ADP
easat-3258	38	11	the	the	PRON
easat-3258	38	12	if	if	SCONJ
easat-3258	38	13	graph	graph	NOUN
easat-3258	38	14	g(v	g(v	PROPN
easat-3258	38	15	,	,	PUNCT
easat-3258	38	16	e	e	NOUN
easat-3258	38	17	)	)	PUNCT
easat-3258	38	18	,	,	PUNCT
easat-3258	38	19	the	the	DET
easat-3258	38	20	graph	graph	NOUN
easat-3258	38	21	is	be	AUX
easat-3258	38	22	denoted	denote	VERB
easat-3258	38	23	as	as	ADP
easat-3258	38	24	(	(	PUNCT
easat-3258	38	25	ki	ki	PROPN
easat-3258	38	26	,	,	PUNCT
easat-3258	38	27	kj	kj	PROPN
easat-3258	38	28	)	)	PUNCT
easat-3258	38	29	ifg	ifg	NOUN
easat-3258	38	30	(	(	PUNCT
easat-3258	38	31	or	or	CCONJ
easat-3258	38	32	)	)	PUNCT
easat-3258	38	33	constant	constant	ADJ
easat-3258	38	34	ifg	ifg	NOUN
easat-3258	38	35	of	of	ADP
easat-3258	38	36	degree	degree	NOUN
easat-3258	38	37	(	(	PUNCT
easat-3258	38	38	ki	ki	PROPN
easat-3258	38	39	,	,	PUNCT
easat-3258	38	40	kj	kj	PROPN
easat-3258	38	41	)	)	PUNCT
easat-3258	38	42	definition	definition	NOUN
easat-3258	38	43	:	:	PUNCT
easat-3258	38	44	2.6	2.6	NUM
easat-3258	38	45	.	.	PUNCT
easat-3258	39	1	[	[	X
easat-3258	39	2	7	7	X
easat-3258	39	3	]	]	PUNCT
easat-3258	39	4	let	let	VERB
easat-3258	39	5	g(v	g(v	PROPN
easat-3258	39	6	,	,	PUNCT
easat-3258	39	7	e	e	NOUN
easat-3258	39	8	)	)	PUNCT
easat-3258	39	9	be	be	AUX
easat-3258	39	10	an	an	DET
easat-3258	39	11	if	if	SCONJ
easat-3258	39	12	graph	graph	NOUN
easat-3258	39	13	with	with	ADP
easat-3258	39	14	g(μ	g(μ	PROPN
easat-3258	39	15	,	,	PUNCT
easat-3258	39	16	γ	γ	NOUN
easat-3258	39	17	)	)	PUNCT
easat-3258	39	18	,	,	PUNCT
easat-3258	39	19	the	the	DET
easat-3258	39	20	total	total	ADJ
easat-3258	39	21	degree	degree	NOUN
easat-3258	39	22	of	of	ADP
easat-3258	39	23	a	a	DET
easat-3258	39	24	vertex	vertex	NOUN
easat-3258	39	25	v	v	ADP
easat-3258	39	26	∈	∈	NOUN
easat-3258	39	27	v	v	NOUN
easat-3258	39	28	is	be	AUX
easat-3258	39	29	defined	define	VERB
easat-3258	39	30	as	as	ADP
easat-3258	39	31	td(u	td(u	PUNCT
easat-3258	39	32	)	)	PUNCT
easat-3258	40	1	=	=	SYM
easat-3258	40	2	∑	∑	PUNCT
easat-3258	40	3	dμ(vi	dμ(vi	PROPN
easat-3258	40	4	,	,	PUNCT
easat-3258	40	5	(	(	PUNCT
easat-3258	40	6	vi	vi	NOUN
easat-3258	40	7	,	,	PUNCT
easat-3258	40	8	vj)∈e	vj)∈e	NOUN
easat-3258	40	9	vj	vj	NOUN
easat-3258	40	10	)	)	PUNCT
easat-3258	40	11	+	+	NUM
easat-3258	40	12	μ(vi	μ(vi	NOUN
easat-3258	40	13	)	)	PUNCT
easat-3258	40	14	,	,	PUNCT
easat-3258	40	15	∑	∑	PUNCT
easat-3258	40	16	dγ(vi	dγ(vi	PROPN
easat-3258	40	17	,	,	PUNCT
easat-3258	40	18	(	(	PUNCT
easat-3258	40	19	vi	vi	NOUN
easat-3258	40	20	,	,	PUNCT
easat-3258	40	21	vj)∈e	vj)∈e	NOUN
easat-3258	40	22	vj	vj	NOUN
easat-3258	40	23	)	)	PUNCT
easat-3258	40	24	+	+	NUM
easat-3258	40	25	γ(vi	γ(vi	NOUN
easat-3258	40	26	)	)	PUNCT
easat-3258	40	27	if	if	SCONJ
easat-3258	40	28	the	the	DET
easat-3258	40	29	total	total	ADJ
easat-3258	40	30	degree	degree	NOUN
easat-3258	40	31	of	of	ADP
easat-3258	40	32	each	each	DET
easat-3258	40	33	vertex	vertex	NOUN
easat-3258	40	34	in	in	ADP
easat-3258	40	35	g	g	PROPN
easat-3258	40	36	is	be	AUX
easat-3258	40	37	the	the	DET
easat-3258	40	38	same	same	ADJ
easat-3258	40	39	and	and	CCONJ
easat-3258	40	40	it	it	PRON
easat-3258	40	41	is	be	AUX
easat-3258	40	42	denoted	denote	VERB
easat-3258	40	43	as	as	ADP
easat-3258	40	44	(	(	PUNCT
easat-3258	40	45	r1	r1	NOUN
easat-3258	40	46	,	,	PUNCT
easat-3258	40	47	r2	r2	PROPN
easat-3258	40	48	)	)	PUNCT
easat-3258	40	49	,	,	PUNCT
easat-3258	40	50	then	then	ADV
easat-3258	40	51	g	g	PROPN
easat-3258	40	52	is	be	AUX
easat-3258	40	53	called	call	VERB
easat-3258	40	54	an	an	PRON
easat-3258	40	55	if	if	SCONJ
easat-3258	40	56	graph	graph	NOUN
easat-3258	40	57	of	of	ADP
easat-3258	40	58	total	total	ADJ
easat-3258	40	59	degree	degree	NOUN
easat-3258	40	60	(	(	PUNCT
easat-3258	40	61	r1	r1	NOUN
easat-3258	40	62	,	,	PUNCT
easat-3258	40	63	r2	r2	PROPN
easat-3258	40	64	)	)	PUNCT
easat-3258	40	65	or	or	CCONJ
easat-3258	40	66	a	a	DET
easat-3258	40	67	(	(	PUNCT
easat-3258	40	68	r1	r1	NOUN
easat-3258	40	69	,	,	PUNCT
easat-3258	40	70	r2	r2	PROPN
easat-3258	40	71	)	)	PUNCT
easat-3258	40	72	totally	totally	ADV
easat-3258	40	73	constant	constant	ADJ
easat-3258	40	74	if	if	SCONJ
easat-3258	40	75	graph	graph	NOUN
easat-3258	40	76	.	.	PUNCT
easat-3258	41	1	definition	definition	NOUN
easat-3258	41	2	:	:	PUNCT
easat-3258	41	3	2.6	2.6	NUM
easat-3258	41	4	.	.	PUNCT
easat-3258	42	1	[	[	X
easat-3258	42	2	6	6	NUM
easat-3258	42	3	]	]	PUNCT
easat-3258	42	4	let	let	AUX
easat-3258	42	5	gi1(v𝐼2	gi1(v𝐼2	VERB
easat-3258	42	6	e𝐼2	e𝐼2	PROPN
easat-3258	42	7	μ𝐼2	μ𝐼2	PROPN
easat-3258	42	8	γ𝐼2	γ𝐼2	PROPN
easat-3258	42	9	)	)	PUNCT
easat-3258	42	10	and	and	CCONJ
easat-3258	42	11	g𝐼2	g𝐼2	PROPN
easat-3258	42	12	(	(	PUNCT
easat-3258	42	13	v𝐼2	v𝐼2	PROPN
easat-3258	42	14	e𝐼2	e𝐼2	PROPN
easat-3258	42	15	μ𝐼2	μ𝐼2	PROPN
easat-3258	42	16	γ𝐼2	γ𝐼2	PROPN
easat-3258	42	17	)	)	PUNCT
easat-3258	42	18	be	be	AUX
easat-3258	42	19	two	two	NUM
easat-3258	42	20	graphs	graph	NOUN
easat-3258	42	21	of	of	ADP
easat-3258	42	22	ifimfgnr	ifimfgnr	PROPN
easat-3258	42	23	i1	i1	PROPN
easat-3258	42	24	and	and	CCONJ
easat-3258	42	25	i2	i2	PROPN
easat-3258	42	26	is	be	AUX
easat-3258	42	27	near	near	ADP
easat-3258	42	28	ring	ring	NOUN
easat-3258	42	29	n∗	n∗	PROPN
easat-3258	42	30	then	then	ADV
easat-3258	42	31	gi1	gi1	PROPN
easat-3258	42	32	∗	∗	NOUN
easat-3258	42	33	gi2	gi2	NOUN
easat-3258	42	34	=	=	SYM
easat-3258	42	35	(	(	PUNCT
easat-3258	42	36	vieiμiγi	vieiμiγi	NOUN
easat-3258	42	37	)	)	PUNCT
easat-3258	42	38	is	be	AUX
easat-3258	42	39	called	call	VERB
easat-3258	42	40	maximal	maximal	ADJ
easat-3258	42	41	product	product	NOUN
easat-3258	42	42	structure	structure	NOUN
easat-3258	42	43	of	of	ADP
easat-3258	42	44	ifmfgnr	ifmfgnr	PROPN
easat-3258	42	45	.	.	PUNCT
easat-3258	43	1	the	the	DET
easat-3258	43	2	set	set	NOUN
easat-3258	43	3	of	of	ADP
easat-3258	43	4	vertices	vertex	NOUN
easat-3258	43	5	vi	vi	NOUN
easat-3258	43	6	=	=	SYM
easat-3258	43	7	v𝐼1	v𝐼1	NOUN
easat-3258	43	8	x	x	PUNCT
easat-3258	43	9	v𝐼2	v𝐼2	ADV
easat-3258	43	10	exist	exist	VERB
easat-3258	43	11	with	with	ADP
easat-3258	43	12	μi(ri	μi(ri	NUM
easat-3258	43	13	,	,	PUNCT
easat-3258	44	1	si	si	NOUN
easat-3258	44	2	)	)	PUNCT
easat-3258	44	3	=	=	SYM
easat-3258	44	4	μ𝐼1	μ𝐼1	PROPN
easat-3258	44	5	(	(	PUNCT
easat-3258	44	6	ri	ri	NOUN
easat-3258	44	7	)	)	PUNCT
easat-3258	44	8	⋁	⋁	PROPN
easat-3258	44	9	μ𝐼2	μ𝐼2	PROPN
easat-3258	44	10	(	(	PUNCT
easat-3258	44	11	si	si	NOUN
easat-3258	44	12	)	)	PUNCT
easat-3258	44	13	and	and	CCONJ
easat-3258	44	14	γi(ri	γi(ri	PROPN
easat-3258	44	15	,	,	PUNCT
easat-3258	44	16	si	si	NOUN
easat-3258	44	17	)	)	PUNCT
easat-3258	44	18	=	=	SYM
easat-3258	44	19	γ𝐼1	γ𝐼1	PROPN
easat-3258	44	20	(	(	PUNCT
easat-3258	44	21	ri	ri	NOUN
easat-3258	44	22	)	)	PUNCT
easat-3258	44	23	⋀	⋀	PROPN
easat-3258	44	24	γ𝐼2	γ𝐼2	PROPN
easat-3258	44	25	(	(	PUNCT
easat-3258	44	26	si	si	NOUN
easat-3258	44	27	)	)	PUNCT
easat-3258	44	28	for	for	ADP
easat-3258	44	29	all	all	DET
easat-3258	44	30	(	(	PUNCT
easat-3258	44	31	ri	ri	NOUN
easat-3258	44	32	,	,	PUNCT
easat-3258	44	33	si	si	NOUN
easat-3258	44	34	)	)	PUNCT
easat-3258	44	35	∈	∈	PROPN
easat-3258	44	36	vi	vi	NOUN
easat-3258	44	37	the	the	DET
easat-3258	44	38	set	set	NOUN
easat-3258	44	39	of	of	ADP
easat-3258	44	40	edges	edge	NOUN
easat-3258	44	41	ei	ei	X
easat-3258	44	42	=	=	PUNCT
easat-3258	44	43	{	{	PUNCT
easat-3258	44	44	(	(	PUNCT
easat-3258	44	45	r1	r1	NOUN
easat-3258	44	46	,	,	PUNCT
easat-3258	44	47	s1)(r2	s1)(r2	NOUN
easat-3258	44	48	,	,	PUNCT
easat-3258	44	49	s2	s2	PROPN
easat-3258	44	50	)	)	PUNCT
easat-3258	44	51	}	}	PUNCT
easat-3258	44	52	/	/	SYM
easat-3258	44	53	r1	r1	PROPN
easat-3258	44	54	=	=	SYM
easat-3258	44	55	r2	r2	PROPN
easat-3258	44	56	and	and	CCONJ
easat-3258	44	57	s1s2	s1s2	PROPN
easat-3258	44	58	∈	∈	PROPN
easat-3258	44	59	e𝐼2	e𝐼2	PROPN
easat-3258	44	60	(	(	PUNCT
easat-3258	44	61	or	or	CCONJ
easat-3258	44	62	)	)	PUNCT
easat-3258	44	63	s1	s1	NOUN
easat-3258	44	64	=	=	SYM
easat-3258	44	65	s2	s2	PROPN
easat-3258	44	66	and	and	CCONJ
easat-3258	44	67	r1	r1	PROPN
easat-3258	44	68	r2	r2	PROPN
easat-3258	44	69	∈	∈	PROPN
easat-3258	44	70	e𝐼1	e𝐼1	PROPN
easat-3258	44	71	exist	exist	VERB
easat-3258	44	72	with	with	ADP
easat-3258	44	73	μi(r1	μi(r1	NOUN
easat-3258	44	74	,	,	PUNCT
easat-3258	44	75	s1	s1	NOUN
easat-3258	44	76	)	)	PUNCT
easat-3258	44	77	(	(	PUNCT
easat-3258	44	78	r2	r2	PROPN
easat-3258	44	79	,	,	PUNCT
easat-3258	44	80	s2	s2	PROPN
easat-3258	44	81	)	)	PUNCT
easat-3258	44	82	=	=	PRON
easat-3258	44	83	{	{	PUNCT
easat-3258	45	1	μ𝐼1	μ𝐼1	PROPN
easat-3258	45	2	(	(	PUNCT
easat-3258	45	3	r1	r1	PROPN
easat-3258	45	4	)	)	PUNCT
easat-3258	45	5	⋁	⋁	PROPN
easat-3258	45	6	μ𝐼2	μ𝐼2	PROPN
easat-3258	45	7	(	(	PUNCT
easat-3258	45	8	s1s2	s1s2	PROPN
easat-3258	45	9	)	)	PUNCT
easat-3258	45	10	where	where	SCONJ
easat-3258	45	11	r1	r1	PROPN
easat-3258	45	12	=	=	PROPN
easat-3258	45	13	r2	r2	PROPN
easat-3258	45	14	&	&	CCONJ
easat-3258	45	15	s1s2	s1s2	PROPN
easat-3258	45	16	∈	∈	PROPN
easat-3258	45	17	e𝐼2	e𝐼2	PROPN
easat-3258	45	18	5791	5791	NUM
easat-3258	45	19	edelweiss	edelweiss	PROPN
easat-3258	45	20	applied	apply	VERB
easat-3258	45	21	science	science	NOUN
easat-3258	45	22	and	and	CCONJ
easat-3258	45	23	technology	technology	NOUN
easat-3258	45	24	issn	issn	PROPN
easat-3258	45	25	:	:	PUNCT
easat-3258	45	26	2576	2576	NUM
easat-3258	45	27	-	-	SYM
easat-3258	45	28	8484	8484	NUM
easat-3258	45	29	vol	vol	NOUN
easat-3258	45	30	.	.	PROPN
easat-3258	45	31	8	8	NUM
easat-3258	45	32	,	,	PUNCT
easat-3258	45	33	no	no	INTJ
easat-3258	45	34	.	.	NOUN
easat-3258	45	35	6	6	NUM
easat-3258	45	36	:	:	PUNCT
easat-3258	45	37	5789	5789	NUM
easat-3258	45	38	-	-	SYM
easat-3258	45	39	5799	5799	NUM
easat-3258	45	40	,	,	PUNCT
easat-3258	45	41	2024	2024	NUM
easat-3258	45	42	doi	doi	NOUN
easat-3258	45	43	:	:	PUNCT
easat-3258	45	44	10.55214/25768484.v8i6.3258	10.55214/25768484.v8i6.3258	NUM
easat-3258	45	45	©	©	PROPN
easat-3258	45	46	2024	2024	NUM
easat-3258	45	47	by	by	ADP
easat-3258	45	48	the	the	DET
easat-3258	45	49	authors	author	NOUN
easat-3258	45	50	;	;	PUNCT
easat-3258	45	51	licensee	licensee	PROPN
easat-3258	45	52	learning	learning	NOUN
easat-3258	45	53	gate	gate	NOUN
easat-3258	45	54	{	{	PUNCT
easat-3258	45	55	μ𝐼2	μ𝐼2	PROPN
easat-3258	45	56	(	(	PUNCT
easat-3258	45	57	s2	s2	PROPN
easat-3258	45	58	)	)	PUNCT
easat-3258	45	59	⋁	⋁	PROPN
easat-3258	45	60	μ𝐼1	μ𝐼1	PROPN
easat-3258	45	61	(	(	PUNCT
easat-3258	45	62	r1r2	r1r2	NOUN
easat-3258	45	63	)	)	PUNCT
easat-3258	45	64	where	where	SCONJ
easat-3258	45	65	s1	s1	PROPN
easat-3258	45	66	=	=	SYM
easat-3258	45	67	s2	s2	PROPN
easat-3258	45	68	&	&	CCONJ
easat-3258	45	69	r1r2	r1r2	VERB
easat-3258	45	70	∈	∈	PROPN
easat-3258	45	71	e𝐼2	e𝐼2	PROPN
easat-3258	45	72	and	and	CCONJ
easat-3258	45	73	γi(r1	γi(r1	PROPN
easat-3258	45	74	,	,	PUNCT
easat-3258	45	75	s1	s1	NOUN
easat-3258	45	76	)	)	PUNCT
easat-3258	45	77	(	(	PUNCT
easat-3258	45	78	r2	r2	PROPN
easat-3258	45	79	,	,	PUNCT
easat-3258	45	80	s2	s2	PROPN
easat-3258	45	81	)	)	PUNCT
easat-3258	45	82	=	=	PRON
easat-3258	45	83	{	{	PUNCT
easat-3258	45	84	γ𝐼1	γ𝐼1	PROPN
easat-3258	45	85	(	(	PUNCT
easat-3258	45	86	r1	r1	PROPN
easat-3258	45	87	)	)	PUNCT
easat-3258	45	88	⋀	⋀	PROPN
easat-3258	45	89	γ𝐼2	γ𝐼2	PROPN
easat-3258	45	90	(	(	PUNCT
easat-3258	45	91	s1s2	s1s2	PROPN
easat-3258	45	92	)	)	PUNCT
easat-3258	45	93	where	where	SCONJ
easat-3258	45	94	r1	r1	PROPN
easat-3258	45	95	=	=	PROPN
easat-3258	45	96	r2	r2	PROPN
easat-3258	45	97	&	&	CCONJ
easat-3258	45	98	s1s2	s1s2	PROPN
easat-3258	45	99	∈	∈	PROPN
easat-3258	45	100	e𝐼2	e𝐼2	PROPN
easat-3258	45	101	{	{	PUNCT
easat-3258	45	102	γ𝐼2	γ𝐼2	PROPN
easat-3258	45	103	(	(	PUNCT
easat-3258	45	104	s2	s2	PROPN
easat-3258	45	105	)	)	PUNCT
easat-3258	45	106	⋁	⋁	PROPN
easat-3258	45	107	γ𝐼1	γ𝐼1	PROPN
easat-3258	45	108	(	(	PUNCT
easat-3258	45	109	r1r2	r1r2	NOUN
easat-3258	45	110	)	)	PUNCT
easat-3258	45	111	where	where	SCONJ
easat-3258	45	112	s1	s1	PROPN
easat-3258	45	113	=	=	SYM
easat-3258	45	114	s2	s2	PROPN
easat-3258	45	115	&	&	CCONJ
easat-3258	45	116	r1r2	r1r2	PROPN
easat-3258	45	117	∈	∈	PROPN
easat-3258	45	118	e𝐼1	e𝐼1	PROPN
easat-3258	45	119	definition	definition	NOUN
easat-3258	45	120	:	:	PUNCT
easat-3258	45	121	2.7	2.7	NUM
easat-3258	45	122	.	.	PUNCT
easat-3258	46	1	[	[	X
easat-3258	46	2	6	6	NUM
easat-3258	46	3	]	]	PUNCT
easat-3258	46	4	the	the	DET
easat-3258	46	5	vertex	vertex	NOUN
easat-3258	46	6	degree	degree	NOUN
easat-3258	46	7	of	of	ADP
easat-3258	46	8	maximal	maximal	ADJ
easat-3258	46	9	product	product	NOUN
easat-3258	46	10	of	of	ADP
easat-3258	46	11	ifmfgnr	ifmfgnr	ADJ
easat-3258	46	12	gi1(v𝐼1	gi1(v𝐼1	PROPN
easat-3258	46	13	e𝐼1	e𝐼1	PROPN
easat-3258	46	14	μ𝐼1	μ𝐼1	PROPN
easat-3258	46	15	γ𝐼1	γ𝐼1	PROPN
easat-3258	46	16	)	)	PUNCT
easat-3258	46	17	and	and	CCONJ
easat-3258	46	18	gi2(v𝐼2	gi2(v𝐼2	ADJ
easat-3258	46	19	e𝐼2	e𝐼2	PROPN
easat-3258	46	20	μ𝐼2	μ𝐼2	PROPN
easat-3258	46	21	γ𝐼2	γ𝐼2	PROPN
easat-3258	46	22	)	)	PUNCT
easat-3258	46	23	is	be	AUX
easat-3258	46	24	given	give	VERB
easat-3258	46	25	by	by	ADP
easat-3258	46	26	:	:	PUNCT
easat-3258	46	27	d(g1	d(g1	PROPN
easat-3258	46	28	∗	∗	PROPN
easat-3258	46	29	g2	g2	PROPN
easat-3258	46	30	)	)	PUNCT
easat-3258	47	1	μi(rj	μi(rj	PROPN
easat-3258	47	2	,	,	PUNCT
easat-3258	47	3	sj	sj	X
easat-3258	47	4	)	)	PUNCT
easat-3258	47	5	=	=	SYM
easat-3258	47	6	∑	∑	PROPN
easat-3258	47	7	μ𝐼1	μ𝐼1	PROPN
easat-3258	47	8	(	(	PUNCT
easat-3258	47	9	rjrk	rjrk	PROPN
easat-3258	47	10	)	)	PUNCT
easat-3258	47	11	⋁	⋁	PROPN
easat-3258	47	12	μ𝐼2	μ𝐼2	PROPN
easat-3258	47	13	(	(	PUNCT
easat-3258	47	14	sj	sj	NOUN
easat-3258	47	15	)	)	PUNCT
easat-3258	47	16	+	+	CCONJ
easat-3258	47	17	∑	∑	PROPN
easat-3258	47	18	μ𝐼2	μ𝐼2	PROPN
easat-3258	47	19	(	(	PUNCT
easat-3258	47	20	sjsi	sjsi	PROPN
easat-3258	47	21	)	)	PUNCT
easat-3258	47	22	⋁	⋁	PROPN
easat-3258	47	23	μ𝐼2	μ𝐼2	PROPN
easat-3258	47	24	(	(	PUNCT
easat-3258	47	25	rj	rj	PROPN
easat-3258	47	26	)	)	PUNCT
easat-3258	47	27	and	and	CCONJ
easat-3258	47	28	d(g1	d(g1	PROPN
easat-3258	47	29	∗	∗	PROPN
easat-3258	47	30	g2	g2	PROPN
easat-3258	47	31	)	)	PUNCT
easat-3258	47	32	γi(rj	γi(rj	PROPN
easat-3258	47	33	,	,	PUNCT
easat-3258	47	34	sj	sj	PROPN
easat-3258	47	35	)	)	PUNCT
easat-3258	47	36	=	=	PUNCT
easat-3258	47	37	∑	∑	PROPN
easat-3258	47	38	γ𝐼1	γ𝐼1	PROPN
easat-3258	47	39	(	(	PUNCT
easat-3258	47	40	rjrk	rjrk	PROPN
easat-3258	47	41	)	)	PUNCT
easat-3258	47	42	⋀	⋀	PROPN
easat-3258	47	43	γ𝐼2	γ𝐼2	PROPN
easat-3258	47	44	(	(	PUNCT
easat-3258	47	45	sj	sj	NOUN
easat-3258	47	46	)	)	PUNCT
easat-3258	47	47	+	+	CCONJ
easat-3258	47	48	∑	∑	PROPN
easat-3258	47	49	γ𝐼2	γ𝐼2	PROPN
easat-3258	47	50	(	(	PUNCT
easat-3258	47	51	sjsi	sjsi	PROPN
easat-3258	47	52	)	)	PUNCT
easat-3258	47	53	⋀	⋀	PROPN
easat-3258	47	54	γ𝐼1	γ𝐼1	PROPN
easat-3258	47	55	(	(	PUNCT
easat-3258	47	56	rj	rj	PROPN
easat-3258	47	57	)	)	PUNCT
easat-3258	47	58	3	3	NUM
easat-3258	47	59	.	.	X
easat-3258	47	60	maximal	maximal	ADJ
easat-3258	47	61	product	product	NOUN
easat-3258	47	62	of	of	ADP
easat-3258	47	63	two	two	NUM
easat-3258	47	64	constant	constant	ADJ
easat-3258	47	65	if	if	SCONJ
easat-3258	47	66	graph	graph	NOUN
easat-3258	47	67	definition	definition	NOUN
easat-3258	47	68	3.1	3.1	NUM
easat-3258	47	69	.	.	PUNCT
easat-3258	48	1	let	let	VERB
easat-3258	48	2	𝐺1(𝑉′	𝐺1(𝑉′	ADV
easat-3258	48	3	,	,	PUNCT
easat-3258	48	4	𝐸′	𝐸′	NOUN
easat-3258	48	5	,	,	PUNCT
easat-3258	48	6	𝜇′	𝜇′	NOUN
easat-3258	48	7	,	,	PUNCT
easat-3258	48	8	𝛾′	𝛾′	NUM
easat-3258	48	9	)	)	PUNCT
easat-3258	48	10	and	and	CCONJ
easat-3258	48	11	𝐺2(𝑉′′	𝐺2(𝑉′′	NOUN
easat-3258	48	12	,	,	PUNCT
easat-3258	48	13	𝐸′′	𝐸′′	ADJ
easat-3258	48	14	,	,	PUNCT
easat-3258	48	15	𝜇′′	𝜇′′	NOUN
easat-3258	48	16	,	,	PUNCT
easat-3258	48	17	𝛾′′	𝛾′′	PROPN
easat-3258	48	18	)	)	PUNCT
easat-3258	48	19	be	be	VERB
easat-3258	48	20	two	two	NUM
easat-3258	48	21	constant	constant	ADJ
easat-3258	48	22	if	if	SCONJ
easat-3258	48	23	graphs	graph	NOUN
easat-3258	48	24	then	then	ADV
easat-3258	48	25	𝐺1	𝐺1	NOUN
easat-3258	48	26	∗	∗	VERB
easat-3258	48	27	𝐺2	𝐺2	NOUN
easat-3258	48	28	=	=	SYM
easat-3258	48	29	(	(	PUNCT
easat-3258	48	30	𝑉∗	𝑉∗	NOUN
easat-3258	48	31	,	,	PUNCT
easat-3258	48	32	𝐸∗	𝐸∗	NOUN
easat-3258	48	33	,	,	PUNCT
easat-3258	48	34	𝜇∗	𝜇∗	NOUN
easat-3258	48	35	,	,	PUNCT
easat-3258	48	36	𝛾∗	𝛾∗	NOUN
easat-3258	48	37	)	)	PUNCT
easat-3258	48	38	is	be	AUX
easat-3258	48	39	the	the	DET
easat-3258	48	40	maximal	maximal	ADJ
easat-3258	48	41	product	product	NOUN
easat-3258	48	42	structure	structure	NOUN
easat-3258	48	43	of	of	ADP
easat-3258	48	44	𝐺1	𝐺1	NOUN
easat-3258	48	45	and	and	CCONJ
easat-3258	48	46	𝐺2	𝐺2	NOUN
easat-3258	48	47	with	with	ADP
easat-3258	48	48	𝑉′𝑋	𝑉′𝑋	PROPN
easat-3258	48	49	𝑉′′	𝑉′′	NOUN
easat-3258	48	50	=	=	SYM
easat-3258	48	51	𝑉∗	𝑉∗	PROPN
easat-3258	48	52	,	,	PUNCT
easat-3258	48	53	the	the	DET
easat-3258	48	54	set	set	NOUN
easat-3258	48	55	of	of	ADP
easat-3258	48	56	vertices	vertex	NOUN
easat-3258	48	57	exist	exist	VERB
easat-3258	48	58	with	with	ADP
easat-3258	48	59	example	example	NOUN
easat-3258	48	60	3.2	3.2	NUM
easat-3258	48	61	.	.	PUNCT
easat-3258	49	1	consider	consider	VERB
easat-3258	49	2	𝐺1(𝑉′	𝐺1(𝑉′	ADV
easat-3258	49	3	,	,	PUNCT
easat-3258	49	4	𝐸′	𝐸′	NOUN
easat-3258	49	5	,	,	PUNCT
easat-3258	49	6	𝜇′	𝜇′	NOUN
easat-3258	49	7	,	,	PUNCT
easat-3258	49	8	𝛾′	𝛾′	NUM
easat-3258	49	9	)	)	PUNCT
easat-3258	49	10	and	and	CCONJ
easat-3258	49	11	𝐺2(𝑉′′	𝐺2(𝑉′′	NOUN
easat-3258	49	12	,	,	PUNCT
easat-3258	49	13	𝐸′′	𝐸′′	ADJ
easat-3258	49	14	,	,	PUNCT
easat-3258	49	15	𝜇′′	𝜇′′	NOUN
easat-3258	49	16	,	,	PUNCT
easat-3258	49	17	𝛾′′	𝛾′′	PROPN
easat-3258	49	18	)	)	PUNCT
easat-3258	49	19	be	be	VERB
easat-3258	49	20	to	to	PART
easat-3258	49	21	constant	constant	ADJ
easat-3258	49	22	if	if	SCONJ
easat-3258	49	23	graphs	graph	NOUN
easat-3258	49	24	and	and	CCONJ
easat-3258	49	25	𝐺(𝑉	𝐺(𝑉	NUM
easat-3258	49	26	,	,	PUNCT
easat-3258	49	27	𝐸	𝐸	PROPN
easat-3258	49	28	,	,	PUNCT
easat-3258	49	29	𝜇	𝜇	ADP
easat-3258	49	30	,	,	PUNCT
easat-3258	49	31	𝛾	𝛾	NOUN
easat-3258	49	32	)	)	PUNCT
easat-3258	49	33	is	be	AUX
easat-3258	49	34	their	their	PRON
easat-3258	49	35	maximal	maximal	ADJ
easat-3258	49	36	product	product	NOUN
easat-3258	49	37	of	of	ADP
easat-3258	49	38	constant	constant	ADJ
easat-3258	49	39	if	if	SCONJ
easat-3258	49	40	graphs	graph	NOUN
easat-3258	49	41	5792	5792	NUM
easat-3258	49	42	edelweiss	edelweiss	PROPN
easat-3258	49	43	applied	apply	VERB
easat-3258	49	44	science	science	NOUN
easat-3258	49	45	and	and	CCONJ
easat-3258	49	46	technology	technology	NOUN
easat-3258	49	47	issn	issn	PROPN
easat-3258	49	48	:	:	PUNCT
easat-3258	49	49	2576	2576	NUM
easat-3258	49	50	-	-	SYM
easat-3258	49	51	8484	8484	NUM
easat-3258	49	52	vol	vol	NOUN
easat-3258	49	53	.	.	PROPN
easat-3258	49	54	8	8	NUM
easat-3258	49	55	,	,	PUNCT
easat-3258	49	56	no	no	INTJ
easat-3258	49	57	.	.	NOUN
easat-3258	50	1	6	6	NUM
easat-3258	50	2	:	:	PUNCT
easat-3258	50	3	5789	5789	NUM
easat-3258	50	4	-	-	SYM
easat-3258	50	5	5799	5799	NUM
easat-3258	50	6	,	,	PUNCT
easat-3258	50	7	2024	2024	NUM
easat-3258	50	8	doi	doi	NOUN
easat-3258	50	9	:	:	PUNCT
easat-3258	50	10	10.55214/25768484.v8i6.3258	10.55214/25768484.v8i6.3258	NUM
easat-3258	50	11	©	©	PROPN
easat-3258	50	12	2024	2024	NUM
easat-3258	50	13	by	by	ADP
easat-3258	50	14	the	the	DET
easat-3258	50	15	authors	author	NOUN
easat-3258	50	16	;	;	PUNCT
easat-3258	50	17	licensee	licensee	PROPN
easat-3258	50	18	learning	learning	NOUN
easat-3258	50	19	gate	gate	PROPN
easat-3258	50	20	example	example	NOUN
easat-3258	50	21	3.3	3.3	NUM
easat-3258	50	22	.	.	PUNCT
easat-3258	51	1	consider	consider	VERB
easat-3258	51	2	the	the	DET
easat-3258	51	3	following	follow	VERB
easat-3258	51	4	two	two	NUM
easat-3258	51	5	constant	constant	ADJ
easat-3258	51	6	if	if	SCONJ
easat-3258	51	7	graphs	graph	NOUN
easat-3258	51	8	g1	g1	NOUN
easat-3258	51	9	and	and	CCONJ
easat-3258	51	10	g2	g2	PROPN
easat-3258	51	11	.	.	PUNCT
easat-3258	52	1	5793	5793	NUM
easat-3258	52	2	edelweiss	edelweiss	PROPN
easat-3258	52	3	applied	apply	VERB
easat-3258	52	4	science	science	NOUN
easat-3258	52	5	and	and	CCONJ
easat-3258	52	6	technology	technology	NOUN
easat-3258	52	7	issn	issn	PROPN
easat-3258	52	8	:	:	PUNCT
easat-3258	52	9	2576	2576	NUM
easat-3258	52	10	-	-	SYM
easat-3258	52	11	8484	8484	NUM
easat-3258	52	12	vol	vol	NOUN
easat-3258	52	13	.	.	PROPN
easat-3258	52	14	8	8	NUM
easat-3258	52	15	,	,	PUNCT
easat-3258	52	16	no	no	INTJ
easat-3258	52	17	.	.	NOUN
easat-3258	52	18	6	6	NUM
easat-3258	52	19	:	:	PUNCT
easat-3258	52	20	5789	5789	NUM
easat-3258	52	21	-	-	SYM
easat-3258	52	22	5799	5799	NUM
easat-3258	52	23	,	,	PUNCT
easat-3258	52	24	2024	2024	NUM
easat-3258	52	25	doi	doi	NOUN
easat-3258	52	26	:	:	PUNCT
easat-3258	52	27	10.55214/25768484.v8i6.3258	10.55214/25768484.v8i6.3258	NUM
easat-3258	52	28	©	©	PROPN
easat-3258	52	29	2024	2024	NUM
easat-3258	52	30	by	by	ADP
easat-3258	52	31	the	the	DET
easat-3258	52	32	authors	author	NOUN
easat-3258	52	33	;	;	PUNCT
easat-3258	52	34	licensee	licensee	PROPN
easat-3258	52	35	learning	learn	VERB
easat-3258	52	36	gate	gate	NOUN
easat-3258	52	37	figure	figure	NOUN
easat-3258	52	38	1	1	NUM
easat-3258	52	39	.	.	PUNCT
easat-3258	52	40	figure	figure	NOUN
easat-3258	52	41	2	2	NUM
easat-3258	52	42	.	.	PUNCT
easat-3258	52	43	let	let	VERB
easat-3258	52	44	us	we	PRON
easat-3258	52	45	find	find	VERB
easat-3258	52	46	the	the	DET
easat-3258	52	47	maximal	maximal	ADJ
easat-3258	52	48	product	product	NOUN
easat-3258	52	49	of	of	ADP
easat-3258	52	50	these	these	DET
easat-3258	52	51	two	two	NUM
easat-3258	52	52	graphs	graph	NOUN
easat-3258	52	53	as	as	ADP
easat-3258	52	54	g.	g.	PROPN
easat-3258	52	55	5794	5794	NUM
easat-3258	52	56	edelweiss	edelweiss	PROPN
easat-3258	52	57	applied	apply	VERB
easat-3258	52	58	science	science	NOUN
easat-3258	52	59	and	and	CCONJ
easat-3258	52	60	technology	technology	NOUN
easat-3258	52	61	issn	issn	PROPN
easat-3258	52	62	:	:	PUNCT
easat-3258	52	63	2576	2576	NUM
easat-3258	52	64	-	-	SYM
easat-3258	52	65	8484	8484	NUM
easat-3258	52	66	vol	vol	NOUN
easat-3258	52	67	.	.	PROPN
easat-3258	52	68	8	8	NUM
easat-3258	52	69	,	,	PUNCT
easat-3258	52	70	no	no	INTJ
easat-3258	52	71	.	.	NOUN
easat-3258	52	72	6	6	NUM
easat-3258	52	73	:	:	PUNCT
easat-3258	52	74	5789	5789	NUM
easat-3258	52	75	-	-	SYM
easat-3258	52	76	5799	5799	NUM
easat-3258	52	77	,	,	PUNCT
easat-3258	52	78	2024	2024	NUM
easat-3258	52	79	doi	doi	NOUN
easat-3258	52	80	:	:	PUNCT
easat-3258	52	81	10.55214/25768484.v8i6.3258	10.55214/25768484.v8i6.3258	NUM
easat-3258	52	82	©	©	PROPN
easat-3258	52	83	2024	2024	NUM
easat-3258	52	84	by	by	ADP
easat-3258	52	85	the	the	DET
easat-3258	52	86	authors	author	NOUN
easat-3258	52	87	;	;	PUNCT
easat-3258	52	88	licensee	licensee	PROPN
easat-3258	52	89	learning	learn	VERB
easat-3258	52	90	gate	gate	NOUN
easat-3258	52	91	consider	consider	VERB
easat-3258	52	92	the	the	DET
easat-3258	52	93	above	above	ADJ
easat-3258	52	94	graph	graph	NOUN
easat-3258	52	95	,	,	PUNCT
easat-3258	52	96	the	the	DET
easat-3258	52	97	degree	degree	NOUN
easat-3258	52	98	of	of	ADP
easat-3258	52	99	the	the	DET
easat-3258	52	100	maximal	maximal	ADJ
easat-3258	52	101	product	product	NOUN
easat-3258	52	102	of	of	ADP
easat-3258	52	103	the	the	DET
easat-3258	52	104	constant	constant	ADJ
easat-3258	52	105	if	if	SCONJ
easat-3258	52	106	graphs	graph	NOUN
easat-3258	52	107	are	be	AUX
easat-3258	52	108	calculated	calculate	VERB
easat-3258	52	109	using	use	VERB
easat-3258	52	110	the	the	DET
easat-3258	52	111	above	above	ADJ
easat-3258	52	112	definition	definition	NOUN
easat-3258	52	113	as	as	SCONJ
easat-3258	52	114	given	give	VERB
easat-3258	52	115	below	below	ADV
easat-3258	52	116	:	:	PUNCT
easat-3258	52	117	d(g1	d(g1	PROPN
easat-3258	52	118	∗	∗	PROPN
easat-3258	52	119	g2)μ(v1xv1′	g2)μ(v1xv1′	PROPN
easat-3258	52	120	)	)	PUNCT
easat-3258	53	1	=	=	SYM
easat-3258	53	2	μ1(v1v2)⋁μ2(v1′	μ1(v1v2)⋁μ2(v1′	NOUN
easat-3258	53	3	)	)	PUNCT
easat-3258	54	1	+	+	NUM
easat-3258	55	1	μ1(v1v4)⋁μ2(v1′	μ1(v1v4)⋁μ2(v1′	X
easat-3258	55	2	)	)	PUNCT
easat-3258	55	3	+	+	NUM
easat-3258	55	4	μ2(v1′v2′	μ2(v1′v2′	NOUN
easat-3258	55	5	)	)	PUNCT
easat-3258	55	6	⋁μ1(v1	⋁μ1(v1	NOUN
easat-3258	55	7	)	)	PUNCT
easat-3258	55	8	+	+	CCONJ
easat-3258	55	9	μ2(v1′v3′)⋁μ1(v1′	μ2(v1′v3′)⋁μ1(v1′	NOUN
easat-3258	55	10	)	)	PUNCT
easat-3258	55	11	=	=	PUNCT
easat-3258	56	1	1.7	1.7	NUM
easat-3258	56	2	d(g1	d(g1	NOUN
easat-3258	56	3	∗	∗	PROPN
easat-3258	56	4	g2)γ(v1xv1′	g2)γ(v1xv1′	PROPN
easat-3258	56	5	)	)	PUNCT
easat-3258	56	6	=	=	SYM
easat-3258	56	7	γ1(v1v2)⋀γ2(v1′	γ1(v1v2)⋀γ2(v1′	PROPN
easat-3258	56	8	)	)	PUNCT
easat-3258	57	1	+	+	CCONJ
easat-3258	58	1	γ1(v1v4)⋀γ2(v1′	γ1(v1v4)⋀γ2(v1′	NOUN
easat-3258	58	2	)	)	PUNCT
easat-3258	58	3	+	+	CCONJ
easat-3258	58	4	γ2(v1′v2′	γ2(v1′v2′	NOUN
easat-3258	58	5	)	)	PUNCT
easat-3258	58	6	⋀γ1(v1	⋀γ1(v1	NOUN
easat-3258	58	7	)	)	PUNCT
easat-3258	58	8	+	+	NUM
easat-3258	58	9	γ2(v1′v3′)⋀γ1(v1′	γ2(v1′v3′)⋀γ1(v1′	NOUN
easat-3258	58	10	)	)	PUNCT
easat-3258	58	11	=	=	SYM
easat-3258	58	12	0.7	0.7	NUM
easat-3258	58	13	(	(	PUNCT
easat-3258	58	14	i.	i.	NOUN
easat-3258	58	15	e	e	NOUN
easat-3258	58	16	)	)	PUNCT
easat-3258	58	17	d(g1	d(g1	VERB
easat-3258	58	18	∗	∗	NOUN
easat-3258	58	19	g2)(v1xv1′	g2)(v1xv1′	NOUN
easat-3258	58	20	)	)	PUNCT
easat-3258	59	1	=	=	PRON
easat-3258	59	2	(	(	PUNCT
easat-3258	59	3	1.7,0.7	1.7,0.7	NUM
easat-3258	59	4	)	)	PUNCT
easat-3258	59	5	d(g1	d(g1	VERB
easat-3258	59	6	∗	∗	PROPN
easat-3258	59	7	g2)μ(v1xv2′	g2)μ(v1xv2′	PROPN
easat-3258	59	8	)	)	PUNCT
easat-3258	60	1	=	=	SYM
easat-3258	60	2	μ1(v1v2)⋁μ2(v2′	μ1(v1v2)⋁μ2(v2′	PROPN
easat-3258	60	3	)	)	PUNCT
easat-3258	60	4	+	+	NUM
easat-3258	60	5	μ1(v1v4)⋁μ2(v2′	μ1(v1v4)⋁μ2(v2′	NUM
easat-3258	60	6	)	)	PUNCT
easat-3258	60	7	+	+	NUM
easat-3258	60	8	μ2(v2′v1′	μ2(v2′v1′	NOUN
easat-3258	60	9	)	)	PUNCT
easat-3258	60	10	⋁μ1(v1	⋁μ1(v1	NOUN
easat-3258	60	11	)	)	PUNCT
easat-3258	60	12	+	+	SYM
easat-3258	60	13	μ2(v2′v3′)⋁μ1(v1′	μ2(v2′v3′)⋁μ1(v1′	PROPN
easat-3258	60	14	)	)	PUNCT
easat-3258	61	1	=	=	PUNCT
easat-3258	62	1	1.8	1.8	NUM
easat-3258	62	2	d(g1	d(g1	NOUN
easat-3258	62	3	∗	∗	NOUN
easat-3258	62	4	g2)γ(v1xv2′	g2)γ(v1xv2′	NOUN
easat-3258	62	5	)	)	PUNCT
easat-3258	62	6	=	=	SYM
easat-3258	63	1	γ1(v1v2)⋀γ2(v2′	γ1(v1v2)⋀γ2(v2′	NUM
easat-3258	63	2	)	)	PUNCT
easat-3258	64	1	+	+	CCONJ
easat-3258	64	2	γ1(v1v4)⋀γ2(v2′	γ1(v1v4)⋀γ2(v2′	NOUN
easat-3258	64	3	)	)	PUNCT
easat-3258	65	1	+	+	CCONJ
easat-3258	65	2	γ2(v2′v1′	γ2(v2′v1′	ADJ
easat-3258	65	3	)	)	PUNCT
easat-3258	65	4	⋀γ1(v1	⋀γ1(v1	NOUN
easat-3258	65	5	)	)	PUNCT
easat-3258	65	6	+	+	NUM
easat-3258	65	7	γ2(v2′v3′)⋀γ1(v1′	γ2(v2′v3′)⋀γ1(v1′	ADJ
easat-3258	65	8	)	)	PUNCT
easat-3258	66	1	=	=	SYM
easat-3258	66	2	0.7	0.7	NUM
easat-3258	66	3	d(g1	d(g1	NOUN
easat-3258	66	4	∗	∗	NOUN
easat-3258	66	5	g2)(v1xv2′	g2)(v1xv2′	NOUN
easat-3258	66	6	)	)	PUNCT
easat-3258	66	7	=	=	PUNCT
easat-3258	67	1	(	(	PUNCT
easat-3258	67	2	1.8,0.7	1.8,0.7	NUM
easat-3258	67	3	)	)	PUNCT
easat-3258	67	4	5795	5795	NUM
easat-3258	67	5	edelweiss	edelweiss	PROPN
easat-3258	67	6	applied	apply	VERB
easat-3258	67	7	science	science	NOUN
easat-3258	67	8	and	and	CCONJ
easat-3258	67	9	technology	technology	NOUN
easat-3258	67	10	issn	issn	PROPN
easat-3258	67	11	:	:	PUNCT
easat-3258	67	12	2576	2576	NUM
easat-3258	67	13	-	-	SYM
easat-3258	67	14	8484	8484	NUM
easat-3258	67	15	vol	vol	NOUN
easat-3258	67	16	.	.	PROPN
easat-3258	67	17	8	8	NUM
easat-3258	67	18	,	,	PUNCT
easat-3258	67	19	no	no	INTJ
easat-3258	67	20	.	.	NOUN
easat-3258	67	21	6	6	NUM
easat-3258	67	22	:	:	PUNCT
easat-3258	67	23	5789	5789	NUM
easat-3258	67	24	-	-	SYM
easat-3258	67	25	5799	5799	NUM
easat-3258	67	26	,	,	PUNCT
easat-3258	67	27	2024	2024	NUM
easat-3258	67	28	doi	doi	NOUN
easat-3258	67	29	:	:	PUNCT
easat-3258	67	30	10.55214/25768484.v8i6.3258	10.55214/25768484.v8i6.3258	NUM
easat-3258	67	31	©	©	PROPN
easat-3258	67	32	2024	2024	NUM
easat-3258	67	33	by	by	ADP
easat-3258	67	34	the	the	DET
easat-3258	67	35	authors	author	NOUN
easat-3258	67	36	;	;	PUNCT
easat-3258	67	37	licensee	licensee	PROPN
easat-3258	67	38	learning	learning	NOUN
easat-3258	67	39	gate	gate	PROPN
easat-3258	67	40	d(g1	d(g1	PROPN
easat-3258	67	41	∗	∗	NOUN
easat-3258	67	42	g2)(v1xv3′	g2)(v1xv3′	NOUN
easat-3258	67	43	)	)	PUNCT
easat-3258	67	44	=	=	SYM
easat-3258	67	45	μ1(v1v2)⋁μ2(v3′	μ1(v1v2)⋁μ2(v3′	PROPN
easat-3258	67	46	)	)	PUNCT
easat-3258	67	47	+	+	NUM
easat-3258	67	48	μ1(v1v4)⋁μ2(v3′	μ1(v1v4)⋁μ2(v3′	NUM
easat-3258	67	49	)	)	PUNCT
easat-3258	68	1	+	+	X
easat-3258	68	2	μ2(v3′v1′	μ2(v3′v1′	X
easat-3258	68	3	)	)	PUNCT
easat-3258	68	4	⋁μ1(v1	⋁μ1(v1	NOUN
easat-3258	68	5	)	)	PUNCT
easat-3258	69	1	+	+	NUM
easat-3258	69	2	μ2(v3′v2′)⋁μ1(v1′	μ2(v3′v2′)⋁μ1(v1′	PROPN
easat-3258	69	3	)	)	PUNCT
easat-3258	69	4	=	=	SYM
easat-3258	70	1	1.6	1.6	NUM
easat-3258	70	2	d(g1	d(g1	NOUN
easat-3258	70	3	∗	∗	NOUN
easat-3258	70	4	g2)γ(v1xv3′	g2)γ(v1xv3′	NOUN
easat-3258	70	5	)	)	PUNCT
easat-3258	70	6	=	=	SYM
easat-3258	70	7	γ1(v1v2)⋀γ2(v3′	γ1(v1v2)⋀γ2(v3′	NOUN
easat-3258	70	8	)	)	PUNCT
easat-3258	71	1	+	+	CCONJ
easat-3258	71	2	γ1(v1v4)⋀γ2(v3′	γ1(v1v4)⋀γ2(v3′	NOUN
easat-3258	71	3	)	)	PUNCT
easat-3258	72	1	+	+	CCONJ
easat-3258	72	2	γ2(v3′v1′	γ2(v3′v1′	ADJ
easat-3258	72	3	)	)	PUNCT
easat-3258	72	4	⋀γ1(v1	⋀γ1(v1	NOUN
easat-3258	72	5	)	)	PUNCT
easat-3258	72	6	+	+	NUM
easat-3258	72	7	γ2(v3′v2′)⋀γ1(v1′	γ2(v3′v2′)⋀γ1(v1′	NOUN
easat-3258	72	8	)	)	PUNCT
easat-3258	72	9	=	=	SYM
easat-3258	72	10	0.6	0.6	NUM
easat-3258	72	11	d(g1	d(g1	VERB
easat-3258	72	12	∗	∗	NOUN
easat-3258	72	13	g2)(v1xv3′	g2)(v1xv3′	NOUN
easat-3258	72	14	)	)	PUNCT
easat-3258	72	15	=	=	PUNCT
easat-3258	72	16	(	(	PUNCT
easat-3258	72	17	1.6,0.6	1.6,0.6	NOUN
easat-3258	72	18	)	)	PUNCT
easat-3258	72	19	likewise	likewise	ADV
easat-3258	72	20	apply	apply	VERB
easat-3258	72	21	the	the	DET
easat-3258	72	22	same	same	ADJ
easat-3258	72	23	technique	technique	NOUN
easat-3258	72	24	to	to	PART
easat-3258	72	25	determine	determine	VERB
easat-3258	72	26	the	the	DET
easat-3258	72	27	degree	degree	NOUN
easat-3258	72	28	of	of	ADP
easat-3258	72	29	each	each	DET
easat-3258	72	30	vertex	vertex	NOUN
easat-3258	72	31	in	in	ADP
easat-3258	72	32	the	the	DET
easat-3258	72	33	maximal	maximal	ADJ
easat-3258	72	34	product	product	NOUN
easat-3258	72	35	.	.	PUNCT
easat-3258	73	1	d(g1	d(g1	PROPN
easat-3258	73	2	∗	∗	NOUN
easat-3258	73	3	g2)(v2xv1′	g2)(v2xv1′	NOUN
easat-3258	73	4	)	)	PUNCT
easat-3258	74	1	=	=	PUNCT
easat-3258	74	2	(	(	PUNCT
easat-3258	74	3	1.9,0.7	1.9,0.7	NUM
easat-3258	74	4	)	)	PUNCT
easat-3258	74	5	,	,	PUNCT
easat-3258	74	6	d(g1	d(g1	VERB
easat-3258	74	7	∗	∗	PROPN
easat-3258	74	8	g2)(v2xv2′	g2)(v2xv2′	PROPN
easat-3258	74	9	)	)	PUNCT
easat-3258	75	1	=	=	PUNCT
easat-3258	75	2	(	(	PUNCT
easat-3258	75	3	2.0,0.7	2.0,0.7	NUM
easat-3258	75	4	)	)	PUNCT
easat-3258	75	5	,	,	PUNCT
easat-3258	75	6	d(g1	d(g1	VERB
easat-3258	75	7	∗	∗	NOUN
easat-3258	75	8	g2)(v2xv3′	g2)(v2xv3′	NOUN
easat-3258	75	9	)	)	PUNCT
easat-3258	75	10	=	=	PUNCT
easat-3258	75	11	(	(	PUNCT
easat-3258	75	12	1.8,0.6	1.8,0.6	NUM
easat-3258	75	13	)	)	PUNCT
easat-3258	75	14	,	,	PUNCT
easat-3258	75	15	d(g1	d(g1	VERB
easat-3258	75	16	∗	∗	NOUN
easat-3258	75	17	g2)(v3xv1′	g2)(v3xv1′	NOUN
easat-3258	75	18	)	)	PUNCT
easat-3258	75	19	=	=	PUNCT
easat-3258	75	20	(	(	PUNCT
easat-3258	75	21	1.7,0.5	1.7,0.5	NUM
easat-3258	75	22	)	)	PUNCT
easat-3258	75	23	,	,	PUNCT
easat-3258	75	24	d(g1	d(g1	VERB
easat-3258	75	25	∗	∗	PROPN
easat-3258	75	26	g2)(v3xv2′	g2)(v3xv2′	NOUN
easat-3258	75	27	)	)	PUNCT
easat-3258	75	28	=	=	PUNCT
easat-3258	75	29	(	(	PUNCT
easat-3258	75	30	1.8,0.5	1.8,0.5	NUM
easat-3258	75	31	)	)	PUNCT
easat-3258	75	32	,	,	PUNCT
easat-3258	75	33	d(g1	d(g1	VERB
easat-3258	75	34	∗	∗	PROPN
easat-3258	75	35	g2)(v3xv3′	g2)(v3xv3′	NOUN
easat-3258	75	36	)	)	PUNCT
easat-3258	75	37	=	=	PUNCT
easat-3258	75	38	(	(	PUNCT
easat-3258	75	39	1.6,0.4	1.6,0.4	NUM
easat-3258	75	40	)	)	PUNCT
easat-3258	75	41	,	,	PUNCT
easat-3258	75	42	d(g1	d(g1	VERB
easat-3258	75	43	∗	∗	PROPN
easat-3258	75	44	g2)(v4xv1′	g2)(v4xv1′	NOUN
easat-3258	75	45	)	)	PUNCT
easat-3258	75	46	=	=	PUNCT
easat-3258	75	47	(	(	PUNCT
easat-3258	75	48	1.9,0.7	1.9,0.7	NUM
easat-3258	75	49	)	)	PUNCT
easat-3258	75	50	,	,	PUNCT
easat-3258	75	51	d(g1	d(g1	VERB
easat-3258	75	52	∗	∗	PROPN
easat-3258	75	53	g2)(v4xv2′	g2)(v4xv2′	NOUN
easat-3258	75	54	)	)	PUNCT
easat-3258	75	55	=	=	PUNCT
easat-3258	76	1	(	(	PUNCT
easat-3258	76	2	2.0,0.7	2.0,0.7	NUM
easat-3258	76	3	)	)	PUNCT
easat-3258	76	4	,	,	PUNCT
easat-3258	76	5	d(g1	d(g1	VERB
easat-3258	76	6	∗	∗	PROPN
easat-3258	76	7	g2)(v4xv3′	g2)(v4xv3′	PROPN
easat-3258	76	8	)	)	PUNCT
easat-3258	76	9	=	=	PUNCT
easat-3258	76	10	(	(	PUNCT
easat-3258	76	11	1.8,0.6	1.8,0.6	NUM
easat-3258	76	12	)	)	PUNCT
easat-3258	76	13	.	.	PUNCT
easat-3258	77	1	the	the	DET
easat-3258	77	2	above	above	ADJ
easat-3258	77	3	example	example	NOUN
easat-3258	77	4	implies	imply	VERB
easat-3258	77	5	the	the	DET
easat-3258	77	6	maximal	maximal	ADJ
easat-3258	77	7	product	product	NOUN
easat-3258	77	8	of	of	ADP
easat-3258	77	9	two	two	NUM
easat-3258	77	10	constant	constant	ADJ
easat-3258	77	11	if	if	SCONJ
easat-3258	77	12	graphs	graph	NOUN
easat-3258	77	13	need	need	AUX
easat-3258	77	14	not	not	PART
easat-3258	77	15	be	be	AUX
easat-3258	77	16	a	a	DET
easat-3258	77	17	constant	constant	ADJ
easat-3258	77	18	if	if	SCONJ
easat-3258	77	19	graphs	graph	NOUN
easat-3258	77	20	.	.	PUNCT
easat-3258	78	1	definition	definition	NOUN
easat-3258	78	2	3.4	3.4	NUM
easat-3258	78	3	.	.	PUNCT
easat-3258	79	1	if	if	SCONJ
easat-3258	79	2	g(𝑉∗	g(𝑉∗	PROPN
easat-3258	79	3	,	,	PUNCT
easat-3258	79	4	𝐸∗	𝐸∗	NOUN
easat-3258	79	5	,	,	PUNCT
easat-3258	79	6	𝜇∗	𝜇∗	NOUN
easat-3258	79	7	,	,	PUNCT
easat-3258	79	8	𝛾∗	𝛾∗	NOUN
easat-3258	79	9	)	)	PUNCT
easat-3258	79	10	is	be	AUX
easat-3258	79	11	the	the	DET
easat-3258	79	12	maximal	maximal	ADJ
easat-3258	79	13	product	product	NOUN
easat-3258	79	14	of	of	ADP
easat-3258	79	15	two	two	NUM
easat-3258	79	16	constant	constant	ADJ
easat-3258	79	17	if	if	SCONJ
easat-3258	79	18	graphs	graph	NOUN
easat-3258	79	19	𝐺1(𝑉′	𝐺1(𝑉′	ADV
easat-3258	79	20	,	,	PUNCT
easat-3258	79	21	𝐸′	𝐸′	NOUN
easat-3258	79	22	,	,	PUNCT
easat-3258	79	23	𝜇′	𝜇′	NOUN
easat-3258	79	24	,	,	PUNCT
easat-3258	79	25	𝛾′	𝛾′	NUM
easat-3258	79	26	)	)	PUNCT
easat-3258	79	27	and	and	CCONJ
easat-3258	79	28	𝐺2(𝑉′′	𝐺2(𝑉′′	NOUN
easat-3258	79	29	,	,	PUNCT
easat-3258	79	30	𝐸′′	𝐸′′	ADJ
easat-3258	79	31	,	,	PUNCT
easat-3258	79	32	𝜇′′	𝜇′′	NOUN
easat-3258	79	33	,	,	PUNCT
easat-3258	79	34	𝛾′′	𝛾′′	PROPN
easat-3258	79	35	)	)	PUNCT
easat-3258	79	36	then	then	ADV
easat-3258	79	37	the	the	DET
easat-3258	79	38	total	total	ADJ
easat-3258	79	39	degree	degree	NOUN
easat-3258	79	40	of	of	ADP
easat-3258	79	41	the	the	DET
easat-3258	79	42	vertices	vertex	NOUN
easat-3258	79	43	of	of	ADP
easat-3258	79	44	g	g	PROPN
easat-3258	79	45	(	(	PUNCT
easat-3258	79	46	𝑢𝑖	𝑢𝑖	INTJ
easat-3258	79	47	′	′	NUM
easat-3258	79	48	,	,	PUNCT
easat-3258	79	49	𝑢𝑗	𝑢𝑗	X
easat-3258	79	50	′′	′′	PROPN
easat-3258	79	51	)	)	PUNCT
easat-3258	79	52	∈	∈	PROPN
easat-3258	79	53	𝑉∗	𝑉∗	NOUN
easat-3258	79	54	is	be	AUX
easat-3258	79	55	defined	define	VERB
easat-3258	79	56	as	as	ADP
easat-3258	79	57	,	,	PUNCT
easat-3258	79	58	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢𝑖	NOUN
easat-3258	79	59	′	′	NOUN
easat-3258	79	60	,	,	PUNCT
easat-3258	79	61	𝑢𝑗	𝑢𝑗	X
easat-3258	79	62	′′	′′	PROPN
easat-3258	79	63	)	)	PUNCT
easat-3258	79	64	=	=	PUNCT
easat-3258	80	1	∑	∑	PUNCT
easat-3258	80	2	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
easat-3258	80	3	{	{	PUNCT
easat-3258	80	4	𝜇′(𝑢𝑖	𝜇′(𝑢𝑖	PROPN
easat-3258	80	5	′𝑢𝑘	′𝑢𝑘	NOUN
easat-3258	80	6	′	′	NUM
easat-3258	80	7	)	)	PUNCT
easat-3258	80	8	,	,	PUNCT
easat-3258	80	9	𝜇′′(𝑢𝑗	𝜇′′(𝑢𝑗	VERB
easat-3258	80	10	′′	′′	PROPN
easat-3258	80	11	)	)	PUNCT
easat-3258	80	12	}	}	PUNCT
easat-3258	81	1	+	+	CCONJ
easat-3258	81	2	∑	∑	PUNCT
easat-3258	81	3	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
easat-3258	81	4	{	{	PUNCT
easat-3258	81	5	𝜇′′(𝑢𝑗	𝜇′′(𝑢𝑗	NOUN
easat-3258	81	6	′′𝑢𝑘	′′𝑢𝑘	PROPN
easat-3258	81	7	′′	′′	PROPN
easat-3258	81	8	)	)	PUNCT
easat-3258	81	9	,	,	PUNCT
easat-3258	81	10	𝜇′(𝑢𝑖	𝜇′(𝑢𝑖	PROPN
easat-3258	81	11	′	′	NUM
easat-3258	81	12	)	)	PUNCT
easat-3258	81	13	}	}	PUNCT
easat-3258	82	1	+	+	NUM
easat-3258	82	2	𝜇∗(𝑢𝑖	𝜇∗(𝑢𝑖	PROPN
easat-3258	82	3	′	′	NOUN
easat-3258	82	4	,	,	PUNCT
easat-3258	82	5	𝑢𝑗	𝑢𝑗	X
easat-3258	82	6	′′	′′	PROPN
easat-3258	82	7	)	)	PUNCT
easat-3258	82	8	where	where	SCONJ
easat-3258	82	9	(	(	PUNCT
easat-3258	82	10	𝑢𝑖	𝑢𝑖	PRON
easat-3258	82	11	′𝑢𝑘	′𝑢𝑘	PROPN
easat-3258	82	12	′	′	NOUN
easat-3258	82	13	)	)	PUNCT
easat-3258	82	14	∈	∈	PROPN
easat-3258	82	15	𝐸′	𝐸′	PROPN
easat-3258	82	16	and	and	CCONJ
easat-3258	82	17	(	(	PUNCT
easat-3258	82	18	𝑢𝑗	𝑢𝑗	NOUN
easat-3258	82	19	′′𝑢𝑘	′′𝑢𝑘	PROPN
easat-3258	82	20	′′	′′	PROPN
easat-3258	82	21	)	)	PUNCT
easat-3258	82	22	∈	∈	PROPN
easat-3258	82	23	𝐸′′	𝐸′′	NOUN
easat-3258	82	24	and	and	CCONJ
easat-3258	82	25	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢𝑖	PROPN
easat-3258	82	26	′	′	NOUN
easat-3258	82	27	,	,	PUNCT
easat-3258	82	28	𝑢𝑗	𝑢𝑗	X
easat-3258	82	29	′′	′′	PROPN
easat-3258	82	30	)	)	PUNCT
easat-3258	82	31	=	=	PUNCT
easat-3258	82	32	∑	∑	PUNCT
easat-3258	82	33	min	min	PROPN
easat-3258	82	34	{	{	PUNCT
easat-3258	82	35	𝛾′(𝑢𝑖	𝛾′(𝑢𝑖	PROPN
easat-3258	82	36	′𝑢𝑘	′𝑢𝑘	PROPN
easat-3258	82	37	′	′	NUM
easat-3258	82	38	)	)	PUNCT
easat-3258	82	39	,	,	PUNCT
easat-3258	82	40	𝛾′′(𝑢𝑗	𝛾′′(𝑢𝑗	PROPN
easat-3258	82	41	′′	′′	PROPN
easat-3258	82	42	)	)	PUNCT
easat-3258	82	43	}	}	PUNCT
easat-3258	83	1	+	+	CCONJ
easat-3258	83	2	∑	∑	NOUN
easat-3258	83	3	𝑚𝑖𝑛{𝛾′′(𝑢𝑗	𝑚𝑖𝑛{𝛾′′(𝑢𝑗	NOUN
easat-3258	83	4	′′𝑢𝑘	′′𝑢𝑘	PROPN
easat-3258	83	5	′′	′′	PROPN
easat-3258	83	6	)	)	PUNCT
easat-3258	83	7	,	,	PUNCT
easat-3258	83	8	𝛾′(𝑢𝑖	𝛾′(𝑢𝑖	NOUN
easat-3258	83	9	′	′	NOUN
easat-3258	83	10	)	)	PUNCT
easat-3258	83	11	}	}	PUNCT
easat-3258	84	1	+	+	CCONJ
easat-3258	84	2	𝛾∗(𝑢𝑖	𝛾∗(𝑢𝑖	PROPN
easat-3258	84	3	′	′	NOUN
easat-3258	84	4	,	,	PUNCT
easat-3258	84	5	𝑢𝑗	𝑢𝑗	X
easat-3258	84	6	′′	′′	PROPN
easat-3258	84	7	)	)	PUNCT
easat-3258	84	8	,	,	PUNCT
easat-3258	84	9	wher	wher	PROPN
easat-3258	84	10	𝑖	𝑖	SYM
easat-3258	84	11	,	,	PUNCT
easat-3258	84	12	𝑗	𝑗	INTJ
easat-3258	84	13	,	,	PUNCT
easat-3258	84	14	𝑘	𝑘	X
easat-3258	84	15	=	=	SYM
easat-3258	84	16	1,2,3	1,2,3	NUM
easat-3258	84	17	…	…	PUNCT
easat-3258	84	18	.	.	PUNCT
easat-3258	85	1	𝑛	𝑛	PRON
easat-3258	85	2	if	if	SCONJ
easat-3258	85	3	each	each	DET
easat-3258	85	4	vertex	vertex	NOUN
easat-3258	85	5	of	of	ADP
easat-3258	85	6	g	g	PROPN
easat-3258	85	7	has	have	VERB
easat-3258	85	8	the	the	DET
easat-3258	85	9	unique	unique	ADJ
easat-3258	85	10	total	total	NOUN
easat-3258	85	11	degree	degree	NOUN
easat-3258	85	12	(	(	PUNCT
easat-3258	85	13	𝑘′	𝑘′	NUM
easat-3258	85	14	,	,	PUNCT
easat-3258	85	15	𝑘′′	𝑘′′	PROPN
easat-3258	85	16	)	)	PUNCT
easat-3258	85	17	then	then	ADV
easat-3258	85	18	g	g	PROPN
easat-3258	85	19	is	be	AUX
easat-3258	85	20	said	say	VERB
easat-3258	85	21	to	to	ADP
easat-3258	85	22	a	a	DET
easat-3258	85	23	maximal	maximal	ADJ
easat-3258	85	24	product	product	NOUN
easat-3258	85	25	of	of	ADP
easat-3258	85	26	if	if	SCONJ
easat-3258	85	27	graphs	graph	NOUN
easat-3258	85	28	of	of	ADP
easat-3258	85	29	total	total	ADJ
easat-3258	85	30	degree	degree	NOUN
easat-3258	85	31	(	(	PUNCT
easat-3258	85	32	𝑘′	𝑘′	NUM
easat-3258	85	33	,	,	PUNCT
easat-3258	85	34	𝑘′′	𝑘′′	PROPN
easat-3258	85	35	)	)	PUNCT
easat-3258	85	36	or	or	CCONJ
easat-3258	85	37	(	(	PUNCT
easat-3258	85	38	𝑘′	𝑘′	NUM
easat-3258	85	39	,	,	PUNCT
easat-3258	85	40	𝑘′′)totally	𝑘′′)totally	ADV
easat-3258	85	41	constant	constant	ADJ
easat-3258	85	42	maximal	maximal	ADJ
easat-3258	85	43	product	product	NOUN
easat-3258	85	44	if	if	SCONJ
easat-3258	85	45	graphs	graph	NOUN
easat-3258	85	46	.	.	PUNCT
easat-3258	86	1	example	example	NOUN
easat-3258	86	2	3.5	3.5	NUM
easat-3258	86	3	consider	consider	VERB
easat-3258	86	4	the	the	DET
easat-3258	86	5	maximal	maximal	ADJ
easat-3258	86	6	product	product	NOUN
easat-3258	86	7	of	of	ADP
easat-3258	86	8	two	two	NUM
easat-3258	86	9	constant	constant	ADJ
easat-3258	86	10	if	if	SCONJ
easat-3258	86	11	graphs	graph	NOUN
easat-3258	86	12	which	which	PRON
easat-3258	86	13	is	be	AUX
easat-3258	86	14	obtained	obtain	VERB
easat-3258	86	15	in	in	ADP
easat-3258	86	16	example	example	NOUN
easat-3258	86	17	3.2	3.2	NUM
easat-3258	86	18	.	.	PUNCT
easat-3258	87	1	the	the	DET
easat-3258	87	2	total	total	ADJ
easat-3258	87	3	degree	degree	NOUN
easat-3258	87	4	of	of	ADP
easat-3258	87	5	all	all	DET
easat-3258	87	6	9	9	NUM
easat-3258	87	7	vertices	vertex	NOUN
easat-3258	87	8	of	of	ADP
easat-3258	87	9	g	g	PROPN
easat-3258	87	10	has	have	AUX
easat-3258	87	11	calculated	calculate	VERB
easat-3258	87	12	as	as	ADP
easat-3258	87	13	follows	follow	VERB
easat-3258	87	14	:	:	PUNCT
easat-3258	87	15	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢1	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢1	NOUN
easat-3258	87	16	′	′	NUM
easat-3258	87	17	,	,	PUNCT
easat-3258	87	18	𝑢1	𝑢1	PROPN
easat-3258	87	19	′′	′′	PROPN
easat-3258	87	20	)	)	PUNCT
easat-3258	87	21	=	=	PUNCT
easat-3258	88	1	(	(	PUNCT
easat-3258	88	2	0.4	0.4	NUM
easat-3258	88	3	+	+	NUM
easat-3258	88	4	0.4	0.4	NUM
easat-3258	88	5	+	+	CCONJ
easat-3258	88	6	0.3	0.3	NUM
easat-3258	88	7	+	+	CCONJ
easat-3258	88	8	0.3	0.3	NUM
easat-3258	88	9	)	)	PUNCT
easat-3258	89	1	+	+	CCONJ
easat-3258	89	2	0.3	0.3	NUM
easat-3258	89	3	=	=	SYM
easat-3258	89	4	1.7	1.7	NUM
easat-3258	89	5	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢1	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢1	NOUN
easat-3258	89	6	′	′	NOUN
easat-3258	89	7	,	,	PUNCT
easat-3258	89	8	𝑢1	𝑢1	PROPN
easat-3258	89	9	′′	′′	PROPN
easat-3258	89	10	)	)	PUNCT
easat-3258	89	11	=	=	PUNCT
easat-3258	90	1	(	(	PUNCT
easat-3258	90	2	0.2	0.2	NUM
easat-3258	90	3	+	+	NUM
easat-3258	90	4	0.2	0.2	NUM
easat-3258	90	5	+	+	NUM
easat-3258	90	6	0.1	0.1	NUM
easat-3258	90	7	+	+	NUM
easat-3258	90	8	0.1	0.1	NUM
easat-3258	90	9	)	)	PUNCT
easat-3258	91	1	+	+	CCONJ
easat-3258	91	2	0.1	0.1	NUM
easat-3258	91	3	=	=	SYM
easat-3258	91	4	0.7	0.7	NUM
easat-3258	91	5	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢1	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢1	NOUN
easat-3258	91	6	′	′	NOUN
easat-3258	91	7	,	,	PUNCT
easat-3258	91	8	𝑢2	𝑢2	PROPN
easat-3258	91	9	′′	′′	PROPN
easat-3258	91	10	)	)	PUNCT
easat-3258	91	11	=	=	PUNCT
easat-3258	92	1	(	(	PUNCT
easat-3258	92	2	0.4	0.4	NUM
easat-3258	92	3	+	+	NUM
easat-3258	92	4	0.4	0.4	NUM
easat-3258	92	5	+	+	NUM
easat-3258	92	6	0.4	0.4	NUM
easat-3258	92	7	+	+	CCONJ
easat-3258	92	8	0.4	0.4	NUM
easat-3258	92	9	)	)	PUNCT
easat-3258	93	1	+	+	CCONJ
easat-3258	93	2	0.4	0.4	NUM
easat-3258	93	3	=	=	SYM
easat-3258	93	4	2.0	2.0	NUM
easat-3258	93	5	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢1	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢1	NOUN
easat-3258	93	6	′	′	NOUN
easat-3258	93	7	,	,	PUNCT
easat-3258	93	8	𝑢2	𝑢2	PROPN
easat-3258	93	9	′′	′′	PROPN
easat-3258	93	10	)	)	PUNCT
easat-3258	93	11	=	=	PUNCT
easat-3258	94	1	(	(	PUNCT
easat-3258	94	2	0.1	0.1	NUM
easat-3258	94	3	+	+	NUM
easat-3258	94	4	0.1	0.1	NUM
easat-3258	94	5	+	+	CCONJ
easat-3258	94	6	0.2	0.2	NUM
easat-3258	94	7	+	+	NUM
easat-3258	94	8	0.2	0.2	NUM
easat-3258	94	9	)	)	PUNCT
easat-3258	95	1	+	+	CCONJ
easat-3258	95	2	0.1	0.1	NUM
easat-3258	95	3	=	=	SYM
easat-3258	95	4	0.7	0.7	NUM
easat-3258	95	5	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢1	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢1	NOUN
easat-3258	95	6	′	′	NOUN
easat-3258	95	7	,	,	PUNCT
easat-3258	95	8	𝑢3	𝑢3	PROPN
easat-3258	95	9	′′	′′	PROPN
easat-3258	95	10	)	)	PUNCT
easat-3258	95	11	=	=	PUNCT
easat-3258	96	1	(	(	PUNCT
easat-3258	96	2	0.4	0.4	NUM
easat-3258	96	3	+	+	NUM
easat-3258	96	4	0.4	0.4	NUM
easat-3258	96	5	+	+	NUM
easat-3258	96	6	0.5	0.5	NUM
easat-3258	96	7	+	+	NUM
easat-3258	96	8	0.5	0.5	NUM
easat-3258	96	9	)	)	PUNCT
easat-3258	96	10	+	+	CCONJ
easat-3258	96	11	0.5	0.5	NUM
easat-3258	96	12	=	=	SYM
easat-3258	96	13	2.3	2.3	NUM
easat-3258	96	14	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢1	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢1	NOUN
easat-3258	96	15	′	′	NOUN
easat-3258	96	16	,	,	PUNCT
easat-3258	96	17	𝑢3	𝑢3	PROPN
easat-3258	96	18	′′	′′	PROPN
easat-3258	96	19	)	)	PUNCT
easat-3258	96	20	=	=	PUNCT
easat-3258	96	21	(	(	PUNCT
easat-3258	96	22	0.2	0.2	NUM
easat-3258	96	23	+	+	NUM
easat-3258	96	24	0.2	0.2	NUM
easat-3258	96	25	+	+	NUM
easat-3258	96	26	0.1	0.1	NUM
easat-3258	96	27	+	+	NUM
easat-3258	96	28	0.1	0.1	NUM
easat-3258	96	29	)	)	PUNCT
easat-3258	97	1	+	+	CCONJ
easat-3258	97	2	0.2	0.2	NUM
easat-3258	97	3	=	=	SYM
easat-3258	97	4	0.8	0.8	NUM
easat-3258	97	5	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢2	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢2	NOUN
easat-3258	97	6	′	′	NUM
easat-3258	97	7	,	,	PUNCT
easat-3258	97	8	𝑢1	𝑢1	PROPN
easat-3258	97	9	′′	′′	PROPN
easat-3258	97	10	)	)	PUNCT
easat-3258	97	11	=	=	SYM
easat-3258	97	12	2.1	2.1	NUM
easat-3258	97	13	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢2	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢2	NOUN
easat-3258	97	14	′	′	NUM
easat-3258	97	15	,	,	PUNCT
easat-3258	97	16	𝑢1	𝑢1	PROPN
easat-3258	97	17	′′	′′	PROPN
easat-3258	97	18	)	)	PUNCT
easat-3258	97	19	=	=	SYM
easat-3258	97	20	0.9	0.9	NUM
easat-3258	97	21	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢2	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢2	NOUN
easat-3258	97	22	′	′	NOUN
easat-3258	97	23	,	,	PUNCT
easat-3258	97	24	𝑢2	𝑢2	PROPN
easat-3258	97	25	′′	′′	PROPN
easat-3258	97	26	)	)	PUNCT
easat-3258	97	27	=	=	SYM
easat-3258	97	28	2.3	2.3	NUM
easat-3258	97	29	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢2	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢2	NOUN
easat-3258	97	30	′	′	NUM
easat-3258	97	31	,	,	PUNCT
easat-3258	97	32	𝑢2	𝑢2	PROPN
easat-3258	97	33	′′	′′	PROPN
easat-3258	97	34	)	)	PUNCT
easat-3258	97	35	=	=	SYM
easat-3258	97	36	0.9	0.9	NUM
easat-3258	97	37	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢2	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢2	NOUN
easat-3258	97	38	′	′	NOUN
easat-3258	97	39	,	,	PUNCT
easat-3258	97	40	𝑢3	𝑢3	PROPN
easat-3258	97	41	′′	′′	PROPN
easat-3258	97	42	)	)	PUNCT
easat-3258	97	43	=	=	SYM
easat-3258	97	44	2.5	2.5	NUM
easat-3258	97	45	5796	5796	NUM
easat-3258	97	46	edelweiss	edelweiss	PROPN
easat-3258	97	47	applied	apply	VERB
easat-3258	97	48	science	science	NOUN
easat-3258	97	49	and	and	CCONJ
easat-3258	97	50	technology	technology	NOUN
easat-3258	97	51	issn	issn	PROPN
easat-3258	97	52	:	:	PUNCT
easat-3258	97	53	2576	2576	NUM
easat-3258	97	54	-	-	SYM
easat-3258	97	55	8484	8484	NUM
easat-3258	97	56	vol	vol	NOUN
easat-3258	97	57	.	.	PROPN
easat-3258	97	58	8	8	NUM
easat-3258	97	59	,	,	PUNCT
easat-3258	97	60	no	no	INTJ
easat-3258	97	61	.	.	NOUN
easat-3258	98	1	6	6	NUM
easat-3258	98	2	:	:	PUNCT
easat-3258	98	3	5789	5789	NUM
easat-3258	98	4	-	-	SYM
easat-3258	98	5	5799	5799	NUM
easat-3258	98	6	,	,	PUNCT
easat-3258	98	7	2024	2024	NUM
easat-3258	98	8	doi	doi	NOUN
easat-3258	98	9	:	:	PUNCT
easat-3258	98	10	10.55214/25768484.v8i6.3258	10.55214/25768484.v8i6.3258	NUM
easat-3258	98	11	©	©	PROPN
easat-3258	98	12	2024	2024	NUM
easat-3258	98	13	by	by	ADP
easat-3258	98	14	the	the	DET
easat-3258	98	15	authors	author	NOUN
easat-3258	98	16	;	;	PUNCT
easat-3258	98	17	licensee	licensee	PROPN
easat-3258	98	18	learning	learning	PROPN
easat-3258	98	19	gate	gate	PROPN
easat-3258	98	20	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢2	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢2	PROPN
easat-3258	98	21	′	′	PROPN
easat-3258	98	22	,	,	PUNCT
easat-3258	98	23	𝑢3	𝑢3	PROPN
easat-3258	98	24	′′	′′	PROPN
easat-3258	98	25	)	)	PUNCT
easat-3258	98	26	=	=	SYM
easat-3258	98	27	1.0	1.0	NUM
easat-3258	98	28	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢3	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢3	NOUN
easat-3258	98	29	′	′	NOUN
easat-3258	98	30	,	,	PUNCT
easat-3258	98	31	𝑢1	𝑢1	PROPN
easat-3258	98	32	′′	′′	PROPN
easat-3258	98	33	)	)	PUNCT
easat-3258	98	34	=	=	SYM
easat-3258	98	35	1.7	1.7	NUM
easat-3258	98	36	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢3	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢3	NOUN
easat-3258	98	37	′	′	NOUN
easat-3258	98	38	,	,	PUNCT
easat-3258	98	39	𝑢1	𝑢1	PROPN
easat-3258	98	40	′′	′′	PROPN
easat-3258	98	41	)	)	PUNCT
easat-3258	98	42	=	=	SYM
easat-3258	98	43	0.5	0.5	NUM
easat-3258	98	44	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢3	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢3	NOUN
easat-3258	98	45	′	′	NOUN
easat-3258	98	46	,	,	PUNCT
easat-3258	98	47	𝑢2	𝑢2	PROPN
easat-3258	98	48	′′	′′	PROPN
easat-3258	98	49	)	)	PUNCT
easat-3258	98	50	=	=	PROPN
easat-3258	98	51	2.0	2.0	NUM
easat-3258	98	52	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢3	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢3	NOUN
easat-3258	98	53	′	′	NOUN
easat-3258	98	54	,	,	PUNCT
easat-3258	98	55	𝑢2	𝑢2	PROPN
easat-3258	98	56	′′	′′	PROPN
easat-3258	98	57	)	)	PUNCT
easat-3258	98	58	=	=	SYM
easat-3258	98	59	0.5	0.5	NUM
easat-3258	98	60	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢3	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢3	NOUN
easat-3258	98	61	′	′	NOUN
easat-3258	98	62	,	,	PUNCT
easat-3258	98	63	𝑢3	𝑢3	PROPN
easat-3258	98	64	′′	′′	PROPN
easat-3258	98	65	)	)	PUNCT
easat-3258	98	66	=	=	PUNCT
easat-3258	98	67	2.3	2.3	NUM
easat-3258	98	68	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢3	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢3	NOUN
easat-3258	98	69	′	′	NOUN
easat-3258	98	70	,	,	PUNCT
easat-3258	98	71	𝑢3	𝑢3	PROPN
easat-3258	98	72	′′	′′	PROPN
easat-3258	98	73	)	)	PUNCT
easat-3258	98	74	=	=	SYM
easat-3258	98	75	0.5	0.5	NUM
easat-3258	98	76	example	example	NOUN
easat-3258	98	77	3.6	3.6	NUM
easat-3258	98	78	the	the	DET
easat-3258	98	79	following	following	ADJ
easat-3258	98	80	example	example	NOUN
easat-3258	98	81	explains	explain	VERB
easat-3258	98	82	the	the	DET
easat-3258	98	83	maximal	maximal	ADJ
easat-3258	98	84	product	product	NOUN
easat-3258	98	85	of	of	ADP
easat-3258	98	86	two	two	NUM
easat-3258	98	87	totally	totally	ADV
easat-3258	98	88	constant	constant	ADJ
easat-3258	98	89	if	if	SCONJ
easat-3258	98	90	graph	graph	NOUN
easat-3258	98	91	need	need	AUX
easat-3258	98	92	not	not	PART
easat-3258	98	93	be	be	AUX
easat-3258	98	94	totally	totally	ADV
easat-3258	98	95	constant	constant	ADJ
easat-3258	98	96	maximal	maximal	ADJ
easat-3258	98	97	product	product	NOUN
easat-3258	98	98	if	if	SCONJ
easat-3258	98	99	graphs	graph	NOUN
easat-3258	98	100	.	.	PUNCT
easat-3258	99	1	5797	5797	NUM
easat-3258	99	2	edelweiss	edelweiss	PROPN
easat-3258	99	3	applied	apply	VERB
easat-3258	99	4	science	science	NOUN
easat-3258	99	5	and	and	CCONJ
easat-3258	99	6	technology	technology	NOUN
easat-3258	99	7	issn	issn	PROPN
easat-3258	99	8	:	:	PUNCT
easat-3258	99	9	2576	2576	NUM
easat-3258	99	10	-	-	SYM
easat-3258	99	11	8484	8484	NUM
easat-3258	99	12	vol	vol	NOUN
easat-3258	99	13	.	.	PROPN
easat-3258	99	14	8	8	NUM
easat-3258	99	15	,	,	PUNCT
easat-3258	99	16	no	no	INTJ
easat-3258	99	17	.	.	NOUN
easat-3258	99	18	6	6	NUM
easat-3258	99	19	:	:	PUNCT
easat-3258	99	20	5789	5789	NUM
easat-3258	99	21	-	-	SYM
easat-3258	99	22	5799	5799	NUM
easat-3258	99	23	,	,	PUNCT
easat-3258	99	24	2024	2024	NUM
easat-3258	99	25	doi	doi	NOUN
easat-3258	99	26	:	:	PUNCT
easat-3258	99	27	10.55214/25768484.v8i6.3258	10.55214/25768484.v8i6.3258	NUM
easat-3258	99	28	©	©	PROPN
easat-3258	99	29	2024	2024	NUM
easat-3258	99	30	by	by	ADP
easat-3258	99	31	the	the	DET
easat-3258	99	32	authors	author	NOUN
easat-3258	99	33	;	;	PUNCT
easat-3258	99	34	licensee	licensee	PROPN
easat-3258	99	35	learning	learning	PROPN
easat-3258	99	36	gate	gate	PROPN
easat-3258	99	37	theorem	theorem	VERB
easat-3258	99	38	3.7	3.7	NUM
easat-3258	99	39	if	if	SCONJ
easat-3258	99	40	𝐺1(𝑉′	𝐺1(𝑉′	ADV
easat-3258	99	41	,	,	PUNCT
easat-3258	99	42	𝐸′	𝐸′	NOUN
easat-3258	99	43	,	,	PUNCT
easat-3258	99	44	𝜇′	𝜇′	NOUN
easat-3258	99	45	,	,	PUNCT
easat-3258	99	46	𝛾′	𝛾′	NUM
easat-3258	99	47	)	)	PUNCT
easat-3258	99	48	and	and	CCONJ
easat-3258	99	49	𝐺2(𝑉′′	𝐺2(𝑉′′	NOUN
easat-3258	99	50	,	,	PUNCT
easat-3258	99	51	𝐸′′	𝐸′′	ADJ
easat-3258	99	52	,	,	PUNCT
easat-3258	99	53	𝜇′′	𝜇′′	NOUN
easat-3258	99	54	,	,	PUNCT
easat-3258	99	55	𝛾′′	𝛾′′	PROPN
easat-3258	99	56	)	)	PUNCT
easat-3258	99	57	are	be	AUX
easat-3258	99	58	two	two	NUM
easat-3258	99	59	constant	constant	ADJ
easat-3258	99	60	if	if	SCONJ
easat-3258	99	61	graphs	graph	NOUN
easat-3258	99	62	such	such	ADJ
easat-3258	99	63	that	that	DET
easat-3258	99	64	𝜇′(𝑢𝑖	𝜇′(𝑢𝑖	PROPN
easat-3258	99	65	′	′	NOUN
easat-3258	99	66	)	)	PUNCT
easat-3258	99	67	≤	≤	NOUN
easat-3258	99	68	𝜇′′(𝑢𝑗	𝜇′′(𝑢𝑗	NOUN
easat-3258	99	69	′′𝑢𝑘	′′𝑢𝑘	PROPN
easat-3258	99	70	′′	′′	PROPN
easat-3258	99	71	)	)	PUNCT
easat-3258	99	72	,	,	PUNCT
easat-3258	99	73	𝜇′(𝑢𝑖	𝜇′(𝑢𝑖	PROPN
easat-3258	99	74	′𝑢𝑗	′𝑢𝑗	NOUN
easat-3258	99	75	′	′	NUM
easat-3258	99	76	)	)	PUNCT
easat-3258	99	77	≤	≤	NOUN
easat-3258	99	78	𝜇′′(𝑢𝑘	𝜇′′(𝑢𝑘	VERB
easat-3258	99	79	′′	′′	PROPN
easat-3258	99	80	)	)	PUNCT
easat-3258	99	81	and	and	CCONJ
easat-3258	99	82	𝛾′(𝑢𝑖	𝛾′(𝑢𝑖	PROPN
easat-3258	99	83	′	′	NOUN
easat-3258	99	84	)	)	PUNCT
easat-3258	99	85	≥	≥	NOUN
easat-3258	99	86	𝛾′′(𝑢𝑗	𝛾′′(𝑢𝑗	NOUN
easat-3258	99	87	′′𝑢𝑘	′′𝑢𝑘	PROPN
easat-3258	99	88	′′	′′	PROPN
easat-3258	99	89	)	)	PUNCT
easat-3258	99	90	,	,	PUNCT
easat-3258	99	91	𝛾′(𝑢𝑖	𝛾′(𝑢𝑖	NOUN
easat-3258	99	92	′𝑢𝑗	′𝑢𝑗	NOUN
easat-3258	99	93	′	′	PROPN
easat-3258	99	94	)	)	PUNCT
easat-3258	99	95	≥	≥	PROPN
easat-3258	99	96	𝛾′′(𝑢𝑘	𝛾′′(𝑢𝑘	PROPN
easat-3258	99	97	′′	′′	PROPN
easat-3258	99	98	)	)	PUNCT
easat-3258	99	99	then	then	ADV
easat-3258	99	100	the	the	DET
easat-3258	99	101	total	total	ADJ
easat-3258	99	102	degree	degree	NOUN
easat-3258	99	103	of	of	ADP
easat-3258	99	104	their	their	PRON
easat-3258	99	105	maximal	maximal	ADJ
easat-3258	99	106	product	product	NOUN
easat-3258	99	107	𝐺∗(𝑉∗	𝐺∗(𝑉∗	NOUN
easat-3258	99	108	,	,	PUNCT
easat-3258	99	109	𝐸∗	𝐸∗	NOUN
easat-3258	99	110	,	,	PUNCT
easat-3258	99	111	𝜇∗	𝜇∗	NOUN
easat-3258	99	112	,	,	PUNCT
easat-3258	99	113	𝛾∗	𝛾∗	NOUN
easat-3258	99	114	)	)	PUNCT
easat-3258	99	115	=	=	PUNCT
easat-3258	99	116	𝐺1	𝐺1	NOUN
easat-3258	99	117	∗	∗	NOUN
easat-3258	99	118	𝐺2	𝐺2	NOUN
easat-3258	99	119	is	be	AUX
easat-3258	99	120	given	give	VERB
easat-3258	99	121	by	by	ADP
easat-3258	99	122	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢𝑖	PROPN
easat-3258	99	123	′	′	NOUN
easat-3258	99	124	,	,	PUNCT
easat-3258	99	125	𝑢𝑗	𝑢𝑗	X
easat-3258	99	126	′′	′′	PROPN
easat-3258	99	127	)	)	PUNCT
easat-3258	99	128	=	=	SYM
easat-3258	99	129	𝑛0(𝑢𝑖	𝑛0(𝑢𝑖	PROPN
easat-3258	99	130	′	′	NUM
easat-3258	99	131	)	)	PUNCT
easat-3258	99	132	𝜇′′(𝑢𝑗	𝜇′′(𝑢𝑗	NOUN
easat-3258	99	133	′′	′′	PROPN
easat-3258	99	134	)	)	PUNCT
easat-3258	100	1	+	+	PROPN
easat-3258	100	2	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇′′(𝑢𝑗	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇′′(𝑢𝑗	PROPN
easat-3258	100	3	′′	′′	NOUN
easat-3258	100	4	)	)	PUNCT
easat-3258	100	5	and	and	CCONJ
easat-3258	100	6	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢𝑖	PROPN
easat-3258	100	7	′	′	NOUN
easat-3258	100	8	,	,	PUNCT
easat-3258	100	9	𝑢𝑗	𝑢𝑗	X
easat-3258	100	10	′′	′′	PROPN
easat-3258	100	11	)	)	PUNCT
easat-3258	100	12	=	=	SYM
easat-3258	100	13	𝑛0(𝑢𝑖	𝑛0(𝑢𝑖	PROPN
easat-3258	100	14	′	′	NUM
easat-3258	100	15	)	)	PUNCT
easat-3258	100	16	𝛾′′(𝑢𝑗	𝛾′′(𝑢𝑗	NOUN
easat-3258	100	17	′′	′′	PROPN
easat-3258	100	18	)	)	PUNCT
easat-3258	101	1	+	+	NUM
easat-3258	101	2	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾′′(𝑢𝑗	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾′′(𝑢𝑗	NOUN
easat-3258	101	3	′′	′′	PROPN
easat-3258	101	4	)	)	PUNCT
easat-3258	101	5	for	for	ADP
easat-3258	101	6	𝑖	𝑖	SYM
easat-3258	101	7	,	,	PUNCT
easat-3258	101	8	𝑗	𝑗	INTJ
easat-3258	101	9	,	,	PUNCT
easat-3258	101	10	𝑘	𝑘	X
easat-3258	101	11	=	=	SYM
easat-3258	101	12	1,2,3	1,2,3	NUM
easat-3258	101	13	…	…	PUNCT
easat-3258	101	14	.	.	PUNCT
easat-3258	102	1	𝑛	𝑛	DET
easat-3258	102	2	proof	proof	NOUN
easat-3258	102	3	:	:	PUNCT
easat-3258	102	4	if	if	SCONJ
easat-3258	102	5	𝐺1(𝑉′	𝐺1(𝑉′	ADV
easat-3258	102	6	,	,	PUNCT
easat-3258	102	7	𝐸′	𝐸′	NOUN
easat-3258	102	8	,	,	PUNCT
easat-3258	102	9	𝜇′	𝜇′	NOUN
easat-3258	102	10	,	,	PUNCT
easat-3258	102	11	𝛾′	𝛾′	NUM
easat-3258	102	12	)	)	PUNCT
easat-3258	102	13	and	and	CCONJ
easat-3258	102	14	𝐺2(𝑉′′	𝐺2(𝑉′′	NOUN
easat-3258	102	15	,	,	PUNCT
easat-3258	102	16	𝐸′′	𝐸′′	ADJ
easat-3258	102	17	,	,	PUNCT
easat-3258	102	18	𝜇′′	𝜇′′	NOUN
easat-3258	102	19	,	,	PUNCT
easat-3258	102	20	𝛾′′	𝛾′′	PROPN
easat-3258	102	21	)	)	PUNCT
easat-3258	102	22	are	be	AUX
easat-3258	102	23	two	two	NUM
easat-3258	102	24	constant	constant	ADJ
easat-3258	102	25	if	if	SCONJ
easat-3258	102	26	graphs	graph	NOUN
easat-3258	102	27	such	such	ADJ
easat-3258	102	28	that	that	DET
easat-3258	102	29	𝜇′(𝑢𝑖	𝜇′(𝑢𝑖	PROPN
easat-3258	102	30	′	′	NOUN
easat-3258	102	31	)	)	PUNCT
easat-3258	102	32	≤	≤	NOUN
easat-3258	102	33	𝜇′′(𝑢𝑗	𝜇′′(𝑢𝑗	NOUN
easat-3258	102	34	′′𝑢𝑘	′′𝑢𝑘	PROPN
easat-3258	102	35	′′	′′	PROPN
easat-3258	102	36	)	)	PUNCT
easat-3258	102	37	,	,	PUNCT
easat-3258	102	38	𝜇′(𝑢𝑖	𝜇′(𝑢𝑖	PROPN
easat-3258	102	39	′𝑢𝑗	′𝑢𝑗	NOUN
easat-3258	102	40	′	′	NUM
easat-3258	102	41	)	)	PUNCT
easat-3258	102	42	≤	≤	NOUN
easat-3258	102	43	𝜇′′(𝑢𝑘	𝜇′′(𝑢𝑘	VERB
easat-3258	102	44	′′	′′	PROPN
easat-3258	102	45	)	)	PUNCT
easat-3258	102	46	then	then	ADV
easat-3258	102	47	the	the	DET
easat-3258	102	48	total	total	ADJ
easat-3258	102	49	degree	degree	NOUN
easat-3258	102	50	of	of	ADP
easat-3258	102	51	the	the	DET
easat-3258	102	52	vertices	vertex	NOUN
easat-3258	102	53	in	in	ADP
easat-3258	102	54	their	their	PRON
easat-3258	102	55	maximal	maximal	ADJ
easat-3258	102	56	product	product	NOUN
easat-3258	102	57	is	be	AUX
easat-3258	102	58	defined	define	VERB
easat-3258	102	59	for	for	ADP
easat-3258	102	60	𝑖	𝑖	SYM
easat-3258	102	61	,	,	PUNCT
easat-3258	102	62	𝑗	𝑗	INTJ
easat-3258	102	63	,	,	PUNCT
easat-3258	102	64	𝑘	𝑘	X
easat-3258	102	65	=	=	SYM
easat-3258	102	66	1,2,3	1,2,3	NUM
easat-3258	102	67	…	…	PUNCT
easat-3258	102	68	.	.	PUNCT
easat-3258	103	1	𝑛	𝑛	PRON
easat-3258	103	2	as	as	ADP
easat-3258	103	3	,	,	PUNCT
easat-3258	103	4	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢𝑖	NOUN
easat-3258	103	5	′	′	NOUN
easat-3258	103	6	,	,	PUNCT
easat-3258	103	7	𝑢𝑗	𝑢𝑗	X
easat-3258	103	8	′′	′′	PROPN
easat-3258	103	9	)	)	PUNCT
easat-3258	103	10	=	=	PUNCT
easat-3258	103	11	∑	∑	PUNCT
easat-3258	103	12	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
easat-3258	103	13	{	{	PUNCT
easat-3258	103	14	𝜇′(𝑢𝑖	𝜇′(𝑢𝑖	PROPN
easat-3258	103	15	′𝑢𝑘	′𝑢𝑘	NOUN
easat-3258	103	16	′	′	NUM
easat-3258	103	17	)	)	PUNCT
easat-3258	103	18	,	,	PUNCT
easat-3258	103	19	𝜇′′(𝑢𝑗	𝜇′′(𝑢𝑗	VERB
easat-3258	103	20	′′	′′	PROPN
easat-3258	103	21	)	)	PUNCT
easat-3258	103	22	}	}	PUNCT
easat-3258	104	1	+	+	CCONJ
easat-3258	104	2	∑	∑	PUNCT
easat-3258	104	3	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
easat-3258	104	4	{	{	PUNCT
easat-3258	104	5	𝜇′′(𝑢𝑗	𝜇′′(𝑢𝑗	NOUN
easat-3258	104	6	′′𝑢𝑘	′′𝑢𝑘	PROPN
easat-3258	104	7	′′	′′	PROPN
easat-3258	104	8	)	)	PUNCT
easat-3258	104	9	,	,	PUNCT
easat-3258	104	10	𝜇′(𝑢𝑖	𝜇′(𝑢𝑖	PROPN
easat-3258	104	11	′	′	NUM
easat-3258	104	12	)	)	PUNCT
easat-3258	104	13	}	}	PUNCT
easat-3258	105	1	+	+	NUM
easat-3258	105	2	𝜇∗(𝑢𝑖	𝜇∗(𝑢𝑖	PROPN
easat-3258	105	3	′	′	NOUN
easat-3258	105	4	,	,	PUNCT
easat-3258	105	5	𝑢𝑗	𝑢𝑗	X
easat-3258	105	6	′′	′′	PROPN
easat-3258	105	7	)	)	PUNCT
easat-3258	105	8	where	where	SCONJ
easat-3258	105	9	(	(	PUNCT
easat-3258	105	10	𝑢𝑖	𝑢𝑖	PRON
easat-3258	105	11	′𝑢𝑘	′𝑢𝑘	PROPN
easat-3258	105	12	′	′	NUM
easat-3258	105	13	)	)	PUNCT
easat-3258	105	14	∈	∈	PROPN
easat-3258	105	15	𝐸′	𝐸′	NOUN
easat-3258	105	16	,	,	PUNCT
easat-3258	105	17	(	(	PUNCT
easat-3258	105	18	𝑢𝑗	𝑢𝑗	NOUN
easat-3258	105	19	′′𝑢𝑘	′′𝑢𝑘	PROPN
easat-3258	105	20	′′	′′	PROPN
easat-3258	105	21	)	)	PUNCT
easat-3258	105	22	∈	∈	PROPN
easat-3258	105	23	𝐸′′	𝐸′′	NOUN
easat-3258	105	24	and	and	CCONJ
easat-3258	105	25	𝑢𝑖	𝑢𝑖	ADP
easat-3258	105	26	′	′	NUM
easat-3258	105	27	=	=	PUNCT
easat-3258	105	28	𝑢𝑗	𝑢𝑗	PROPN
easat-3258	105	29	′	′	NOUN
easat-3258	105	30	,	,	PUNCT
easat-3258	105	31	𝑢𝑖	𝑢𝑖	VERB
easat-3258	105	32	′′	′′	PROPN
easat-3258	105	33	=	=	PROPN
easat-3258	105	34	𝑢𝑗′′	𝑢𝑗′′	PROPN
easat-3258	105	35	=	=	PUNCT
easat-3258	105	36	∑	∑	PROPN
easat-3258	105	37	𝜇′′(𝑢𝑗	𝜇′′(𝑢𝑗	PROPN
easat-3258	105	38	′′	′′	PROPN
easat-3258	105	39	)	)	PUNCT
easat-3258	106	1	+	+	CCONJ
easat-3258	106	2	∑	∑	PUNCT
easat-3258	106	3	𝜇′′(𝑢𝑗	𝜇′′(𝑢𝑗	NOUN
easat-3258	106	4	′′𝑢𝑘	′′𝑢𝑘	PROPN
easat-3258	106	5	′′	′′	PROPN
easat-3258	106	6	)	)	PUNCT
easat-3258	107	1	+	+	NUM
easat-3258	107	2	𝜇∗(𝑢𝑖	𝜇∗(𝑢𝑖	PROPN
easat-3258	107	3	′	′	NOUN
easat-3258	107	4	,	,	PUNCT
easat-3258	107	5	𝑢𝑗	𝑢𝑗	X
easat-3258	107	6	′′	′′	PROPN
easat-3258	107	7	)	)	PUNCT
easat-3258	107	8	=	=	SYM
easat-3258	107	9	𝑛0(𝑢𝑖	𝑛0(𝑢𝑖	PROPN
easat-3258	107	10	′	′	NUM
easat-3258	107	11	)	)	PUNCT
easat-3258	107	12	𝜇′′(𝑢𝑗	𝜇′′(𝑢𝑗	NOUN
easat-3258	107	13	′′	′′	PROPN
easat-3258	107	14	)	)	PUNCT
easat-3258	108	1	+	+	PROPN
easat-3258	108	2	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇′′(𝑢𝑗	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇′′(𝑢𝑗	PROPN
easat-3258	108	3	′′	′′	PROPN
easat-3258	108	4	)	)	PUNCT
easat-3258	108	5	5798	5798	NUM
easat-3258	108	6	edelweiss	edelweiss	PROPN
easat-3258	108	7	applied	apply	VERB
easat-3258	108	8	science	science	NOUN
easat-3258	108	9	and	and	CCONJ
easat-3258	108	10	technology	technology	NOUN
easat-3258	108	11	issn	issn	PROPN
easat-3258	108	12	:	:	PUNCT
easat-3258	108	13	2576	2576	NUM
easat-3258	108	14	-	-	SYM
easat-3258	108	15	8484	8484	NUM
easat-3258	108	16	vol	vol	NOUN
easat-3258	108	17	.	.	PROPN
easat-3258	108	18	8	8	NUM
easat-3258	108	19	,	,	PUNCT
easat-3258	108	20	no	no	INTJ
easat-3258	108	21	.	.	NOUN
easat-3258	108	22	6	6	NUM
easat-3258	108	23	:	:	PUNCT
easat-3258	108	24	5789	5789	NUM
easat-3258	108	25	-	-	SYM
easat-3258	108	26	5799	5799	NUM
easat-3258	108	27	,	,	PUNCT
easat-3258	108	28	2024	2024	NUM
easat-3258	108	29	doi	doi	NOUN
easat-3258	108	30	:	:	PUNCT
easat-3258	108	31	10.55214/25768484.v8i6.3258	10.55214/25768484.v8i6.3258	NUM
easat-3258	108	32	©	©	PROPN
easat-3258	108	33	2024	2024	NUM
easat-3258	108	34	by	by	ADP
easat-3258	108	35	the	the	DET
easat-3258	108	36	authors	author	NOUN
easat-3258	108	37	;	;	PUNCT
easat-3258	108	38	licensee	licensee	PROPN
easat-3258	108	39	learning	learn	VERB
easat-3258	108	40	gate	gate	PROPN
easat-3258	108	41	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢𝑖	PROPN
easat-3258	108	42	′	′	PROPN
easat-3258	108	43	,	,	PUNCT
easat-3258	108	44	𝑢𝑗	𝑢𝑗	X
easat-3258	108	45	′′	′′	PROPN
easat-3258	108	46	)	)	PUNCT
easat-3258	108	47	=	=	PUNCT
easat-3258	108	48	∑	∑	PROPN
easat-3258	108	49	𝑚𝑖𝑛	𝑚𝑖𝑛	PROPN
easat-3258	108	50	{	{	PUNCT
easat-3258	108	51	𝛾′(𝑢𝑖	𝛾′(𝑢𝑖	NOUN
easat-3258	108	52	′𝑢𝑘	′𝑢𝑘	PROPN
easat-3258	108	53	′	′	NUM
easat-3258	108	54	)	)	PUNCT
easat-3258	108	55	,	,	PUNCT
easat-3258	108	56	𝛾′′(𝑢𝑗	𝛾′′(𝑢𝑗	PROPN
easat-3258	108	57	′′	′′	PROPN
easat-3258	108	58	)	)	PUNCT
easat-3258	108	59	}	}	PUNCT
easat-3258	109	1	+	+	CCONJ
easat-3258	109	2	∑	∑	PROPN
easat-3258	109	3	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
easat-3258	109	4	{	{	PUNCT
easat-3258	109	5	𝛾′′(𝑢𝑗	𝛾′′(𝑢𝑗	NOUN
easat-3258	109	6	′′𝑢𝑘	′′𝑢𝑘	PROPN
easat-3258	109	7	′′	′′	PROPN
easat-3258	109	8	)	)	PUNCT
easat-3258	109	9	,	,	PUNCT
easat-3258	109	10	𝛾′(𝑢𝑖	𝛾′(𝑢𝑖	NOUN
easat-3258	109	11	′	′	NOUN
easat-3258	109	12	)	)	PUNCT
easat-3258	109	13	}	}	PUNCT
easat-3258	110	1	+	+	CCONJ
easat-3258	110	2	𝛾∗(𝑢𝑖	𝛾∗(𝑢𝑖	PROPN
easat-3258	110	3	′	′	NOUN
easat-3258	110	4	,	,	PUNCT
easat-3258	110	5	𝑢𝑗	𝑢𝑗	X
easat-3258	110	6	′′	′′	PROPN
easat-3258	110	7	)	)	PUNCT
easat-3258	110	8	where	where	SCONJ
easat-3258	110	9	(	(	PUNCT
easat-3258	110	10	𝑢𝑖	𝑢𝑖	PRON
easat-3258	110	11	′𝑢𝑘	′𝑢𝑘	PROPN
easat-3258	110	12	′	′	NUM
easat-3258	110	13	)	)	PUNCT
easat-3258	110	14	∈	∈	PROPN
easat-3258	110	15	𝐸′	𝐸′	NOUN
easat-3258	110	16	,	,	PUNCT
easat-3258	110	17	(	(	PUNCT
easat-3258	110	18	𝑢𝑗	𝑢𝑗	NOUN
easat-3258	110	19	′′𝑢𝑘	′′𝑢𝑘	PROPN
easat-3258	110	20	′′	′′	PROPN
easat-3258	110	21	)	)	PUNCT
easat-3258	110	22	∈	∈	PROPN
easat-3258	110	23	𝐸′′	𝐸′′	NOUN
easat-3258	110	24	and	and	CCONJ
easat-3258	110	25	𝑢𝑖	𝑢𝑖	ADP
easat-3258	110	26	′	′	NUM
easat-3258	110	27	=	=	PUNCT
easat-3258	110	28	𝑢𝑗	𝑢𝑗	PROPN
easat-3258	110	29	′	′	NOUN
easat-3258	110	30	,	,	PUNCT
easat-3258	110	31	𝑢𝑖	𝑢𝑖	VERB
easat-3258	110	32	′′	′′	PROPN
easat-3258	110	33	=	=	PROPN
easat-3258	110	34	𝑢𝑗′′	𝑢𝑗′′	PROPN
easat-3258	110	35	=	=	SYM
easat-3258	110	36	∑	∑	PROPN
easat-3258	110	37	𝛾′′(𝑢𝑗	𝛾′′(𝑢𝑗	NOUN
easat-3258	110	38	′′	′′	PROPN
easat-3258	110	39	)	)	PUNCT
easat-3258	111	1	+	+	CCONJ
easat-3258	111	2	∑	∑	PROPN
easat-3258	111	3	𝛾′′(𝑢𝑗	𝛾′′(𝑢𝑗	NOUN
easat-3258	111	4	′′𝑢𝑘	′′𝑢𝑘	PROPN
easat-3258	111	5	′′	′′	PROPN
easat-3258	111	6	)	)	PUNCT
easat-3258	112	1	+	+	CCONJ
easat-3258	112	2	𝛾∗(𝑢𝑖	𝛾∗(𝑢𝑖	PROPN
easat-3258	112	3	′	′	NOUN
easat-3258	112	4	,	,	PUNCT
easat-3258	112	5	𝑢𝑗	𝑢𝑗	X
easat-3258	112	6	′′	′′	PROPN
easat-3258	112	7	)	)	PUNCT
easat-3258	112	8	=	=	SYM
easat-3258	112	9	𝑛0(𝑢𝑖	𝑛0(𝑢𝑖	PROPN
easat-3258	112	10	′	′	NUM
easat-3258	112	11	)	)	PUNCT
easat-3258	112	12	𝛾′′(𝑢𝑗	𝛾′′(𝑢𝑗	NOUN
easat-3258	112	13	′′	′′	PROPN
easat-3258	112	14	)	)	PUNCT
easat-3258	113	1	+	+	NUM
easat-3258	113	2	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾′′(𝑢𝑗	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾′′(𝑢𝑗	NOUN
easat-3258	113	3	′′	′′	PROPN
easat-3258	113	4	)	)	PUNCT
easat-3258	113	5	here	here	ADV
easat-3258	113	6	𝑛0(𝑢𝑖	𝑛0(𝑢𝑖	PROPN
easat-3258	113	7	′	′	NOUN
easat-3258	113	8	)	)	PUNCT
easat-3258	113	9	is	be	AUX
easat-3258	113	10	the	the	DET
easat-3258	113	11	number	number	NOUN
easat-3258	113	12	of	of	ADP
easat-3258	113	13	edges	edge	NOUN
easat-3258	113	14	incident	incident	NOUN
easat-3258	113	15	at	at	ADP
easat-3258	113	16	𝑢𝑖	𝑢𝑖	X
easat-3258	113	17	′	′	NUM
easat-3258	113	18	in	in	ADP
easat-3258	113	19	𝐺1(𝑉′	𝐺1(𝑉′	NOUN
easat-3258	113	20	,	,	PUNCT
easat-3258	113	21	𝐸′	𝐸′	NOUN
easat-3258	113	22	,	,	PUNCT
easat-3258	113	23	𝜇′	𝜇′	NOUN
easat-3258	113	24	,	,	PUNCT
easat-3258	113	25	𝛾′	𝛾′	NUM
easat-3258	113	26	)	)	PUNCT
easat-3258	113	27	theorem	theorem	VERB
easat-3258	113	28	3.8	3.8	NUM
easat-3258	113	29	if	if	SCONJ
easat-3258	113	30	𝐺1(𝑉′	𝐺1(𝑉′	ADV
easat-3258	113	31	,	,	PUNCT
easat-3258	113	32	𝐸′	𝐸′	NOUN
easat-3258	113	33	,	,	PUNCT
easat-3258	113	34	𝜇′	𝜇′	NOUN
easat-3258	113	35	,	,	PUNCT
easat-3258	113	36	𝛾′	𝛾′	NUM
easat-3258	113	37	)	)	PUNCT
easat-3258	113	38	and	and	CCONJ
easat-3258	113	39	𝐺2(𝑉′′	𝐺2(𝑉′′	NOUN
easat-3258	113	40	,	,	PUNCT
easat-3258	113	41	𝐸′′	𝐸′′	ADJ
easat-3258	113	42	,	,	PUNCT
easat-3258	113	43	𝜇′′	𝜇′′	NOUN
easat-3258	113	44	,	,	PUNCT
easat-3258	113	45	𝛾′′	𝛾′′	PROPN
easat-3258	113	46	)	)	PUNCT
easat-3258	113	47	are	be	AUX
easat-3258	113	48	two	two	NUM
easat-3258	113	49	constant	constant	ADJ
easat-3258	113	50	if	if	SCONJ
easat-3258	113	51	graphs	graph	NOUN
easat-3258	113	52	such	such	ADJ
easat-3258	113	53	that	that	DET
easat-3258	113	54	𝜇′(𝑢𝑖	𝜇′(𝑢𝑖	PROPN
easat-3258	113	55	′	′	NOUN
easat-3258	113	56	)	)	PUNCT
easat-3258	113	57	≤	≤	NOUN
easat-3258	113	58	𝜇′′(𝑢𝑗	𝜇′′(𝑢𝑗	NOUN
easat-3258	113	59	′′𝑢𝑘	′′𝑢𝑘	PROPN
easat-3258	113	60	′′	′′	PROPN
easat-3258	113	61	)	)	PUNCT
easat-3258	113	62	,	,	PUNCT
easat-3258	113	63	𝜇′(𝑢𝑖	𝜇′(𝑢𝑖	PROPN
easat-3258	113	64	′𝑢𝑗	′𝑢𝑗	NOUN
easat-3258	113	65	′	′	NUM
easat-3258	113	66	)	)	PUNCT
easat-3258	113	67	≤	≤	NOUN
easat-3258	113	68	𝜇′′(𝑢𝑘	𝜇′′(𝑢𝑘	VERB
easat-3258	113	69	′′	′′	PROPN
easat-3258	113	70	)	)	PUNCT
easat-3258	113	71	and	and	CCONJ
easat-3258	113	72	𝛾′(𝑢𝑖	𝛾′(𝑢𝑖	PROPN
easat-3258	113	73	′	′	NOUN
easat-3258	113	74	)	)	PUNCT
easat-3258	113	75	≥	≥	NOUN
easat-3258	113	76	𝛾′′(𝑢𝑗	𝛾′′(𝑢𝑗	NOUN
easat-3258	113	77	′′𝑢𝑘	′′𝑢𝑘	PROPN
easat-3258	113	78	′′	′′	PROPN
easat-3258	113	79	)	)	PUNCT
easat-3258	113	80	,	,	PUNCT
easat-3258	113	81	𝛾′	𝛾′	PROPN
easat-3258	113	82	(	(	PUNCT
easat-3258	113	83	𝑢𝑖	𝑢𝑖	NOUN
easat-3258	113	84	′𝑢𝑗	′𝑢𝑗	PROPN
easat-3258	113	85	′	′	PROPN
easat-3258	113	86	)	)	PUNCT
easat-3258	113	87	≥	≥	PROPN
easat-3258	113	88	𝛾′′(𝑢𝑘	𝛾′′(𝑢𝑘	PROPN
easat-3258	113	89	′′	′′	PROPN
easat-3258	113	90	)	)	PUNCT
easat-3258	113	91	with	with	ADP
easat-3258	113	92	second	second	ADJ
easat-3258	113	93	constant	constant	ADJ
easat-3258	113	94	if	if	SCONJ
easat-3258	113	95	graph	graph	NOUN
easat-3258	113	96	is	be	AUX
easat-3258	113	97	(	(	PUNCT
easat-3258	113	98	𝐶1	𝐶1	PROPN
easat-3258	113	99	∗∗	∗∗	NOUN
easat-3258	113	100	,	,	PUNCT
easat-3258	113	101	𝐶2	𝐶2	X
easat-3258	113	102	∗∗	∗∗	PROPN
easat-3258	113	103	)	)	PUNCT
easat-3258	113	104	then	then	ADV
easat-3258	113	105	the	the	DET
easat-3258	113	106	total	total	ADJ
easat-3258	113	107	degree	degree	NOUN
easat-3258	113	108	of	of	ADP
easat-3258	113	109	the	the	DET
easat-3258	113	110	vertices	vertex	NOUN
easat-3258	113	111	of	of	ADP
easat-3258	113	112	their	their	PRON
easat-3258	113	113	maximal	maximal	ADJ
easat-3258	113	114	product	product	NOUN
easat-3258	113	115	is	be	AUX
easat-3258	113	116	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢𝑖	NOUN
easat-3258	113	117	′	′	NOUN
easat-3258	113	118	,	,	PUNCT
easat-3258	113	119	𝑢𝑗	𝑢𝑗	X
easat-3258	113	120	′′	′′	PROPN
easat-3258	113	121	)	)	PUNCT
easat-3258	114	1	=	=	SYM
easat-3258	114	2	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇′′(𝑢𝑗	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇′′(𝑢𝑗	PROPN
easat-3258	114	3	′′	′′	PROPN
easat-3258	114	4	)	)	PUNCT
easat-3258	114	5	+	+	NUM
easat-3258	114	6	𝑛0(𝑢𝑖	𝑛0(𝑢𝑖	PROPN
easat-3258	114	7	′)𝐶1	′)𝐶1	PROPN
easat-3258	114	8	∗∗	∗∗	PROPN
easat-3258	114	9	and	and	CCONJ
easat-3258	114	10	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢𝑖	PROPN
easat-3258	114	11	′	′	NOUN
easat-3258	114	12	,	,	PUNCT
easat-3258	114	13	𝑢𝑗	𝑢𝑗	X
easat-3258	114	14	′′	′′	PROPN
easat-3258	114	15	)	)	PUNCT
easat-3258	114	16	=	=	PROPN
easat-3258	114	17	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾′′(𝑢𝑗	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾′′(𝑢𝑗	NOUN
easat-3258	114	18	′′	′′	PROPN
easat-3258	114	19	)	)	PUNCT
easat-3258	114	20	+	+	NUM
easat-3258	114	21	𝑛0(𝑢𝑖	𝑛0(𝑢𝑖	PROPN
easat-3258	114	22	′)𝐶2	′)𝐶2	PROPN
easat-3258	114	23	∗∗	∗∗	PROPN
easat-3258	114	24	theorem	theorem	VERB
easat-3258	114	25	3.9	3.9	NUM
easat-3258	114	26	if	if	SCONJ
easat-3258	114	27	𝐺1(𝑉′	𝐺1(𝑉′	ADV
easat-3258	114	28	,	,	PUNCT
easat-3258	114	29	𝐸′	𝐸′	NOUN
easat-3258	114	30	,	,	PUNCT
easat-3258	114	31	𝜇′	𝜇′	NOUN
easat-3258	114	32	,	,	PUNCT
easat-3258	114	33	𝛾′	𝛾′	NUM
easat-3258	114	34	)	)	PUNCT
easat-3258	114	35	and	and	CCONJ
easat-3258	114	36	𝐺2(𝑉′′	𝐺2(𝑉′′	NOUN
easat-3258	114	37	,	,	PUNCT
easat-3258	114	38	𝐸′′	𝐸′′	ADJ
easat-3258	114	39	,	,	PUNCT
easat-3258	114	40	𝜇′′	𝜇′′	NOUN
easat-3258	114	41	,	,	PUNCT
easat-3258	114	42	𝛾′′	𝛾′′	PROPN
easat-3258	114	43	)	)	PUNCT
easat-3258	114	44	are	be	AUX
easat-3258	114	45	two	two	NUM
easat-3258	114	46	constant	constant	ADJ
easat-3258	114	47	if	if	SCONJ
easat-3258	114	48	graphs	graph	NOUN
easat-3258	114	49	such	such	ADJ
easat-3258	114	50	that	that	DET
easat-3258	114	51	𝜇′′(𝑢𝑖	𝜇′′(𝑢𝑖	NOUN
easat-3258	114	52	′′	′′	NOUN
easat-3258	114	53	)	)	PUNCT
easat-3258	114	54	≤	≤	NUM
easat-3258	114	55	𝜇′(𝑢𝑗	𝜇′(𝑢𝑗	VERB
easat-3258	114	56	′𝑢𝑘	′𝑢𝑘	NOUN
easat-3258	114	57	′	′	NUM
easat-3258	114	58	)	)	PUNCT
easat-3258	114	59	,	,	PUNCT
easat-3258	114	60	𝜇′′(𝑢𝑖	𝜇′′(𝑢𝑖	NOUN
easat-3258	114	61	′′𝑢𝑗	′′𝑢𝑗	PROPN
easat-3258	114	62	′′	′′	PROPN
easat-3258	114	63	)	)	PUNCT
easat-3258	114	64	≤	≤	PROPN
easat-3258	114	65	𝜇′(𝑢𝑘	𝜇′(𝑢𝑘	PROPN
easat-3258	114	66	′	′	NOUN
easat-3258	114	67	)	)	PUNCT
easat-3258	114	68	and	and	CCONJ
easat-3258	114	69	𝛾′′(𝑢𝑖	𝛾′′(𝑢𝑖	PROPN
easat-3258	114	70	′′	′′	PROPN
easat-3258	114	71	)	)	PUNCT
easat-3258	114	72	≥	≥	PROPN
easat-3258	114	73	𝛾′(𝑢𝑗	𝛾′(𝑢𝑗	PROPN
easat-3258	114	74	′𝑢𝑘	′𝑢𝑘	NOUN
easat-3258	114	75	′	′	NUM
easat-3258	114	76	)	)	PUNCT
easat-3258	114	77	,	,	PUNCT
easat-3258	114	78	𝛾′′(𝑢𝑖	𝛾′′(𝑢𝑖	PROPN
easat-3258	114	79	′′𝑢𝑗	′′𝑢𝑗	PROPN
easat-3258	114	80	′′	′′	PROPN
easat-3258	114	81	)	)	PUNCT
easat-3258	114	82	≥	≥	NOUN
easat-3258	114	83	𝛾′(𝑢𝑘	𝛾′(𝑢𝑘	PROPN
easat-3258	114	84	′	′	PROPN
easat-3258	114	85	)	)	PUNCT
easat-3258	114	86	then	then	ADV
easat-3258	114	87	the	the	DET
easat-3258	114	88	total	total	ADJ
easat-3258	114	89	degree	degree	NOUN
easat-3258	114	90	of	of	ADP
easat-3258	114	91	the	the	DET
easat-3258	114	92	vertices	vertex	NOUN
easat-3258	114	93	in	in	ADP
easat-3258	114	94	their	their	PRON
easat-3258	114	95	maximal	maximal	ADJ
easat-3258	114	96	product	product	NOUN
easat-3258	114	97	g(𝑉∗	g(𝑉∗	PROPN
easat-3258	114	98	,	,	PUNCT
easat-3258	114	99	𝐸∗	𝐸∗	NOUN
easat-3258	114	100	,	,	PUNCT
easat-3258	114	101	𝜇∗	𝜇∗	NOUN
easat-3258	114	102	,	,	PUNCT
easat-3258	114	103	𝛾∗	𝛾∗	NOUN
easat-3258	114	104	)	)	PUNCT
easat-3258	114	105	=	=	PUNCT
easat-3258	114	106	𝐺1	𝐺1	NOUN
easat-3258	114	107	∗	∗	NOUN
easat-3258	114	108	𝐺2	𝐺2	NOUN
easat-3258	114	109	is	be	AUX
easat-3258	114	110	given	give	VERB
easat-3258	114	111	by	by	ADP
easat-3258	114	112	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢𝑖	PROPN
easat-3258	114	113	′	′	NOUN
easat-3258	114	114	,	,	PUNCT
easat-3258	114	115	𝑢𝑗	𝑢𝑗	X
easat-3258	114	116	′′	′′	PROPN
easat-3258	114	117	)	)	PUNCT
easat-3258	114	118	=	=	SYM
easat-3258	114	119	𝑛0(𝑢𝑗	𝑛0(𝑢𝑗	NUM
easat-3258	114	120	′′	′′	PROPN
easat-3258	114	121	)	)	PUNCT
easat-3258	114	122	𝜇′(𝑢𝑖	𝜇′(𝑢𝑖	PROPN
easat-3258	114	123	′	′	NUM
easat-3258	114	124	)	)	PUNCT
easat-3258	114	125	+	+	NOUN
easat-3258	114	126	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇′(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇′(𝑢𝑖	NOUN
easat-3258	114	127	′	′	NUM
easat-3258	114	128	)	)	PUNCT
easat-3258	114	129	and	and	CCONJ
easat-3258	114	130	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢𝑖	PROPN
easat-3258	114	131	′	′	NOUN
easat-3258	114	132	,	,	PUNCT
easat-3258	114	133	𝑢𝑗	𝑢𝑗	X
easat-3258	114	134	′′	′′	PROPN
easat-3258	114	135	)	)	PUNCT
easat-3258	114	136	=	=	SYM
easat-3258	114	137	𝑛0(𝑢𝑗	𝑛0(𝑢𝑗	NUM
easat-3258	114	138	′′	′′	PROPN
easat-3258	114	139	)	)	PUNCT
easat-3258	114	140	𝛾′(𝑢𝑖	𝛾′(𝑢𝑖	NOUN
easat-3258	114	141	′	′	NOUN
easat-3258	114	142	)	)	PUNCT
easat-3258	115	1	+	+	CCONJ
easat-3258	115	2	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾′(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾′(𝑢𝑖	CCONJ
easat-3258	115	3	′	′	NOUN
easat-3258	115	4	)	)	PUNCT
easat-3258	115	5	for	for	ADP
easat-3258	115	6	𝑖	𝑖	SYM
easat-3258	115	7	,	,	PUNCT
easat-3258	115	8	𝑗	𝑗	INTJ
easat-3258	115	9	,	,	PUNCT
easat-3258	115	10	𝑘	𝑘	X
easat-3258	115	11	=	=	SYM
easat-3258	115	12	1,2,3	1,2,3	NUM
easat-3258	115	13	…	…	PUNCT
easat-3258	115	14	.	.	PUNCT
easat-3258	116	1	𝑛	𝑛	DET
easat-3258	116	2	proof	proof	NOUN
easat-3258	116	3	:	:	PUNCT
easat-3258	116	4	let	let	VERB
easat-3258	116	5	𝐺1(𝑉′	𝐺1(𝑉′	ADV
easat-3258	116	6	,	,	PUNCT
easat-3258	116	7	𝐸′	𝐸′	NOUN
easat-3258	116	8	,	,	PUNCT
easat-3258	116	9	𝜇′	𝜇′	NOUN
easat-3258	116	10	,	,	PUNCT
easat-3258	116	11	𝛾′	𝛾′	NUM
easat-3258	116	12	)	)	PUNCT
easat-3258	116	13	and	and	CCONJ
easat-3258	116	14	𝐺2(𝑉′′	𝐺2(𝑉′′	NOUN
easat-3258	116	15	,	,	PUNCT
easat-3258	116	16	𝐸′′	𝐸′′	ADJ
easat-3258	116	17	,	,	PUNCT
easat-3258	116	18	𝜇′′	𝜇′′	NOUN
easat-3258	116	19	,	,	PUNCT
easat-3258	116	20	𝛾′′	𝛾′′	PROPN
easat-3258	116	21	)	)	PUNCT
easat-3258	116	22	are	be	AUX
easat-3258	116	23	two	two	NUM
easat-3258	116	24	constant	constant	ADJ
easat-3258	116	25	if	if	SCONJ
easat-3258	116	26	graphs	graph	NOUN
easat-3258	116	27	such	such	ADJ
easat-3258	116	28	that	that	DET
easat-3258	116	29	𝜇′′(𝑢𝑖	𝜇′′(𝑢𝑖	NOUN
easat-3258	116	30	′′	′′	NOUN
easat-3258	116	31	)	)	PUNCT
easat-3258	116	32	≤	≤	NUM
easat-3258	116	33	𝜇′(𝑢𝑗	𝜇′(𝑢𝑗	VERB
easat-3258	116	34	′𝑢𝑘	′𝑢𝑘	NOUN
easat-3258	116	35	′	′	NUM
easat-3258	116	36	)	)	PUNCT
easat-3258	116	37	,	,	PUNCT
easat-3258	116	38	𝜇′′(𝑢𝑖	𝜇′′(𝑢𝑖	NOUN
easat-3258	116	39	′′𝑢𝑗	′′𝑢𝑗	PROPN
easat-3258	116	40	′′	′′	PROPN
easat-3258	116	41	)	)	PUNCT
easat-3258	116	42	≤	≤	PROPN
easat-3258	116	43	𝜇′(𝑢𝑘	𝜇′(𝑢𝑘	PROPN
easat-3258	116	44	′	′	NOUN
easat-3258	116	45	)	)	PUNCT
easat-3258	116	46	and	and	CCONJ
easat-3258	116	47	𝛾′′(𝑢𝑖	𝛾′′(𝑢𝑖	PROPN
easat-3258	116	48	′′	′′	PROPN
easat-3258	116	49	)	)	PUNCT
easat-3258	116	50	≥	≥	PROPN
easat-3258	116	51	𝛾′(𝑢𝑗	𝛾′(𝑢𝑗	PROPN
easat-3258	116	52	′𝑢𝑘	′𝑢𝑘	NOUN
easat-3258	116	53	′	′	NUM
easat-3258	116	54	)	)	PUNCT
easat-3258	116	55	,	,	PUNCT
easat-3258	116	56	𝛾′′(𝑢𝑖	𝛾′′(𝑢𝑖	PROPN
easat-3258	116	57	′′𝑢𝑗	′′𝑢𝑗	PROPN
easat-3258	116	58	′′	′′	PROPN
easat-3258	116	59	)	)	PUNCT
easat-3258	116	60	≥	≥	NOUN
easat-3258	116	61	𝛾′(𝑢𝑘	𝛾′(𝑢𝑘	PROPN
easat-3258	116	62	′	′	NOUN
easat-3258	116	63	)	)	PUNCT
easat-3258	116	64	then	then	ADV
easat-3258	116	65	by	by	ADP
easat-3258	116	66	definition	definition	NOUN
easat-3258	116	67	of	of	ADP
easat-3258	116	68	total	total	ADJ
easat-3258	116	69	degree	degree	NOUN
easat-3258	116	70	,	,	PUNCT
easat-3258	116	71	their	their	PRON
easat-3258	116	72	maximal	maximal	ADJ
easat-3258	116	73	product	product	NOUN
easat-3258	116	74	𝐺1	𝐺1	NOUN
easat-3258	116	75	∗	∗	NOUN
easat-3258	116	76	𝐺2	𝐺2	NOUN
easat-3258	116	77	=	=	PUNCT
easat-3258	116	78	g(𝑉∗	g(𝑉∗	PROPN
easat-3258	116	79	,	,	PUNCT
easat-3258	116	80	𝐸∗	𝐸∗	NOUN
easat-3258	116	81	,	,	PUNCT
easat-3258	116	82	𝜇∗	𝜇∗	NOUN
easat-3258	116	83	,	,	PUNCT
easat-3258	116	84	𝛾∗	𝛾∗	NOUN
easat-3258	116	85	)	)	PUNCT
easat-3258	116	86	is	be	AUX
easat-3258	116	87	obtained	obtain	VERB
easat-3258	116	88	as	as	ADP
easat-3258	116	89	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢𝑖	PROPN
easat-3258	116	90	′	′	NOUN
easat-3258	116	91	,	,	PUNCT
easat-3258	116	92	𝑢𝑗	𝑢𝑗	X
easat-3258	116	93	′′	′′	PROPN
easat-3258	116	94	)	)	PUNCT
easat-3258	116	95	=	=	PUNCT
easat-3258	117	1	∑	∑	PUNCT
easat-3258	117	2	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
easat-3258	117	3	{	{	PUNCT
easat-3258	117	4	𝜇′(𝑢𝑖	𝜇′(𝑢𝑖	PROPN
easat-3258	117	5	′𝑢𝑘	′𝑢𝑘	NOUN
easat-3258	117	6	′	′	NUM
easat-3258	117	7	)	)	PUNCT
easat-3258	117	8	,	,	PUNCT
easat-3258	117	9	𝜇′′(𝑢𝑗	𝜇′′(𝑢𝑗	VERB
easat-3258	117	10	′′	′′	PROPN
easat-3258	117	11	)	)	PUNCT
easat-3258	117	12	}	}	PUNCT
easat-3258	118	1	+	+	CCONJ
easat-3258	118	2	∑	∑	PUNCT
easat-3258	118	3	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
easat-3258	118	4	{	{	PUNCT
easat-3258	118	5	𝜇′′(𝑢𝑗	𝜇′′(𝑢𝑗	NOUN
easat-3258	118	6	′′𝑢𝑘	′′𝑢𝑘	PROPN
easat-3258	118	7	′′	′′	PROPN
easat-3258	118	8	)	)	PUNCT
easat-3258	118	9	,	,	PUNCT
easat-3258	118	10	𝜇′(𝑢𝑖	𝜇′(𝑢𝑖	PROPN
easat-3258	118	11	′	′	NUM
easat-3258	118	12	)	)	PUNCT
easat-3258	118	13	}	}	PUNCT
easat-3258	119	1	+	+	NUM
easat-3258	119	2	𝜇∗(𝑢𝑖	𝜇∗(𝑢𝑖	PROPN
easat-3258	119	3	′	′	NOUN
easat-3258	119	4	,	,	PUNCT
easat-3258	119	5	𝑢𝑗	𝑢𝑗	X
easat-3258	119	6	′′	′′	PROPN
easat-3258	119	7	)	)	PUNCT
easat-3258	119	8	where	where	SCONJ
easat-3258	119	9	(	(	PUNCT
easat-3258	119	10	𝑢𝑖	𝑢𝑖	PRON
easat-3258	119	11	′𝑢𝑘	′𝑢𝑘	PROPN
easat-3258	119	12	′	′	NUM
easat-3258	119	13	)	)	PUNCT
easat-3258	119	14	∈	∈	PROPN
easat-3258	119	15	𝐸′	𝐸′	NOUN
easat-3258	119	16	,	,	PUNCT
easat-3258	119	17	(	(	PUNCT
easat-3258	119	18	𝑢𝑗	𝑢𝑗	NOUN
easat-3258	119	19	′′𝑢𝑘	′′𝑢𝑘	PROPN
easat-3258	119	20	′′	′′	PROPN
easat-3258	119	21	)	)	PUNCT
easat-3258	119	22	∈	∈	PROPN
easat-3258	119	23	𝐸′′	𝐸′′	NOUN
easat-3258	119	24	and	and	CCONJ
easat-3258	119	25	𝑢𝑖	𝑢𝑖	ADP
easat-3258	119	26	′	′	NUM
easat-3258	119	27	=	=	PUNCT
easat-3258	119	28	𝑢𝑗	𝑢𝑗	PROPN
easat-3258	119	29	′	′	NOUN
easat-3258	119	30	,	,	PUNCT
easat-3258	119	31	𝑢𝑖	𝑢𝑖	VERB
easat-3258	119	32	′′	′′	PROPN
easat-3258	119	33	=	=	PROPN
easat-3258	119	34	𝑢𝑗′′	𝑢𝑗′′	PROPN
easat-3258	119	35	=	=	SYM
easat-3258	119	36	∑	∑	PROPN
easat-3258	119	37	𝜇′(𝑢𝑗	𝜇′(𝑢𝑗	PROPN
easat-3258	119	38	′𝑢𝑘	′𝑢𝑘	NOUN
easat-3258	119	39	′	′	NUM
easat-3258	119	40	)	)	PUNCT
easat-3258	120	1	+	+	CCONJ
easat-3258	120	2	∑	∑	PROPN
easat-3258	120	3	𝜇′(𝑢𝑖	𝜇′(𝑢𝑖	PROPN
easat-3258	120	4	′	′	NUM
easat-3258	120	5	)	)	PUNCT
easat-3258	121	1	+	+	CCONJ
easat-3258	121	2	𝜇∗(𝑢𝑖	𝜇∗(𝑢𝑖	PROPN
easat-3258	121	3	′	′	NOUN
easat-3258	121	4	,	,	PUNCT
easat-3258	121	5	𝑢𝑗	𝑢𝑗	X
easat-3258	121	6	′′	′′	PROPN
easat-3258	121	7	)	)	PUNCT
easat-3258	121	8	=	=	PUNCT
easat-3258	122	1	∑	∑	PUNCT
easat-3258	122	2	𝜇′(𝑢𝑗	𝜇′(𝑢𝑗	PROPN
easat-3258	122	3	′𝑢𝑘	′𝑢𝑘	NOUN
easat-3258	122	4	′	′	NUM
easat-3258	122	5	)	)	PUNCT
easat-3258	123	1	+	+	CCONJ
easat-3258	123	2	∑	∑	PROPN
easat-3258	123	3	𝜇′(𝑢𝑖	𝜇′(𝑢𝑖	PROPN
easat-3258	123	4	′	′	NUM
easat-3258	123	5	)	)	PUNCT
easat-3258	124	1	+	+	CCONJ
easat-3258	124	2	max	max	PROPN
easat-3258	124	3	{	{	PUNCT
easat-3258	124	4	𝜇′(𝑢𝑖	𝜇′(𝑢𝑖	PROPN
easat-3258	124	5	′	′	NUM
easat-3258	124	6	)	)	PUNCT
easat-3258	124	7	,	,	PUNCT
easat-3258	124	8	𝜇′′(𝑢𝑗	𝜇′′(𝑢𝑗	VERB
easat-3258	124	9	′′	′′	PROPN
easat-3258	124	10	)	)	PUNCT
easat-3258	124	11	}	}	PUNCT
easat-3258	125	1	=	=	SYM
easat-3258	125	2	𝑛0(𝑢𝑗	𝑛0(𝑢𝑗	NUM
easat-3258	125	3	′′)𝜇′(𝑢𝑖	′′)𝜇′(𝑢𝑖	NOUN
easat-3258	125	4	′	′	NUM
easat-3258	125	5	)	)	PUNCT
easat-3258	126	1	+	+	NOUN
easat-3258	126	2	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇′(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇′(𝑢𝑖	NOUN
easat-3258	126	3	′	′	NOUN
easat-3258	126	4	)	)	PUNCT
easat-3258	126	5	similarly	similarly	ADV
easat-3258	126	6	,	,	PUNCT
easat-3258	126	7	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢𝑖	PROPN
easat-3258	126	8	′	′	NOUN
easat-3258	126	9	,	,	PUNCT
easat-3258	126	10	𝑢𝑗	𝑢𝑗	X
easat-3258	126	11	′′	′′	PROPN
easat-3258	126	12	)	)	PUNCT
easat-3258	126	13	=	=	PUNCT
easat-3258	127	1	∑	∑	PUNCT
easat-3258	127	2	min	min	PROPN
easat-3258	127	3	{	{	PUNCT
easat-3258	127	4	𝛾′(𝑢𝑖	𝛾′(𝑢𝑖	PROPN
easat-3258	127	5	′𝑢𝑘	′𝑢𝑘	PROPN
easat-3258	127	6	′	′	NUM
easat-3258	127	7	)	)	PUNCT
easat-3258	127	8	,	,	PUNCT
easat-3258	127	9	𝛾′′(𝑢𝑗	𝛾′′(𝑢𝑗	PROPN
easat-3258	127	10	′′	′′	PROPN
easat-3258	127	11	)	)	PUNCT
easat-3258	127	12	}	}	PUNCT
easat-3258	128	1	+	+	CCONJ
easat-3258	128	2	∑	∑	NOUN
easat-3258	128	3	𝑚𝑖𝑛{𝛾′′(𝑢𝑗	𝑚𝑖𝑛{𝛾′′(𝑢𝑗	NOUN
easat-3258	128	4	′′𝑢𝑘	′′𝑢𝑘	PROPN
easat-3258	128	5	′′	′′	PROPN
easat-3258	128	6	)	)	PUNCT
easat-3258	128	7	,	,	PUNCT
easat-3258	128	8	𝛾′(𝑢𝑖	𝛾′(𝑢𝑖	NOUN
easat-3258	128	9	′	′	NOUN
easat-3258	128	10	)	)	PUNCT
easat-3258	128	11	}	}	PUNCT
easat-3258	129	1	+	+	CCONJ
easat-3258	129	2	𝛾∗(𝑢𝑖	𝛾∗(𝑢𝑖	PROPN
easat-3258	129	3	′	′	NOUN
easat-3258	129	4	,	,	PUNCT
easat-3258	129	5	𝑢𝑗	𝑢𝑗	X
easat-3258	129	6	′′	′′	PROPN
easat-3258	129	7	)	)	PUNCT
easat-3258	129	8	,	,	PUNCT
easat-3258	129	9	where	where	SCONJ
easat-3258	129	10	(	(	PUNCT
easat-3258	129	11	𝑢𝑖	𝑢𝑖	PRON
easat-3258	129	12	′𝑢𝑘	′𝑢𝑘	PROPN
easat-3258	129	13	′	′	NUM
easat-3258	129	14	)	)	PUNCT
easat-3258	129	15	∈	∈	PROPN
easat-3258	129	16	𝐸′	𝐸′	NOUN
easat-3258	129	17	,	,	PUNCT
easat-3258	129	18	(	(	PUNCT
easat-3258	129	19	𝑢𝑗	𝑢𝑗	NOUN
easat-3258	129	20	′′𝑢𝑘	′′𝑢𝑘	PROPN
easat-3258	129	21	′′	′′	PROPN
easat-3258	129	22	)	)	PUNCT
easat-3258	129	23	∈	∈	PROPN
easat-3258	129	24	𝐸′′	𝐸′′	NOUN
easat-3258	129	25	and	and	CCONJ
easat-3258	129	26	𝑢𝑖	𝑢𝑖	ADP
easat-3258	129	27	′	′	NUM
easat-3258	129	28	=	=	PUNCT
easat-3258	129	29	𝑢𝑗	𝑢𝑗	PROPN
easat-3258	129	30	′	′	NOUN
easat-3258	129	31	,	,	PUNCT
easat-3258	129	32	𝑢𝑖	𝑢𝑖	VERB
easat-3258	129	33	′′	′′	PROPN
easat-3258	129	34	=	=	PROPN
easat-3258	129	35	𝑢𝑗′′	𝑢𝑗′′	PROPN
easat-3258	129	36	=	=	SYM
easat-3258	129	37	∑	∑	PROPN
easat-3258	129	38	𝛾′(𝑢𝑖	𝛾′(𝑢𝑖	PROPN
easat-3258	129	39	′𝑢𝑘	′𝑢𝑘	NOUN
easat-3258	129	40	′	′	NUM
easat-3258	129	41	)	)	PUNCT
easat-3258	130	1	+	+	CCONJ
easat-3258	130	2	∑	∑	PROPN
easat-3258	130	3	𝛾′(𝑢𝑖	𝛾′(𝑢𝑖	NOUN
easat-3258	130	4	′	′	NOUN
easat-3258	130	5	)	)	PUNCT
easat-3258	131	1	+	+	CCONJ
easat-3258	131	2	𝛾∗(𝑢𝑖	𝛾∗(𝑢𝑖	PROPN
easat-3258	131	3	′	′	NOUN
easat-3258	131	4	,	,	PUNCT
easat-3258	131	5	𝑢𝑗	𝑢𝑗	X
easat-3258	131	6	′′	′′	PROPN
easat-3258	131	7	)	)	PUNCT
easat-3258	131	8	5799	5799	NUM
easat-3258	131	9	edelweiss	edelweiss	PROPN
easat-3258	131	10	applied	apply	VERB
easat-3258	131	11	science	science	NOUN
easat-3258	131	12	and	and	CCONJ
easat-3258	131	13	technology	technology	NOUN
easat-3258	131	14	issn	issn	PROPN
easat-3258	131	15	:	:	PUNCT
easat-3258	131	16	2576	2576	NUM
easat-3258	131	17	-	-	SYM
easat-3258	131	18	8484	8484	NUM
easat-3258	131	19	vol	vol	NOUN
easat-3258	131	20	.	.	PROPN
easat-3258	131	21	8	8	NUM
easat-3258	131	22	,	,	PUNCT
easat-3258	131	23	no	no	INTJ
easat-3258	131	24	.	.	NOUN
easat-3258	131	25	6	6	NUM
easat-3258	131	26	:	:	PUNCT
easat-3258	131	27	5789	5789	NUM
easat-3258	131	28	-	-	SYM
easat-3258	131	29	5799	5799	NUM
easat-3258	131	30	,	,	PUNCT
easat-3258	131	31	2024	2024	NUM
easat-3258	131	32	doi	doi	NOUN
easat-3258	131	33	:	:	PUNCT
easat-3258	131	34	10.55214/25768484.v8i6.3258	10.55214/25768484.v8i6.3258	NUM
easat-3258	131	35	©	©	PROPN
easat-3258	131	36	2024	2024	NUM
easat-3258	131	37	by	by	ADP
easat-3258	131	38	the	the	DET
easat-3258	131	39	authors	author	NOUN
easat-3258	131	40	;	;	PUNCT
easat-3258	131	41	licensee	licensee	NOUN
easat-3258	131	42	learning	learning	NOUN
easat-3258	131	43	gate	gate	NOUN
easat-3258	131	44	=	=	SYM
easat-3258	131	45	∑	∑	PUNCT
easat-3258	131	46	𝛾′(𝑢𝑖	𝛾′(𝑢𝑖	PROPN
easat-3258	131	47	′𝑢𝑘	′𝑢𝑘	NOUN
easat-3258	131	48	′	′	NUM
easat-3258	131	49	)	)	PUNCT
easat-3258	132	1	+	+	CCONJ
easat-3258	132	2	∑	∑	PROPN
easat-3258	132	3	𝛾′(𝑢𝑖	𝛾′(𝑢𝑖	NOUN
easat-3258	132	4	′	′	NOUN
easat-3258	132	5	)	)	PUNCT
easat-3258	133	1	+	+	CCONJ
easat-3258	133	2	min{𝜇′(𝑢𝑖	min{𝜇′(𝑢𝑖	PROPN
easat-3258	133	3	′	′	NUM
easat-3258	133	4	)	)	PUNCT
easat-3258	133	5	,	,	PUNCT
easat-3258	133	6	𝜇′′(𝑢𝑗	𝜇′′(𝑢𝑗	VERB
easat-3258	133	7	′′	′′	PROPN
easat-3258	133	8	)	)	PUNCT
easat-3258	133	9	}	}	PUNCT
easat-3258	133	10	=	=	SYM
easat-3258	133	11	𝑛0(𝑢𝑗	𝑛0(𝑢𝑗	NUM
easat-3258	133	12	′′	′′	PROPN
easat-3258	133	13	)	)	PUNCT
easat-3258	133	14	𝛾′(𝑢𝑖	𝛾′(𝑢𝑖	NOUN
easat-3258	133	15	′	′	NOUN
easat-3258	133	16	)	)	PUNCT
easat-3258	134	1	+	+	CCONJ
easat-3258	134	2	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾′(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾′(𝑢𝑖	CCONJ
easat-3258	134	3	′	′	NOUN
easat-3258	134	4	)	)	PUNCT
easat-3258	134	5	hence	hence	ADV
easat-3258	134	6	𝑛0(𝑢𝑗	𝑛0(𝑢𝑗	NUM
easat-3258	134	7	′′	′′	PROPN
easat-3258	134	8	)	)	PUNCT
easat-3258	134	9	is	be	AUX
easat-3258	134	10	the	the	DET
easat-3258	134	11	number	number	NOUN
easat-3258	134	12	of	of	ADP
easat-3258	134	13	edges	edge	NOUN
easat-3258	134	14	incident	incident	NOUN
easat-3258	134	15	at	at	ADP
easat-3258	134	16	𝑢𝑗	𝑢𝑗	NOUN
easat-3258	134	17	′′	′′	PROPN
easat-3258	134	18	in	in	ADP
easat-3258	134	19	𝐺2(𝑉′′	𝐺2(𝑉′′	NOUN
easat-3258	134	20	,	,	PUNCT
easat-3258	134	21	𝐸′′	𝐸′′	ADJ
easat-3258	134	22	,	,	PUNCT
easat-3258	134	23	𝜇′′	𝜇′′	NOUN
easat-3258	134	24	,	,	PUNCT
easat-3258	134	25	𝛾′′	𝛾′′	NOUN
easat-3258	134	26	)	)	PUNCT
easat-3258	134	27	constant	constant	ADJ
easat-3258	134	28	if	if	SCONJ
easat-3258	134	29	graphs	graph	NOUN
easat-3258	134	30	.	.	PUNCT
easat-3258	135	1	theorem	theorem	VERB
easat-3258	135	2	3.10	3.10	NUM
easat-3258	135	3	if	if	SCONJ
easat-3258	135	4	𝐺1(𝑉′	𝐺1(𝑉′	ADV
easat-3258	135	5	,	,	PUNCT
easat-3258	135	6	𝐸′	𝐸′	NOUN
easat-3258	135	7	,	,	PUNCT
easat-3258	135	8	𝜇′	𝜇′	NOUN
easat-3258	135	9	,	,	PUNCT
easat-3258	135	10	𝛾′	𝛾′	NUM
easat-3258	135	11	)	)	PUNCT
easat-3258	135	12	and	and	CCONJ
easat-3258	135	13	𝐺2(𝑉′′	𝐺2(𝑉′′	NOUN
easat-3258	135	14	,	,	PUNCT
easat-3258	135	15	𝐸′′	𝐸′′	ADJ
easat-3258	135	16	,	,	PUNCT
easat-3258	135	17	𝜇′′	𝜇′′	NOUN
easat-3258	135	18	,	,	PUNCT
easat-3258	135	19	𝛾′′	𝛾′′	PROPN
easat-3258	135	20	)	)	PUNCT
easat-3258	135	21	are	be	AUX
easat-3258	135	22	two	two	NUM
easat-3258	135	23	constant	constant	ADJ
easat-3258	135	24	if	if	SCONJ
easat-3258	135	25	graphs	graph	NOUN
easat-3258	135	26	such	such	ADJ
easat-3258	135	27	that	that	DET
easat-3258	135	28	𝜇′′(𝑢𝑖	𝜇′′(𝑢𝑖	NOUN
easat-3258	135	29	′′	′′	NOUN
easat-3258	135	30	)	)	PUNCT
easat-3258	135	31	≤	≤	NUM
easat-3258	135	32	𝜇′(𝑢𝑗	𝜇′(𝑢𝑗	VERB
easat-3258	135	33	′𝑢𝑘	′𝑢𝑘	NOUN
easat-3258	135	34	′	′	NUM
easat-3258	135	35	)	)	PUNCT
easat-3258	135	36	,	,	PUNCT
easat-3258	135	37	𝜇′′(𝑢𝑖	𝜇′′(𝑢𝑖	NOUN
easat-3258	135	38	′′𝑢𝑗	′′𝑢𝑗	PROPN
easat-3258	135	39	′′	′′	PROPN
easat-3258	135	40	)	)	PUNCT
easat-3258	135	41	≤	≤	PROPN
easat-3258	135	42	𝜇′(𝑢𝑘	𝜇′(𝑢𝑘	PROPN
easat-3258	135	43	′	′	NOUN
easat-3258	135	44	)	)	PUNCT
easat-3258	135	45	and	and	CCONJ
easat-3258	135	46	𝛾′′(𝑢𝑖	𝛾′′(𝑢𝑖	PROPN
easat-3258	135	47	′′	′′	PROPN
easat-3258	135	48	)	)	PUNCT
easat-3258	135	49	≥	≥	PROPN
easat-3258	135	50	𝛾′(𝑢𝑗	𝛾′(𝑢𝑗	PROPN
easat-3258	135	51	′𝑢𝑘	′𝑢𝑘	NOUN
easat-3258	135	52	′	′	NUM
easat-3258	135	53	)	)	PUNCT
easat-3258	135	54	,	,	PUNCT
easat-3258	135	55	𝛾′′	𝛾′′	NOUN
easat-3258	135	56	(	(	PUNCT
easat-3258	135	57	𝑢𝑖	𝑢𝑖	X
easat-3258	135	58	′′𝑢𝑗	′′𝑢𝑗	PROPN
easat-3258	135	59	′′	′′	PROPN
easat-3258	135	60	)	)	PUNCT
easat-3258	135	61	≥	≥	NOUN
easat-3258	135	62	𝛾′(𝑢𝑘	𝛾′(𝑢𝑘	PROPN
easat-3258	135	63	′	′	NOUN
easat-3258	135	64	)	)	PUNCT
easat-3258	135	65	with	with	ADP
easat-3258	135	66	second	second	ADJ
easat-3258	135	67	constant	constant	ADJ
easat-3258	135	68	if	if	SCONJ
easat-3258	135	69	graph	graph	NOUN
easat-3258	135	70	is	be	AUX
easat-3258	135	71	(	(	PUNCT
easat-3258	135	72	𝐶1	𝐶1	NOUN
easat-3258	135	73	∗	∗	NOUN
easat-3258	135	74	,	,	PUNCT
easat-3258	135	75	𝐶2	𝐶2	ADJ
easat-3258	135	76	∗	∗	NOUN
easat-3258	135	77	)	)	PUNCT
easat-3258	135	78	then	then	ADV
easat-3258	135	79	their	their	PRON
easat-3258	135	80	maximal	maximal	ADJ
easat-3258	135	81	product	product	NOUN
easat-3258	135	82	has	have	VERB
easat-3258	135	83	the	the	DET
easat-3258	135	84	total	total	ADJ
easat-3258	135	85	degree	degree	NOUN
easat-3258	135	86	as	as	ADP
easat-3258	135	87	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇∗(𝑢𝑖	PROPN
easat-3258	135	88	′	′	NOUN
easat-3258	135	89	,	,	PUNCT
easat-3258	135	90	𝑢𝑗	𝑢𝑗	X
easat-3258	135	91	′′	′′	PROPN
easat-3258	135	92	)	)	PUNCT
easat-3258	135	93	=	=	SYM
easat-3258	135	94	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇′(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝜇′(𝑢𝑖	NUM
easat-3258	135	95	′	′	NUM
easat-3258	135	96	)	)	PUNCT
easat-3258	136	1	+	+	NUM
easat-3258	136	2	𝑛0(𝑢𝑗	𝑛0(𝑢𝑗	NUM
easat-3258	136	3	′′)𝐶1	′′)𝐶1	NOUN
easat-3258	136	4	∗	∗	NOUN
easat-3258	136	5	and	and	CCONJ
easat-3258	136	6	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾∗(𝑢𝑖	PROPN
easat-3258	136	7	′	′	NOUN
easat-3258	136	8	,	,	PUNCT
easat-3258	136	9	𝑢𝑗	𝑢𝑗	X
easat-3258	136	10	′′	′′	PROPN
easat-3258	136	11	)	)	PUNCT
easat-3258	136	12	=	=	SYM
easat-3258	136	13	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾′(𝑢𝑖	𝑡𝑜𝑡𝑎𝑙𝑑𝑒𝑔𝛾′(𝑢𝑖	PROPN
easat-3258	136	14	′	′	NOUN
easat-3258	136	15	)	)	PUNCT
easat-3258	137	1	+	+	NUM
easat-3258	137	2	𝑛0(𝑢𝑗	𝑛0(𝑢𝑗	NUM
easat-3258	137	3	′′)𝐶2	′′)𝐶2	NOUN
easat-3258	137	4	∗	∗	NOUN
easat-3258	137	5	4	4	NUM
easat-3258	137	6	.	.	PUNCT
easat-3258	137	7	conclusion	conclusion	NOUN
easat-3258	137	8	the	the	DET
easat-3258	137	9	total	total	ADJ
easat-3258	137	10	degree	degree	NOUN
easat-3258	137	11	of	of	ADP
easat-3258	137	12	the	the	DET
easat-3258	137	13	vertices	vertex	NOUN
easat-3258	137	14	of	of	ADP
easat-3258	137	15	the	the	DET
easat-3258	137	16	maximal	maximal	ADJ
easat-3258	137	17	product	product	NOUN
easat-3258	137	18	of	of	ADP
easat-3258	137	19	two	two	NUM
easat-3258	137	20	constant	constant	ADJ
easat-3258	137	21	if	if	SCONJ
easat-3258	137	22	graphs	graph	NOUN
easat-3258	137	23	has	have	AUX
easat-3258	137	24	been	be	AUX
easat-3258	137	25	explained	explain	VERB
easat-3258	137	26	with	with	ADP
easat-3258	137	27	definitions	definition	NOUN
easat-3258	137	28	,	,	PUNCT
easat-3258	137	29	examples	example	NOUN
easat-3258	137	30	and	and	CCONJ
easat-3258	137	31	theorems	theorem	NOUN
easat-3258	137	32	.	.	PUNCT
easat-3258	138	1	also	also	ADV
easat-3258	138	2	,	,	PUNCT
easat-3258	138	3	theorems	theorem	NOUN
easat-3258	138	4	on	on	ADP
easat-3258	138	5	different	different	ADJ
easat-3258	138	6	conditions	condition	NOUN
easat-3258	138	7	related	relate	VERB
easat-3258	138	8	to	to	ADP
easat-3258	138	9	two	two	NUM
easat-3258	138	10	different	different	ADJ
easat-3258	138	11	constant	constant	ADJ
easat-3258	138	12	if	if	SCONJ
easat-3258	138	13	graphs	graph	NOUN
easat-3258	138	14	on	on	ADP
easat-3258	138	15	membership	membership	NOUN
easat-3258	138	16	and	and	CCONJ
easat-3258	138	17	non	non	ADJ
easat-3258	138	18	membership	membership	NOUN
easat-3258	138	19	values	value	NOUN
easat-3258	138	20	are	be	AUX
easat-3258	138	21	proved	prove	VERB
easat-3258	138	22	explicitly	explicitly	ADV
easat-3258	138	23	.	.	PUNCT
easat-3258	139	1	copyright	copyright	NOUN
easat-3258	139	2	:	:	PUNCT
easat-3258	139	3	©	©	PROPN
easat-3258	139	4	2024	2024	NUM
easat-3258	139	5	by	by	ADP
easat-3258	139	6	the	the	DET
easat-3258	139	7	authors	author	NOUN
easat-3258	139	8	.	.	PUNCT
easat-3258	140	1	this	this	DET
easat-3258	140	2	article	article	NOUN
easat-3258	140	3	is	be	AUX
easat-3258	140	4	an	an	DET
easat-3258	140	5	open	open	ADJ
easat-3258	140	6	access	access	NOUN
easat-3258	140	7	article	article	NOUN
easat-3258	140	8	distributed	distribute	VERB
easat-3258	140	9	under	under	ADP
easat-3258	140	10	the	the	DET
easat-3258	140	11	terms	term	NOUN
easat-3258	140	12	and	and	CCONJ
easat-3258	140	13	conditions	condition	NOUN
easat-3258	140	14	of	of	ADP
easat-3258	140	15	the	the	DET
easat-3258	140	16	creative	creative	ADJ
easat-3258	140	17	commons	common	NOUN
easat-3258	140	18	attribution	attribution	NOUN
easat-3258	140	19	(	(	PUNCT
easat-3258	140	20	cc	cc	NOUN
easat-3258	140	21	by	by	ADP
easat-3258	140	22	)	)	PUNCT
easat-3258	140	23	license	license	NOUN
easat-3258	140	24	(	(	PUNCT
easat-3258	140	25	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-3258	140	26	)	)	PUNCT
easat-3258	140	27	.	.	PUNCT
easat-3258	141	1	references	reference	NOUN
easat-3258	141	2	[	[	X
easat-3258	141	3	1	1	NUM
easat-3258	141	4	]	]	PUNCT
easat-3258	141	5	atanassov	atanassov	NOUN
easat-3258	141	6	,	,	PUNCT
easat-3258	141	7	k.	k.	PROPN
easat-3258	141	8	t.	t.	PROPN
easat-3258	141	9	(	(	PUNCT
easat-3258	141	10	1986	1986	NUM
easat-3258	141	11	)	)	PUNCT
easat-3258	141	12	.	.	PUNCT
easat-3258	142	1	intuitionistic	intuitionistic	ADJ
easat-3258	142	2	fuzzy	fuzzy	ADJ
easat-3258	142	3	sets	set	NOUN
easat-3258	142	4	.	.	PUNCT
easat-3258	143	1	fuzzy	fuzzy	ADJ
easat-3258	143	2	sets	set	NOUN
easat-3258	143	3	and	and	CCONJ
easat-3258	143	4	systems	system	NOUN
easat-3258	143	5	,	,	PUNCT
easat-3258	143	6	20(1	20(1	NUM
easat-3258	143	7	)	)	PUNCT
easat-3258	143	8	,	,	PUNCT
easat-3258	143	9	87	87	NUM
easat-3258	143	10	-	-	SYM
easat-3258	143	11	96	96	NUM
easat-3258	143	12	.	.	PUNCT
easat-3258	144	1	[	[	X
easat-3258	144	2	2	2	NUM
easat-3258	144	3	]	]	PUNCT
easat-3258	144	4	atanassov	atanassov	NOUN
easat-3258	144	5	,	,	PUNCT
easat-3258	144	6	k.	k.	PROPN
easat-3258	144	7	t.	t.	PROPN
easat-3258	144	8	(	(	PUNCT
easat-3258	144	9	1999	1999	NUM
easat-3258	144	10	)	)	PUNCT
easat-3258	144	11	.	.	PUNCT
easat-3258	145	1	intuitionistic	intuitionistic	ADJ
easat-3258	145	2	fuzzy	fuzzy	ADJ
easat-3258	145	3	sets	set	NOUN
easat-3258	145	4	.	.	PUNCT
easat-3258	146	1	in	in	ADP
easat-3258	146	2	intuitionistic	intuitionistic	ADJ
easat-3258	146	3	fuzzy	fuzzy	ADJ
easat-3258	146	4	sets	set	NOUN
easat-3258	146	5	(	(	PUNCT
easat-3258	146	6	pp.1	pp.1	NOUN
easat-3258	146	7	-	-	PUNCT
easat-3258	146	8	137	137	NUM
easat-3258	146	9	)	)	PUNCT
easat-3258	146	10	.	.	PUNCT
easat-3258	147	1	physica	physica	PROPN
easat-3258	147	2	-	-	PUNCT
easat-3258	147	3	verlag	verlag	PROPN
easat-3258	147	4	hd	hd	PROPN
easat-3258	147	5	.	.	PUNCT
easat-3258	148	1	[	[	X
easat-3258	148	2	3	3	X
easat-3258	148	3	]	]	PUNCT
easat-3258	148	4	atanassov.k	atanassov.k	PROPN
easat-3258	148	5	&	&	CCONJ
easat-3258	148	6	shannon	shannon	PROPN
easat-3258	148	7	.	.	PUNCT
easat-3258	149	1	a	a	DET
easat-3258	149	2	,	,	PUNCT
easat-3258	149	3	on	on	ADP
easat-3258	149	4	a	a	DET
easat-3258	149	5	generalisation	generalisation	NOUN
easat-3258	149	6	of	of	ADP
easat-3258	149	7	intuitionistic	intuitionistic	ADJ
easat-3258	149	8	fuzzy	fuzzy	ADJ
easat-3258	149	9	graph	graph	NOUN
easat-3258	149	10	,	,	PUNCT
easat-3258	149	11	notes	note	NOUN
easat-3258	149	12	on	on	ADP
easat-3258	149	13	intuitionistic	intuitionistic	ADJ
easat-3258	149	14	fuzzy	fuzzy	ADJ
easat-3258	149	15	sets	set	NOUN
easat-3258	149	16	,	,	PUNCT
easat-3258	149	17	8	8	NUM
easat-3258	149	18	(	(	PUNCT
easat-3258	149	19	2002	2002	NUM
easat-3258	149	20	)	)	PUNCT
easat-3258	149	21	,	,	PUNCT
easat-3258	149	22	7378	7378	NUM
easat-3258	150	1	[	[	X
easat-3258	150	2	4	4	X
easat-3258	150	3	]	]	X
easat-3258	150	4	karunambigai	karunambigai	PROPN
easat-3258	150	5	.	.	PROPN
easat-3258	150	6	m.	m.	PROPN
easat-3258	150	7	g	g	PROPN
easat-3258	150	8	&	&	CCONJ
easat-3258	150	9	parvathi	parvathi	PROPN
easat-3258	150	10	.	.	PUNCT
easat-3258	151	1	r	r	NOUN
easat-3258	151	2	(	(	PUNCT
easat-3258	151	3	2006	2006	NUM
easat-3258	151	4	)	)	PUNCT
easat-3258	151	5	,	,	PUNCT
easat-3258	151	6	intuitionistic	intuitionistic	ADJ
easat-3258	151	7	fuzzy	fuzzy	ADJ
easat-3258	151	8	graphs	graph	NOUN
easat-3258	151	9	,	,	PUNCT
easat-3258	151	10	proceedings	proceeding	NOUN
easat-3258	151	11	of	of	ADP
easat-3258	151	12	9th	9th	ADJ
easat-3258	151	13	fuzzy	fuzzy	ADJ
easat-3258	151	14	days	day	NOUN
easat-3258	151	15	international	international	ADJ
easat-3258	151	16	conference	conference	NOUN
easat-3258	151	17	on	on	ADP
easat-3258	151	18	computational	computational	ADJ
easat-3258	151	19	intelligence	intelligence	NOUN
easat-3258	151	20	,	,	PUNCT
easat-3258	151	21	theory	theory	NOUN
easat-3258	151	22	and	and	CCONJ
easat-3258	151	23	applications	application	NOUN
easat-3258	151	24	,	,	PUNCT
easat-3258	151	25	springer	springer	NOUN
easat-3258	151	26	-	-	PUNCT
easat-3258	151	27	verlage	verlage	NOUN
easat-3258	151	28	,	,	PUNCT
easat-3258	151	29	20	20	NUM
easat-3258	151	30	,	,	PUNCT
easat-3258	151	31	(	(	PUNCT
easat-3258	151	32	2006	2006	NUM
easat-3258	151	33	)	)	PUNCT
easat-3258	151	34	,	,	PUNCT
easat-3258	151	35	139150	139150	NUM
easat-3258	152	1	[	[	X
easat-3258	152	2	5	5	X
easat-3258	152	3	]	]	X
easat-3258	152	4	karunambigai	karunambigai	PROPN
easat-3258	152	5	.	.	PROPN
easat-3258	152	6	m.	m.	PROPN
easat-3258	152	7	g	g	PROPN
easat-3258	152	8	,	,	PUNCT
easat-3258	152	9	parvathi	parvathi	PROPN
easat-3258	152	10	.	.	PUNCT
easat-3258	153	1	r	r	NOUN
easat-3258	153	2	&	&	CCONJ
easat-3258	153	3	bhuvaneswari	bhuvaneswari	NOUN
easat-3258	153	4	.	.	PUNCT
easat-3258	154	1	r	r	NOUN
easat-3258	154	2	(	(	PUNCT
easat-3258	154	3	2011	2011	NUM
easat-3258	154	4	)	)	PUNCT
easat-3258	154	5	.	.	PUNCT
easat-3258	155	1	notes	note	NOUN
easat-3258	155	2	on	on	ADP
easat-3258	155	3	intuitionistic	intuitionistic	ADJ
easat-3258	155	4	fuzzy	fuzzy	ADJ
easat-3258	155	5	sets	set	NOUN
easat-3258	155	6	,	,	PUNCT
easat-3258	155	7	vol	vol	NOUN
easat-3258	155	8	17	17	NUM
easat-3258	155	9	,	,	PUNCT
easat-3258	155	10	37	37	NUM
easat-3258	155	11	-	-	SYM
easat-3258	155	12	47	47	NUM
easat-3258	156	1	[	[	X
easat-3258	156	2	6	6	NUM
easat-3258	156	3	]	]	PUNCT
easat-3258	156	4	mala	mala	X
easat-3258	156	5	.	.	PUNCT
easat-3258	157	1	s.k	s.k	PROPN
easat-3258	157	2	,	,	PUNCT
easat-3258	157	3	shanmugapriya	shanmugapriya	PROPN
easat-3258	157	4	.	.	PUNCT
easat-3258	158	1	s.s	s.s	PROPN
easat-3258	158	2	&	&	CCONJ
easat-3258	158	3	santhoshkumar	santhoshkumar	PROPN
easat-3258	158	4	.	.	PUNCT
easat-3258	159	1	s	s	X
easat-3258	159	2	,	,	PUNCT
easat-3258	159	3	intuitionistic	intuitionistic	ADJ
easat-3258	159	4	fuzzy	fuzzy	ADJ
easat-3258	159	5	ideals	ideal	NOUN
easat-3258	159	6	of	of	ADP
easat-3258	159	7	m𝛤groups	m𝛤groups	PROPN
easat-3258	159	8	in	in	ADP
easat-3258	159	9	near	near	ADJ
easat-3258	159	10	rings	ring	NOUN
easat-3258	159	11	as	as	ADP
easat-3258	159	12	maximal	maximal	ADJ
easat-3258	159	13	product	product	NOUN
easat-3258	159	14	of	of	ADP
easat-3258	159	15	graphs	graph	NOUN
easat-3258	159	16	,	,	PUNCT
easat-3258	159	17	turkish	turkish	ADJ
easat-3258	159	18	journal	journal	NOUN
easat-3258	159	19	of	of	ADP
easat-3258	159	20	computer	computer	NOUN
easat-3258	159	21	and	and	CCONJ
easat-3258	159	22	mathematics	mathematic	NOUN
easat-3258	159	23	education	education	NOUN
easat-3258	159	24	vol.12	vol.12	NOUN
easat-3258	159	25	no	no	NOUN
easat-3258	159	26	.	.	PROPN
easat-3258	159	27	7	7	NUM
easat-3258	159	28	(	(	PUNCT
easat-3258	159	29	2021	2021	NUM
easat-3258	159	30	)	)	PUNCT
easat-3258	159	31	,	,	PUNCT
easat-3258	159	32	17771782	17771782	NUM
easat-3258	160	1	[	[	X
easat-3258	160	2	7	7	NUM
easat-3258	160	3	]	]	X
easat-3258	160	4	parvathy	parvathy	NOUN
easat-3258	160	5	.	.	PUNCT
easat-3258	161	1	r	r	X
easat-3258	161	2	,	,	PUNCT
easat-3258	161	3	karunambigai	karunambigai	PROPN
easat-3258	161	4	&	&	CCONJ
easat-3258	161	5	atanassov	atanassov	PROPN
easat-3258	161	6	.	.	PUNCT
easat-3258	162	1	k	k	X
easat-3258	162	2	,	,	PUNCT
easat-3258	162	3	operations	operation	NOUN
easat-3258	162	4	on	on	ADP
easat-3258	162	5	intuitionistic	intuitionistic	ADJ
easat-3258	162	6	fuzzy	fuzzy	ADJ
easat-3258	162	7	graph	graph	NOUN
easat-3258	162	8	,	,	PUNCT
easat-3258	162	9	proceedings	proceeding	NOUN
easat-3258	162	10	of	of	ADP
easat-3258	162	11	ieee	ieee	PROPN
easat-3258	162	12	international	international	ADJ
easat-3258	162	13	conference	conference	NOUN
easat-3258	162	14	on	on	ADP
easat-3258	162	15	fuzzy	fuzzy	ADJ
easat-3258	162	16	systems	system	NOUN
easat-3258	162	17	,	,	PUNCT
easat-3258	162	18	august	august	PROPN
easat-3258	162	19	2009	2009	NUM
easat-3258	162	20	,	,	PUNCT
easat-3258	162	21	1396	1396	NUM
easat-3258	162	22	-	-	SYM
easat-3258	162	23	1401	1401	NUM
easat-3258	162	24	[	[	X
easat-3258	162	25	8	8	NUM
easat-3258	162	26	]	]	SYM
easat-3258	162	27	sitara	sitara	PROPN
easat-3258	162	28	,	,	PUNCT
easat-3258	162	29	muhannad	muhannad	PROPN
easat-3258	162	30	akram	akram	PROPN
easat-3258	162	31	,	,	PUNCT
easat-3258	162	32	and	and	CCONJ
easat-3258	162	33	muhammad	muhammad	PROPN
easat-3258	162	34	yusaf	yusaf	PROPN
easat-3258	162	35	,	,	PUNCT
easat-3258	162	36	fuzzy	fuzzy	ADJ
easat-3258	162	37	graph	graph	NOUN
easat-3258	162	38	structures	structure	NOUN
easat-3258	162	39	with	with	ADP
easat-3258	162	40	application	application	NOUN
easat-3258	162	41	,	,	PUNCT
easat-3258	162	42	mdpi	mdpi	PROPN
easat-3258	162	43	,	,	PUNCT
easat-3258	162	44	vol	vol	VERB
easat-3258	162	45	7	7	NUM
easat-3258	162	46	issue	issue	NOUN
easat-3258	162	47	1	1	NUM
easat-3258	162	48	,	,	PUNCT
easat-3258	162	49	1	1	NUM
easat-3258	162	50	-	-	SYM
easat-3258	162	51	22	22	NUM
easat-3258	163	1	[	[	X
easat-3258	163	2	9	9	NUM
easat-3258	163	3	]	]	SYM
easat-3258	163	4	zadeh	zadeh	PROPN
easat-3258	163	5	,	,	PUNCT
easat-3258	163	6	l.	l.	PROPN
easat-3258	163	7	a.	a.	PROPN
easat-3258	163	8	(	(	PUNCT
easat-3258	163	9	1965	1965	NUM
easat-3258	163	10	)	)	PUNCT
easat-3258	163	11	.	.	PUNCT
easat-3258	164	1	fuzzy	fuzzy	ADJ
easat-3258	164	2	sets	set	NOUN
easat-3258	164	3	,	,	PUNCT
easat-3258	164	4	information	information	NOUN
easat-3258	164	5	science	science	NOUN
easat-3258	164	6	,	,	PUNCT
easat-3258	164	7	8	8	NUM
easat-3258	164	8	(	(	PUNCT
easat-3258	164	9	1965	1965	NUM
easat-3258	164	10	)	)	PUNCT
easat-3258	164	11	,	,	PUNCT
easat-3258	164	12	338	338	NUM
easat-3258	164	13	353	353	NUM
easat-3258	164	14	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	NOUN