id	sid	tid	token	lemma	pos
iajs-2009	1	1	microsoft	microsoft	PROPN
iajs-2009	1	2	word	word	PROPN
iajs-2009	1	3	160	160	NUM
iajs-2009	1	4	-	-	SYM
iajs-2009	1	5	170	170	NUM
iajs-2009	1	6	mathematics	mathematic	NOUN
iajs-2009	1	7	|	|	ADV
iajs-2009	1	8	160	160	NUM
iajs-2009	1	9	ibn	ibn	PROPN
iajs-2009	1	10	al	al	PROPN
iajs-2009	1	11	-	-	PUNCT
iajs-2009	1	12	haitham	haitham	PROPN
iajs-2009	1	13	jour	jour	X
iajs-2009	1	14	.	.	PROPN
iajs-2009	2	1	for	for	ADP
iajs-2009	2	2	pure	pure	ADJ
iajs-2009	2	3	&	&	CCONJ
iajs-2009	2	4	appl	appl	PROPN
iajs-2009	2	5	.	.	PUNCT
iajs-2009	3	1	sci	sci	PROPN
iajs-2009	3	2	.	.	PROPN
iajs-2009	3	3	ihjpas	ihjpas	PROPN
iajs-2009	3	4	https://doi.org/10.30526/31.3.2009	https://doi.org/10.30526/31.3.2009	PROPN
iajs-2009	3	5	vol	vol	NOUN
iajs-2009	3	6	.	.	PROPN
iajs-2009	4	1	31	31	NUM
iajs-2009	5	1	(	(	PUNCT
iajs-2009	5	2	3	3	NUM
iajs-2009	5	3	)	)	SYM
iajs-2009	5	4	2018	2018	NUM
iajs-2009	5	5	study	study	NOUN
iajs-2009	5	6	of	of	ADP
iajs-2009	5	7	two	two	NUM
iajs-2009	5	8	types	type	NOUN
iajs-2009	5	9	finite	finite	VERB
iajs-2009	5	10	graphs	graph	NOUN
iajs-2009	5	11	in	in	ADP
iajs-2009	5	12	ku	ku	NOUN
iajs-2009	5	13	-	-	PUNCT
iajs-2009	5	14	semigroups	semigroups	PROPN
iajs-2009	5	15	elaf	elaf	PROPN
iajs-2009	5	16	r.	r.	PROPN
iajs-2009	5	17	hasan	hasan	PROPN
iajs-2009	5	18	math88012@gmail.com	math88012@gmail.com	PROPN
iajs-2009	6	1	fatema	fatema	PROPN
iajs-2009	6	2	f.	f.	PROPN
iajs-2009	6	3	kareem	kareem	PROPN
iajs-2009	6	4	fa_sa20072000@yahoo.com	fa_sa20072000@yahoo.com	PROPN
iajs-2009	6	5	department	department	PROPN
iajs-2009	6	6	of	of	ADP
iajs-2009	6	7	mathematics	mathematics	PROPN
iajs-2009	6	8	,	,	PUNCT
iajs-2009	6	9	college	college	NOUN
iajs-2009	6	10	of	of	ADP
iajs-2009	6	11	education	education	NOUN
iajs-2009	6	12	for	for	ADP
iajs-2009	6	13	pure	pure	ADJ
iajs-2009	6	14	science	science	NOUN
iajs-2009	6	15	ibn	ibn	PROPN
iajs-2009	6	16	al	al	PROPN
iajs-2009	6	17	-	-	PUNCT
iajs-2009	6	18	haitham	haitham	PROPN
iajs-2009	6	19	,	,	PUNCT
iajs-2009	6	20	university	university	PROPN
iajs-2009	6	21	of	of	ADP
iajs-2009	6	22	baghdad	baghdad	PROPN
iajs-2009	6	23	,	,	PUNCT
iajs-2009	6	24	baghdad	baghdad	PROPN
iajs-2009	6	25	,	,	PUNCT
iajs-2009	6	26	iraq	iraq	PROPN
iajs-2009	6	27	.	.	PUNCT
iajs-2009	7	1	article	article	NOUN
iajs-2009	7	2	history	history	NOUN
iajs-2009	7	3	:	:	PUNCT
iajs-2009	7	4	received	receive	VERB
iajs-2009	7	5	25	25	NUM
iajs-2009	7	6	june	june	PROPN
iajs-2009	7	7	2018	2018	NUM
iajs-2009	7	8	,	,	PUNCT
iajs-2009	7	9	accepted	accept	VERB
iajs-2009	7	10	18	18	NUM
iajs-2009	7	11	july	july	PROPN
iajs-2009	7	12	2018	2018	NUM
iajs-2009	7	13	,	,	PUNCT
iajs-2009	7	14	published	publish	VERB
iajs-2009	7	15	december	december	PROPN
iajs-2009	7	16	2018	2018	NUM
iajs-2009	7	17	abstract	abstract	ADV
iajs-2009	7	18	in	in	ADP
iajs-2009	7	19	this	this	DET
iajs-2009	7	20	ˑresearch	ˑresearch	NOUN
iajs-2009	7	21	,	,	PUNCT
iajs-2009	7	22	we	we	PRON
iajs-2009	7	23	present	present	VERB
iajs-2009	7	24	theˑ	theˑ	NOUN
iajs-2009	7	25	notion	notion	NOUN
iajs-2009	7	26	of	of	ADP
iajs-2009	7	27	the	the	DET
iajs-2009	7	28	ˑgraph	ˑgraph	NOUN
iajs-2009	7	29	for	for	ADP
iajs-2009	7	30	a	a	DET
iajs-2009	7	31	ku	ku	PROPN
iajs-2009	7	32	-	-	PUNCT
iajs-2009	7	33	semigroup	semigroup	NOUN
iajs-2009	7	34	x	x	X
iajs-2009	7	35	as	as	SCONJ
iajs-2009	7	36	theˑ	theˑ	NOUN
iajs-2009	7	37	undirected	undirected	ADJ
iajs-2009	7	38	simple	simple	ADJ
iajs-2009	7	39	graphˑ	graphˑ	NOUN
iajs-2009	7	40	with	with	ADP
iajs-2009	7	41	the	the	DET
iajs-2009	7	42	vertices	vertex	NOUN
iajs-2009	7	43	are	be	AUX
iajs-2009	7	44	the	the	DET
iajs-2009	7	45	elementsˑ	elementsˑ	NOUN
iajs-2009	7	46	of	of	ADP
iajs-2009	7	47	x	x	PUNCT
iajs-2009	7	48	and	and	CCONJ
iajs-2009	7	49	weˑˑstudy	weˑˑstudy	VERB
iajs-2009	7	50	the	the	DET
iajs-2009	7	51	ˑgraph	ˑgraph	NOUN
iajs-2009	7	52	ofˑ	ofˑ	PRON
iajs-2009	7	53	equivalence	equivalence	NOUN
iajs-2009	7	54	classes	class	NOUN
iajs-2009	7	55	ofˑ	ofˑ	PRON
iajs-2009	7	56	x	x	PUNCT
iajs-2009	7	57	which	which	PRON
iajs-2009	7	58	is	be	AUX
iajs-2009	7	59	determinedˑ	determinedˑ	VERB
iajs-2009	7	60	by	by	ADP
iajs-2009	7	61	theˑ	theˑ	NOUN
iajs-2009	7	62	definition	definition	NOUN
iajs-2009	7	63	equivalenceˑ	equivalenceˑ	VERB
iajs-2009	7	64	relation	relation	PROPN
iajs-2009	7	65	ofˑ	ofˑ	ADP
iajs-2009	7	66	these	these	DET
iajs-2009	7	67	verticesˑ	verticesˑ	NOUN
iajs-2009	7	68	,	,	PUNCT
iajs-2009	7	69	andˑ	andˑ	NOUN
iajs-2009	7	70	then	then	ADV
iajs-2009	7	71	some	some	DET
iajs-2009	7	72	related	related	ADJ
iajs-2009	7	73	ˑproperties	ˑpropertie	NOUN
iajs-2009	7	74	areˑ	areˑ	NOUN
iajs-2009	7	75	given	give	VERB
iajs-2009	7	76	.	.	PUNCT
iajs-2009	8	1	several	several	ADJ
iajs-2009	8	2	examples	example	NOUN
iajs-2009	8	3	are	be	AUX
iajs-2009	8	4	presented	present	VERB
iajs-2009	8	5	and	and	CCONJ
iajs-2009	8	6	some	some	DET
iajs-2009	8	7	theorems	theorem	NOUN
iajs-2009	8	8	are	be	AUX
iajs-2009	8	9	proved	prove	VERB
iajs-2009	8	10	.	.	PUNCT
iajs-2009	9	1	byˑ	byˑ	PROPN
iajs-2009	9	2	usingˑ	usingˑ	PROPN
iajs-2009	9	3	the	the	DET
iajs-2009	9	4	definitionˑ	definitionˑ	NOUN
iajs-2009	9	5	ofˑ	ofˑ	NOUN
iajs-2009	9	6	isomorphicˑ	isomorphicˑ	NOUN
iajs-2009	9	7	graph	graph	NOUN
iajs-2009	9	8	,	,	PUNCT
iajs-2009	9	9	ˑwe	ˑwe	PROPN
iajs-2009	9	10	showˑ	showˑ	NOUN
iajs-2009	9	11	thatˑ	thatˑ	NOUN
iajs-2009	9	12	the	the	DET
iajs-2009	9	13	graphˑ	graphˑ	NOUN
iajs-2009	9	14	of	of	ADP
iajs-2009	9	15	equivalence	equivalence	NOUN
iajs-2009	9	16	ˑclasses	ˑclasse	NOUN
iajs-2009	9	17	ˑand	ˑand	CCONJ
iajs-2009	9	18	the	the	DET
iajs-2009	9	19	ˑgraphˑofˑa	ˑgraphˑofˑa	PROPN
iajs-2009	9	20	ku	ku	PROPN
iajs-2009	9	21	-	-	PUNCT
iajs-2009	9	22	semigroup	semigroup	PROPN
iajs-2009	9	23	ˑ	ˑ	PROPN
iajs-2009	9	24	areˑ	areˑ	PROPN
iajs-2009	9	25	theˑ	theˑ	NOUN
iajs-2009	9	26	sameˑ	sameˑ	PROPN
iajs-2009	9	27	,	,	PUNCT
iajs-2009	9	28	in	in	ADP
iajs-2009	9	29	special	special	ADJ
iajs-2009	9	30	cases	case	NOUN
iajs-2009	9	31	.	.	PUNCT
iajs-2009	10	1	key	key	ADJ
iajs-2009	10	2	words	word	NOUN
iajs-2009	10	3	:	:	PUNCT
iajs-2009	10	4	ku	ku	PROPN
iajs-2009	10	5	-	-	PUNCT
iajs-2009	10	6	algebra	algebra	PROPN
iajs-2009	10	7	,	,	PUNCT
iajs-2009	10	8	ku	ku	PROPN
iajs-2009	10	9	-	-	PUNCT
iajs-2009	10	10	semigroup	semigroup	PROPN
iajs-2009	10	11	,	,	PUNCT
iajs-2009	10	12	graph	graph	NOUN
iajs-2009	10	13	,	,	PUNCT
iajs-2009	10	14	annihilator	annihilator	NOUN
iajs-2009	10	15	.	.	PUNCT
iajs-2009	11	1	1.introduction	1.introduction	NUM
iajs-2009	11	2	mathematicians	mathematician	NOUN
iajs-2009	11	3	prabpayak	prabpayak	NOUN
iajs-2009	11	4	andˑ	andˑ	NOUN
iajs-2009	11	5	leerawat	leerawat	NOUN
iajs-2009	12	1	[	[	X
iajs-2009	12	2	1	1	NUM
iajs-2009	12	3	,	,	PUNCT
iajs-2009	12	4	ˑ2	ˑ2	PROPN
iajs-2009	12	5	]	]	PUNCT
iajs-2009	12	6	constructed	construct	VERB
iajs-2009	12	7	algebraicˑ	algebraicˑ	ADJ
iajs-2009	12	8	structure	structure	NOUN
iajs-2009	12	9	whichˑ	whichˑ	VERB
iajs-2009	12	10	isˑ	isˑ	NOUN
iajs-2009	12	11	calledˑˑku	calledˑˑku	NOUN
iajs-2009	12	12	-	-	PUNCT
iajs-2009	12	13	algebra	algebra	NOUN
iajs-2009	13	1	and	and	CCONJ
iajs-2009	13	2	they	they	PRON
iajs-2009	13	3	ˑintroduced	ˑintroduce	VERB
iajs-2009	13	4	the	the	DET
iajs-2009	13	5	conceptˑ	conceptˑ	PROPN
iajs-2009	13	6	of	of	ADP
iajs-2009	13	7	ˑa	ˑa	PROPN
iajs-2009	13	8	homomorphism	homomorphism	PROPN
iajs-2009	13	9	of	of	ADP
iajs-2009	13	10	ˑku	ˑku	NOUN
iajs-2009	13	11	-	-	PUNCT
iajs-2009	13	12	algebra	algebra	NOUN
iajs-2009	13	13	.	.	PUNCT
iajs-2009	14	1	kareem	kareem	PROPN
iajs-2009	14	2	and	and	CCONJ
iajs-2009	14	3	ˑhasan	ˑhasan	VERB
iajs-2009	14	4	[	[	X
iajs-2009	14	5	3	3	X
iajs-2009	14	6	]	]	PUNCT
iajs-2009	14	7	introduced	introduce	VERB
iajs-2009	14	8	a	a	DET
iajs-2009	14	9	new	new	ADJ
iajs-2009	14	10	class	class	NOUN
iajs-2009	14	11	of	of	ADP
iajs-2009	14	12	algebras	algebras	PROPN
iajs-2009	14	13	related	relate	VERB
iajs-2009	14	14	to	to	ADP
iajs-2009	14	15	ku	ku	NOUN
iajs-2009	14	16	-	-	PUNCT
iajs-2009	14	17	algebras	algebras	PROPN
iajs-2009	14	18	and	and	CCONJ
iajs-2009	14	19	semigroups	semigroup	NOUN
iajs-2009	14	20	,	,	PUNCT
iajs-2009	14	21	called	call	VERB
iajs-2009	14	22	a	a	DET
iajs-2009	14	23	ku	ku	PROPN
iajs-2009	14	24	-	-	PUNCT
iajs-2009	14	25	semigroup	semigroup	PROPN
iajs-2009	14	26	.	.	PUNCT
iajs-2009	15	1	they	they	PRON
iajs-2009	15	2	defined	define	VERB
iajs-2009	15	3	some	some	DET
iajs-2009	15	4	types	type	NOUN
iajs-2009	15	5	of	of	ADP
iajs-2009	15	6	ideals	ideal	NOUN
iajs-2009	15	7	and	and	CCONJ
iajs-2009	15	8	discussed	discuss	VERB
iajs-2009	15	9	few	few	ADJ
iajs-2009	15	10	properties	property	NOUN
iajs-2009	15	11	.	.	PUNCT
iajs-2009	16	1	the	the	DET
iajs-2009	16	2	study	study	NOUN
iajs-2009	16	3	of	of	ADP
iajs-2009	16	4	graph	graph	NOUN
iajs-2009	16	5	theory	theory	NOUN
iajs-2009	16	6	and	and	CCONJ
iajs-2009	16	7	its	its	PRON
iajs-2009	16	8	properties	property	NOUN
iajs-2009	16	9	are	be	AUX
iajs-2009	16	10	topics	topic	NOUN
iajs-2009	16	11	of	of	ADP
iajs-2009	16	12	interest	interest	NOUN
iajs-2009	16	13	in	in	ADP
iajs-2009	16	14	algebraic	algebraic	ADJ
iajs-2009	16	15	structures	structure	NOUN
iajs-2009	16	16	.	.	PUNCT
iajs-2009	17	1	beck	beck	NOUN
iajs-2009	17	2	in	in	ADP
iajs-2009	17	3	[	[	X
iajs-2009	17	4	4	4	NUM
iajs-2009	17	5	]	]	PUNCT
iajs-2009	17	6	introduced	introduce	VERB
iajs-2009	17	7	the	the	DET
iajs-2009	17	8	graph	graph	NOUN
iajs-2009	17	9	of	of	ADP
iajs-2009	17	10	commutative	commutative	ADJ
iajs-2009	17	11	ring	ring	NOUN
iajs-2009	17	12	by	by	SCONJ
iajs-2009	17	13	studied	study	VERB
iajs-2009	17	14	the	the	DET
iajs-2009	17	15	ˑzerodivisor	ˑzerodivisor	NOUN
iajs-2009	17	16	graphs	graph	NOUN
iajs-2009	17	17	of	of	ADP
iajs-2009	17	18	thisˑ	thisˑ	NOUN
iajs-2009	17	19	ring	ring	NOUN
iajs-2009	17	20	.	.	PUNCT
iajs-2009	18	1	many	many	ADJ
iajs-2009	18	2	mathematicians	mathematician	NOUN
iajs-2009	18	3	studied	study	VERB
iajs-2009	18	4	a	a	DET
iajs-2009	18	5	graph	graph	NOUN
iajs-2009	18	6	of	of	ADP
iajs-2009	18	7	a	a	DET
iajs-2009	18	8	commutative	commutative	ADJ
iajs-2009	18	9	ring	ring	NOUN
iajs-2009	18	10	by	by	ADP
iajs-2009	18	11	different	different	ADJ
iajs-2009	18	12	ways	way	NOUN
iajs-2009	18	13	;	;	PUNCT
iajs-2009	18	14	see	see	VERB
iajs-2009	18	15	[	[	X
iajs-2009	18	16	510	510	NUM
iajs-2009	18	17	]	]	PUNCT
iajs-2009	18	18	.	.	PUNCT
iajs-2009	19	1	in	in	ADP
iajs-2009	19	2	[	[	X
iajs-2009	19	3	11	11	NUM
iajs-2009	19	4	]	]	PUNCT
iajs-2009	19	5	,	,	PUNCT
iajs-2009	19	6	jun	jun	PROPN
iajs-2009	19	7	and	and	CCONJ
iajs-2009	19	8	leeˑ	leeˑ	PROPN
iajs-2009	19	9	introduced	introduce	VERB
iajs-2009	19	10	theˑ	theˑ	NOUN
iajs-2009	19	11	concept	concept	NOUN
iajs-2009	19	12	of	of	ADP
iajs-2009	19	13	theˑ	theˑ	NOUN
iajs-2009	19	14	associated	associate	VERB
iajs-2009	19	15	graphˑ	graphˑ	NOUN
iajs-2009	19	16	of	of	ADP
iajs-2009	19	17	ˑbck	ˑbck	PROPN
iajs-2009	19	18	/	/	SYM
iajs-2009	19	19	bci	bci	NOUN
iajs-2009	19	20	-	-	ADJ
iajs-2009	19	21	algebra	algebra	NOUN
iajs-2009	19	22	andˑ	andˑ	NOUN
iajs-2009	19	23	they	they	PRON
iajs-2009	19	24	provedˑ	provedˑ	VERB
iajs-2009	19	25	that	that	SCONJ
iajs-2009	19	26	:	:	PUNCT
iajs-2009	19	27	if	if	SCONJ
iajs-2009	19	28	x	x	PRON
iajs-2009	19	29	ˑis	ˑi	VERB
iajs-2009	19	30	a	a	DET
iajs-2009	19	31	bck-ˑalgebra	bck-ˑalgebra	NOUN
iajs-2009	19	32	,	,	PUNCT
iajs-2009	19	33	ˑthen	ˑthen	SCONJ
iajs-2009	19	34	theˑ	theˑ	NOUN
iajs-2009	19	35	associatedˑ	associatedˑ	NOUN
iajs-2009	19	36	graph	graph	NOUN
iajs-2009	19	37	ofˑ	ofˑ	X
iajs-2009	19	38	x	x	SYM
iajs-2009	19	39	isˑ	isˑ	NOUN
iajs-2009	19	40	connected	connect	VERB
iajs-2009	19	41	but	but	CCONJ
iajs-2009	19	42	ˑif	ˑif	ADV
iajs-2009	20	1	x	x	PUNCT
iajs-2009	20	2	is	be	AUX
iajs-2009	20	3	a	a	DET
iajs-2009	20	4	bci	bci	NOUN
iajs-2009	20	5	-	-	NOUN
iajs-2009	20	6	algebra	algebra	NOUN
iajs-2009	20	7	,	,	PUNCT
iajs-2009	20	8	then	then	ADV
iajs-2009	20	9	it	it	PRON
iajs-2009	20	10	's	be	AUX
iajs-2009	20	11	not	not	PART
iajs-2009	20	12	connected	connect	VERB
iajs-2009	20	13	.	.	PUNCT
iajs-2009	21	1	zahiri	zahiri	NOUN
iajs-2009	21	2	and	and	CCONJ
iajs-2009	21	3	borzooei	borzooei	PROPN
iajs-2009	22	1	[	[	X
iajs-2009	22	2	12	12	NUM
iajs-2009	22	3	]	]	PUNCT
iajs-2009	22	4	introduced	introduce	VERB
iajs-2009	22	5	aˑnewˑgraph	aˑnewˑgraph	NOUN
iajs-2009	22	6	of	of	ADP
iajs-2009	22	7	a	a	DET
iajs-2009	22	8	bciˑ-algebraˑ	bciˑ-algebraˑ	ADJ
iajs-2009	22	9	x	x	PUNCT
iajs-2009	22	10	andˑ	andˑ	NOUN
iajs-2009	22	11	they	they	PRON
iajs-2009	22	12	definedˑ	definedˑ	VERB
iajs-2009	22	13	the	the	DET
iajs-2009	22	14	concept	concept	NOUN
iajs-2009	22	15	ofˑ	ofˑ	PRON
iajs-2009	22	16	a-ˑdivisor	a-ˑdivisor	NOUN
iajs-2009	22	17	of	of	ADP
iajs-2009	22	18	bci-ˑalgebraˑ	bci-ˑalgebraˑ	ADJ
iajs-2009	22	19	x	x	X
iajs-2009	22	20	.	.	PUNCT
iajs-2009	23	1	ˑmostafa	ˑmostafa	PROPN
iajs-2009	23	2	and	and	CCONJ
iajs-2009	23	3	kareem	kareem	X
iajs-2009	24	1	[	[	X
iajs-2009	24	2	13	13	NUM
iajs-2009	24	3	]	]	PUNCT
iajs-2009	24	4	introduced	introduce	VERB
iajs-2009	24	5	the	the	DET
iajs-2009	24	6	graphˑ	graphˑ	NOUN
iajs-2009	24	7	of	of	ADP
iajs-2009	24	8	aˑ	aˑ	ADP
iajs-2009	24	9	commutative	commutative	ADJ
iajs-2009	24	10	isˑ-algebra	isˑ-algebra	NOUN
iajs-2009	24	11	ˑx	ˑx	PROPN
iajs-2009	24	12	,	,	PUNCT
iajs-2009	24	13	denotedˑ	denotedˑ	VERB
iajs-2009	24	14	by	by	ADP
iajs-2009	24	15	(x	(x	PROPN
iajs-2009	24	16	)	)	PUNCT
iajs-2009	24	17	and	and	CCONJ
iajs-2009	24	18	studiedˑ	studiedˑ	VERB
iajs-2009	24	19	the	the	DET
iajs-2009	24	20	graph	graph	NOUN
iajs-2009	24	21	of	of	ADP
iajs-2009	24	22	ˑequivalenceˑ	ˑequivalenceˑ	NOUN
iajs-2009	24	23	classes	class	NOUN
iajs-2009	24	24	of	of	ADP
iajs-2009	24	25	x.	x.	NOUN
iajs-2009	24	26	in	in	ADP
iajs-2009	24	27	thisˑ	thisˑ	NOUN
iajs-2009	24	28	research	research	NOUN
iajs-2009	24	29	,	,	PUNCT
iajs-2009	24	30	we	we	PRON
iajs-2009	24	31	introduceˑ	introduceˑ	VERB
iajs-2009	24	32	the	the	DET
iajs-2009	24	33	idea	idea	NOUN
iajs-2009	24	34	ofˑ	ofˑ	NOUN
iajs-2009	24	35	graph	graph	NOUN
iajs-2009	24	36	for	for	ADP
iajs-2009	24	37	a	a	DET
iajs-2009	24	38	ku-ˑsemigroup	ku-ˑsemigroup	NOUN
iajs-2009	24	39	.	.	PUNCT
iajs-2009	25	1	we	we	PRON
iajs-2009	25	2	defineˑ	defineˑ	VERB
iajs-2009	25	3	the	the	DET
iajs-2009	25	4	graph	graph	NOUN
iajs-2009	25	5	as	as	ADP
iajs-2009	25	6	the	the	DET
iajs-2009	25	7	ˑundirected	ˑundirecte	VERB
iajs-2009	25	8	graph	graph	NOUN
iajs-2009	25	9	with	with	ADP
iajs-2009	25	10	ˑthe	ˑthe	DET
iajs-2009	25	11	vertices	vertex	NOUN
iajs-2009	25	12	are	be	AUX
iajs-2009	25	13	the	the	DET
iajs-2009	25	14	elements	element	NOUN
iajs-2009	25	15	ˑin	ˑin	VERB
iajs-2009	25	16	ku-ˑsemigroupˑ	ku-ˑsemigroupˑ	VERB
iajs-2009	25	17	x	x	SYM
iajs-2009	25	18	ˑ	ˑ	NOUN
iajs-2009	25	19	and	and	CCONJ
iajs-2009	25	20	forˑ	forˑ	VERB
iajs-2009	25	21	distinct	distinct	ADJ
iajs-2009	25	22	vertices	vertice	VERB
iajs-2009	26	1	ˑ	ˑ	NOUN
iajs-2009	26	2	x	x	NOUN
iajs-2009	26	3	andˑ	andˑ	NOUN
iajs-2009	26	4	y	y	PROPN
iajs-2009	26	5	ˑare	ˑare	VERB
iajs-2009	26	6	adjacentˑˑif	adjacentˑˑif	ADV
iajs-2009	26	7	and	and	CCONJ
iajs-2009	26	8	onlyˑ	onlyˑ	ADJ
iajs-2009	26	9	ifˑ	ifˑ	NOUN
iajs-2009	26	10	}	}	PUNCT
iajs-2009	26	11	0	0	NUM
iajs-2009	26	12	{	{	PUNCT
iajs-2009	26	13	}	}	PUNCT
iajs-2009	26	14	)	)	PUNCT
iajs-2009	26	15	,	,	PUNCT
iajs-2009	26	16	(	(	PUNCT
iajs-2009	26	17	{	{	PUNCT
iajs-2009	26	18	}	}	NUM
iajs-2009	26	19	)	)	PUNCT
iajs-2009	26	20	,	,	PUNCT
iajs-2009	26	21	(	(	PUNCT
iajs-2009	26	22	{	{	PUNCT
iajs-2009	26	23			NUM
iajs-2009	26	24	yxlyxr	yxlyxr	PROPN
iajs-2009	26	25	ˑ.ˑmoreoverˑ,ˑ	ˑ.ˑmoreoverˑ,ˑ	PROPN
iajs-2009	26	26	weˑ	weˑ	PROPN
iajs-2009	26	27	studyˑ	studyˑ	VERB
iajs-2009	26	28	the	the	DET
iajs-2009	26	29	other	other	ADJ
iajs-2009	26	30	graph	graph	NOUN
iajs-2009	26	31	namely	namely	ADV
iajs-2009	26	32	,	,	PUNCT
iajs-2009	26	33	graph	graph	NOUN
iajs-2009	26	34	ofˑˑequivalenceˑ	ofˑˑequivalenceˑ	ADJ
iajs-2009	26	35	classesˑ	classesˑ	NOUN
iajs-2009	26	36	of	of	ADP
iajs-2009	26	37	x	x	PROPN
iajs-2009	26	38	byˑ	byˑ	PROPN
iajs-2009	26	39	definition	definition	NOUN
iajs-2009	26	40	of	of	ADP
iajs-2009	26	41	equivalenceˑ	equivalenceˑ	ADJ
iajs-2009	26	42	relation	relation	PROPN
iajs-2009	26	43	ofˑ	ofˑ	PRON
iajs-2009	26	44	these	these	DET
iajs-2009	26	45	verticesˑ	verticesˑ	NOUN
iajs-2009	26	46	andˑ	andˑ	NOUN
iajs-2009	26	47	then	then	ADV
iajs-2009	26	48	some	some	DET
iajs-2009	26	49	related	related	ADJ
iajs-2009	26	50	ˑproperties	ˑpropertie	NOUN
iajs-2009	26	51	areˑ	areˑ	NOUN
iajs-2009	26	52	given	give	VERB
iajs-2009	26	53	.	.	PUNCT
iajs-2009	27	1	2.preliminaries	2.preliminaries	NUM
iajs-2009	27	2	inˑ	inˑ	NOUN
iajs-2009	27	3	this	this	DET
iajs-2009	27	4	section	section	NOUN
iajs-2009	27	5	,	,	PUNCT
iajs-2009	27	6	we	we	PRON
iajs-2009	27	7	present	present	VERB
iajs-2009	27	8	some	some	DET
iajs-2009	27	9	definitions	definition	NOUN
iajs-2009	27	10	and	and	CCONJ
iajs-2009	27	11	background	background	NOUN
iajs-2009	27	12	about	about	ADP
iajs-2009	27	13	a	a	DET
iajs-2009	27	14	ku	ku	NOUN
iajs-2009	27	15	-	-	PUNCT
iajs-2009	27	16	algebra	algebra	PROPN
iajs-2009	27	17	and	and	CCONJ
iajs-2009	27	18	kusemigroup	kusemigroup	NOUN
iajs-2009	27	19	.	.	PUNCT
iajs-2009	28	1	definition	definition	NOUN
iajs-2009	28	2	1[1	1[1	NUM
iajs-2009	28	3	-	-	SYM
iajs-2009	28	4	2	2	NUM
iajs-2009	28	5	]	]	PUNCT
iajs-2009	28	6	.	.	PUNCT
iajs-2009	29	1	algebra	algebra	NOUN
iajs-2009	29	2	)	)	PUNCT
iajs-2009	29	3	0	0	NUM
iajs-2009	29	4	,	,	PUNCT
iajs-2009	29	5	,	,	PUNCT
iajs-2009	29	6	(	(	PUNCT
iajs-2009	29	7	x	x	NOUN
iajs-2009	29	8	is	be	AUX
iajs-2009	29	9	called	call	VERB
iajs-2009	29	10	a	a	DET
iajs-2009	29	11	ku	ku	NOUN
iajs-2009	29	12	-	-	PUNCT
iajs-2009	29	13	algebra	algebra	PROPN
iajs-2009	29	14	if	if	SCONJ
iajs-2009	29	15	it	it	PRON
iajs-2009	29	16	satisfies	satisfy	VERB
iajs-2009	29	17	the	the	DET
iajs-2009	29	18	following	follow	VERB
iajs-2009	29	19	axioms	axiom	NOUN
iajs-2009	29	20	:	:	PUNCT
iajs-2009	29	21	mathematics	mathematic	NOUN
iajs-2009	29	22	|	|	ADV
iajs-2009	29	23	161	161	NUM
iajs-2009	29	24	ibn	ibn	PROPN
iajs-2009	29	25	al	al	PROPN
iajs-2009	29	26	-	-	PUNCT
iajs-2009	29	27	haitham	haitham	PROPN
iajs-2009	29	28	jour	jour	X
iajs-2009	29	29	.	.	PROPN
iajs-2009	30	1	for	for	ADP
iajs-2009	30	2	pure	pure	ADJ
iajs-2009	30	3	&	&	CCONJ
iajs-2009	30	4	appl	appl	PROPN
iajs-2009	30	5	.	.	PUNCT
iajs-2009	31	1	sci	sci	PROPN
iajs-2009	31	2	.	.	PROPN
iajs-2009	31	3	ihjpas	ihjpas	PROPN
iajs-2009	31	4	https://doi.org/10.30526/31.3.2009	https://doi.org/10.30526/31.3.2009	PROPN
iajs-2009	31	5	vol	vol	NOUN
iajs-2009	31	6	.	.	PROPN
iajs-2009	32	1	31	31	NUM
iajs-2009	33	1	(	(	PUNCT
iajs-2009	33	2	3	3	NUM
iajs-2009	33	3	)	)	PUNCT
iajs-2009	33	4	2018	2018	NUM
iajs-2009	33	5	(	(	PUNCT
iajs-2009	33	6	1ku	1ku	X
iajs-2009	33	7	)	)	PUNCT
iajs-2009	33	8	0	0	NUM
iajs-2009	33	9	)	)	PUNCT
iajs-2009	33	10	]	]	PUNCT
iajs-2009	33	11	(	(	PUNCT
iajs-2009	33	12	)	)	PUNCT
iajs-2009	33	13	)	)	PUNCT
iajs-2009	34	1	[	[	X
iajs-2009	34	2	(	(	PUNCT
iajs-2009	34	3	)	)	PUNCT
iajs-2009	34	4	(	(	PUNCT
iajs-2009	34	5			NUM
iajs-2009	34	6	zxzyyx	zxzyyx	NOUN
iajs-2009	34	7	,	,	PUNCT
iajs-2009	34	8	(	(	PUNCT
iajs-2009	34	9	2ku	2ku	ADJ
iajs-2009	34	10	)	)	PUNCT
iajs-2009	34	11	00	00	PUNCT
iajs-2009	35	1	x	x	NOUN
iajs-2009	35	2	,	,	PUNCT
iajs-2009	35	3	(	(	PUNCT
iajs-2009	35	4	3ku	3ku	ADJ
iajs-2009	35	5	)	)	PUNCT
iajs-2009	35	6	xx	xx	NUM
iajs-2009	35	7	0	0	NUM
iajs-2009	35	8	,	,	PUNCT
iajs-2009	35	9	(	(	PUNCT
iajs-2009	35	10	4ku	4ku	NOUN
iajs-2009	35	11	)	)	PUNCT
iajs-2009	35	12	0	0	NOUN
iajs-2009	35	13	yx	yx	NOUN
iajs-2009	35	14	and	and	CCONJ
iajs-2009	35	15	0	0	NOUN
iajs-2009	35	16	xy	xy	PROPN
iajs-2009	35	17	implies	imply	VERB
iajs-2009	35	18	yx	yx	NOUN
iajs-2009	35	19			NUM
iajs-2009	35	20	,	,	PUNCT
iajs-2009	35	21	(	(	PUNCT
iajs-2009	35	22	5ku	5ku	NOUN
iajs-2009	35	23	)	)	PUNCT
iajs-2009	35	24	0	0	NOUN
iajs-2009	35	25	xx	xx	NUM
iajs-2009	35	26	.	.	PUNCT
iajs-2009	36	1	on	on	ADP
iajs-2009	36	2	aˑ	aˑ	ADP
iajs-2009	36	3	ku	ku	PROPN
iajs-2009	36	4	-	-	PUNCT
iajs-2009	36	5	algebraˑ	algebraˑ	PROPN
iajs-2009	36	6	x	x	X
iajs-2009	36	7	,	,	PUNCT
iajs-2009	36	8	we	we	PRON
iajs-2009	36	9	can	can	AUX
iajs-2009	36	10	defineˑ	defineˑ	VERB
iajs-2009	36	11	a	a	DET
iajs-2009	36	12	binary	binary	NOUN
iajs-2009	36	13	relationˑ	relationˑ	PROPN
iajs-2009	36	14	by	by	ADP
iajs-2009	36	15	ˑputting	ˑputte	VERB
iajs-2009	36	16	0	0	NUM
iajs-2009	36	17	xyyx	xyyx	PROPN
iajs-2009	36	18	.	.	PUNCT
iajs-2009	37	1	ˑthen	ˑthen	ADV
iajs-2009	37	2	)	)	PUNCT
iajs-2009	37	3	,	,	PUNCT
iajs-2009	37	4	(	(	PUNCT
iajs-2009	37	5	x	x	PROPN
iajs-2009	37	6	is	be	AUX
iajs-2009	37	7	a	a	DET
iajs-2009	37	8	partially	partially	ADV
iajs-2009	37	9	ˑordered	ˑordere	VERB
iajs-2009	37	10	set	set	NOUN
iajs-2009	37	11	ˑand	ˑand	CCONJ
iajs-2009	37	12	0	0	NUM
iajs-2009	37	13	is	be	AUX
iajs-2009	37	14	ˑits	ˑit	NOUN
iajs-2009	37	15	smallestˑ	smallestˑ	NOUN
iajs-2009	37	16	element	element	NOUN
iajs-2009	37	17	.	.	PUNCT
iajs-2009	38	1	thusˑ	thusˑ	VERB
iajs-2009	38	2	)	)	PUNCT
iajs-2009	38	3	0	0	NUM
iajs-2009	38	4	,	,	PUNCT
iajs-2009	38	5	,	,	PUNCT
iajs-2009	38	6	(	(	PUNCT
iajs-2009	38	7	x	x	NOUN
iajs-2009	38	8	satisfies	satisfy	VERB
iajs-2009	38	9	the	the	DET
iajs-2009	38	10	followingˑ	followingˑ	NOUN
iajs-2009	38	11	conditions	condition	NOUN
iajs-2009	38	12	.	.	PUNCT
iajs-2009	39	1	for	for	ADP
iajs-2009	39	2	allˑ	allˑ	NOUN
iajs-2009	39	3	xzyx	xzyx	PROPN
iajs-2009	39	4			PROPN
iajs-2009	39	5	,	,	PUNCT
iajs-2009	39	6	,	,	PUNCT
iajs-2009	39	7	,	,	PUNCT
iajs-2009	39	8	weˑ	weˑ	VERB
iajs-2009	39	9	that	that	SCONJ
iajs-2009	39	10	(	(	PUNCT
iajs-2009	39	11	\1	\1	PROPN
iajs-2009	39	12	ku	ku	PROPN
iajs-2009	39	13	)	)	PUNCT
iajs-2009	39	14	)	)	PUNCT
iajs-2009	39	15	(	(	PUNCT
iajs-2009	39	16	)	)	PUNCT
iajs-2009	39	17	(	(	PUNCT
iajs-2009	39	18	)	)	PUNCT
iajs-2009	39	19	(	(	PUNCT
iajs-2009	39	20	yxzxzy	yxzxzy	PROPN
iajs-2009	39	21			PROPN
iajs-2009	39	22	,	,	PUNCT
iajs-2009	39	23	(	(	PUNCT
iajs-2009	39	24	\2	\2	X
iajs-2009	39	25	ku	ku	PROPN
iajs-2009	39	26	)	)	PUNCT
iajs-2009	39	27	x0	x0	NOUN
iajs-2009	39	28	,	,	PUNCT
iajs-2009	39	29	(	(	PUNCT
iajs-2009	39	30	\3	\3	X
iajs-2009	39	31	ku	ku	PROPN
iajs-2009	39	32	)	)	PUNCT
iajs-2009	39	33	xyyx	xyyx	PROPN
iajs-2009	39	34			PROPN
iajs-2009	39	35	,	,	PUNCT
iajs-2009	39	36	implies	imply	VERB
iajs-2009	39	37	yx	yx	NOUN
iajs-2009	39	38			NUM
iajs-2009	39	39	,	,	PUNCT
iajs-2009	40	1	(	(	PUNCT
iajs-2009	40	2	\4	\4	PROPN
iajs-2009	40	3	ku	ku	PROPN
iajs-2009	40	4	)	)	PUNCT
iajs-2009	40	5	xxy	xxy	PROPN
iajs-2009	40	6			PROPN
iajs-2009	40	7	.ˑ	.ˑ	PROPN
iajs-2009	40	8	ˑtheoremˑ2ˑ[14].ˑin	ˑtheoremˑ2ˑ[14].ˑin	VERB
iajs-2009	40	9	a	a	DET
iajs-2009	40	10	kuˑ-algebra	kuˑ-algebra	NOUN
iajs-2009	40	11	x	x	X
iajs-2009	40	12	.	.	PUNCT
iajs-2009	41	1	ˑtheˑ	ˑtheˑ	PROPN
iajs-2009	41	2	followingˑ	followingˑ	PROPN
iajs-2009	41	3	axiomsˑ	axiomsˑ	NOUN
iajs-2009	41	4	are	be	AUX
iajs-2009	41	5	satisfied	satisfied	ADJ
iajs-2009	41	6	,	,	PUNCT
iajs-2009	41	7	for	for	ADP
iajs-2009	41	8	all	all	PRON
iajs-2009	41	9	xzyx	xzyx	ADP
iajs-2009	41	10			NOUN
iajs-2009	41	11	,	,	PUNCT
iajs-2009	41	12	,	,	PUNCT
iajs-2009	41	13	(	(	PUNCT
iajs-2009	41	14	1	1	X
iajs-2009	41	15	)	)	PUNCT
iajs-2009	41	16	yx	yx	NOUN
iajs-2009	41	17			NUM
iajs-2009	41	18	ˑimplyˑ	ˑimplyˑ	VERB
iajs-2009	41	19	zxzy	zxzy	NOUN
iajs-2009	41	20			NOUN
iajs-2009	41	21	,	,	PUNCT
iajs-2009	41	22	(	(	PUNCT
iajs-2009	41	23	2	2	NUM
iajs-2009	41	24	)	)	PUNCT
iajs-2009	41	25	)	)	PUNCT
iajs-2009	41	26	(	(	PUNCT
iajs-2009	41	27	)	)	PUNCT
iajs-2009	41	28	(	(	PUNCT
iajs-2009	41	29	zxyzyx	zxyzyx	NOUN
iajs-2009	41	30			NOUN
iajs-2009	41	31	,	,	PUNCT
iajs-2009	41	32	ˑfor	ˑfor	ADP
iajs-2009	41	33	allˑ	allˑ	NOUN
iajs-2009	41	34	xzyx	xzyx	PROPN
iajs-2009	41	35			PROPN
iajs-2009	41	36	,	,	PUNCT
iajs-2009	41	37	,	,	PUNCT
iajs-2009	41	38	,	,	PUNCT
iajs-2009	41	39	(	(	PUNCT
iajs-2009	41	40	3	3	X
iajs-2009	41	41	)	)	PUNCT
iajs-2009	41	42	yxxy	yxxy	NOUN
iajs-2009	41	43			PROPN
iajs-2009	41	44	)	)	PUNCT
iajs-2009	41	45	)	)	PUNCT
iajs-2009	42	1	(	(	PUNCT
iajs-2009	42	2	(	(	PUNCT
iajs-2009	42	3	ˑ.ˑ	ˑ.ˑ	X
iajs-2009	42	4	definition	definition	NOUN
iajs-2009	42	5	3	3	NUM
iajs-2009	42	6	[	[	X
iajs-2009	42	7	1	1	NUM
iajs-2009	42	8	-	-	SYM
iajs-2009	42	9	2	2	NUM
iajs-2009	42	10	]	]	PUNCT
iajs-2009	42	11	.	.	PUNCT
iajs-2009	43	1	ˑa	ˑa	PROPN
iajs-2009	43	2	non-ˑempty	non-ˑempty	ADJ
iajs-2009	43	3	subsetˑ	subsetˑ	PROPN
iajs-2009	44	1	i	i	PRON
iajs-2009	44	2	of	of	ADP
iajs-2009	44	3	a	a	DET
iajs-2009	44	4	ku	ku	NOUN
iajs-2009	44	5	-	-	PUNCT
iajs-2009	44	6	algebra	algebra	PROPN
iajs-2009	44	7	)	)	PUNCT
iajs-2009	44	8	0	0	NUM
iajs-2009	44	9	,	,	PUNCT
iajs-2009	44	10	,	,	PUNCT
iajs-2009	44	11	(	(	PUNCT
iajs-2009	44	12	x	x	NOUN
iajs-2009	44	13	is	be	AUX
iajs-2009	44	14	calledˑˑan	calledˑˑan	ADJ
iajs-2009	44	15	ˑideal	ˑideal	NOUN
iajs-2009	44	16	of	of	ADP
iajs-2009	44	17	x	x	PRON
iajs-2009	44	18	if	if	SCONJ
iajs-2009	44	19	ˑfor	ˑfor	ADP
iajs-2009	44	20	anyˑ	anyˑ	PROPN
iajs-2009	44	21	xyx	xyx	PROPN
iajs-2009	44	22			PROPN
iajs-2009	44	23	,	,	PUNCT
iajs-2009	44	24	,	,	PUNCT
iajs-2009	44	25	then	then	ADV
iajs-2009	44	26	(	(	PUNCT
iajs-2009	44	27	i	i	NOUN
iajs-2009	44	28	)	)	PUNCT
iajs-2009	44	29	i0	i0	PUNCT
iajs-2009	45	1	and	and	CCONJ
iajs-2009	45	2	(	(	PUNCT
iajs-2009	45	3	ii	ii	NOUN
iajs-2009	45	4	)	)	PUNCT
iajs-2009	45	5	ixyx	ixyx	ADJ
iajs-2009	45	6			NOUN
iajs-2009	45	7	,	,	PUNCT
iajs-2009	45	8	imply	imply	VERB
iajs-2009	45	9	that	that	SCONJ
iajs-2009	45	10	iy	iy	NOUN
iajs-2009	45	11	.ˑˑ	.ˑˑ	PUNCT
iajs-2009	45	12	definition	definition	NOUN
iajs-2009	45	13	4	4	NUM
iajs-2009	45	14	[	[	X
iajs-2009	45	15	1	1	NUM
iajs-2009	45	16	-	-	SYM
iajs-2009	45	17	2].ˑlet	2].ˑlet	NUM
iajs-2009	45	18	i	i	PRON
iajs-2009	45	19	be	be	VERB
iajs-2009	45	20	a	a	DET
iajs-2009	45	21	nonempty	nonempty	ADJ
iajs-2009	45	22	subset	subset	NOUN
iajs-2009	45	23	of	of	ADP
iajs-2009	45	24	a	a	DET
iajs-2009	45	25	ku	ku	NOUN
iajs-2009	45	26	-	-	PUNCT
iajs-2009	45	27	algebra	algebra	PROPN
iajs-2009	45	28	x	x	X
iajs-2009	45	29	.	.	PUNCT
iajs-2009	46	1	then	then	ADV
iajs-2009	46	2	i	i	PRON
iajs-2009	46	3	is	be	AUX
iajs-2009	46	4	said	say	VERB
iajs-2009	46	5	to	to	PART
iajs-2009	46	6	be	be	AUX
iajs-2009	46	7	a	a	DET
iajs-2009	46	8	ku	ku	NOUN
iajs-2009	46	9	-	-	PUNCT
iajs-2009	46	10	ideal	ideal	NOUN
iajs-2009	46	11	of	of	ADP
iajs-2009	46	12	x	x	SYM
iajs-2009	46	13	,	,	PUNCT
iajs-2009	46	14	if	if	SCONJ
iajs-2009	46	15	)	)	PUNCT
iajs-2009	46	16	(	(	PUNCT
iajs-2009	46	17	1i	1i	NOUN
iajs-2009	46	18	i0	i0	PUNCT
iajs-2009	46	19	and	and	CCONJ
iajs-2009	46	20	)	)	PUNCT
iajs-2009	46	21	(	(	PUNCT
iajs-2009	46	22	2i	2i	NUM
iajs-2009	46	23	xzyx	xzyx	PROPN
iajs-2009	46	24			PROPN
iajs-2009	46	25	,	,	PUNCT
iajs-2009	46	26	,	,	PUNCT
iajs-2009	46	27	,	,	PUNCT
iajs-2009	46	28	izyx	izyx	NOUN
iajs-2009	46	29			NOUN
iajs-2009	46	30	)	)	PUNCT
iajs-2009	46	31	(	(	PUNCT
iajs-2009	46	32	and	and	CCONJ
iajs-2009	46	33	iy	iy	PRON
iajs-2009	46	34	imply	imply	VERB
iajs-2009	46	35	that	that	SCONJ
iajs-2009	46	36	izx	izx	NOUN
iajs-2009	46	37			NOUN
iajs-2009	46	38	.	.	PUNCT
iajs-2009	47	1	ˑˑdefinition	ˑˑdefinition	NOUN
iajs-2009	47	2	5[15].ˑa	5[15].ˑa	NOUN
iajs-2009	47	3	ku-ˑalgebraˑ	ku-ˑalgebraˑ	NOUN
iajs-2009	47	4	)	)	PUNCT
iajs-2009	47	5	0	0	NUM
iajs-2009	47	6	,	,	PUNCT
iajs-2009	47	7	,	,	PUNCT
iajs-2009	47	8	(	(	PUNCT
iajs-2009	47	9	x	x	NOUN
iajs-2009	47	10	ˑis	ˑis	PROPN
iajs-2009	47	11	saidˑˑto	saidˑˑto	PROPN
iajs-2009	47	12	beˑa	beˑa	PROPN
iajs-2009	47	13	commutativeˑifˑitˑsatisfiesˑ	commutativeˑifˑitˑsatisfiesˑ	NOUN
iajs-2009	47	14	:	:	PUNCT
iajs-2009	47	15	for	for	ADP
iajs-2009	47	16	all	all	DET
iajs-2009	47	17	ˑ	ˑ	NOUN
iajs-2009	47	18	yx	yx	NOUN
iajs-2009	47	19	,	,	PUNCT
iajs-2009	47	20	in	in	ADP
iajs-2009	47	21	x	x	SYM
iajs-2009	47	22	,	,	PUNCT
iajs-2009	47	23	yyxxxy	yyxxxy	NOUN
iajs-2009	47	24			NOUN
iajs-2009	47	25	)	)	PUNCT
iajs-2009	47	26	(	(	PUNCT
iajs-2009	47	27	)	)	PUNCT
iajs-2009	47	28	(	(	PUNCT
iajs-2009	47	29	,	,	PUNCT
iajs-2009	47	30	where	where	SCONJ
iajs-2009	47	31	xxyyx	xxyyx	PROPN
iajs-2009	47	32			NOUN
iajs-2009	47	33	)	)	PUNCT
iajs-2009	47	34	(	(	PUNCT
iajs-2009	47	35	,	,	PUNCT
iajs-2009	47	36	i.e.	i.e.	X
iajs-2009	47	37	xyyx	xyyx	PROPN
iajs-2009	47	38			PROPN
iajs-2009	47	39	.ˑˑ	.ˑˑ	PUNCT
iajs-2009	48	1	lemma	lemma	PROPN
iajs-2009	48	2	6ˑ[15	6ˑ[15	PROPN
iajs-2009	48	3	]	]	PUNCT
iajs-2009	48	4	.	.	PUNCT
iajs-2009	49	1	if	if	SCONJ
iajs-2009	49	2	x	x	PRON
iajs-2009	49	3	is	be	AUX
iajs-2009	49	4	a	a	DET
iajs-2009	49	5	commutative	commutative	ADJ
iajs-2009	49	6	ku	ku	NOUN
iajs-2009	49	7	-	-	PUNCT
iajs-2009	49	8	algebra	algebra	PROPN
iajs-2009	49	9	,	,	PUNCT
iajs-2009	49	10	then	then	ADV
iajs-2009	49	11	)	)	PUNCT
iajs-2009	49	12	(	(	PUNCT
iajs-2009	49	13	)	)	PUNCT
iajs-2009	49	14	(	(	PUNCT
iajs-2009	49	15	)	)	PUNCT
iajs-2009	49	16	(	(	PUNCT
iajs-2009	49	17	zxyxzyx	zxyxzyx	INTJ
iajs-2009	49	18			NOUN
iajs-2009	49	19	.	.	PUNCT
iajs-2009	49	20	example	example	NOUN
iajs-2009	50	1	7[15	7[15	NUM
iajs-2009	50	2	]	]	PUNCT
iajs-2009	50	3	.	.	PUNCT
iajs-2009	51	1	let	let	VERB
iajs-2009	51	2	e}d	e}d	NOUN
iajs-2009	51	3	,	,	PUNCT
iajs-2009	51	4	c	c	X
iajs-2009	51	5	,	,	PUNCT
iajs-2009	51	6	b	b	NOUN
iajs-2009	51	7	,	,	PUNCT
iajs-2009	51	8	a,0,{x	a,0,{x	NOUN
iajs-2009	51	9	ˑbe	ˑbe	NOUN
iajs-2009	51	10	a	a	DET
iajs-2009	51	11	set	set	NOUN
iajs-2009	51	12	,	,	PUNCT
iajs-2009	51	13	with	with	ADP
iajs-2009	51	14	the	the	DET
iajs-2009	51	15	operation	operation	NUM
iajs-2009	51	16	defined	define	VERB
iajs-2009	51	17	by	by	ADP
iajs-2009	51	18	the	the	DET
iajs-2009	51	19	following	follow	VERB
iajs-2009	51	20	table	table	NOUN
iajs-2009	51	21	:	:	PUNCT
iajs-2009	52	1	mathematics	mathematic	NOUN
iajs-2009	52	2	|	|	ADV
iajs-2009	52	3	162	162	NUM
iajs-2009	52	4	ibn	ibn	PROPN
iajs-2009	52	5	al	al	PROPN
iajs-2009	52	6	-	-	PUNCT
iajs-2009	52	7	haitham	haitham	PROPN
iajs-2009	52	8	jour	jour	X
iajs-2009	52	9	.	.	PROPN
iajs-2009	52	10	for	for	ADP
iajs-2009	52	11	pure	pure	ADJ
iajs-2009	52	12	&	&	CCONJ
iajs-2009	52	13	appl	appl	PROPN
iajs-2009	52	14	.	.	PUNCT
iajs-2009	53	1	sci	sci	PROPN
iajs-2009	53	2	.	.	PROPN
iajs-2009	53	3	ihjpas	ihjpas	PROPN
iajs-2009	53	4	https://doi.org/10.30526/31.3.2009	https://doi.org/10.30526/31.3.2009	PROPN
iajs-2009	53	5	vol	vol	NOUN
iajs-2009	53	6	.	.	PROPN
iajs-2009	54	1	31	31	NUM
iajs-2009	55	1	(	(	PUNCT
iajs-2009	55	2	3	3	NUM
iajs-2009	55	3	)	)	PUNCT
iajs-2009	55	4	2018	2018	NUM
iajs-2009	55	5	thenˑ	thenˑ	NOUN
iajs-2009	55	6	)	)	PUNCT
iajs-2009	55	7	0	0	NUM
iajs-2009	55	8	,	,	PUNCT
iajs-2009	55	9	,	,	PUNCT
iajs-2009	55	10	(	(	PUNCT
iajs-2009	55	11	x	x	NOUN
iajs-2009	55	12	is	be	AUX
iajs-2009	55	13	aˑku	aˑku	NOUN
iajs-2009	55	14	-	-	PUNCT
iajs-2009	55	15	algebra	algebra	NOUN
iajs-2009	55	16	andˑku	andˑku	NOUN
iajs-2009	55	17	-	-	PUNCT
iajs-2009	55	18	commutative	commutative	ADJ
iajs-2009	55	19	.	.	PUNCT
iajs-2009	56	1	definition	definition	NOUN
iajs-2009	56	2	8	8	NUM
iajs-2009	57	1	[	[	X
iajs-2009	57	2	3	3	NUM
iajs-2009	57	3	]	]	PUNCT
iajs-2009	57	4	.	.	PUNCT
iajs-2009	58	1	a	a	DET
iajs-2009	58	2	ku	ku	PROPN
iajs-2009	58	3	-	-	PUNCT
iajs-2009	58	4	semigroup	semigroup	PROPN
iajs-2009	58	5	is	be	AUX
iajs-2009	58	6	a	a	DET
iajs-2009	58	7	nonempty	nonempty	ADV
iajs-2009	58	8	set	set	VERB
iajs-2009	58	9	x	x	PUNCT
iajs-2009	58	10	with	with	ADP
iajs-2009	58	11	twoˑbinary	twoˑbinary	ADJ
iajs-2009	58	12	operations	operation	NOUN
iajs-2009	59	1	,	,	NOUN
iajs-2009	59	2	ˑand	ˑand	NOUN
iajs-2009	59	3	constantˑ	constantˑ	NOUN
iajs-2009	59	4	0	0	NUM
iajs-2009	60	1	satisfying	satisfy	VERB
iajs-2009	60	2	ˑtheˑfollowing	ˑtheˑfollowe	VERB
iajs-2009	60	3	axiomsˑ	axiomsˑ	NOUN
iajs-2009	60	4	(	(	PUNCT
iajs-2009	60	5	i	i	NOUN
iajs-2009	60	6	)	)	PUNCT
iajs-2009	60	7	)	)	PUNCT
iajs-2009	60	8	0	0	NUM
iajs-2009	60	9	,	,	PUNCT
iajs-2009	60	10	,	,	PUNCT
iajs-2009	60	11	(	(	PUNCT
iajs-2009	60	12	x	x	VERB
iajs-2009	60	13	isˑˑa	isˑˑa	NOUN
iajs-2009	60	14	ku-ˑalgebra	ku-ˑalgebra	NOUN
iajs-2009	60	15	,	,	PUNCT
iajs-2009	60	16	(	(	PUNCT
iajs-2009	60	17	ii	ii	NOUN
iajs-2009	60	18	)	)	PUNCT
iajs-2009	60	19	)	)	PUNCT
iajs-2009	60	20	,	,	PUNCT
iajs-2009	60	21	(	(	PUNCT
iajs-2009	60	22	x	x	NOUN
iajs-2009	60	23	is	be	AUX
iajs-2009	60	24	aˑˑsemigroup	aˑˑsemigroup	ADJ
iajs-2009	60	25	,	,	PUNCT
iajs-2009	60	26	(	(	PUNCT
iajs-2009	60	27	iii)the	iii)the	DET
iajs-2009	60	28	ˑoperation	ˑoperation	NOUN
iajs-2009	60	29			PROPN
iajs-2009	60	30	is	be	AUX
iajs-2009	60	31	ˑdistributiveˑ(on	ˑdistributiveˑ(on	VERB
iajs-2009	60	32	bothˑ	bothˑ	ADJ
iajs-2009	60	33	sides	side	NOUN
iajs-2009	60	34	)	)	PUNCT
iajs-2009	60	35	over	over	ADP
iajs-2009	60	36	theˑˑoperation	theˑˑoperation	NUM
iajs-2009	60	37	,	,	PUNCT
iajs-2009	60	38	i.e.	i.e.	X
iajs-2009	60	39	)	)	PUNCT
iajs-2009	60	40	(	(	PUNCT
iajs-2009	60	41	)	)	PUNCT
iajs-2009	60	42	(	(	PUNCT
iajs-2009	60	43	)	)	PUNCT
iajs-2009	60	44	(	(	PUNCT
iajs-2009	60	45	)	)	PUNCT
iajs-2009	60	46	(	(	PUNCT
iajs-2009	60	47	)	)	PUNCT
iajs-2009	60	48	(	(	PUNCT
iajs-2009	60	49	)	)	PUNCT
iajs-2009	60	50	(	(	PUNCT
iajs-2009	60	51	zyzxzyxandzxyxzyx	zyzxzyxandzxyxzyx	NOUN
iajs-2009	60	52			PROPN
iajs-2009	60	53			NUM
iajs-2009	60	54	,	,	PUNCT
iajs-2009	60	55	for	for	ADP
iajs-2009	60	56	all	all	PRON
iajs-2009	60	57	xzyx	xzyx	ADP
iajs-2009	60	58			NOUN
iajs-2009	60	59	,	,	PUNCT
iajs-2009	60	60	,	,	PUNCT
iajs-2009	60	61	.	.	PUNCT
iajs-2009	61	1	example	example	NOUN
iajs-2009	61	2	9[3	9[3	NUM
iajs-2009	61	3	]	]	PUNCT
iajs-2009	61	4	.	.	PUNCT
iajs-2009	62	1	let	let	VERB
iajs-2009	62	2	}	}	PUNCT
iajs-2009	62	3	3,2,1,0{x	3,2,1,0{x	NUM
iajs-2009	62	4	beˑa	beˑa	NOUN
iajs-2009	62	5	set	set	NOUN
iajs-2009	62	6	.	.	PUNCT
iajs-2009	63	1	define	define	VERB
iajs-2009	63	2			PROPN
iajs-2009	63	3	-ˑoperation	-ˑoperation	NOUN
iajs-2009	63	4	and	and	CCONJ
iajs-2009	63	5			PROPN
iajs-2009	63	6	-ˑoperation	-ˑoperation	NOUN
iajs-2009	63	7	by	by	ADP
iajs-2009	63	8	the	the	DET
iajs-2009	63	9	following	follow	VERB
iajs-2009	63	10	tables	table	NOUN
iajs-2009	63	11	then	then	ADV
iajs-2009	63	12	,	,	PUNCT
iajs-2009	63	13	)	)	PUNCT
iajs-2009	63	14	0	0	NUM
iajs-2009	63	15	,	,	PUNCT
iajs-2009	63	16	,	,	PUNCT
iajs-2009	63	17	,	,	PUNCT
iajs-2009	63	18	(	(	PUNCT
iajs-2009	63	19	x	x	VERB
iajs-2009	63	20	is	be	AUX
iajs-2009	63	21	a	a	DET
iajs-2009	63	22	ku	ku	PROPN
iajs-2009	63	23	-	-	PUNCT
iajs-2009	63	24	semigroup	semigroup	PROPN
iajs-2009	63	25	.	.	PUNCT
iajs-2009	64	1	proposition	proposition	NOUN
iajs-2009	64	2	10[3	10[3	NUM
iajs-2009	64	3	]	]	PUNCT
iajs-2009	64	4	.	.	PUNCT
iajs-2009	65	1	let	let	VERB
iajs-2009	65	2	)	)	PUNCT
iajs-2009	65	3	0	0	NUM
iajs-2009	65	4	,	,	PUNCT
iajs-2009	65	5	,	,	PUNCT
iajs-2009	65	6	,	,	PUNCT
iajs-2009	65	7	(	(	PUNCT
iajs-2009	65	8	x	x	PRON
iajs-2009	65	9	be	be	VERB
iajs-2009	65	10	a	a	DET
iajs-2009	65	11	ku	ku	PROPN
iajs-2009	65	12	-	-	PUNCT
iajs-2009	65	13	semigroup	semigroup	PROPN
iajs-2009	65	14	.	.	PUNCT
iajs-2009	66	1	the	the	DET
iajs-2009	66	2	followingˑaxioms	followingˑaxiom	NOUN
iajs-2009	66	3	areˑsatisfied	areˑsatisfie	VERB
iajs-2009	66	4	.	.	PUNCT
iajs-2009	67	1	for	for	ADP
iajs-2009	67	2	all	all	PRON
iajs-2009	67	3	xzyx	xzyx	ADP
iajs-2009	67	4			NOUN
iajs-2009	67	5	,	,	PUNCT
iajs-2009	67	6	,	,	PUNCT
iajs-2009	67	7	,	,	PUNCT
iajs-2009	67	8	(	(	PUNCT
iajs-2009	67	9	1	1	NUM
iajs-2009	67	10	)	)	PUNCT
iajs-2009	67	11	00	00	PUNCT
iajs-2009	67	12	x	x	NOUN
iajs-2009	67	13	and	and	CCONJ
iajs-2009	67	14	00	00	NUM
iajs-2009	67	15	x	x	NOUN
iajs-2009	67	16	,	,	PUNCT
iajs-2009	67	17	(	(	PUNCT
iajs-2009	67	18	2	2	X
iajs-2009	67	19	)	)	PUNCT
iajs-2009	67	20	if	if	SCONJ
iajs-2009	67	21	yx	yx	ADP
iajs-2009	67	22			NOUN
iajs-2009	67	23	implyˑ	implyˑ	VERB
iajs-2009	67	24	yzxz	yzxz	NOUN
iajs-2009	67	25			PUNCT
iajs-2009	67	26			PROPN
iajs-2009	67	27	and	and	CCONJ
iajs-2009	67	28	zyzx	zyzx	PROPN
iajs-2009	67	29			PUNCT
iajs-2009	67	30			NOUN
iajs-2009	67	31	,	,	PUNCT
iajs-2009	67	32	(	(	PUNCT
iajs-2009	67	33	3	3	NUM
iajs-2009	67	34	)	)	PUNCT
iajs-2009	67	35	)	)	PUNCT
iajs-2009	67	36	(	(	PUNCT
iajs-2009	67	37	)	)	PUNCT
iajs-2009	67	38	(	(	PUNCT
iajs-2009	67	39	)	)	PUNCT
iajs-2009	67	40	(	(	PUNCT
iajs-2009	67	41	)	)	PUNCT
iajs-2009	67	42	(	(	PUNCT
iajs-2009	67	43	)	)	PUNCT
iajs-2009	67	44	(	(	PUNCT
iajs-2009	67	45	)	)	PUNCT
iajs-2009	67	46	(	(	PUNCT
iajs-2009	67	47	zyzxzyxandzxyxzyx	zyzxzyxandzxyxzyx	NOUN
iajs-2009	67	48			PROPN
iajs-2009	67	49			NOUN
iajs-2009	67	50	.	.	PUNCT
iajs-2009	68	1	3.a	3.a	NUM
iajs-2009	68	2	graph	graph	NOUN
iajs-2009	68	3	ofˑku	ofˑku	NOUN
iajs-2009	68	4	-	-	PUNCT
iajs-2009	68	5	semigroups	semigroup	NOUN
iajs-2009	68	6	in	in	ADP
iajs-2009	68	7	thisˑ	thisˑ	NOUN
iajs-2009	68	8	part	part	NOUN
iajs-2009	68	9	,	,	PUNCT
iajs-2009	68	10	we	we	PRON
iajs-2009	68	11	introduceˑ	introduceˑ	VERB
iajs-2009	68	12	the	the	DET
iajs-2009	68	13	conceptsˑ	conceptsˑ	NOUN
iajs-2009	68	14	of	of	ADP
iajs-2009	68	15	graph	graph	NOUN
iajs-2009	68	16	ku	ku	NOUN
iajs-2009	68	17	-	-	PUNCT
iajs-2009	68	18	semigroupsˑ	semigroupsˑ	NOUN
iajs-2009	68	19	x	x	NOUN
iajs-2009	68	20	and	and	CCONJ
iajs-2009	68	21	theˑ	theˑ	NOUN
iajs-2009	68	22	graph	graph	NOUN
iajs-2009	68	23	of	of	ADP
iajs-2009	68	24	equivalence	equivalence	NOUN
iajs-2009	68	25	ˑclasses	ˑclasse	NOUN
iajs-2009	68	26	of	of	ADP
iajs-2009	68	27	x	x	X
iajs-2009	68	28	.	.	PUNCT
iajs-2009	69	1	we	we	PRON
iajs-2009	69	2	ˑrecall	ˑrecall	VERB
iajs-2009	69	3	some	some	DET
iajs-2009	69	4	definitions	definition	NOUN
iajs-2009	69	5	ˑand	ˑand	CCONJ
iajs-2009	69	6	basic	basic	ADJ
iajs-2009	69	7	ˑfacts	ˑfact	NOUN
iajs-2009	69	8	.	.	PUNCT
iajs-2009	70	1	for	for	ADP
iajs-2009	70	2	aˑ	aˑ	ADP
iajs-2009	70	3	graph	graph	NOUN
iajs-2009	70	4	g	g	PROPN
iajs-2009	70	5	ˑ	ˑ	NOUN
iajs-2009	70	6	,	,	PUNCT
iajs-2009	70	7	we	we	PRON
iajs-2009	70	8	ˑdenotedˑ	ˑdenotedˑ	VERB
iajs-2009	70	9	theˑ	theˑ	NOUN
iajs-2009	70	10	set	set	VERB
iajs-2009	70	11	of	of	ADP
iajs-2009	70	12	ˑvertices	ˑvertice	NOUN
iajs-2009	70	13	ˑof	ˑof	INTJ
iajs-2009	70	14	g	g	PROPN
iajs-2009	70	15	ˑasˑ	ˑasˑ	NOUN
iajs-2009	70	16	)	)	PUNCT
iajs-2009	70	17	(	(	PUNCT
iajs-2009	70	18	gv	gv	ADP
iajs-2009	70	19	and	and	CCONJ
iajs-2009	70	20	ˑthe	ˑthe	DET
iajs-2009	70	21	ˑset	ˑset	NOUN
iajs-2009	70	22	ˑof	ˑof	ADV
iajs-2009	70	23	edgesˑ	edgesˑ	ADJ
iajs-2009	70	24	as	as	ADP
iajs-2009	70	25	)	)	PUNCT
iajs-2009	70	26	(	(	PUNCT
iajs-2009	70	27	ge	ge	PROPN
iajs-2009	70	28	.	.	PUNCT
iajs-2009	71	1	an	an	DET
iajs-2009	71	2	edge	edge	NOUN
iajs-2009	71	3	to	to	PART
iajs-2009	71	4	be	be	AUX
iajs-2009	71	5			PROPN
iajs-2009	71	6	0	0	NUM
iajs-2009	71	7	aˑ	aˑ	ADP
iajs-2009	71	8	b	b	NOUN
iajs-2009	71	9	c	c	NOUN
iajs-2009	71	10	d	d	X
iajs-2009	71	11	e	e	X
iajs-2009	71	12	0	0	NUM
iajs-2009	71	13	0	0	NUM
iajs-2009	71	14	a	a	DET
iajs-2009	71	15	bˑ	bˑ	PROPN
iajs-2009	71	16	c	c	PROPN
iajs-2009	71	17	d	d	PROPN
iajs-2009	71	18	e	e	PROPN
iajs-2009	71	19	a	a	PRON
iajs-2009	71	20	0	0	NUM
iajs-2009	71	21	0	0	NUM
iajs-2009	71	22	b	b	NOUN
iajs-2009	71	23	c	c	NOUN
iajs-2009	71	24	bˑ	bˑ	PROPN
iajs-2009	71	25	c	c	PROPN
iajs-2009	71	26	b	b	PROPN
iajs-2009	71	27	0	0	PUNCT
iajs-2009	71	28	a	a	DET
iajs-2009	71	29	0ˑ	0ˑ	ADJ
iajs-2009	71	30	b	b	NOUN
iajs-2009	71	31	aˑ	aˑ	ADP
iajs-2009	71	32	d	d	PROPN
iajs-2009	71	33	c	c	NOUN
iajs-2009	71	34	0	0	NUM
iajs-2009	71	35	aˑ	aˑ	ADP
iajs-2009	71	36	0	0	NUM
iajs-2009	71	37	0	0	NUM
iajs-2009	72	1	a	a	DET
iajs-2009	72	2	a	a	DET
iajs-2009	72	3	d	d	NOUN
iajs-2009	72	4	0	0	PUNCT
iajs-2009	72	5	0ˑ	0ˑ	ADJ
iajs-2009	72	6	0	0	NUM
iajs-2009	72	7	b	b	NOUN
iajs-2009	72	8	0	0	NUM
iajs-2009	72	9	b	b	PROPN
iajs-2009	72	10	e	e	X
iajs-2009	72	11	0	0	NUM
iajs-2009	72	12	0	0	NUM
iajs-2009	72	13	0	0	NUM
iajs-2009	72	14	0	0	NUM
iajs-2009	72	15	0	0	NUM
iajs-2009	72	16	0	0	NUM
iajs-2009	73	1	*	*	SYM
iajs-2009	73	2	0	0	NUM
iajs-2009	74	1	1	1	NUM
iajs-2009	74	2	2	2	NUM
iajs-2009	74	3	3	3	NUM
iajs-2009	74	4	0	0	NUM
iajs-2009	74	5	0	0	NUM
iajs-2009	74	6	1	1	NUM
iajs-2009	74	7	2	2	NUM
iajs-2009	74	8	3	3	NUM
iajs-2009	74	9	1	1	NUM
iajs-2009	74	10	0	0	NUM
iajs-2009	74	11	0	0	NUM
iajs-2009	74	12	0	0	NUM
iajs-2009	74	13	2	2	NUM
iajs-2009	74	14	2	2	NUM
iajs-2009	74	15	0	0	NUM
iajs-2009	74	16	2	2	NUM
iajs-2009	74	17	0	0	NUM
iajs-2009	74	18	1	1	NUM
iajs-2009	74	19	3	3	NUM
iajs-2009	74	20	0	0	NUM
iajs-2009	74	21	0	0	NUM
iajs-2009	74	22	0	0	NUM
iajs-2009	74	23	0	0	NUM
iajs-2009	74	24			NOUN
iajs-2009	74	25	0	0	NUM
iajs-2009	74	26	1	1	NUM
iajs-2009	74	27	2	2	NUM
iajs-2009	74	28	3	3	NUM
iajs-2009	74	29	0	0	NUM
iajs-2009	74	30	0	0	NUM
iajs-2009	74	31	0	0	NUM
iajs-2009	74	32	0	0	NUM
iajs-2009	74	33	0	0	NUM
iajs-2009	74	34	1	1	NUM
iajs-2009	74	35	0	0	NUM
iajs-2009	74	36	1	1	NUM
iajs-2009	74	37	0	0	NUM
iajs-2009	74	38	1	1	NUM
iajs-2009	74	39	2	2	NUM
iajs-2009	74	40	0	0	NUM
iajs-2009	74	41	0	0	NUM
iajs-2009	74	42	2	2	NUM
iajs-2009	74	43	2	2	NUM
iajs-2009	74	44	3	3	NUM
iajs-2009	74	45	0	0	NUM
iajs-2009	74	46	1	1	NUM
iajs-2009	74	47	2	2	NUM
iajs-2009	74	48	3	3	NUM
iajs-2009	74	49	mathematics	mathematic	NOUN
iajs-2009	74	50	|	|	ADV
iajs-2009	74	51	163	163	NUM
iajs-2009	74	52	ibn	ibn	PROPN
iajs-2009	74	53	al	al	PROPN
iajs-2009	74	54	-	-	PUNCT
iajs-2009	74	55	haitham	haitham	PROPN
iajs-2009	74	56	jour	jour	X
iajs-2009	74	57	.	.	PROPN
iajs-2009	74	58	for	for	ADP
iajs-2009	74	59	pure	pure	ADJ
iajs-2009	74	60	&	&	CCONJ
iajs-2009	74	61	appl	appl	PROPN
iajs-2009	74	62	.	.	PUNCT
iajs-2009	75	1	sci	sci	PROPN
iajs-2009	75	2	.	.	PROPN
iajs-2009	75	3	ihjpas	ihjpas	PROPN
iajs-2009	75	4	https://doi.org/10.30526/31.3.2009	https://doi.org/10.30526/31.3.2009	PROPN
iajs-2009	75	5	vol	vol	NOUN
iajs-2009	75	6	.	.	PROPN
iajs-2009	76	1	31	31	NUM
iajs-2009	77	1	(	(	PUNCT
iajs-2009	77	2	3	3	NUM
iajs-2009	77	3	)	)	PUNCT
iajs-2009	77	4	2018	2018	NUM
iajs-2009	77	5	associated	associate	VERB
iajs-2009	77	6	with	with	ADP
iajs-2009	77	7	a	a	DET
iajs-2009	77	8	vertex	vertex	NOUN
iajs-2009	77	9	pair	pair	NOUN
iajs-2009	77	10	ji	ji	PROPN
iajs-2009	77	11	xx	xx	NOUN
iajs-2009	77	12			PROPN
iajs-2009	77	13	;	;	PUNCT
iajs-2009	77	14	such	such	DET
iajs-2009	77	15	an	an	DET
iajs-2009	77	16	edge	edge	NOUN
iajs-2009	77	17	having	have	VERB
iajs-2009	77	18	the	the	DET
iajs-2009	77	19	same	same	ADJ
iajs-2009	77	20	vertex	vertex	NOUN
iajs-2009	77	21	as	as	SCONJ
iajs-2009	77	22	end	end	NOUN
iajs-2009	77	23	vertices	vertex	NOUN
iajs-2009	77	24	are	be	AUX
iajs-2009	77	25	called	call	VERB
iajs-2009	77	26	a	a	DET
iajs-2009	77	27	loop	loop	NOUN
iajs-2009	77	28	.	.	PUNCT
iajs-2009	78	1	also	also	ADV
iajs-2009	78	2	if	if	SCONJ
iajs-2009	78	3	more	more	ADJ
iajs-2009	78	4	than	than	ADP
iajs-2009	78	5	one	one	NUM
iajs-2009	78	6	edge	edge	NOUN
iajs-2009	78	7	to	to	PART
iajs-2009	78	8	be	be	AUX
iajs-2009	78	9	associated	associate	VERB
iajs-2009	78	10	with	with	ADP
iajs-2009	78	11	a	a	DET
iajs-2009	78	12	given	give	VERB
iajs-2009	78	13	pair	pair	NOUN
iajs-2009	78	14	of	of	ADP
iajs-2009	78	15	vertices	vertex	NOUN
iajs-2009	78	16	,	,	PUNCT
iajs-2009	78	17	then	then	ADV
iajs-2009	78	18	edges	edge	NOUN
iajs-2009	78	19	referred	refer	VERB
iajs-2009	78	20	to	to	ADP
iajs-2009	78	21	as	as	SCONJ
iajs-2009	78	22	parallel	parallel	ADJ
iajs-2009	78	23	edges.a	edges.a	PUNCT
iajs-2009	78	24	simple	simple	ADJ
iajs-2009	78	25	graph	graph	NOUN
iajs-2009	78	26	is	be	AUX
iajs-2009	78	27	a	a	DET
iajs-2009	78	28	graph	graph	NOUN
iajs-2009	78	29	that	that	PRON
iajs-2009	78	30	has	have	VERB
iajs-2009	78	31	neither	neither	CCONJ
iajs-2009	78	32	loops	loop	NOUN
iajs-2009	78	33	nor	nor	CCONJ
iajs-2009	78	34	parallel	parallel	ADJ
iajs-2009	78	35	edges	edge	NOUN
iajs-2009	78	36	.	.	PUNCT
iajs-2009	79	1	a	a	DET
iajs-2009	79	2	graphˑ	graphˑ	ADJ
iajs-2009	79	3	g	g	NOUN
iajs-2009	79	4	is	be	AUX
iajs-2009	79	5	ˑsaid	ˑsaid	VERB
iajs-2009	79	6	to	to	PART
iajs-2009	79	7	be	be	AUX
iajs-2009	79	8	complete	complete	ADJ
iajs-2009	79	9	ˑ	ˑ	NOUN
iajs-2009	79	10	if	if	SCONJ
iajs-2009	79	11	everyˑ	everyˑ	VERB
iajs-2009	79	12	two	two	NUM
iajs-2009	79	13	distinct	distinct	ADJ
iajs-2009	79	14	ˑvertices	ˑvertice	NOUN
iajs-2009	79	15	areˑ	areˑ	VERB
iajs-2009	79	16	joined	join	VERB
iajs-2009	79	17	byˑ	byˑ	PROPN
iajs-2009	79	18	exactly	exactly	ADV
iajs-2009	79	19	one	one	NUM
iajs-2009	79	20	ˑedge	ˑedge	NOUN
iajs-2009	79	21	.	.	PUNCT
iajs-2009	80	1	ˑa	ˑa	PROPN
iajs-2009	80	2	ˑgraph	ˑgraph	PROPN
iajs-2009	80	3	ˑ	ˑ	PROPN
iajs-2009	80	4	g	g	NOUN
iajs-2009	80	5	is	be	AUX
iajs-2009	80	6	said	say	VERB
iajs-2009	80	7	ˑto	ˑto	NOUN
iajs-2009	80	8	be	be	AUX
iajs-2009	80	9	ˑbipartite	ˑbipartite	NOUN
iajs-2009	80	10	graph	graph	VERB
iajs-2009	80	11	ˑif	ˑif	ADV
iajs-2009	80	12	its	its	PRON
iajs-2009	80	13	vertex	vertex	NOUN
iajs-2009	80	14	ˑset	ˑset	NOUN
iajs-2009	80	15	)	)	PUNCT
iajs-2009	80	16	(	(	PUNCT
iajs-2009	80	17	gv	gv	AUX
iajs-2009	80	18	can	can	AUX
iajs-2009	80	19	ˑbe	ˑbe	VERB
iajs-2009	80	20	partitionedˑ	partitionedˑ	VERB
iajs-2009	80	21	into	into	ADP
iajs-2009	80	22	disjointˑ	disjointˑ	ADJ
iajs-2009	80	23	subsets	subset	NOUN
iajs-2009	80	24	1v	1v	NUM
iajs-2009	80	25	andˑ	andˑ	ADJ
iajs-2009	80	26	2v	2v	PROPN
iajs-2009	80	27	such	such	ADJ
iajs-2009	80	28	thatˑ	thatˑ	NOUN
iajs-2009	80	29	,	,	PUNCT
iajs-2009	80	30	every	every	DET
iajs-2009	80	31	edge	edge	NOUN
iajs-2009	80	32	of	of	ADP
iajs-2009	80	33	ˑ	ˑ	PROPN
iajs-2009	80	34	g	g	PROPN
iajs-2009	80	35	joinsˑ	joinsˑ	PROPN
iajs-2009	80	36	a	a	DET
iajs-2009	80	37	vertexˑ	vertexˑ	NOUN
iajs-2009	80	38	of	of	ADP
iajs-2009	80	39	1v	1v	NUM
iajs-2009	80	40	withˑ	withˑ	NOUN
iajs-2009	80	41	aˑ	aˑ	ADP
iajs-2009	80	42	vertex	vertex	NOUN
iajs-2009	80	43	ofˑ	ofˑ	X
iajs-2009	80	44	2v	2v	PROPN
iajs-2009	80	45	.	.	PUNCT
iajs-2009	81	1	soˑ	soˑ	PROPN
iajs-2009	81	2	,	,	PUNCT
iajs-2009	81	3	g	g	PROPN
iajs-2009	81	4	ˑ	ˑ	PROPN
iajs-2009	81	5	is	be	AUX
iajs-2009	81	6	calledˑ	calledˑ	VERB
iajs-2009	81	7	a	a	DET
iajs-2009	81	8	completeˑ	completeˑ	PROPN
iajs-2009	81	9	bipartiteˑˑ	bipartiteˑˑ	NOUN
iajs-2009	81	10	graphˑ	graphˑ	NOUN
iajs-2009	81	11	if	if	SCONJ
iajs-2009	81	12	every	every	DET
iajs-2009	81	13	vertexˑ	vertexˑ	NOUN
iajs-2009	81	14	in	in	ADP
iajs-2009	81	15	ˑone	ˑone	PROPN
iajs-2009	81	16	of	of	ADP
iajs-2009	81	17	theˑˑbipartition	theˑˑbipartition	NOUN
iajs-2009	81	18	subsetˑ	subsetˑ	PROPN
iajs-2009	81	19	isˑ	isˑ	NOUN
iajs-2009	81	20	joined	join	VERB
iajs-2009	81	21	to	to	ADP
iajs-2009	81	22	ˑevery	ˑevery	PROPN
iajs-2009	81	23	vertexˑ	vertexˑ	PROPN
iajs-2009	81	24	inˑ	inˑ	PROPN
iajs-2009	81	25	theˑ	theˑ	NOUN
iajs-2009	81	26	otherˑ	otherˑ	ADJ
iajs-2009	81	27	bipartition	bipartition	NOUN
iajs-2009	81	28	ˑˑsubset	ˑˑsubset	NOUN
iajs-2009	81	29	.	.	PUNCT
iajs-2009	82	1	if	if	SCONJ
iajs-2009	82	2	1v	1v	NUM
iajs-2009	82	3	andˑ	andˑ	ADJ
iajs-2009	82	4	2v	2v	PROPN
iajs-2009	82	5	haveˑ	haveˑ	VERB
iajs-2009	82	6	m	m	PROPN
iajs-2009	82	7	and	and	CCONJ
iajs-2009	82	8	n	n	PRON
iajs-2009	82	9	ˑvertices	ˑvertice	NOUN
iajs-2009	82	10	ˑrespectivelyˑ	ˑrespectivelyˑ	VERB
iajs-2009	82	11	,	,	PUNCT
iajs-2009	82	12	then	then	ADV
iajs-2009	82	13	a	a	DET
iajs-2009	82	14	completeˑˑ	completeˑˑ	NOUN
iajs-2009	82	15	bipartite	bipartite	PROPN
iajs-2009	82	16	ˑgraphˑ	ˑgraphˑ	NOUN
iajs-2009	82	17	will	will	AUX
iajs-2009	82	18	be	be	AUX
iajs-2009	82	19	denotedˑ	denotedˑ	VERB
iajs-2009	82	20	by	by	ADP
iajs-2009	82	21	nmk	nmk	NOUN
iajs-2009	82	22	,	,	PUNCT
iajs-2009	82	23	.	.	PUNCT
iajs-2009	83	1	consequently	consequently	ADV
iajs-2009	83	2	,	,	PUNCT
iajs-2009	83	3	a	a	DET
iajs-2009	83	4	star	star	NOUN
iajs-2009	83	5	ˑgraph	ˑgraph	NOUN
iajs-2009	83	6	is	be	AUX
iajs-2009	83	7	aˑ	aˑ	ADP
iajs-2009	83	8	complete	complete	ADJ
iajs-2009	83	9	bipartiteˑ	bipartiteˑ	NOUN
iajs-2009	83	10	graph	graph	NOUN
iajs-2009	83	11	ofˑ	ofˑ	PRON
iajs-2009	83	12	the	the	DET
iajs-2009	83	13	form	form	NOUN
iajs-2009	83	14	nk	nk	PROPN
iajs-2009	83	15	,	,	PUNCT
iajs-2009	83	16	1	1	NUM
iajs-2009	83	17	.ˑ	.ˑ	NOUN
iajs-2009	83	18	a	a	DET
iajs-2009	83	19	ˑgraph	ˑgraph	NOUN
iajs-2009	83	20	ˑgˑ	ˑgˑ	PROPN
iajs-2009	83	21	is	be	AUX
iajs-2009	83	22	saidˑ	saidˑ	NOUN
iajs-2009	83	23	to	to	PART
iajs-2009	83	24	beˑ	beˑ	VERB
iajs-2009	83	25	a	a	DET
iajs-2009	83	26	connected	connect	VERB
iajs-2009	83	27	if	if	SCONJ
iajs-2009	83	28	ˑthere	ˑthere	ADV
iajs-2009	83	29	is	be	AUX
iajs-2009	83	30	ˑa	ˑa	ADJ
iajs-2009	83	31	pathˑˑ	pathˑˑ	NOUN
iajs-2009	83	32	between	between	ADP
iajs-2009	83	33	anyˑ	anyˑ	NOUN
iajs-2009	83	34	given	give	VERB
iajs-2009	83	35	pairs	pair	NOUN
iajs-2009	83	36	ofˑ	ofˑ	NOUN
iajs-2009	83	37	vertices	vertex	NOUN
iajs-2009	83	38	,	,	PUNCT
iajs-2009	83	39	otherwiseˑ	otherwiseˑ	VERB
iajs-2009	83	40	the	the	DET
iajs-2009	83	41	graph	graph	NOUN
iajs-2009	83	42	is	be	AUX
iajs-2009	83	43	a	a	DET
iajs-2009	83	44	ˑdisconnected	ˑdisconnecte	VERB
iajs-2009	83	45	.	.	PUNCT
iajs-2009	84	1	the	the	DET
iajs-2009	84	2	neighborsˑ	neighborsˑ	NOUN
iajs-2009	84	3	of	of	ADP
iajs-2009	84	4	a	a	DET
iajs-2009	84	5	vertex	vertex	NOUN
iajs-2009	84	6	x	x	SYM
iajs-2009	84	7	inˑ	inˑ	VERB
iajs-2009	84	8	a	a	DET
iajs-2009	84	9	graphˑ	graphˑ	ADJ
iajs-2009	84	10	g	g	NOUN
iajs-2009	84	11	,	,	PUNCT
iajs-2009	84	12	denoted	denote	VERB
iajs-2009	84	13	ˑby	ˑby	ADV
iajs-2009	84	14	)	)	PUNCT
iajs-2009	84	15	(	(	PUNCT
iajs-2009	84	16	xn	xn	PROPN
iajs-2009	84	17	ˑare	ˑare	VERB
iajs-2009	84	18	the	the	DET
iajs-2009	84	19	set	set	ADJ
iajs-2009	84	20	ofˑ	ofˑ	NOUN
iajs-2009	84	21	vertices	vertex	NOUN
iajs-2009	84	22	that	that	PRON
iajs-2009	84	23	are	be	AUX
iajs-2009	84	24	ˑadjacent	ˑadjacent	ADJ
iajs-2009	84	25	to	to	ADP
iajs-2009	84	26	x	x	X
iajs-2009	84	27	.	.	PUNCT
iajs-2009	85	1	a	a	DET
iajs-2009	85	2	graph	graph	NOUN
iajs-2009	85	3	ˑh	ˑh	VERB
iajs-2009	85	4	is	be	AUX
iajs-2009	85	5	called	call	VERB
iajs-2009	85	6	a	a	DET
iajs-2009	85	7	subgraphˑ	subgraphˑ	NOUN
iajs-2009	85	8	of	of	ADP
iajs-2009	85	9	g	g	PROPN
iajs-2009	85	10	ˑ	ˑ	NOUN
iajs-2009	85	11	if	if	SCONJ
iajs-2009	85	12	)	)	PUNCT
iajs-2009	85	13	(	(	PUNCT
iajs-2009	85	14	)	)	PUNCT
iajs-2009	85	15	(	(	PUNCT
iajs-2009	85	16	gvhv	gvhv	NOUN
iajs-2009	85	17			PROPN
iajs-2009	85	18	ˑand	ˑand	PROPN
iajs-2009	85	19	)	)	PUNCT
iajs-2009	85	20	(	(	PUNCT
iajs-2009	85	21	)	)	PUNCT
iajs-2009	85	22	(	(	PUNCT
iajs-2009	85	23	gehe	gehe	NOUN
iajs-2009	85	24			PROPN
iajs-2009	85	25	.ˑ	.ˑ	PROPN
iajs-2009	86	1	two	two	NUM
iajs-2009	86	2	graphs	graph	NOUN
iajs-2009	86	3	1	1	NUM
iajs-2009	86	4	g	g	NOUN
iajs-2009	86	5	andˑ	andˑ	ADJ
iajs-2009	86	6	2	2	NUM
iajs-2009	86	7	g	g	NOUN
iajs-2009	86	8	are	be	AUX
iajs-2009	86	9	saidˑ	saidˑ	NOUN
iajs-2009	86	10	to	to	PART
iajs-2009	86	11	be	be	AUX
iajs-2009	86	12	isomorphicˑ	isomorphicˑ	PRON
iajs-2009	86	13	if	if	SCONJ
iajs-2009	86	14	there	there	PRON
iajs-2009	86	15	exists	exist	VERB
iajs-2009	86	16	ˑa	ˑa	ADJ
iajs-2009	86	17	bijective	bijective	ADJ
iajs-2009	86	18	mappingˑ	mappingˑ	NOUN
iajs-2009	86	19	)	)	PUNCT
iajs-2009	86	20	(	(	PUNCT
iajs-2009	86	21	)	)	PUNCT
iajs-2009	86	22	(:	(:	VERB
iajs-2009	86	23	21	21	NUM
iajs-2009	86	24	gvgvf	gvgvf	ADJ
iajs-2009	86	25			NOUN
iajs-2009	86	26	such	such	ADJ
iajs-2009	86	27	thatˑ	thatˑ	NOUN
iajs-2009	86	28	)	)	PUNCT
iajs-2009	86	29	(	(	PUNCT
iajs-2009	86	30	1geyx	1geyx	NUM
iajs-2009	86	31			NUM
iajs-2009	86	32	then	then	ADV
iajs-2009	86	33	ˑ	ˑ	NOUN
iajs-2009	86	34	)	)	PUNCT
iajs-2009	86	35	(	(	PUNCT
iajs-2009	86	36	)	)	PUNCT
iajs-2009	86	37	(	(	PUNCT
iajs-2009	86	38	)	)	PUNCT
iajs-2009	86	39	(	(	PUNCT
iajs-2009	86	40	2geyfxf	2geyfxf	NUM
iajs-2009	86	41			NUM
iajs-2009	86	42	.	.	PUNCT
iajs-2009	87	1	for	for	ADP
iajs-2009	87	2	more	more	ADJ
iajs-2009	87	3	ˑdetails	ˑdetail	NOUN
iajs-2009	87	4	we	we	PRON
iajs-2009	87	5	refer	refer	VERB
iajs-2009	87	6	ˑto	ˑto	NOUN
iajs-2009	88	1	[	[	X
iajs-2009	88	2	16	16	NUM
iajs-2009	88	3	]	]	X
iajs-2009	88	4	ˑ.	ˑ.	NOUN
iajs-2009	88	5	definitionˑ11	definitionˑ11	PROPN
iajs-2009	88	6	.	.	PUNCT
iajs-2009	89	1	letˑ	letˑ	ADJ
iajs-2009	89	2	a	a	DET
iajs-2009	89	3	be	be	NOUN
iajs-2009	89	4	aˑ	aˑ	ADP
iajs-2009	89	5	subset	subset	NOUN
iajs-2009	89	6	of	of	ADP
iajs-2009	89	7	a	a	DET
iajs-2009	89	8	kusemigroup	kusemigroup	NOUN
iajs-2009	89	9	ˑ	ˑ	NOUN
iajs-2009	89	10	)	)	PUNCT
iajs-2009	89	11	0	0	NUM
iajs-2009	89	12	,	,	PUNCT
iajs-2009	89	13	,	,	PUNCT
iajs-2009	89	14	,	,	PUNCT
iajs-2009	89	15	(	(	PUNCT
iajs-2009	89	16	x	x	X
iajs-2009	89	17	,	,	PUNCT
iajs-2009	89	18	then	then	ADV
iajs-2009	89	19	ˑwe	ˑwe	VERB
iajs-2009	89	20	define	define	VERB
iajs-2009	89	21	the	the	DET
iajs-2009	89	22	followingˑ	followingˑ	NOUN
iajs-2009	89	23	}	}	PUNCT
iajs-2009	89	24	,	,	PUNCT
iajs-2009	89	25	0,0	0,0	NOUN
iajs-2009	89	26	:	:	PUNCT
iajs-2009	89	27	{	{	PUNCT
iajs-2009	89	28	)	)	PUNCT
iajs-2009	89	29	(	(	PUNCT
iajs-2009	89	30	aaaxaxxxal	aaaxaxxxal	PROPN
iajs-2009	89	31			PROPN
iajs-2009	90	1			PROPN
iajs-2009	90	2	,	,	PUNCT
iajs-2009	90	3	ˑ	ˑ	PRON
iajs-2009	90	4	ˑ	ˑ	NOUN
iajs-2009	90	5	}	}	PUNCT
iajs-2009	90	6	,	,	PUNCT
iajs-2009	90	7	0,0	0,0	NOUN
iajs-2009	90	8	:	:	PUNCT
iajs-2009	90	9	{	{	PUNCT
iajs-2009	90	10	)	)	PUNCT
iajs-2009	90	11	(	(	PUNCT
iajs-2009	90	12	aaxaxaxxar	aaxaxaxxar	PROPN
iajs-2009	90	13			PUNCT
iajs-2009	91	1			PROPN
iajs-2009	91	2	.	.	PUNCT
iajs-2009	92	1	if	if	SCONJ
iajs-2009	92	2	ˑ	ˑ	X
iajs-2009	92	3	}	}	PUNCT
iajs-2009	92	4	{	{	PUNCT
iajs-2009	92	5	aa	aa	NOUN
iajs-2009	92	6			PROPN
iajs-2009	92	7	ˑ	ˑ	NOUN
iajs-2009	92	8	,	,	PUNCT
iajs-2009	92	9	then	then	ADV
iajs-2009	92	10	weˑ	weˑ	PROPN
iajs-2009	92	11	write	write	PROPN
iajs-2009	92	12	)	)	PUNCT
iajs-2009	92	13	(	(	PUNCT
iajs-2009	92	14	al	al	PROPN
iajs-2009	92	15	and	and	CCONJ
iajs-2009	92	16	)	)	PUNCT
iajs-2009	92	17	(	(	PUNCT
iajs-2009	92	18	ar	ar	NOUN
iajs-2009	92	19	ˑinstead	ˑinstead	NOUN
iajs-2009	92	20	of	of	ADP
iajs-2009	92	21	}	}	PUNCT
iajs-2009	92	22	)	)	PUNCT
iajs-2009	92	23	(	(	PUNCT
iajs-2009	92	24	{	{	PUNCT
iajs-2009	92	25	al	al	PROPN
iajs-2009	92	26	ˑand	ˑand	PROPN
iajs-2009	92	27	}	}	PUNCT
iajs-2009	92	28	)	)	PUNCT
iajs-2009	92	29	(	(	PUNCT
iajs-2009	92	30	{	{	PUNCT
iajs-2009	92	31	ar	ar	NOUN
iajs-2009	92	32	,	,	PUNCT
iajs-2009	92	33	ˑrespectively	ˑrespectively	ADV
iajs-2009	92	34	.	.	PUNCT
iajs-2009	93	1	proposition12.ˑ	proposition12.ˑ	PROPN
iajs-2009	93	2	let	let	VERB
iajs-2009	93	3	a	a	DET
iajs-2009	93	4	ˑand	ˑand	NOUN
iajs-2009	93	5	b	b	AUX
iajs-2009	93	6	be	be	AUX
iajs-2009	93	7	non	non	ADJ
iajs-2009	93	8	-	-	ADJ
iajs-2009	93	9	empty	empty	ADJ
iajs-2009	93	10	subsetsˑ	subsetsˑ	NOUN
iajs-2009	93	11	in	in	ADP
iajs-2009	93	12	)	)	PUNCT
iajs-2009	93	13	0	0	NUM
iajs-2009	93	14	,	,	PUNCT
iajs-2009	93	15	,	,	PUNCT
iajs-2009	93	16	,	,	PUNCT
iajs-2009	93	17	(	(	PUNCT
iajs-2009	93	18	x	x	X
iajs-2009	93	19	,	,	PUNCT
iajs-2009	93	20	then	then	ADV
iajs-2009	93	21	the	the	DET
iajs-2009	93	22	ˑfollowing	ˑfollowing	ADJ
iajs-2009	93	23	statements	statement	NOUN
iajs-2009	93	24	areˑ	areˑ	VERB
iajs-2009	93	25	true	true	ADJ
iajs-2009	93	26	:	:	PUNCT
iajs-2009	93	27	(	(	PUNCT
iajs-2009	93	28	1	1	NUM
iajs-2009	93	29	)	)	PUNCT
iajs-2009	93	30	)	)	PUNCT
iajs-2009	94	1	]	]	PUNCT
iajs-2009	94	2	(	(	PUNCT
iajs-2009	94	3	[	[	PUNCT
iajs-2009	94	4	alra	alra	NOUN
iajs-2009	94	5			PROPN
iajs-2009	94	6	andˑ	andˑ	NOUN
iajs-2009	94	7	)	)	PUNCT
iajs-2009	94	8	]	]	PUNCT
iajs-2009	94	9	(	(	PUNCT
iajs-2009	94	10	[	[	PUNCT
iajs-2009	94	11	arla	arla	NOUN
iajs-2009	94	12			PROPN
iajs-2009	94	13	,	,	PUNCT
iajs-2009	94	14	(	(	PUNCT
iajs-2009	94	15	2	2	X
iajs-2009	94	16	)	)	PUNCT
iajs-2009	94	17	ˑif	ˑif	DET
iajs-2009	94	18	ba	ba	PROPN
iajs-2009	94	19	,	,	PUNCT
iajs-2009	94	20	thenˑ	thenˑ	PROPN
iajs-2009	94	21	)	)	PUNCT
iajs-2009	94	22	(	(	PUNCT
iajs-2009	94	23	)	)	PUNCT
iajs-2009	94	24	(	(	PUNCT
iajs-2009	94	25	arbr	arbr	NOUN
iajs-2009	94	26			PROPN
iajs-2009	94	27	and	and	CCONJ
iajs-2009	94	28	ˑ	ˑ	NOUN
iajs-2009	94	29	)	)	PUNCT
iajs-2009	94	30	(	(	PUNCT
iajs-2009	94	31	)	)	PUNCT
iajs-2009	94	32	(	(	PUNCT
iajs-2009	94	33	albl	albl	NOUN
iajs-2009	94	34			PROPN
iajs-2009	94	35	,	,	PUNCT
iajs-2009	94	36	(	(	PUNCT
iajs-2009	94	37	3	3	X
iajs-2009	94	38	)	)	PUNCT
iajs-2009	94	39	ˑ	ˑ	NOUN
iajs-2009	94	40	)	)	PUNCT
iajs-2009	95	1	]	]	PUNCT
iajs-2009	95	2	]	]	X
iajs-2009	95	3	(	(	PUNCT
iajs-2009	95	4	[	[	X
iajs-2009	95	5	[	[	X
iajs-2009	95	6	)	)	PUNCT
iajs-2009	95	7	(	(	PUNCT
iajs-2009	95	8	arlrar	arlrar	NOUN
iajs-2009	95	9			PROPN
iajs-2009	95	10	ˑˑ	ˑˑ	NOUN
iajs-2009	95	11	andˑ	andˑ	ADJ
iajs-2009	95	12	)	)	PUNCT
iajs-2009	95	13	]	]	X
iajs-2009	96	1	]	]	X
iajs-2009	96	2	(	(	PUNCT
iajs-2009	96	3	[	[	X
iajs-2009	96	4	[	[	X
iajs-2009	96	5	)	)	PUNCT
iajs-2009	96	6	(	(	PUNCT
iajs-2009	96	7	alrlal	alrlal	PROPN
iajs-2009	96	8			NOUN
iajs-2009	96	9	.	.	PUNCT
iajs-2009	97	1	(	(	PUNCT
iajs-2009	97	2	4	4	X
iajs-2009	97	3	)	)	PUNCT
iajs-2009	97	4	ˑ	ˑ	NOUN
iajs-2009	97	5	)	)	PUNCT
iajs-2009	97	6	(	(	PUNCT
iajs-2009	97	7	)	)	PUNCT
iajs-2009	97	8	(	(	PUNCT
iajs-2009	97	9	)	)	PUNCT
iajs-2009	97	10	(	(	PUNCT
iajs-2009	97	11	brarbar	brarbar	VERB
iajs-2009	97	12			ADJ
iajs-2009	98	1			PROPN
iajs-2009	98	2	ˑˑandˑ	ˑˑandˑ	ADJ
iajs-2009	98	3	)	)	PUNCT
iajs-2009	98	4	(	(	PUNCT
iajs-2009	98	5	)	)	PUNCT
iajs-2009	98	6	(	(	PUNCT
iajs-2009	98	7	)	)	PUNCT
iajs-2009	98	8	(	(	PUNCT
iajs-2009	98	9	blalbal	blalbal	ADJ
iajs-2009	98	10			ADJ
iajs-2009	98	11			PROPN
iajs-2009	98	12	(	(	PUNCT
iajs-2009	98	13	5	5	NUM
iajs-2009	98	14	)	)	PUNCT
iajs-2009	98	15	ˑ	ˑ	NOUN
iajs-2009	98	16	)	)	PUNCT
iajs-2009	98	17	(	(	PUNCT
iajs-2009	98	18	)	)	PUNCT
iajs-2009	98	19	(	(	PUNCT
iajs-2009	98	20	)	)	PUNCT
iajs-2009	98	21	(	(	PUNCT
iajs-2009	98	22	barbrar	barbrar	NOUN
iajs-2009	98	23			ADJ
iajs-2009	98	24			PROPN
iajs-2009	98	25	ˑand	ˑand	PROPN
iajs-2009	98	26	)	)	PUNCT
iajs-2009	98	27	(	(	PUNCT
iajs-2009	98	28	)	)	PUNCT
iajs-2009	98	29	(	(	PUNCT
iajs-2009	98	30	)	)	PUNCT
iajs-2009	98	31	(	(	PUNCT
iajs-2009	98	32	balblal	balblal	X
iajs-2009	98	33			ADJ
iajs-2009	98	34			PROPN
iajs-2009	98	35	proof	proof	NOUN
iajs-2009	98	36	.	.	PUNCT
iajs-2009	99	1	(	(	PUNCT
iajs-2009	99	2	1	1	X
iajs-2009	99	3	)	)	PUNCT
iajs-2009	99	4	let	let	VERB
iajs-2009	99	5	ˑ	ˑ	NOUN
iajs-2009	99	6	aa	aa	NOUN
iajs-2009	99	7	ˑand	ˑand	NOUN
iajs-2009	99	8	)	)	PUNCT
iajs-2009	99	9	(	(	PUNCT
iajs-2009	99	10	alx	alx	INTJ
iajs-2009	99	11	,	,	PUNCT
iajs-2009	99	12	ˑthen	ˑthen	ADV
iajs-2009	99	13	0,0	0,0	NUM
iajs-2009	99	14			NOUN
iajs-2009	99	15	axax	axax	NOUN
iajs-2009	99	16			PROPN
iajs-2009	99	17	.	.	PUNCT
iajs-2009	100	1	it	it	PRON
iajs-2009	100	2	follows	follow	VERB
iajs-2009	100	3	that	that	PRON
iajs-2009	100	4	)	)	PUNCT
iajs-2009	101	1	]	]	PUNCT
iajs-2009	101	2	(	(	PUNCT
iajs-2009	101	3	[	[	PUNCT
iajs-2009	101	4	alra	alra	NOUN
iajs-2009	101	5	,	,	PUNCT
iajs-2009	101	6	hence	hence	ADV
iajs-2009	101	7	)	)	PUNCT
iajs-2009	101	8	]	]	PUNCT
iajs-2009	101	9	(	(	PUNCT
iajs-2009	101	10	[	[	PUNCT
iajs-2009	101	11	alra	alra	NOUN
iajs-2009	101	12			PROPN
iajs-2009	101	13	.	.	PUNCT
iajs-2009	102	1	similarlyˑ	similarlyˑ	PROPN
iajs-2009	102	2	,	,	PUNCT
iajs-2009	102	3	)	)	PUNCT
iajs-2009	102	4	]	]	PUNCT
iajs-2009	102	5	(	(	PUNCT
iajs-2009	102	6	[	[	PUNCT
iajs-2009	102	7	arla	arla	PROPN
iajs-2009	102	8			PROPN
iajs-2009	102	9	.	.	PUNCT
iajs-2009	103	1	(	(	PUNCT
iajs-2009	103	2	2	2	X
iajs-2009	103	3	)	)	PUNCT
iajs-2009	103	4	suppose	suppose	VERB
iajs-2009	103	5	thatˑ	thatˑ	NOUN
iajs-2009	103	6	ba	ba	PROPN
iajs-2009	103	7	and	and	CCONJ
iajs-2009	103	8	)	)	PUNCT
iajs-2009	103	9	(	(	PUNCT
iajs-2009	103	10	brx	brx	PROPN
iajs-2009	103	11	,	,	PUNCT
iajs-2009	103	12	ˑthen	ˑthen	ADV
iajs-2009	103	13	0,0	0,0	NUM
iajs-2009	103	14			NOUN
iajs-2009	103	15	xbxb	xbxb	VERB
iajs-2009	103	16			PROPN
iajs-2009	103	17	for	for	ADP
iajs-2009	103	18	all	all	DET
iajs-2009	103	19	bb	bb	NOUN
iajs-2009	103	20	.	.	PUNCT
iajs-2009	104	1	abxbxbtherforebabut	abxbxbtherforebabut	PROPN
iajs-2009	104	2			NUM
iajs-2009	104	3	0,0	0,0	NOUN
iajs-2009	104	4	,	,	PUNCT
iajs-2009	104	5			PROPN
iajs-2009	104	6	.	.	PUNCT
iajs-2009	105	1	so	so	ADV
iajs-2009	105	2	)	)	PUNCT
iajs-2009	105	3	(	(	PUNCT
iajs-2009	105	4	arx	arx	PROPN
iajs-2009	105	5	,	,	PUNCT
iajs-2009	105	6	ˑ	ˑ	NOUN
iajs-2009	105	7	hence	hence	ADV
iajs-2009	105	8	)	)	PUNCT
iajs-2009	105	9	(	(	PUNCT
iajs-2009	105	10	)	)	PUNCT
iajs-2009	105	11	(	(	PUNCT
iajs-2009	105	12	arbr	arbr	NOUN
iajs-2009	105	13			PROPN
iajs-2009	105	14	.	.	PUNCT
iajs-2009	106	1	similarly,ˑ	similarly,ˑ	X
iajs-2009	106	2	)	)	PUNCT
iajs-2009	106	3	(	(	PUNCT
iajs-2009	106	4	)	)	PUNCT
iajs-2009	106	5	(	(	PUNCT
iajs-2009	106	6	albl	albl	NOUN
iajs-2009	106	7			PROPN
iajs-2009	106	8	.	.	PUNCT
iajs-2009	107	1	(	(	PUNCT
iajs-2009	107	2	3	3	X
iajs-2009	107	3	)	)	PUNCT
iajs-2009	107	4	by	by	ADP
iajs-2009	107	5	usingˑ	usingˑ	NOUN
iajs-2009	107	6	(	(	PUNCT
iajs-2009	107	7	1	1	NUM
iajs-2009	107	8	)	)	PUNCT
iajs-2009	107	9	andˑ	andˑ	NOUN
iajs-2009	107	10	(	(	PUNCT
iajs-2009	107	11	2	2	X
iajs-2009	107	12	)	)	PUNCT
iajs-2009	107	13	we	we	PRON
iajs-2009	107	14	have	have	VERB
iajs-2009	107	15	ˑ	ˑ	NOUN
iajs-2009	107	16	)	)	PUNCT
iajs-2009	107	17	]	]	PUNCT
iajs-2009	107	18	(	(	PUNCT
iajs-2009	107	19	[	[	PUNCT
iajs-2009	107	20	alra	alra	NOUN
iajs-2009	107	21			NOUN
iajs-2009	107	22	ˑand	ˑand	CCONJ
iajs-2009	107	23	)	)	PUNCT
iajs-2009	107	24	]	]	PUNCT
iajs-2009	107	25	(	(	PUNCT
iajs-2009	107	26	[	[	PUNCT
iajs-2009	107	27	arla	arla	PROPN
iajs-2009	107	28			PROPN
iajs-2009	107	29	ˑimpliesˑˑ	ˑimpliesˑˑ	PROPN
iajs-2009	107	30	that	that	SCONJ
iajs-2009	107	31	byˑ	byˑ	NOUN
iajs-2009	107	32	(	(	PUNCT
iajs-2009	107	33	2	2	NUM
iajs-2009	107	34	)	)	PUNCT
iajs-2009	107	35	)	)	PUNCT
iajs-2009	107	36	(	(	PUNCT
iajs-2009	107	37	)	)	PUNCT
iajs-2009	108	1	]	]	X
iajs-2009	108	2	]	]	X
iajs-2009	108	3	(	(	PUNCT
iajs-2009	108	4	[	[	X
iajs-2009	108	5	[	[	PUNCT
iajs-2009	108	6	alalrl	alalrl	NOUN
iajs-2009	108	7			PROPN
iajs-2009	108	8	and	and	CCONJ
iajs-2009	108	9	)	)	PUNCT
iajs-2009	108	10	(	(	PUNCT
iajs-2009	108	11	)	)	PUNCT
iajs-2009	108	12	]	]	X
iajs-2009	108	13	]	]	X
iajs-2009	108	14	(	(	PUNCT
iajs-2009	108	15	[	[	X
iajs-2009	108	16	[	[	PUNCT
iajs-2009	108	17	ararlr	ararlr	NOUN
iajs-2009	108	18			PROPN
iajs-2009	108	19	.	.	PUNCT
iajs-2009	109	1	if	if	SCONJ
iajs-2009	109	2	ˑˑweˑ	ˑˑweˑ	X
iajs-2009	109	3	applyˑ	applyˑ	ADV
iajs-2009	109	4	(	(	PUNCT
iajs-2009	109	5	1	1	NUM
iajs-2009	109	6	)	)	PUNCT
iajs-2009	109	7	to	to	PART
iajs-2009	109	8	)	)	PUNCT
iajs-2009	109	9	(	(	PUNCT
iajs-2009	109	10	al	al	PROPN
iajs-2009	109	11	and	and	CCONJ
iajs-2009	109	12	ˑ	ˑ	PROPN
iajs-2009	109	13	)	)	PUNCT
iajs-2009	109	14	(	(	PUNCT
iajs-2009	109	15	ar	ar	PROPN
iajs-2009	109	16	,	,	PUNCT
iajs-2009	109	17	then	then	ADV
iajs-2009	109	18	mathematics	mathematics	PROPN
iajs-2009	109	19	|	|	ADV
iajs-2009	109	20	164	164	NUM
iajs-2009	109	21	ibn	ibn	PROPN
iajs-2009	109	22	al	al	PROPN
iajs-2009	109	23	-	-	PUNCT
iajs-2009	109	24	haitham	haitham	PROPN
iajs-2009	109	25	jour	jour	X
iajs-2009	109	26	.	.	PROPN
iajs-2009	109	27	for	for	ADP
iajs-2009	109	28	pure	pure	ADJ
iajs-2009	109	29	&	&	CCONJ
iajs-2009	109	30	appl	appl	PROPN
iajs-2009	109	31	.	.	PUNCT
iajs-2009	110	1	sci	sci	PROPN
iajs-2009	110	2	.	.	PROPN
iajs-2009	110	3	ihjpas	ihjpas	PROPN
iajs-2009	110	4	https://doi.org/10.30526/31.3.2009	https://doi.org/10.30526/31.3.2009	PROPN
iajs-2009	110	5	vol	vol	NOUN
iajs-2009	110	6	.	.	PROPN
iajs-2009	111	1	31	31	NUM
iajs-2009	112	1	(	(	PUNCT
iajs-2009	112	2	3	3	NUM
iajs-2009	112	3	)	)	PUNCT
iajs-2009	112	4	2018	2018	NUM
iajs-2009	112	5	)	)	PUNCT
iajs-2009	113	1	]	]	PUNCT
iajs-2009	113	2	]	]	X
iajs-2009	113	3	(	(	PUNCT
iajs-2009	113	4	[	[	X
iajs-2009	113	5	[	[	X
iajs-2009	113	6	)	)	PUNCT
iajs-2009	113	7	(	(	PUNCT
iajs-2009	113	8	alrlal	alrlal	X
iajs-2009	113	9			PROPN
iajs-2009	113	10	andˑ	andˑ	NOUN
iajs-2009	113	11	)	)	PUNCT
iajs-2009	114	1	]	]	PUNCT
iajs-2009	114	2	]	]	X
iajs-2009	114	3	(	(	PUNCT
iajs-2009	114	4	[	[	X
iajs-2009	114	5	[	[	X
iajs-2009	114	6	)	)	PUNCT
iajs-2009	114	7	(	(	PUNCT
iajs-2009	114	8	arlrar	arlrar	NOUN
iajs-2009	114	9			PROPN
iajs-2009	114	10	.	.	PUNCT
iajs-2009	115	1	henceˑˑ	henceˑˑ	PROPN
iajs-2009	115	2	)	)	PUNCT
iajs-2009	116	1	]	]	X
iajs-2009	116	2	]	]	X
iajs-2009	116	3	(	(	PUNCT
iajs-2009	116	4	[	[	X
iajs-2009	116	5	[	[	X
iajs-2009	116	6	)	)	PUNCT
iajs-2009	116	7	(	(	PUNCT
iajs-2009	116	8	arlrar	arlrar	NOUN
iajs-2009	116	9			PROPN
iajs-2009	116	10	andˑ	andˑ	NOUN
iajs-2009	116	11	)	)	PUNCT
iajs-2009	117	1	]	]	PUNCT
iajs-2009	117	2	]	]	X
iajs-2009	117	3	(	(	PUNCT
iajs-2009	117	4	[	[	X
iajs-2009	117	5	[	[	X
iajs-2009	117	6	)	)	PUNCT
iajs-2009	117	7	(	(	PUNCT
iajs-2009	117	8	alrlal	alrlal	PROPN
iajs-2009	117	9			NOUN
iajs-2009	117	10	.	.	PUNCT
iajs-2009	118	1	(	(	PUNCT
iajs-2009	118	2	4	4	X
iajs-2009	118	3	)	)	PUNCT
iajs-2009	118	4	sinceˑ	sinceˑ	NOUN
iajs-2009	118	5	baa	baa	PROPN
iajs-2009	118	6			PROPN
iajs-2009	118	7	and	and	CCONJ
iajs-2009	118	8	bab	bab	PROPN
iajs-2009	118	9			PROPN
iajs-2009	118	10	,	,	PUNCT
iajs-2009	118	11	weˑ	weˑ	PROPN
iajs-2009	118	12	have	have	VERB
iajs-2009	118	13	by	by	ADP
iajs-2009	118	14	ˑpart	ˑpart	NOUN
iajs-2009	118	15	(	(	PUNCT
iajs-2009	118	16	2	2	NUM
iajs-2009	118	17	)	)	PUNCT
iajs-2009	118	18	of	of	ADP
iajs-2009	118	19	ˑproposition	ˑproposition	NOUN
iajs-2009	118	20	3.2	3.2	NUM
iajs-2009	118	21	thatˑ	thatˑ	NOUN
iajs-2009	118	22	,	,	PUNCT
iajs-2009	118	23	)	)	PUNCT
iajs-2009	118	24	(	(	PUNCT
iajs-2009	118	25	)	)	PUNCT
iajs-2009	118	26	(	(	PUNCT
iajs-2009	118	27	arbar	arbar	NOUN
iajs-2009	118	28			PROPN
iajs-2009	118	29	and	and	CCONJ
iajs-2009	118	30	)	)	PUNCT
iajs-2009	118	31	(	(	PUNCT
iajs-2009	118	32	)	)	PUNCT
iajs-2009	118	33	(	(	PUNCT
iajs-2009	118	34	brbar	brbar	NOUN
iajs-2009	118	35			NUM
iajs-2009	118	36	,	,	PUNCT
iajs-2009	118	37	hence	hence	ADV
iajs-2009	118	38	)	)	PUNCT
iajs-2009	118	39	(	(	PUNCT
iajs-2009	118	40	)	)	PUNCT
iajs-2009	118	41	(	(	PUNCT
iajs-2009	118	42	)	)	PUNCT
iajs-2009	118	43	(	(	PUNCT
iajs-2009	118	44	)	)	PUNCT
iajs-2009	118	45	(	(	PUNCT
iajs-2009	118	46	ibrarbar	ibrarbar	PROPN
iajs-2009	118	47			PROPN
iajs-2009	118	48			ADJ
iajs-2009	118	49	converselyˑ	converselyˑ	NOUN
iajs-2009	118	50	,	,	PUNCT
iajs-2009	118	51	ifˑ	ifˑ	NOUN
iajs-2009	118	52	)	)	PUNCT
iajs-2009	118	53	(	(	PUNCT
iajs-2009	118	54	)	)	PUNCT
iajs-2009	118	55	(	(	PUNCT
iajs-2009	118	56	brarx	brarx	PROPN
iajs-2009	118	57			PROPN
iajs-2009	118	58	,	,	PUNCT
iajs-2009	118	59	ˑthen	ˑthen	ADV
iajs-2009	118	60	)	)	PUNCT
iajs-2009	118	61	(	(	PUNCT
iajs-2009	118	62	)	)	PUNCT
iajs-2009	118	63	(	(	PUNCT
iajs-2009	118	64	brxandarx	brxandarx	ADV
iajs-2009	118	65			X
iajs-2009	118	66	,	,	PUNCT
iajs-2009	118	67	ˑ	ˑ	AUX
iajs-2009	118	68	therefore	therefore	ADV
iajs-2009	118	69	aaxaxa	aaxaxa	VERB
iajs-2009	118	70			PRON
iajs-2009	118	71	,	,	PUNCT
iajs-2009	118	72	0,0	0,0	NUM
iajs-2009	118	73			PROPN
iajs-2009	118	74	andˑ	andˑ	NOUN
iajs-2009	118	75	bbxbxb	bbxbxb	NOUN
iajs-2009	118	76			PROPN
iajs-2009	118	77	,	,	PUNCT
iajs-2009	118	78	0,0	0,0	NUM
iajs-2009	118	79			PROPN
iajs-2009	118	80	.	.	PUNCT
iajs-2009	119	1	butˑ	butˑ	PROPN
iajs-2009	119	2	ˑifˑ	ˑifˑ	PROPN
iajs-2009	119	3			PROPN
iajs-2009	119	4	bac	bac	NOUN
iajs-2009	119	5			NOUN
iajs-2009	119	6	,	,	PUNCT
iajs-2009	119	7	ˑthen	ˑthen	ADV
iajs-2009	119	8	)	)	PUNCT
iajs-2009	119	9	(	(	PUNCT
iajs-2009	119	10	,	,	PUNCT
iajs-2009	119	11	0,0	0,0	NUM
iajs-2009	119	12	bacxcxc	bacxcxc	PROPN
iajs-2009	119	13			NOUN
iajs-2009	119	14			PROPN
iajs-2009	119	15	weˑ	weˑ	PROPN
iajs-2009	119	16	haveˑ	haveˑ	PROPN
iajs-2009	119	17	)	)	PUNCT
iajs-2009	119	18	(	(	PUNCT
iajs-2009	119	19	barx	barx	NOUN
iajs-2009	119	20			NOUN
iajs-2009	119	21	,	,	PUNCT
iajs-2009	119	22	henceˑ	henceˑ	NOUN
iajs-2009	119	23	)	)	PUNCT
iajs-2009	119	24	(	(	PUNCT
iajs-2009	119	25	)	)	PUNCT
iajs-2009	119	26	(	(	PUNCT
iajs-2009	119	27	)	)	PUNCT
iajs-2009	119	28	(	(	PUNCT
iajs-2009	119	29	)	)	PUNCT
iajs-2009	119	30	(	(	PUNCT
iajs-2009	119	31	iibarbrar	iibarbrar	NOUN
iajs-2009	119	32			PROPN
iajs-2009	119	33			NOUN
iajs-2009	119	34	fromˑ	fromˑ	NOUN
iajs-2009	119	35	(	(	PUNCT
iajs-2009	119	36	i)ˑ	i)ˑ	X
iajs-2009	119	37	and	and	CCONJ
iajs-2009	119	38	(	(	PUNCT
iajs-2009	119	39	ii	ii	NOUN
iajs-2009	119	40	)	)	PUNCT
iajs-2009	119	41	,	,	PUNCT
iajs-2009	119	42	ˑwe	ˑwe	PROPN
iajs-2009	119	43	have	have	VERB
iajs-2009	119	44	)	)	PUNCT
iajs-2009	119	45	(	(	PUNCT
iajs-2009	119	46	)	)	PUNCT
iajs-2009	119	47	(	(	PUNCT
iajs-2009	119	48	)	)	PUNCT
iajs-2009	119	49	(	(	PUNCT
iajs-2009	119	50	brarbar	brarbar	VERB
iajs-2009	119	51			ADV
iajs-2009	119	52			PROPN
iajs-2009	119	53	.ˑ	.ˑ	NOUN
iajs-2009	119	54	similarly	similarly	ADV
iajs-2009	119	55	,	,	PUNCT
iajs-2009	119	56	)	)	PUNCT
iajs-2009	119	57	(	(	PUNCT
iajs-2009	119	58	)	)	PUNCT
iajs-2009	119	59	(	(	PUNCT
iajs-2009	119	60	)	)	PUNCT
iajs-2009	119	61	(	(	PUNCT
iajs-2009	119	62	blalbal	blalbal	ADJ
iajs-2009	119	63			ADJ
iajs-2009	119	64			PROPN
iajs-2009	119	65	.	.	PUNCT
iajs-2009	120	1	(	(	PUNCT
iajs-2009	120	2	5	5	X
iajs-2009	120	3	)	)	PUNCT
iajs-2009	120	4	we	we	PRON
iajs-2009	120	5	ˑhave	ˑhave	VERB
iajs-2009	120	6	baa	baa	PROPN
iajs-2009	120	7			PROPN
iajs-2009	120	8	,	,	PUNCT
iajs-2009	120	9	bab	bab	PROPN
iajs-2009	120	10			PROPN
iajs-2009	120	11	ˑ	ˑ	NOUN
iajs-2009	120	12	from	from	ADP
iajs-2009	120	13	(	(	PUNCT
iajs-2009	120	14	2	2	NUM
iajs-2009	120	15	)	)	PUNCT
iajs-2009	120	16	)	)	PUNCT
iajs-2009	121	1	(	(	PUNCT
iajs-2009	121	2	)	)	PUNCT
iajs-2009	121	3	(	(	PUNCT
iajs-2009	121	4	barar	barar	NOUN
iajs-2009	121	5			NOUN
iajs-2009	121	6	and	and	CCONJ
iajs-2009	121	7	)	)	PUNCT
iajs-2009	121	8	(	(	PUNCT
iajs-2009	121	9	)	)	PUNCT
iajs-2009	121	10	(	(	PUNCT
iajs-2009	121	11	barbr	barbr	PROPN
iajs-2009	121	12			PROPN
iajs-2009	121	13	which	which	PRON
iajs-2009	121	14	impliesˑ	impliesˑ	VERB
iajs-2009	121	15	that	that	PRON
iajs-2009	121	16	)	)	PUNCT
iajs-2009	121	17	(	(	PUNCT
iajs-2009	121	18	)	)	PUNCT
iajs-2009	121	19	(	(	PUNCT
iajs-2009	121	20	)	)	PUNCT
iajs-2009	121	21	(	(	PUNCT
iajs-2009	121	22	barbrar	barbrar	NOUN
iajs-2009	121	23			ADJ
iajs-2009	121	24			PROPN
iajs-2009	121	25	.	.	PUNCT
iajs-2009	122	1	similarlyˑ	similarlyˑ	PROPN
iajs-2009	122	2	,	,	PUNCT
iajs-2009	122	3	)	)	PUNCT
iajs-2009	122	4	(	(	PUNCT
iajs-2009	122	5	)	)	PUNCT
iajs-2009	122	6	(	(	PUNCT
iajs-2009	122	7	)	)	PUNCT
iajs-2009	122	8	(	(	PUNCT
iajs-2009	122	9	balblal	balblal	X
iajs-2009	122	10			ADJ
iajs-2009	122	11			PROPN
iajs-2009	122	12	.ˑ	.ˑ	PROPN
iajs-2009	122	13	example	example	NOUN
iajs-2009	123	1	ˑ13.ˑ	ˑ13.ˑ	ADJ
iajs-2009	123	2	letˑ	letˑ	PROPN
iajs-2009	123	3	}	}	PUNCT
iajs-2009	123	4	3,2,1,0{x	3,2,1,0{x	NUM
iajs-2009	123	5	beˑa	beˑa	PROPN
iajs-2009	123	6	ˑsetˑ.	ˑsetˑ.	PROPN
iajs-2009	123	7	define	define	VERB
iajs-2009	123	8			PROPN
iajs-2009	123	9	-ˑoperation	-ˑoperation	NOUN
iajs-2009	123	10	and	and	CCONJ
iajs-2009	123	11			PROPN
iajs-2009	123	12	-ˑoperation	-ˑoperation	NOUN
iajs-2009	123	13	by	by	ADP
iajs-2009	123	14	the	the	DET
iajs-2009	123	15	following	follow	VERB
iajs-2009	123	16	tables	table	NOUN
iajs-2009	123	17	then	then	ADV
iajs-2009	123	18	)	)	PUNCT
iajs-2009	123	19	0	0	NUM
iajs-2009	123	20	,	,	PUNCT
iajs-2009	123	21	,	,	PUNCT
iajs-2009	123	22	,	,	PUNCT
iajs-2009	123	23	(	(	PUNCT
iajs-2009	123	24	x	x	VERB
iajs-2009	123	25	is	be	AUX
iajs-2009	123	26	a	a	DET
iajs-2009	123	27	ku	ku	PROPN
iajs-2009	123	28	-	-	PUNCT
iajs-2009	123	29	semigroup	semigroup	NOUN
iajs-2009	123	30	.	.	PUNCT
iajs-2009	124	1	we	we	PRON
iajs-2009	124	2	have	have	VERB
iajs-2009	124	3	the	the	DET
iajs-2009	124	4	following	follow	VERB
iajs-2009	124	5	}	}	PUNCT
iajs-2009	124	6	3,0{})2,1({})2,0({})1,0	3,0{})2,1({})2,0({})1,0	PROPN
iajs-2009	124	7	(	(	PUNCT
iajs-2009	124	8	{	{	PUNCT
iajs-2009	124	9			NOUN
iajs-2009	124	10	rrr	rrr	NOUN
iajs-2009	124	11	,	,	PUNCT
iajs-2009	124	12	}	}	PUNCT
iajs-2009	124	13	2,0{})3,0	2,0{})3,0	X
iajs-2009	124	14	(	(	PUNCT
iajs-2009	124	15	{	{	PUNCT
iajs-2009	124	16	r	r	NOUN
iajs-2009	124	17	and	and	CCONJ
iajs-2009	124	18	}	}	PUNCT
iajs-2009	124	19	0{})3,2({})3,1	0{})3,2({})3,1	NUM
iajs-2009	124	20	(	(	PUNCT
iajs-2009	124	21	{	{	PUNCT
iajs-2009	124	22			NUM
iajs-2009	124	23	rr	rr	NOUN
iajs-2009	124	24	.	.	PUNCT
iajs-2009	125	1	also	also	ADV
iajs-2009	125	2	,	,	PUNCT
iajs-2009	125	3	}	}	PUNCT
iajs-2009	125	4	2,1,0{})3,0({},0{})2,1({},3,0{})2,0({},0{})1,0	2,1,0{})3,0({},0{})2,1({},3,0{})2,0({},0{})1,0	NUM
iajs-2009	125	5	(	(	PUNCT
iajs-2009	125	6	{	{	PUNCT
iajs-2009	125	7			ADP
iajs-2009	125	8	llll	llll	NOUN
iajs-2009	125	9	and	and	CCONJ
iajs-2009	125	10	}	}	PUNCT
iajs-2009	125	11	0{})3,2({})3,1	0{})3,2({})3,1	NUM
iajs-2009	125	12	(	(	PUNCT
iajs-2009	125	13	{	{	PUNCT
iajs-2009	125	14			NUM
iajs-2009	125	15	ll	ll	NOUN
iajs-2009	125	16	.	.	PUNCT
iajs-2009	126	1	remark	remark	VERB
iajs-2009	126	2	14	14	NUM
iajs-2009	126	3	.	.	PUNCT
iajs-2009	127	1	if	if	SCONJ
iajs-2009	127	2	)	)	PUNCT
iajs-2009	127	3	0	0	NUM
iajs-2009	127	4	,	,	PUNCT
iajs-2009	127	5	,	,	PUNCT
iajs-2009	127	6	,	,	PUNCT
iajs-2009	127	7	(	(	PUNCT
iajs-2009	127	8	x	x	VERB
iajs-2009	127	9	is	be	AUX
iajs-2009	127	10	a	a	DET
iajs-2009	127	11	ku	ku	PROPN
iajs-2009	127	12	-	-	PUNCT
iajs-2009	127	13	semigroup	semigroup	PROPN
iajs-2009	127	14	,	,	PUNCT
iajs-2009	127	15	then	then	ADV
iajs-2009	127	16	(	(	PUNCT
iajs-2009	127	17	i	i	NOUN
iajs-2009	127	18	)	)	PUNCT
iajs-2009	127	19	xrl	xrl	ADV
iajs-2009	127	20			NUM
iajs-2009	127	21	}	}	PUNCT
iajs-2009	127	22	)	)	PUNCT
iajs-2009	128	1	0({})0	0({})0	X
iajs-2009	128	2	(	(	PUNCT
iajs-2009	128	3	{	{	PUNCT
iajs-2009	128	4	,	,	PUNCT
iajs-2009	128	5	(	(	PUNCT
iajs-2009	128	6	ii	ii	NOUN
iajs-2009	128	7	)	)	PUNCT
iajs-2009	128	8	}	}	PUNCT
iajs-2009	128	9	0	0	NUM
iajs-2009	128	10	{	{	PUNCT
iajs-2009	128	11	}	}	PUNCT
iajs-2009	128	12	)	)	PUNCT
iajs-2009	128	13	(	(	PUNCT
iajs-2009	128	14	{	{	PUNCT
iajs-2009	128	15	}	}	PUNCT
iajs-2009	128	16	)	)	PUNCT
iajs-2009	128	17	(	(	PUNCT
iajs-2009	128	18	{	{	PUNCT
iajs-2009	128	19			NUM
iajs-2009	128	20	xrxl	xrxl	NOUN
iajs-2009	128	21	.	.	PUNCT
iajs-2009	129	1	proof	proof	NOUN
iajs-2009	129	2	.	.	PUNCT
iajs-2009	130	1	ˑclear	ˑclear	NOUN
iajs-2009	130	2	.	.	PUNCT
iajs-2009	131	1	lemma	lemma	PROPN
iajs-2009	131	2	ˑ15.ˑ	ˑ15.ˑ	PROPN
iajs-2009	131	3	let	let	VERB
iajs-2009	131	4	)	)	PUNCT
iajs-2009	131	5	0	0	NUM
iajs-2009	131	6	,	,	PUNCT
iajs-2009	131	7	,	,	PUNCT
iajs-2009	131	8	,	,	PUNCT
iajs-2009	131	9	(	(	PUNCT
iajs-2009	131	10	x	x	VERB
iajs-2009	131	11	ˑbe	ˑbe	VERB
iajs-2009	131	12	a	a	DET
iajs-2009	131	13	ku-ˑsemigroup	ku-ˑsemigroup	NOUN
iajs-2009	131	14	and	and	CCONJ
iajs-2009	131	15	aˑ	aˑ	ADP
iajs-2009	131	16	ku	ku	PROPN
iajs-2009	131	17	-	-	PUNCT
iajs-2009	131	18	algebra	algebra	PROPN
iajs-2009	131	19	beˑ	beˑ	NOUN
iajs-2009	131	20	a	a	DET
iajs-2009	131	21	commutative	commutative	ADJ
iajs-2009	131	22	,	,	PUNCT
iajs-2009	131	23	then	then	ADV
iajs-2009	131	24	forˑ	forˑ	VERB
iajs-2009	131	25	any	any	DET
iajs-2009	131	26	elements	element	NOUN
iajs-2009	131	27	ˑ	ˑ	ADP
iajs-2009	131	28	a	a	PRON
iajs-2009	131	29	and	and	CCONJ
iajs-2009	131	30	b	b	NOUN
iajs-2009	131	31	of	of	ADP
iajs-2009	131	32	x	x	SYM
iajs-2009	131	33	.	.	PUNCT
iajs-2009	132	1	if	if	SCONJ
iajs-2009	132	2	0ba	0ba	X
iajs-2009	132	3	,	,	PUNCT
iajs-2009	132	4	ˑthen	ˑthen	ADV
iajs-2009	132	5	}	}	PUNCT
iajs-2009	132	6	)	)	PUNCT
iajs-2009	132	7	(	(	PUNCT
iajs-2009	132	8	{	{	PUNCT
iajs-2009	132	9	}	}	PUNCT
iajs-2009	132	10	)	)	PUNCT
iajs-2009	132	11	(	(	PUNCT
iajs-2009	132	12	{	{	PUNCT
iajs-2009	132	13	blal	blal	NOUN
iajs-2009	132	14			PROPN
iajs-2009	132	15	.	.	PUNCT
iajs-2009	133	1	proof.ˑˑsupposeˑ	proof.ˑˑsupposeˑ	NOUN
iajs-2009	133	2	ˑthat	ˑthat	NOUN
iajs-2009	133	3	0ba	0ba	INTJ
iajs-2009	133	4	.	.	PUNCT
iajs-2009	134	1	let	let	VERB
iajs-2009	134	2	0,0	0,0	NOUN
iajs-2009	134	3	}	}	PUNCT
iajs-2009	134	4	)	)	PUNCT
iajs-2009	134	5	(	(	PUNCT
iajs-2009	134	6	{	{	PUNCT
iajs-2009	134	7			NUM
iajs-2009	134	8	axaxalx	axaxalx	X
iajs-2009	134	9			PROPN
iajs-2009	134	10	,	,	PUNCT
iajs-2009	134	11	then	then	ADV
iajs-2009	134	12	by	by	ADP
iajs-2009	134	13	lemma	lemma	PROPN
iajs-2009	134	14	6	6	NUM
iajs-2009	134	15	)	)	PUNCT
iajs-2009	134	16	(	(	PUNCT
iajs-2009	134	17	)	)	PUNCT
iajs-2009	134	18	(	(	PUNCT
iajs-2009	134	19	0)()()(0	0)()()(0	NUM
iajs-2009	134	20	bxbxbxaxbax	bxbxbxaxbax	ADJ
iajs-2009	134	21			PROPN
iajs-2009	134	22	and	and	CCONJ
iajs-2009	134	23	*	*	SYM
iajs-2009	134	24	0	0	NUM
iajs-2009	134	25	1	1	NUM
iajs-2009	134	26	2	2	NUM
iajs-2009	134	27	3	3	NUM
iajs-2009	134	28	0	0	NUM
iajs-2009	134	29	0	0	NUM
iajs-2009	134	30	1	1	NUM
iajs-2009	134	31	2	2	NUM
iajs-2009	134	32	3	3	NUM
iajs-2009	134	33	1	1	NUM
iajs-2009	134	34	0	0	NUM
iajs-2009	134	35	0	0	NUM
iajs-2009	134	36	1	1	NUM
iajs-2009	134	37	3	3	NUM
iajs-2009	134	38	2	2	NUM
iajs-2009	134	39	0	0	NUM
iajs-2009	134	40	0	0	NUM
iajs-2009	134	41	0	0	NUM
iajs-2009	134	42	3	3	NUM
iajs-2009	134	43	3	3	NUM
iajs-2009	134	44	0	0	NUM
iajs-2009	134	45	1	1	NUM
iajs-2009	134	46	2	2	NUM
iajs-2009	134	47	0	0	NUM
iajs-2009	134	48			NOUN
iajs-2009	134	49	0	0	NUM
iajs-2009	134	50	1	1	NUM
iajs-2009	134	51	2	2	NUM
iajs-2009	134	52	3	3	NUM
iajs-2009	134	53	0	0	NUM
iajs-2009	134	54	0	0	NUM
iajs-2009	134	55	0	0	NUM
iajs-2009	134	56	0	0	NUM
iajs-2009	134	57	0	0	NUM
iajs-2009	134	58	1	1	NUM
iajs-2009	134	59	0	0	NUM
iajs-2009	134	60	1	1	NUM
iajs-2009	134	61	0	0	NUM
iajs-2009	134	62	0	0	NUM
iajs-2009	134	63	2	2	NUM
iajs-2009	134	64	0	0	NUM
iajs-2009	134	65	0	0	NUM
iajs-2009	134	66	2	2	NUM
iajs-2009	134	67	0	0	NUM
iajs-2009	134	68	3	3	NUM
iajs-2009	134	69	0	0	NUM
iajs-2009	134	70	3	3	NUM
iajs-2009	134	71	0	0	NUM
iajs-2009	134	72	0	0	NUM
iajs-2009	134	73	mathematics	mathematic	NOUN
iajs-2009	134	74	|	|	ADV
iajs-2009	134	75	165	165	NUM
iajs-2009	134	76	ibn	ibn	PROPN
iajs-2009	134	77	al	al	PROPN
iajs-2009	134	78	-	-	PUNCT
iajs-2009	134	79	haitham	haitham	PROPN
iajs-2009	134	80	jour	jour	X
iajs-2009	134	81	.	.	PROPN
iajs-2009	135	1	for	for	ADP
iajs-2009	135	2	pure	pure	ADJ
iajs-2009	135	3	&	&	CCONJ
iajs-2009	135	4	appl	appl	PROPN
iajs-2009	135	5	.	.	PUNCT
iajs-2009	136	1	sci	sci	PROPN
iajs-2009	136	2	.	.	PROPN
iajs-2009	136	3	ihjpas	ihjpas	PROPN
iajs-2009	136	4	https://doi.org/10.30526/31.3.2009	https://doi.org/10.30526/31.3.2009	PROPN
iajs-2009	136	5	vol	vol	NOUN
iajs-2009	136	6	.	.	PROPN
iajs-2009	137	1	31	31	NUM
iajs-2009	138	1	(	(	PUNCT
iajs-2009	138	2	3	3	NUM
iajs-2009	138	3	)	)	PUNCT
iajs-2009	138	4	2018	2018	NUM
iajs-2009	138	5	)	)	PUNCT
iajs-2009	139	1	(	(	PUNCT
iajs-2009	139	2	)	)	PUNCT
iajs-2009	139	3	(	(	PUNCT
iajs-2009	139	4	0)()()(0	0)()()(0	NUM
iajs-2009	139	5	bxbxbxaxbax	bxbxbxaxbax	ADJ
iajs-2009	139	6			PROPN
iajs-2009	139	7			NOUN
iajs-2009	139	8	.	.	PUNCT
iajs-2009	140	1	it	it	PRON
iajs-2009	140	2	follows	follow	VERB
iajs-2009	140	3	that	that	PRON
iajs-2009	140	4	}	}	PUNCT
iajs-2009	140	5	)	)	PUNCT
iajs-2009	140	6	(	(	PUNCT
iajs-2009	140	7	{	{	PUNCT
iajs-2009	140	8	blx	blx	PROPN
iajs-2009	140	9	,	,	PUNCT
iajs-2009	140	10	hence	hence	ADV
iajs-2009	140	11	}	}	PUNCT
iajs-2009	140	12	)	)	PUNCT
iajs-2009	140	13	(	(	PUNCT
iajs-2009	140	14	{	{	PUNCT
iajs-2009	140	15	}	}	PUNCT
iajs-2009	140	16	)	)	PUNCT
iajs-2009	140	17	(	(	PUNCT
iajs-2009	140	18	{	{	PUNCT
iajs-2009	140	19	blal	blal	PROPN
iajs-2009	140	20			PROPN
iajs-2009	140	21	.	.	PUNCT
iajs-2009	141	1	lemma16	lemma16	PROPN
iajs-2009	141	2	.	.	PUNCT
iajs-2009	142	1	if	if	SCONJ
iajs-2009	142	2	a	a	PRON
iajs-2009	142	3	is	be	AUX
iajs-2009	142	4	a	a	DET
iajs-2009	142	5	subset	subset	NOUN
iajs-2009	142	6	ofˑ	ofˑ	ADP
iajs-2009	142	7	a	a	DET
iajs-2009	142	8	ku-ˑsemigroup	ku-ˑsemigroup	NOUN
iajs-2009	142	9	)	)	PUNCT
iajs-2009	142	10	0	0	NUM
iajs-2009	142	11	,	,	PUNCT
iajs-2009	142	12	,	,	PUNCT
iajs-2009	142	13	,	,	PUNCT
iajs-2009	142	14	(	(	PUNCT
iajs-2009	142	15	x	x	VERB
iajs-2009	142	16	and	and	CCONJ
iajs-2009	142	17	a	a	DET
iajs-2009	142	18	ku-ˑalgebra	ku-ˑalgebra	NOUN
iajs-2009	142	19	is	be	AUX
iajs-2009	142	20	aˑ	aˑ	ADP
iajs-2009	142	21	commutative	commutative	ADJ
iajs-2009	142	22	,	,	PUNCT
iajs-2009	142	23	then	then	ADV
iajs-2009	142	24	)	)	PUNCT
iajs-2009	142	25	(	(	PUNCT
iajs-2009	142	26	ar	ar	PROPN
iajs-2009	142	27	is	be	AUX
iajs-2009	142	28	anˑ	anˑ	NOUN
iajs-2009	142	29	ideal	ideal	ADJ
iajs-2009	142	30	of	of	ADP
iajs-2009	142	31	x	x	X
iajs-2009	142	32	.	.	PUNCT
iajs-2009	143	1	proof	proof	NOUN
iajs-2009	143	2	.	.	PUNCT
iajs-2009	144	1	for	for	ADP
iajs-2009	144	2	any	any	DET
iajs-2009	144	3	aa	aa	NOUN
iajs-2009	144	4	,	,	PUNCT
iajs-2009	144	5	we	we	PRON
iajs-2009	144	6	have	have	VERB
iajs-2009	144	7	0)0(0	0)0(0	PROPN
iajs-2009	144	8			NOUN
iajs-2009	144	9	aaaaa	aaaaa	NOUN
iajs-2009	144	10	and	and	CCONJ
iajs-2009	144	11	00	00	NUM
iajs-2009	144	12	a	a	NOUN
iajs-2009	144	13	.	.	PUNCT
iajs-2009	145	1	hence	hence	ADV
iajs-2009	145	2	)	)	PUNCT
iajs-2009	145	3	(	(	PUNCT
iajs-2009	145	4	0	0	NUM
iajs-2009	145	5	ar	ar	NOUN
iajs-2009	145	6	.	.	PUNCT
iajs-2009	146	1	let	let	VERB
iajs-2009	146	2	)	)	PUNCT
iajs-2009	146	3	(	(	PUNCT
iajs-2009	146	4	)	)	PUNCT
iajs-2009	146	5	,	,	PUNCT
iajs-2009	146	6	(	(	PUNCT
iajs-2009	146	7	arxaryx	arxaryx	NOUN
iajs-2009	146	8			ADP
iajs-2009	146	9	,	,	PUNCT
iajs-2009	146	10	then	then	ADV
iajs-2009	146	11	0	0	NUM
iajs-2009	146	12	)	)	PUNCT
iajs-2009	146	13	(	(	PUNCT
iajs-2009	146	14			VERB
iajs-2009	146	15	yxa	yxa	NOUN
iajs-2009	146	16	,	,	PUNCT
iajs-2009	146	17	0	0	NUM
iajs-2009	146	18	)	)	PUNCT
iajs-2009	146	19	(	(	PUNCT
iajs-2009	146	20			NOUN
iajs-2009	146	21	yxa	yxa	PROPN
iajs-2009	146	22			PROPN
iajs-2009	146	23	which	which	PRON
iajs-2009	146	24	implies	imply	VERB
iajs-2009	146	25	that	that	SCONJ
iajs-2009	146	26	by	by	ADP
iajs-2009	146	27	lemma6	lemma6	PROPN
iajs-2009	146	28	0	0	NUM
iajs-2009	146	29	)	)	PUNCT
iajs-2009	146	30	(	(	PUNCT
iajs-2009	146	31	)	)	PUNCT
iajs-2009	146	32	(	(	PUNCT
iajs-2009	146	33			NUM
iajs-2009	146	34	yaxa	yaxa	NOUN
iajs-2009	146	35	and	and	CCONJ
iajs-2009	146	36	since	since	SCONJ
iajs-2009	146	37	)	)	PUNCT
iajs-2009	146	38	(	(	PUNCT
iajs-2009	146	39	arx	arx	PROPN
iajs-2009	146	40	,	,	PUNCT
iajs-2009	146	41	then	then	ADV
iajs-2009	146	42	0)(0	0)(0	NUM
iajs-2009	146	43			PUNCT
iajs-2009	146	44	ya	ya	PROPN
iajs-2009	146	45	,	,	PUNCT
iajs-2009	146	46	hence	hence	ADV
iajs-2009	146	47	0	0	X
iajs-2009	146	48	ya	ya	PRON
iajs-2009	146	49	.	.	PUNCT
iajs-2009	147	1	also	also	ADV
iajs-2009	147	2	,	,	PUNCT
iajs-2009	147	3	0	0	NUM
iajs-2009	147	4	)	)	PUNCT
iajs-2009	147	5	(	(	PUNCT
iajs-2009	147	6	)	)	PUNCT
iajs-2009	147	7	(	(	PUNCT
iajs-2009	147	8			NOUN
iajs-2009	147	9	yaxa	yaxa	NOUN
iajs-2009	147	10			PROPN
iajs-2009	147	11	and	and	CCONJ
iajs-2009	147	12	since	since	SCONJ
iajs-2009	147	13	)	)	PUNCT
iajs-2009	147	14	(	(	PUNCT
iajs-2009	147	15	arx	arx	PROPN
iajs-2009	147	16	,	,	PUNCT
iajs-2009	147	17	0)(0	0)(0	NUM
iajs-2009	147	18			PROPN
iajs-2009	147	19	ya	ya	PROPN
iajs-2009	147	20			PROPN
iajs-2009	147	21	,	,	PUNCT
iajs-2009	147	22	hence	hence	ADV
iajs-2009	147	23	0ya	0ya	PROPN
iajs-2009	147	24			PROPN
iajs-2009	147	25	,	,	PUNCT
iajs-2009	147	26	i.e.	i.e.	X
iajs-2009	147	27	)	)	PUNCT
iajs-2009	147	28	(	(	PUNCT
iajs-2009	147	29	ary	ary	PROPN
iajs-2009	147	30	.	.	PUNCT
iajs-2009	148	1	which	which	PRON
iajs-2009	148	2	implies	imply	VERB
iajs-2009	148	3	that	that	PRON
iajs-2009	148	4	)	)	PUNCT
iajs-2009	148	5	(	(	PUNCT
iajs-2009	148	6	ar	ar	PROPN
iajs-2009	148	7	is	be	AUX
iajs-2009	148	8	ˑan	ˑan	PROPN
iajs-2009	148	9	ideal	ideal	ADJ
iajs-2009	148	10	ˑofˑ	ˑofˑ	NOUN
iajs-2009	148	11	x	x	X
iajs-2009	148	12	.	.	PUNCT
iajs-2009	149	1	definitionˑ	definitionˑ	NOUN
iajs-2009	149	2	17.ˑ	17.ˑ	NUM
iajs-2009	149	3	a	a	DET
iajs-2009	149	4	graph	graph	NOUN
iajs-2009	149	5	of	of	ADP
iajs-2009	149	6	aˑ	aˑ	ADP
iajs-2009	149	7	ku	ku	PROPN
iajs-2009	149	8	-	-	PUNCT
iajs-2009	149	9	semigroup	semigroup	PROPN
iajs-2009	149	10	x	x	X
iajs-2009	149	11	,	,	PUNCT
iajs-2009	149	12	ˑdenoted	ˑdenote	VERB
iajs-2009	149	13	by	by	ADP
iajs-2009	149	14	ˑω	ˑω	ADP
iajs-2009	149	15	𝑋	𝑋	PROPN
iajs-2009	149	16	is	be	AUX
iajs-2009	149	17	ˑ	ˑ	PRON
iajs-2009	149	18	a	a	DET
iajs-2009	149	19	simple	simple	ADJ
iajs-2009	149	20	graph	graph	NOUN
iajs-2009	149	21	whoseˑ	whoseˑ	ADJ
iajs-2009	149	22	vertices	vertex	NOUN
iajs-2009	149	23	areˑ	areˑ	VERB
iajs-2009	149	24	the	the	DET
iajs-2009	149	25	elements	element	NOUN
iajs-2009	150	1	ˑof	ˑof	NOUN
iajs-2009	150	2	x	x	PUNCT
iajs-2009	150	3	and	and	CCONJ
iajs-2009	150	4	ˑtwo	ˑtwo	ADJ
iajs-2009	150	5	distinctˑ	distinctˑ	PROPN
iajs-2009	150	6	elements	elements	PROPN
iajs-2009	150	7	xyx	xyx	PROPN
iajs-2009	150	8			PROPN
iajs-2009	150	9	,	,	PUNCT
iajs-2009	150	10	areˑ	areˑ	PROPN
iajs-2009	150	11	adjacentˑ	adjacentˑ	PROPN
iajs-2009	150	12	ifˑ	ifˑ	PROPN
iajs-2009	150	13	andˑ	andˑ	PROPN
iajs-2009	150	14	onlyˑ	onlyˑ	ADJ
iajs-2009	150	15	ifˑˑ	ifˑˑ	PROPN
iajs-2009	150	16	}	}	PUNCT
iajs-2009	150	17	0	0	NUM
iajs-2009	150	18	{	{	PUNCT
iajs-2009	150	19	}	}	PUNCT
iajs-2009	150	20	)	)	PUNCT
iajs-2009	150	21	,	,	PUNCT
iajs-2009	150	22	(	(	PUNCT
iajs-2009	150	23	{	{	PUNCT
iajs-2009	150	24	}	}	NUM
iajs-2009	150	25	)	)	PUNCT
iajs-2009	150	26	,	,	PUNCT
iajs-2009	150	27	(	(	PUNCT
iajs-2009	150	28	{	{	PUNCT
iajs-2009	150	29			NUM
iajs-2009	150	30	yxlyxr	yxlyxr	NOUN
iajs-2009	150	31	.	.	PUNCT
iajs-2009	151	1	exampleˑ	exampleˑ	PROPN
iajs-2009	151	2	18.ˑ	18.ˑ	NUM
iajs-2009	151	3	letˑ	letˑ	ADJ
iajs-2009	151	4	}	}	PUNCT
iajs-2009	151	5	,	,	PUNCT
iajs-2009	151	6	,	,	PUNCT
iajs-2009	151	7	,	,	PUNCT
iajs-2009	151	8	,	,	PUNCT
iajs-2009	151	9	0	0	NUM
iajs-2009	151	10	{	{	PUNCT
iajs-2009	151	11	dcbax	dcbax	NOUN
iajs-2009	151	12			PROPN
iajs-2009	151	13	ˑbeˑaˑ	ˑbeˑaˑ	ADJ
iajs-2009	151	14	setˑ.ˑ	setˑ.ˑ	AUX
iajs-2009	151	15	define	define	VERB
iajs-2009	151	16			PROPN
iajs-2009	151	17	-ˑoperation	-ˑoperation	NOUN
iajs-2009	151	18	andˑ	andˑ	NOUN
iajs-2009	151	19			PROPN
iajs-2009	151	20	-ˑoperation	-ˑoperation	NOUN
iajs-2009	151	21	by	by	ADP
iajs-2009	151	22	ˑthe	ˑthe	DET
iajs-2009	151	23	followingˑ	followingˑ	NOUN
iajs-2009	151	24	tables	table	NOUN
iajs-2009	151	25	thenˑ	thenˑ	NOUN
iajs-2009	151	26	)	)	PUNCT
iajs-2009	151	27	0	0	NUM
iajs-2009	151	28	,	,	PUNCT
iajs-2009	151	29	,	,	PUNCT
iajs-2009	151	30	,	,	PUNCT
iajs-2009	151	31	(	(	PUNCT
iajs-2009	151	32	x	x	VERB
iajs-2009	151	33	is	be	AUX
iajs-2009	151	34	a	a	DET
iajs-2009	151	35	ku	ku	PROPN
iajs-2009	151	36	-	-	PUNCT
iajs-2009	151	37	semigroup	semigroup	PROPN
iajs-2009	151	38	.	.	PUNCT
iajs-2009	152	1	so	so	ADV
iajs-2009	152	2	ˑ	ˑ	NOUN
iajs-2009	152	3	}	}	PUNCT
iajs-2009	152	4	,	,	PUNCT
iajs-2009	152	5	,	,	PUNCT
iajs-2009	152	6	,	,	PUNCT
iajs-2009	152	7	0{}),0	0{}),0	PROPN
iajs-2009	152	8	(	(	PUNCT
iajs-2009	152	9	{	{	PUNCT
iajs-2009	152	10	dcar	dcar	NOUN
iajs-2009	152	11			NOUN
iajs-2009	152	12	}	}	PUNCT
iajs-2009	152	13	,	,	PUNCT
iajs-2009	152	14	0{}),({}),0	0{}),({}),0	NOUN
iajs-2009	152	15	(	(	PUNCT
iajs-2009	152	16	{	{	PUNCT
iajs-2009	152	17	cbarbr	cbarbr	NOUN
iajs-2009	152	18			NUM
iajs-2009	152	19	}	}	PUNCT
iajs-2009	152	20	,	,	PUNCT
iajs-2009	152	21	,	,	PUNCT
iajs-2009	152	22	0{}),0	0{}),0	PROPN
iajs-2009	152	23	(	(	PUNCT
iajs-2009	152	24	{	{	PUNCT
iajs-2009	152	25	bacr	bacr	NOUN
iajs-2009	152	26			PROPN
iajs-2009	152	27	,	,	PUNCT
iajs-2009	152	28	}	}	PUNCT
iajs-2009	152	29	0{}),({}),({}),({}),({}),({}),0	0{}),({}),({}),({}),({}),({}),0	NUM
iajs-2009	152	30	(	(	PUNCT
iajs-2009	152	31	{	{	PUNCT
iajs-2009	152	32			ADV
iajs-2009	152	33	dcrdbrcbrdarcardr	dcrdbrcbrdarcardr	ADV
iajs-2009	152	34	.	.	PUNCT
iajs-2009	153	1	also	also	ADV
iajs-2009	153	2	,	,	PUNCT
iajs-2009	153	3	}	}	PUNCT
iajs-2009	153	4	0{}),({}),({}),({}),({}),({}),0	0{}),({}),({}),({}),({}),({}),0	NUM
iajs-2009	153	5	(	(	PUNCT
iajs-2009	153	6	{	{	PUNCT
iajs-2009	154	1			NOUN
iajs-2009	154	2	dcldblcbldalcaldl	dcldblcbldalcaldl	NOUN
iajs-2009	154	3	.	.	PUNCT
iajs-2009	155	1	byˑ	byˑ	PROPN
iajs-2009	155	2	definition17	definition17	PROPN
iajs-2009	155	3	,	,	PUNCT
iajs-2009	155	4	we	we	PRON
iajs-2009	155	5	determineˑ	determineˑ	VERB
iajs-2009	155	6	the	the	DET
iajs-2009	155	7	graphˑ	graphˑ	NOUN
iajs-2009	155	8	of	of	ADP
iajs-2009	155	9	ˑ	ˑ	NOUN
iajs-2009	155	10	x	x	X
iajs-2009	155	11	asˑ	asˑ	NOUN
iajs-2009	155	12	followsˑ	followsˑ	NOUN
iajs-2009	155	13	:	:	PUNCT
iajs-2009	155	14	ˑthe	ˑthe	DET
iajs-2009	155	15	ˑset	ˑset	NOUN
iajs-2009	155	16	ˑofˑ	ˑofˑ	NOUN
iajs-2009	155	17	vertices	vertex	NOUN
iajs-2009	155	18	ˑis	ˑi	VERB
iajs-2009	155	19	ˑ	ˑ	NOUN
iajs-2009	155	20	}	}	PUNCT
iajs-2009	155	21	,	,	PUNCT
iajs-2009	155	22	,	,	PUNCT
iajs-2009	155	23	,	,	PUNCT
iajs-2009	155	24	,	,	PUNCT
iajs-2009	155	25	0	0	NUM
iajs-2009	155	26	{	{	PUNCT
iajs-2009	155	27	)	)	PUNCT
iajs-2009	155	28	(	(	PUNCT
iajs-2009	155	29	dcbaxv	dcbaxv	NOUN
iajs-2009	155	30			PROPN
iajs-2009	155	31	ˑˑandˑˑˑ	ˑˑandˑˑˑ	ADJ
iajs-2009	155	32	theˑ	theˑ	NOUN
iajs-2009	155	33	set	set	VERB
iajs-2009	155	34	ˑof	ˑof	PROPN
iajs-2009	155	35	ˑedgesˑˑis	ˑedgesˑˑis	PROPN
iajs-2009	155	36	ˑ	ˑ	PROPN
iajs-2009	155	37	}	}	PUNCT
iajs-2009	155	38	,	,	PUNCT
iajs-2009	155	39	,	,	PUNCT
iajs-2009	155	40	,	,	PUNCT
iajs-2009	155	41	,	,	PUNCT
iajs-2009	155	42	,	,	PUNCT
iajs-2009	155	43	0	0	NUM
iajs-2009	155	44	{	{	PUNCT
iajs-2009	155	45	)	)	PUNCT
iajs-2009	155	46	(	(	PUNCT
iajs-2009	155	47	dcdbcbdacadxe	dcdbcbdacadxe	PROPN
iajs-2009	155	48			NOUN
iajs-2009	155	49	.	.	PUNCT
iajs-2009	156	1	theˑ	theˑ	NOUN
iajs-2009	156	2	figure	figure	NOUN
iajs-2009	156	3	(	(	PUNCT
iajs-2009	156	4	1	1	NUM
iajs-2009	156	5	)	)	PUNCT
iajs-2009	156	6	ˑshowsˑ	ˑshowsˑ	NOUN
iajs-2009	156	7	the	the	DET
iajs-2009	156	8	graphˑ	graphˑ	ADJ
iajs-2009	156	9	ω	ω	NUM
iajs-2009	156	10	𝑋	𝑋	PROPN
iajs-2009	156	11	.	.	PUNCT
iajs-2009	157	1	ˑ	ˑ	PROPN
iajs-2009	157	2			PROPN
iajs-2009	157	3	0	0	NUM
iajs-2009	158	1	a	a	DET
iajs-2009	158	2	b	b	NOUN
iajs-2009	158	3	c	c	NOUN
iajs-2009	158	4	d	d	SYM
iajs-2009	158	5	0ˑ	0ˑ	NOUN
iajs-2009	158	6	0	0	NUM
iajs-2009	158	7	ˑ	ˑ	PROPN
iajs-2009	158	8	a	a	DET
iajs-2009	158	9	b	b	NOUN
iajs-2009	158	10	ˑ	ˑ	NOUN
iajs-2009	158	11	c	c	NOUN
iajs-2009	158	12	d	d	NOUN
iajs-2009	158	13	a	a	DET
iajs-2009	158	14	ˑ	ˑ	NOUN
iajs-2009	158	15	0	0	NUM
iajs-2009	158	16	0	0	NUM
iajs-2009	158	17	ˑ	ˑ	NOUN
iajs-2009	158	18	a	a	DET
iajs-2009	158	19	ˑ	ˑ	NOUN
iajs-2009	158	20	c	c	NOUN
iajs-2009	158	21	d	d	NOUN
iajs-2009	158	22	ˑ	ˑ	PROPN
iajs-2009	158	23	b	b	PROPN
iajs-2009	158	24	0	0	NUM
iajs-2009	158	25	0	0	NUM
iajs-2009	158	26	0	0	NUM
iajs-2009	159	1	c	c	NOUN
iajs-2009	159	2	d	d	X
iajs-2009	159	3	ˑ	ˑ	NOUN
iajs-2009	159	4	c	c	NOUN
iajs-2009	159	5	0	0	NUM
iajs-2009	159	6	a	a	PRON
iajs-2009	159	7	ˑ	ˑ	NOUN
iajs-2009	159	8	b	b	NOUN
iajs-2009	159	9	0	0	NUM
iajs-2009	159	10	ˑ	ˑ	NOUN
iajs-2009	159	11	d	d	NOUN
iajs-2009	159	12	ˑ	ˑ	NOUN
iajs-2009	159	13	d	d	PROPN
iajs-2009	159	14	0	0	PUNCT
iajs-2009	159	15	a	a	DET
iajs-2009	159	16	ˑ	ˑ	NOUN
iajs-2009	159	17	b	b	NOUN
iajs-2009	159	18	c	c	NOUN
iajs-2009	159	19	0	0	PUNCT
iajs-2009	160	1			PROPN
iajs-2009	160	2	0	0	NUM
iajs-2009	160	3	a	a	DET
iajs-2009	160	4	b	b	NOUN
iajs-2009	160	5	c	c	NOUN
iajs-2009	160	6	d	d	NOUN
iajs-2009	160	7	0	0	NUM
iajs-2009	160	8	ˑ	ˑ	NOUN
iajs-2009	160	9	0	0	NUM
iajs-2009	160	10	0	0	NUM
iajs-2009	160	11	ˑ	ˑ	NOUN
iajs-2009	160	12	0	0	NUM
iajs-2009	160	13	0	0	NUM
iajs-2009	160	14	ˑ	ˑ	NOUN
iajs-2009	160	15	0	0	NUM
iajs-2009	160	16	a	a	DET
iajs-2009	160	17	0	0	NUM
iajs-2009	160	18	0	0	NUM
iajs-2009	160	19	0	0	NUM
iajs-2009	160	20	0	0	NUM
iajs-2009	161	1	a	a	DET
iajs-2009	161	2	b	b	NOUN
iajs-2009	161	3	ˑ	ˑ	NOUN
iajs-2009	161	4	0	0	NUM
iajs-2009	161	5	0	0	NUM
iajs-2009	161	6	ˑ	ˑ	NOUN
iajs-2009	161	7	0	0	NUM
iajs-2009	161	8	0	0	NUM
iajs-2009	161	9	b	b	X
iajs-2009	161	10	c	c	NOUN
iajs-2009	161	11	0	0	NUM
iajs-2009	161	12	0	0	NUM
iajs-2009	161	13	0	0	NUM
iajs-2009	162	1	b	b	X
iajs-2009	162	2	c	c	NOUN
iajs-2009	162	3	d	d	PROPN
iajs-2009	162	4	0	0	NUM
iajs-2009	162	5	ˑ	ˑ	PROPN
iajs-2009	162	6	a	a	DET
iajs-2009	162	7	b	b	NOUN
iajs-2009	162	8	ˑ	ˑ	NOUN
iajs-2009	162	9	c	c	NOUN
iajs-2009	162	10	d	d	NOUN
iajs-2009	162	11	mathematics	mathematic	NOUN
iajs-2009	162	12	|	|	ADV
iajs-2009	162	13	166	166	NUM
iajs-2009	162	14	ibn	ibn	PROPN
iajs-2009	162	15	al	al	PROPN
iajs-2009	162	16	-	-	PUNCT
iajs-2009	162	17	haitham	haitham	PROPN
iajs-2009	162	18	jour	jour	X
iajs-2009	162	19	.	.	PROPN
iajs-2009	163	1	for	for	ADP
iajs-2009	163	2	pure	pure	ADJ
iajs-2009	163	3	&	&	CCONJ
iajs-2009	163	4	appl	appl	PROPN
iajs-2009	163	5	.	.	PUNCT
iajs-2009	164	1	sci	sci	PROPN
iajs-2009	164	2	.	.	PROPN
iajs-2009	164	3	ihjpas	ihjpas	PROPN
iajs-2009	164	4	https://doi.org/10.30526/31.3.2009	https://doi.org/10.30526/31.3.2009	PROPN
iajs-2009	164	5	vol	vol	NOUN
iajs-2009	164	6	.	.	PROPN
iajs-2009	165	1	31	31	NUM
iajs-2009	166	1	(	(	PUNCT
iajs-2009	166	2	3	3	NUM
iajs-2009	166	3	)	)	SYM
iajs-2009	166	4	2018	2018	NUM
iajs-2009	166	5	figure	figure	VERB
iajs-2009	166	6	1.the	1.the	DET
iajs-2009	166	7	graphˑω	graphˑω	NOUN
iajs-2009	166	8	𝑋	𝑋	PROPN
iajs-2009	166	9	example	example	NOUN
iajs-2009	166	10	19	19	NUM
iajs-2009	166	11	.	.	PUNCT
iajs-2009	167	1	ˑlet	ˑlet	NOUN
iajs-2009	168	1	}	}	PUNCT
iajs-2009	168	2	3,2,1,0{x	3,2,1,0{x	NUM
iajs-2009	168	3	beˑaˑ	beˑaˑ	NOUN
iajs-2009	168	4	set	set	VERB
iajs-2009	168	5	in	in	ADP
iajs-2009	168	6	example13	example13	NOUN
iajs-2009	168	7	.	.	PUNCT
iajs-2009	169	1	ˑthe	ˑthe	DET
iajs-2009	169	2	set	set	NOUN
iajs-2009	169	3	of	of	ADP
iajs-2009	169	4	vertices	vertex	NOUN
iajs-2009	169	5	ˑis	ˑis	PROPN
iajs-2009	169	6	}	}	PUNCT
iajs-2009	169	7	3,2,1,0	3,2,1,0	NUM
iajs-2009	169	8	{	{	PUNCT
iajs-2009	169	9	and	and	CCONJ
iajs-2009	169	10	the	the	DET
iajs-2009	169	11	set	set	NOUN
iajs-2009	169	12	of	of	ADP
iajs-2009	169	13	edges	edge	NOUN
iajs-2009	169	14	is	be	AUX
iajs-2009	169	15	1	1	NUM
iajs-2009	169	16	3	3	NUM
iajs-2009	169	17	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
iajs-2009	169	18	2	2	NUM
iajs-2009	169	19	3	3	NUM
iajs-2009	169	20	.	.	PUNCT
iajs-2009	170	1	theˑ	theˑ	NOUN
iajs-2009	170	2	figure	figure	NOUN
iajs-2009	170	3	(	(	PUNCT
iajs-2009	170	4	2	2	NUM
iajs-2009	170	5	)	)	PUNCT
iajs-2009	170	6	showsˑ	showsˑ	NOUN
iajs-2009	170	7	the	the	DET
iajs-2009	170	8	ˑ	ˑ	NOUN
iajs-2009	170	9	graph	graph	NOUN
iajs-2009	170	10	ˑω	ˑω	ADP
iajs-2009	170	11	𝑋	𝑋	PROPN
iajs-2009	170	12	.	.	PUNCT
iajs-2009	171	1	figure	figure	NOUN
iajs-2009	171	2	2	2	NUM
iajs-2009	171	3	.	.	PUNCT
iajs-2009	172	1	the	the	DET
iajs-2009	172	2	graphˑω	graphˑω	NOUN
iajs-2009	172	3	𝑋	𝑋	PROPN
iajs-2009	172	4	theorem	theorem	VERB
iajs-2009	172	5	20	20	NUM
iajs-2009	172	6	.	.	PUNCT
iajs-2009	173	1	a	a	DET
iajs-2009	173	2	disconnected	disconnected	ADJ
iajs-2009	173	3	graph	graph	NOUN
iajs-2009	173	4	can	can	AUX
iajs-2009	173	5	not	not	PART
iajs-2009	173	6	be	be	AUX
iajs-2009	173	7	a	a	DET
iajs-2009	173	8	graph	graph	NOUN
iajs-2009	173	9	of	of	ADP
iajs-2009	173	10	any	any	DET
iajs-2009	173	11	ku	ku	NOUN
iajs-2009	173	12	-	-	PUNCT
iajs-2009	173	13	semigroups	semigroup	NOUN
iajs-2009	173	14	𝑋.	𝑋.	PROPN
iajs-2009	173	15	proof	proof	NOUN
iajs-2009	173	16	.	.	PUNCT
iajs-2009	174	1	suppose	suppose	VERB
iajs-2009	174	2	g	g	PROPN
iajs-2009	174	3	is	be	AUX
iajs-2009	174	4	a	a	DET
iajs-2009	174	5	disconnected	disconnected	ADJ
iajs-2009	174	6	graph	graph	NOUN
iajs-2009	174	7	with	with	ADP
iajs-2009	174	8	components	component	NOUN
iajs-2009	174	9	1	1	NUM
iajs-2009	174	10	g	g	NOUN
iajs-2009	174	11	and	and	CCONJ
iajs-2009	174	12	2	2	NUM
iajs-2009	174	13	g	g	NOUN
iajs-2009	174	14	.	.	PUNCT
iajs-2009	175	1	let	let	VERB
iajs-2009	175	2	ˑ𝐺	ˑ𝐺	PROPN
iajs-2009	175	3	ω	ω	PROPN
iajs-2009	175	4	𝑋	𝑋	PROPN
iajs-2009	175	5	ˑ	ˑ	PROPN
iajs-2009	175	6	beˑ	beˑ	NOUN
iajs-2009	175	7	a	a	DET
iajs-2009	175	8	graphˑ	graphˑ	NOUN
iajs-2009	175	9	of	of	ADP
iajs-2009	175	10	ˑ	ˑ	NOUN
iajs-2009	175	11	ku-ˑsemigroups𝑋.	ku-ˑsemigroups𝑋.	NOUN
iajs-2009	175	12	then	then	ADV
iajs-2009	175	13	,	,	PUNCT
iajs-2009	175	14	there	there	PRON
iajs-2009	175	15	exist	exist	VERB
iajs-2009	175	16	vertices	vertex	NOUN
iajs-2009	175	17	1gx	1gx	PROPN
iajs-2009	175	18	and	and	CCONJ
iajs-2009	175	19	2gy	2gy	NUM
iajs-2009	175	20	such	such	ADJ
iajs-2009	175	21	that	that	SCONJ
iajs-2009	175	22	there	there	PRON
iajs-2009	175	23	is	be	VERB
iajs-2009	175	24	no	no	DET
iajs-2009	175	25	path	path	NOUN
iajs-2009	175	26	between	between	ADP
iajs-2009	175	27	𝑥	𝑥	PROPN
iajs-2009	175	28	and	and	CCONJ
iajs-2009	175	29	𝑦.	𝑦.	PROPN
iajs-2009	175	30	let	let	VERB
iajs-2009	175	31	1ga	1ga	NUM
iajs-2009	175	32	and	and	CCONJ
iajs-2009	175	33	2gb	2gb	PROPN
iajs-2009	175	34	be	be	AUX
iajs-2009	175	35	vertices	vertex	NOUN
iajs-2009	175	36	adjacent	adjacent	ADJ
iajs-2009	175	37	to	to	ADP
iajs-2009	175	38	1gx	1gx	PROPN
iajs-2009	175	39	and	and	CCONJ
iajs-2009	175	40	2gy	2gy	PROPN
iajs-2009	175	41	,	,	PUNCT
iajs-2009	175	42	respectively	respectively	ADV
iajs-2009	175	43	.	.	PUNCT
iajs-2009	176	1	then	then	ADV
iajs-2009	176	2	𝑥	𝑥	X
iajs-2009	176	3			PROPN
iajs-2009	176	4	𝑎	𝑎	X
iajs-2009	176	5	𝑎𝑥	𝑎𝑥	NOUN
iajs-2009	176	6	0	0	NUM
iajs-2009	176	7	,	,	PUNCT
iajs-2009	176	8	𝑥a	𝑥a	PUNCT
iajs-2009	177	1	a𝑥	a𝑥	NOUN
iajs-2009	177	2	0	0	PUNCT
iajs-2009	178	1	and	and	CCONJ
iajs-2009	178	2	𝑦	𝑦	PRON
iajs-2009	178	3			PROPN
iajs-2009	178	4	𝑏	𝑏	PROPN
iajs-2009	178	5	𝑏𝑦	𝑏𝑦	PROPN
iajs-2009	178	6	0	0	NUM
iajs-2009	178	7	,	,	PUNCT
iajs-2009	178	8	𝑦b	𝑦b	NOUN
iajs-2009	179	1	b𝑦	b𝑦	NOUN
iajs-2009	179	2	0	0	X
iajs-2009	179	3	.	.	PUNCT
iajs-2009	180	1	if	if	SCONJ
iajs-2009	180	2			AUX
iajs-2009	180	3	𝑏	𝑏	PROPN
iajs-2009	180	4	𝑏𝑎	𝑏𝑎	PROPN
iajs-2009	180	5	𝑧	𝑧	PART
iajs-2009	180	6	,	,	PUNCT
iajs-2009	180	7	𝑎b	𝑎b	ADJ
iajs-2009	180	8	b𝑎	b𝑎	X
iajs-2009	180	9	z	z	NOUN
iajs-2009	180	10	,	,	PUNCT
iajs-2009	180	11	for	for	ADP
iajs-2009	180	12	ˑsomeˑz	ˑsomeˑz	ADJ
iajs-2009	180	13	𝑋.	𝑋.	PROPN
iajs-2009	180	14	then	then	ADV
iajs-2009	180	15	𝑥	𝑥	ADV
iajs-2009	180	16	𝑧	𝑧	ADV
iajs-2009	180	17	𝑧𝑥	𝑧𝑥	NOUN
iajs-2009	180	18	0	0	NUM
iajs-2009	180	19	,	,	PUNCT
iajs-2009	180	20	𝑦	𝑦	VERB
iajs-2009	180	21	𝑧	𝑧	PRON
iajs-2009	180	22	𝑧𝑦	𝑧𝑦	PROPN
iajs-2009	180	23	0	0	NUM
iajs-2009	180	24	,	,	PUNCT
iajs-2009	180	25	𝑥z	𝑥z	PUNCT
iajs-2009	180	26	z𝑥	z𝑥	NOUN
iajs-2009	180	27	0	0	NUM
iajs-2009	180	28	,	,	PUNCT
iajs-2009	180	29	yz	yz	NOUN
iajs-2009	180	30	z𝑦	z𝑦	NOUN
iajs-2009	180	31	0	0	NUM
iajs-2009	180	32	.	.	PUNCT
iajs-2009	181	1	thus	thus	ADV
iajs-2009	181	2	z	z	X
iajs-2009	181	3	is	be	AUX
iajs-2009	181	4	a	a	DET
iajs-2009	181	5	common	common	ADJ
iajs-2009	181	6	neighbor	neighbor	NOUN
iajs-2009	181	7	of	of	ADP
iajs-2009	181	8	𝑥	𝑥	PROPN
iajs-2009	181	9	and	and	CCONJ
iajs-2009	181	10	𝑦	𝑦	NOUN
iajs-2009	181	11	,	,	PUNCT
iajs-2009	181	12	that	that	PRON
iajs-2009	181	13	is	be	AUX
iajs-2009	181	14	a	a	DET
iajs-2009	181	15	contradiction	contradiction	NOUN
iajs-2009	181	16	.	.	PUNCT
iajs-2009	182	1	hence	hence	ADV
iajs-2009	182	2	,	,	PUNCT
iajs-2009	182	3	a	a	DET
iajs-2009	182	4	disconnected	disconnected	ADJ
iajs-2009	182	5	graph	graph	NOUN
iajs-2009	182	6	can	can	AUX
iajs-2009	182	7	not	not	PART
iajs-2009	182	8	be	be	AUX
iajs-2009	182	9	a	a	DET
iajs-2009	182	10	graph	graph	NOUN
iajs-2009	182	11	of	of	ADP
iajs-2009	182	12	any	any	DET
iajs-2009	182	13	ku	ku	NOUN
iajs-2009	182	14	-	-	PUNCT
iajs-2009	182	15	semigroups	semigroup	NOUN
iajs-2009	182	16	.	.	PUNCT
iajs-2009	182	17	definition21	definition21	PROPN
iajs-2009	182	18	.	.	PUNCT
iajs-2009	183	1	let	let	VERB
iajs-2009	183	2	x	x	PRON
iajs-2009	183	3	be	be	AUX
iajs-2009	183	4	a	a	DET
iajs-2009	183	5	ku	ku	PROPN
iajs-2009	183	6	-	-	PUNCT
iajs-2009	183	7	semigroup	semigroup	PROPN
iajs-2009	183	8	.	.	PUNCT
iajs-2009	184	1	forˑ	forˑ	PROPN
iajs-2009	184	2	any	any	DET
iajs-2009	184	3	xx	xx	PROPN
iajs-2009	184	4	,	,	PUNCT
iajs-2009	184	5	we	we	PRON
iajs-2009	184	6	have	have	AUX
iajs-2009	184	7	}	}	PUNCT
iajs-2009	184	8	}	}	PUNCT
iajs-2009	184	9	0	0	NUM
iajs-2009	184	10	{	{	PUNCT
iajs-2009	184	11	}	}	PUNCT
iajs-2009	184	12	)	)	PUNCT
iajs-2009	184	13	,	,	PUNCT
iajs-2009	184	14	(	(	PUNCT
iajs-2009	184	15	{	{	PUNCT
iajs-2009	184	16	}	}	NUM
iajs-2009	184	17	)	)	PUNCT
iajs-2009	184	18	,	,	PUNCT
iajs-2009	184	19	(	(	PUNCT
iajs-2009	184	20	{	{	PUNCT
iajs-2009	184	21	:	:	PUNCT
iajs-2009	184	22	{	{	PUNCT
iajs-2009	184	23	)	)	PUNCT
iajs-2009	184	24	(	(	PUNCT
iajs-2009	184	25			X
iajs-2009	184	26	yxlyxrxyxann	yxlyxrxyxann	PROPN
iajs-2009	185	1	ˑis	ˑis	PROPN
iajs-2009	185	2	called	call	VERB
iajs-2009	185	3	ˑthe	ˑthe	DET
iajs-2009	185	4	set	set	NOUN
iajs-2009	185	5	of	of	ADP
iajs-2009	185	6	annihilator	annihilator	NOUN
iajs-2009	185	7	of	of	ADP
iajs-2009	185	8	x	x	PROPN
iajs-2009	185	9	.	.	PUNCT
iajs-2009	186	1	lemma	lemma	PROPN
iajs-2009	186	2	22	22	NUM
iajs-2009	186	3	.	.	PUNCT
iajs-2009	187	1	let	let	VERB
iajs-2009	187	2	x	x	PRON
iajs-2009	187	3	be	be	AUX
iajs-2009	187	4	a	a	DET
iajs-2009	187	5	ku	ku	PROPN
iajs-2009	187	6	-	-	PUNCT
iajs-2009	187	7	semigroup	semigroup	PROPN
iajs-2009	187	8	and	and	CCONJ
iajs-2009	187	9	)	)	PUNCT
iajs-2009	187	10	(	(	PUNCT
iajs-2009	187	11	xann	xann	PROPN
iajs-2009	187	12	ˑbe	ˑbe	PROPN
iajs-2009	187	13	ˑthe	ˑthe	DET
iajs-2009	187	14	setˑ	setˑ	PROPN
iajs-2009	187	15	of	of	ADP
iajs-2009	187	16	annihilator	annihilator	PROPN
iajs-2009	187	17	of	of	ADP
iajs-2009	187	18	x	x	PROPN
iajs-2009	187	19	.	.	PUNCT
iajs-2009	188	1	then	then	ADV
iajs-2009	188	2	(	(	PUNCT
iajs-2009	188	3	i	i	NOUN
iajs-2009	188	4	)	)	PUNCT
iajs-2009	188	5	xxxannx	xxxannx	PROPN
iajs-2009	188	6			PROPN
iajs-2009	188	7	)	)	PUNCT
iajs-2009	188	8	(	(	PUNCT
iajs-2009	188	9	,	,	PUNCT
iajs-2009	188	10	(	(	PUNCT
iajs-2009	188	11	ii	ii	NOUN
iajs-2009	188	12	)	)	PUNCT
iajs-2009	188	13	thereˑ	thereˑ	NOUN
iajs-2009	188	14	is	be	AUX
iajs-2009	188	15	anˑ	anˑ	NOUN
iajs-2009	188	16	edgeˑ	edgeˑ	NOUN
iajs-2009	188	17	connectingˑ	connectingˑ	NOUN
iajs-2009	188	18	x	x	PUNCT
iajs-2009	188	19	and	and	CCONJ
iajs-2009	188	20	y	y	PROPN
iajs-2009	188	21	if	if	SCONJ
iajs-2009	188	22	ˑand	ˑand	CCONJ
iajs-2009	188	23	onlyˑ	onlyˑ	ADJ
iajs-2009	188	24	if	if	SCONJ
iajs-2009	188	25	ˑ	ˑ	NOUN
iajs-2009	188	26	)	)	PUNCT
iajs-2009	188	27	(	(	PUNCT
iajs-2009	188	28	yannx	yannx	X
iajs-2009	188	29	ˑand	ˑand	ADP
iajs-2009	188	30	ˑ	ˑ	NOUN
iajs-2009	188	31	)	)	PUNCT
iajs-2009	188	32	(	(	PUNCT
iajs-2009	188	33	xanny	xanny	PROPN
iajs-2009	188	34	.	.	PUNCT
iajs-2009	189	1	mathematics	mathematic	NOUN
iajs-2009	189	2	|	|	ADV
iajs-2009	189	3	167	167	NUM
iajs-2009	189	4	ibn	ibn	PROPN
iajs-2009	189	5	al	al	PROPN
iajs-2009	189	6	-	-	PUNCT
iajs-2009	189	7	haitham	haitham	PROPN
iajs-2009	189	8	jour	jour	X
iajs-2009	189	9	.	.	PROPN
iajs-2009	190	1	for	for	ADP
iajs-2009	190	2	pure	pure	ADJ
iajs-2009	190	3	&	&	CCONJ
iajs-2009	190	4	appl	appl	PROPN
iajs-2009	190	5	.	.	PUNCT
iajs-2009	191	1	sci	sci	PROPN
iajs-2009	191	2	.	.	PROPN
iajs-2009	191	3	ihjpas	ihjpas	PROPN
iajs-2009	191	4	https://doi.org/10.30526/31.3.2009	https://doi.org/10.30526/31.3.2009	PROPN
iajs-2009	191	5	vol	vol	NOUN
iajs-2009	191	6	.	.	PROPN
iajs-2009	192	1	31	31	NUM
iajs-2009	193	1	(	(	PUNCT
iajs-2009	193	2	3	3	NUM
iajs-2009	193	3	)	)	SYM
iajs-2009	193	4	2018	2018	NUM
iajs-2009	193	5	proof	proof	NOUN
iajs-2009	193	6	.	.	PUNCT
iajs-2009	194	1	(	(	PUNCT
iajs-2009	194	2	i	i	NOUN
iajs-2009	194	3	)	)	PUNCT
iajs-2009	194	4	clear	clear	ADJ
iajs-2009	194	5	by	by	ADP
iajs-2009	194	6	definition	definition	NOUN
iajs-2009	194	7	17	17	NUM
iajs-2009	194	8	.	.	PUNCT
iajs-2009	195	1	(	(	PUNCT
iajs-2009	195	2	ii	ii	NOUN
iajs-2009	195	3	):	):	PUNCT
iajs-2009	195	4	suppose	suppose	VERB
iajs-2009	195	5	that	that	SCONJ
iajs-2009	195	6	)	)	PUNCT
iajs-2009	195	7	(	(	PUNCT
iajs-2009	195	8	yannx	yannx	PROPN
iajs-2009	195	9	or	or	CCONJ
iajs-2009	195	10	)	)	PUNCT
iajs-2009	195	11	(	(	PUNCT
iajs-2009	195	12	xanny	xanny	PROPN
iajs-2009	195	13	,	,	PUNCT
iajs-2009	195	14	then	then	ADV
iajs-2009	195	15	}	}	PUNCT
iajs-2009	195	16	0	0	NUM
iajs-2009	195	17	{	{	PUNCT
iajs-2009	195	18	}	}	PUNCT
iajs-2009	195	19	)	)	PUNCT
iajs-2009	195	20	,	,	PUNCT
iajs-2009	195	21	(	(	PUNCT
iajs-2009	195	22	{	{	PUNCT
iajs-2009	195	23	}	}	NUM
iajs-2009	195	24	)	)	PUNCT
iajs-2009	195	25	,	,	PUNCT
iajs-2009	195	26	(	(	PUNCT
iajs-2009	195	27	{	{	PUNCT
iajs-2009	195	28			X
iajs-2009	195	29	yxlyxr	yxlyxr	NOUN
iajs-2009	195	30	.	.	PUNCT
iajs-2009	196	1	it	it	PRON
iajs-2009	196	2	implies	imply	VERB
iajs-2009	196	3	thatˑ	thatˑ	NOUN
iajs-2009	196	4	thereˑ	thereˑ	NOUN
iajs-2009	196	5	is	be	AUX
iajs-2009	196	6	no	no	DET
iajs-2009	196	7	ˑedge	ˑedge	NOUN
iajs-2009	196	8	connectingˑ	connectingˑ	NOUN
iajs-2009	196	9	x	x	PUNCT
iajs-2009	196	10	andˑ	andˑ	NOUN
iajs-2009	196	11	y	y	PROPN
iajs-2009	196	12	,	,	PUNCT
iajs-2009	196	13	thisˑ	thisˑ	NOUN
iajs-2009	196	14	is	be	AUX
iajs-2009	196	15	aˑ	aˑ	ADP
iajs-2009	196	16	contradiction	contradiction	NOUN
iajs-2009	196	17	.	.	PUNCT
iajs-2009	197	1	thus	thus	ADV
iajs-2009	197	2	)	)	PUNCT
iajs-2009	197	3	(	(	PUNCT
iajs-2009	197	4	yannx	yannx	NOUN
iajs-2009	197	5	and	and	CCONJ
iajs-2009	197	6	)	)	PUNCT
iajs-2009	197	7	(	(	PUNCT
iajs-2009	197	8	xanny	xanny	PROPN
iajs-2009	197	9	.	.	PUNCT
iajs-2009	198	1	conversely	conversely	ADV
iajs-2009	198	2	,	,	PUNCT
iajs-2009	198	3	suppose	suppose	VERB
iajs-2009	198	4	that	that	SCONJ
iajs-2009	198	5	)	)	PUNCT
iajs-2009	198	6	(	(	PUNCT
iajs-2009	198	7	yannx	yannx	NOUN
iajs-2009	198	8	and	and	CCONJ
iajs-2009	198	9	)	)	PUNCT
iajs-2009	198	10	(	(	PUNCT
iajs-2009	198	11	xanny	xanny	NOUN
iajs-2009	198	12	,	,	PUNCT
iajs-2009	198	13	then	then	ADV
iajs-2009	198	14	}	}	PUNCT
iajs-2009	198	15	0	0	NUM
iajs-2009	198	16	{	{	PUNCT
iajs-2009	198	17	}	}	PUNCT
iajs-2009	198	18	)	)	PUNCT
iajs-2009	198	19	,	,	PUNCT
iajs-2009	198	20	(	(	PUNCT
iajs-2009	198	21	{	{	PUNCT
iajs-2009	198	22	}	}	NUM
iajs-2009	198	23	)	)	PUNCT
iajs-2009	198	24	,	,	PUNCT
iajs-2009	198	25	(	(	PUNCT
iajs-2009	198	26	{	{	PUNCT
iajs-2009	198	27			NUM
iajs-2009	198	28	yxlyxr	yxlyxr	NOUN
iajs-2009	198	29	.	.	PUNCT
iajs-2009	199	1	it	it	PRON
iajs-2009	199	2	implies	imply	VERB
iajs-2009	199	3	that	that	SCONJ
iajs-2009	199	4	ˑthere	ˑthere	ADV
iajs-2009	199	5	is	be	AUX
iajs-2009	199	6	ˑan	ˑan	ADJ
iajs-2009	199	7	edgeˑ	edgeˑ	NOUN
iajs-2009	199	8	connectingˑ	connectingˑ	NOUN
iajs-2009	199	9	x	x	PUNCT
iajs-2009	199	10	andˑ	andˑ	NOUN
iajs-2009	199	11	y	y	PROPN
iajs-2009	199	12	.	.	PUNCT
iajs-2009	200	1	definition	definition	NOUN
iajs-2009	200	2	23.ˑ	23.ˑ	NUM
iajs-2009	200	3	define	define	VERB
iajs-2009	200	4	aˑ	aˑ	ADP
iajs-2009	200	5	relationˑ	relationˑ	PROPN
iajs-2009	200	6	on	on	ADP
iajs-2009	200	7	a	a	DET
iajs-2009	200	8	kuˑ-semigroupˑ	kuˑ-semigroupˑ	NOUN
iajs-2009	200	9	x	x	PUNCT
iajs-2009	200	10	as	as	ADP
iajs-2009	200	11	followsˑ	followsˑ	NOUN
iajs-2009	200	12	:	:	PUNCT
iajs-2009	200	13	x1	x1	PROPN
iajs-2009	200	14	x2	x2	PROPN
iajs-2009	200	15	ifˑ	ifˑ	VERB
iajs-2009	200	16	and	and	CCONJ
iajs-2009	200	17	only	only	ADV
iajs-2009	200	18	ˑif	ˑif	ADV
iajs-2009	200	19	ˑ	ˑ	X
iajs-2009	200	20	xxxxannxann	xxxxannxann	PROPN
iajs-2009	200	21			PROPN
iajs-2009	200	22	2121	2121	NUM
iajs-2009	200	23	,	,	PUNCT
iajs-2009	200	24	)	)	PUNCT
iajs-2009	200	25	,	,	PUNCT
iajs-2009	200	26	(	(	PUNCT
iajs-2009	200	27	)	)	PUNCT
iajs-2009	200	28	(	(	PUNCT
iajs-2009	200	29	.	.	PUNCT
iajs-2009	201	1	lemma	lemma	PROPN
iajs-2009	201	2	24	24	NUM
iajs-2009	201	3	.	.	PUNCT
iajs-2009	202	1	ˑthe	ˑthe	DET
iajs-2009	202	2	relation	relation	NOUN
iajs-2009	202	3	ˑ	ˑ	PROPN
iajs-2009	202	4	(	(	PUNCT
iajs-2009	202	5	from	from	ADP
iajs-2009	202	6	definition23	definition23	NOUN
iajs-2009	202	7	)	)	PUNCT
iajs-2009	202	8	is	be	AUX
iajs-2009	202	9	ˑan	ˑan	PROPN
iajs-2009	202	10	equivalenceˑ	equivalenceˑ	ADJ
iajs-2009	202	11	relation	relation	PROPN
iajs-2009	202	12	ˑon	ˑon	PROPN
iajs-2009	202	13	x	x	NOUN
iajs-2009	202	14	.	.	PUNCT
iajs-2009	203	1	proof.ˑ	proof.ˑ	PROPN
iajs-2009	203	2	clear	clear	ADJ
iajs-2009	203	3	.	.	PUNCT
iajs-2009	204	1	4	4	X
iajs-2009	204	2	.	.	X
iajs-2009	204	3	a	a	DET
iajs-2009	204	4	graphˑ	graphˑ	NOUN
iajs-2009	204	5	of	of	ADP
iajs-2009	204	6	equivalenceˑclasses	equivalenceˑclasse	NOUN
iajs-2009	204	7	ofˑ	ofˑ	PRON
iajs-2009	204	8	ku-ˑsemigroups	ku-ˑsemigroups	PROPN
iajs-2009	204	9	nowˑ	nowˑ	PROPN
iajs-2009	204	10	,	,	PUNCT
iajs-2009	204	11	we	we	PRON
iajs-2009	204	12	introduceˑ	introduceˑ	VERB
iajs-2009	204	13	ˑthe	ˑthe	DET
iajs-2009	204	14	graphˑ	graphˑ	NOUN
iajs-2009	204	15	of	of	ADP
iajs-2009	204	16	ˑequivalence	ˑequivalence	NOUN
iajs-2009	204	17	classesˑ	classesˑ	NOUN
iajs-2009	204	18	of	of	ADP
iajs-2009	204	19	aˑ	aˑ	ADP
iajs-2009	204	20	kuˑ-ˑsemigroup	kuˑ-ˑsemigroup	NOUN
iajs-2009	204	21	x	x	PUNCT
iajs-2009	204	22	,	,	PUNCT
iajs-2009	204	23	ˑwhich	ˑwhich	PROPN
iajs-2009	204	24	is	be	AUX
iajs-2009	204	25	constructedˑ	constructedˑ	VERB
iajs-2009	204	26	fromˑ	fromˑ	PROPN
iajs-2009	204	27	classes	class	NOUN
iajs-2009	204	28	ofˑˑ	ofˑˑ	VERB
iajs-2009	204	29	equivalence	equivalence	NOUN
iajs-2009	204	30	relationˑ	relationˑ	NOUN
iajs-2009	204	31	~	~	PUNCT
iajs-2009	204	32	ˑin	ˑin	ADJ
iajs-2009	204	33	ˑdefinitionˑ	ˑdefinitionˑ	NOUN
iajs-2009	204	34	23	23	NUM
iajs-2009	204	35	.	.	PUNCT
iajs-2009	205	1	for	for	ADP
iajs-2009	205	2	xyx	xyx	PROPN
iajs-2009	205	3			PROPN
iajs-2009	205	4	,	,	PUNCT
iajs-2009	205	5	,	,	PUNCT
iajs-2009	205	6	ˑwe	ˑwe	PROPN
iajs-2009	205	7	say	say	VERB
iajs-2009	205	8	thatˑ	thatˑ	NOUN
iajs-2009	205	9	x	x	X
iajs-2009	205	10	~	~	PUNCT
iajs-2009	205	11	y	y	NOUN
iajs-2009	205	12	if	if	SCONJ
iajs-2009	205	13	andˑ	andˑ	VERB
iajs-2009	205	14	only	only	ADV
iajs-2009	205	15	ifˑ	ifˑ	NOUN
iajs-2009	205	16	)	)	PUNCT
iajs-2009	205	17	(	(	PUNCT
iajs-2009	205	18	)	)	PUNCT
iajs-2009	205	19	(	(	PUNCT
iajs-2009	205	20	yannxann	yannxann	PROPN
iajs-2009	205	21			NOUN
iajs-2009	205	22	.	.	PUNCT
iajs-2009	206	1	as	as	SCONJ
iajs-2009	206	2	denoted	denote	VERB
iajs-2009	206	3	ˑin	ˑin	NOUN
iajs-2009	206	4	(	(	PUNCT
iajs-2009	206	5	lemma	lemma	PROPN
iajs-2009	206	6	4	4	NUM
iajs-2009	206	7	)	)	PUNCT
iajs-2009	206	8	,	,	PUNCT
iajs-2009	207	1	~	~	PUNCT
iajs-2009	207	2	is	be	AUX
iajs-2009	207	3	anˑ	anˑ	NOUN
iajs-2009	207	4	equivalenceˑ	equivalenceˑ	PROPN
iajs-2009	207	5	relation	relation	PROPN
iajs-2009	207	6	.	.	PUNCT
iajs-2009	208	1	furthermoreˑ	furthermoreˑ	PROPN
iajs-2009	208	2	,	,	PUNCT
iajs-2009	208	3	ifˑ	ifˑ	X
iajs-2009	208	4	]	]	PUNCT
iajs-2009	209	1	[	[	X
iajs-2009	209	2	x	x	X
iajs-2009	209	3	denotes	denotes	PROPN
iajs-2009	209	4	theˑclass	theˑclass	NOUN
iajs-2009	209	5	of	of	ADP
iajs-2009	209	6	x	x	PRON
iajs-2009	209	7	,	,	PUNCT
iajs-2009	209	8	thenˑ	thenˑ	VERB
iajs-2009	209	9	the	the	DET
iajs-2009	209	10	product	product	NOUN
iajs-2009	209	11	ˑ	ˑ	NOUN
iajs-2009	209	12	]	]	X
iajs-2009	210	1	[	[	X
iajs-2009	210	2	]	]	X
iajs-2009	210	3	[	[	X
iajs-2009	210	4	]	]	X
iajs-2009	210	5	[	[	PUNCT
iajs-2009	210	6	yxyx	yxyx	NOUN
iajs-2009	210	7			PROPN
iajs-2009	210	8			PROPN
iajs-2009	210	9	andˑ	andˑ	ADJ
iajs-2009	210	10	]	]	X
iajs-2009	210	11	[	[	X
iajs-2009	210	12	]	]	X
iajs-2009	210	13	[	[	X
iajs-2009	210	14	]	]	X
iajs-2009	210	15	[	[	PUNCT
iajs-2009	210	16	yxyx	yxyx	ADJ
iajs-2009	210	17			PROPN
iajs-2009	210	18	.	.	PUNCT
iajs-2009	211	1	definition25.ˑthe	definition25.ˑthe	PROPN
iajs-2009	211	2	graphˑ	graphˑ	NOUN
iajs-2009	211	3	of	of	ADP
iajs-2009	211	4	equivalence	equivalence	NOUN
iajs-2009	211	5	ˑclasses	ˑclasse	NOUN
iajs-2009	211	6	of	of	ADP
iajs-2009	211	7	ˑa	ˑa	DET
iajs-2009	211	8	ku	ku	PROPN
iajs-2009	211	9	-	-	PUNCT
iajs-2009	211	10	semigroupˑ	semigroupˑ	PROPN
iajs-2009	211	11	x	x	NOUN
iajs-2009	211	12	,	,	PUNCT
iajs-2009	211	13	denoted	denote	VERB
iajs-2009	211	14	by	by	ADP
iajs-2009	211	15	ˑˑ	ˑˑ	PROPN
iajs-2009	211	16	x	x	PRON
iajs-2009	211	17	is	be	AUX
iajs-2009	211	18	the	the	DET
iajs-2009	211	19	undirected	undirected	ADJ
iajs-2009	211	20	simpleˑˑgraph	simpleˑˑgraph	NOUN
iajs-2009	211	21	whoseˑ	whoseˑ	NOUN
iajs-2009	211	22	vertices	vertice	VERB
iajs-2009	211	23	ˑareˑ	ˑareˑ	NOUN
iajs-2009	211	24	theˑ	theˑ	NOUN
iajs-2009	211	25	set	set	VERB
iajs-2009	211	26	of	of	ADP
iajs-2009	211	27	ˑequivalenceˑˑclasses	ˑequivalenceˑˑclasse	NOUN
iajs-2009	211	28	ˑ	ˑ	PUNCT
iajs-2009	211	29	xxx	xxx	ADJ
iajs-2009	211	30			NOUN
iajs-2009	211	31	]	]	PUNCT
iajs-2009	211	32	;	;	PUNCT
iajs-2009	211	33	[	[	PUNCT
iajs-2009	211	34	ˑ	ˑ	NOUN
iajs-2009	211	35	and	and	CCONJ
iajs-2009	211	36	twoˑˑdistinctˑ	twoˑˑdistinctˑ	NOUN
iajs-2009	211	37	classesˑˑ	classesˑˑ	NOUN
iajs-2009	211	38	]	]	X
iajs-2009	212	1	[	[	X
iajs-2009	212	2	]	]	X
iajs-2009	212	3	,	,	PUNCT
iajs-2009	212	4	[	[	PUNCT
iajs-2009	212	5	yx	yx	NOUN
iajs-2009	212	6	are	be	AUX
iajs-2009	212	7	ˑadjacentˑ	ˑadjacentˑ	NOUN
iajs-2009	212	8	in	in	ADP
iajs-2009	212	9	ˑ	ˑ	PROPN
iajs-2009	212	10			PROPN
iajs-2009	212	11	x	x	PUNCT
iajs-2009	212	12	ˑ	ˑ	NOUN
iajs-2009	212	13	if	if	SCONJ
iajs-2009	212	14	ˑandˑ	ˑandˑ	ADJ
iajs-2009	212	15	only	only	ADV
iajs-2009	212	16	ifˑ	ifˑ	NOUN
iajs-2009	212	17	}	}	PUNCT
iajs-2009	212	18	0	0	NUM
iajs-2009	212	19	{	{	PUNCT
iajs-2009	212	20	]	]	X
iajs-2009	212	21	[	[	X
iajs-2009	212	22	]	]	X
iajs-2009	212	23	[	[	PUNCT
iajs-2009	212	24	yx	yx	X
iajs-2009	212	25			PROPN
iajs-2009	212	26	and	and	CCONJ
iajs-2009	212	27	}	}	PUNCT
iajs-2009	212	28	.0	.0	NUM
iajs-2009	212	29	{	{	PUNCT
iajs-2009	212	30	]	]	X
iajs-2009	212	31	[	[	X
iajs-2009	212	32	]	]	X
iajs-2009	212	33	[	[	PUNCT
iajs-2009	212	34			NUM
iajs-2009	212	35	yx	yx	PROPN
iajs-2009	212	36	example	example	NOUN
iajs-2009	212	37	26.ˑ	26.ˑ	NUM
iajs-2009	212	38	let	let	VERB
iajs-2009	212	39	}	}	PUNCT
iajs-2009	212	40	,	,	PUNCT
iajs-2009	212	41	,	,	PUNCT
iajs-2009	212	42	,	,	PUNCT
iajs-2009	212	43	0	0	NUM
iajs-2009	212	44	{	{	PUNCT
iajs-2009	212	45	cbax	cbax	PROPN
iajs-2009	212	46			PROPN
iajs-2009	212	47	beˑˑa	beˑˑa	PROPN
iajs-2009	212	48	set	set	VERB
iajs-2009	212	49	.	.	PUNCT
iajs-2009	213	1	define	define	VERB
iajs-2009	213	2			PROPN
iajs-2009	213	3	-ˑˑoperation	-ˑˑoperation	PROPN
iajs-2009	213	4	and	and	CCONJ
iajs-2009	213	5			PROPN
iajs-2009	213	6	-ˑˑoperation	-ˑˑoperation	NOUN
iajs-2009	213	7	by	by	ADP
iajs-2009	213	8	the	the	DET
iajs-2009	213	9	following	follow	VERB
iajs-2009	213	10	tables	table	NOUN
iajs-2009	213	11	thenˑ	thenˑ	VERB
iajs-2009	213	12	)	)	PUNCT
iajs-2009	213	13	0	0	NUM
iajs-2009	213	14	,	,	PUNCT
iajs-2009	213	15	,	,	PUNCT
iajs-2009	213	16	,	,	PUNCT
iajs-2009	213	17	(	(	PUNCT
iajs-2009	213	18	x	x	VERB
iajs-2009	213	19	is	be	AUX
iajs-2009	213	20	aˑ	aˑ	ADP
iajs-2009	213	21	ku-ˑsemigroup	ku-ˑsemigroup	NOUN
iajs-2009	213	22	.	.	PUNCT
iajs-2009	214	1	we	we	PRON
iajs-2009	214	2	haveˑ	haveˑ	VERB
iajs-2009	214	3	the	the	DET
iajs-2009	214	4	set	set	NOUN
iajs-2009	214	5	of	of	ADP
iajs-2009	214	6	ˑvertices	ˑvertice	NOUN
iajs-2009	214	7	is	be	AUX
iajs-2009	214	8	ˑv	ˑv	ADP
iajs-2009	214	9	ω	ω	NUM
iajs-2009	214	10	𝑋	𝑋	PROPN
iajs-2009	214	11	0	0	NUM
iajs-2009	214	12	,	,	PUNCT
iajs-2009	214	13	𝑎	𝑎	NOUN
iajs-2009	214	14	,	,	PUNCT
iajs-2009	214	15	𝑏	𝑏	NOUN
iajs-2009	214	16	,	,	PUNCT
iajs-2009	214	17	𝑐	𝑐	NOUN
iajs-2009	214	18	ˑ	ˑ	NOUN
iajs-2009	214	19	and	and	CCONJ
iajs-2009	214	20	ˑthe	ˑthe	DET
iajs-2009	214	21	ˑset	ˑset	NOUN
iajs-2009	214	22	of	of	ADP
iajs-2009	214	23	edges	edge	NOUN
iajs-2009	214	24	ˑis	ˑis	VERB
iajs-2009	214	25	ˑe	ˑe	PROPN
iajs-2009	214	26	ω	ω	PROPN
iajs-2009	214	27	𝑋	𝑋	PROPN
iajs-2009	214	28	0	0	NUM
iajs-2009	214	29	𝑎,0	𝑎,0	NUM
iajs-2009	214	30	𝑏,𝑎	𝑏,𝑎	PROPN
iajs-2009	214	31	𝑏,ˑ𝑎	𝑏,ˑ𝑎	PROPN
iajs-2009	214	32	𝑐,𝑏	𝑐,𝑏	PROPN
iajs-2009	215	1	𝑐	𝑐	PROPN
iajs-2009	215	2	.ˑ	.ˑ	NOUN
iajs-2009	215	3	soˑ	soˑ	PROPN
iajs-2009	215	4	,	,	PUNCT
iajs-2009	215	5	the	the	DET
iajs-2009	215	6	set	set	NOUN
iajs-2009	215	7	ˑof	ˑof	NOUN
iajs-2009	215	8	vertices	vertice	VERB
iajs-2009	215	9	ˑof	ˑof	NUM
iajs-2009	215	10	ˑ	ˑ	PROPN
iajs-2009	215	11	𝑋	𝑋	PROPN
iajs-2009	215	12	is	be	AUX
iajs-2009	215	13	]	]	PUNCT
iajs-2009	215	14	}	}	PUNCT
iajs-2009	215	15	[	[	X
iajs-2009	215	16	]	]	X
iajs-2009	215	17	,	,	PUNCT
iajs-2009	215	18	[	[	X
iajs-2009	215	19	]	]	X
iajs-2009	215	20	,	,	PUNCT
iajs-2009	215	21	0	0	NUM
iajs-2009	215	22	{	{	PUNCT
iajs-2009	215	23	[	[	PUNCT
iajs-2009	215	24	ba	ba	NOUN
iajs-2009	215	25	ˑsince	ˑsince	NOUN
iajs-2009	215	26	}	}	PUNCT
iajs-2009	215	27	,	,	PUNCT
iajs-2009	215	28	,	,	PUNCT
iajs-2009	215	29	{	{	PUNCT
iajs-2009	215	30	)	)	PUNCT
iajs-2009	215	31	0	0	NUM
iajs-2009	215	32	(	(	PUNCT
iajs-2009	215	33	baann	baann	NOUN
iajs-2009	215	34			PROPN
iajs-2009	215	35	}	}	PUNCT
iajs-2009	215	36	,	,	PUNCT
iajs-2009	215	37	,	,	PUNCT
iajs-2009	215	38	0	0	NUM
iajs-2009	215	39	{	{	PUNCT
iajs-2009	215	40	)	)	PUNCT
iajs-2009	215	41	(	(	PUNCT
iajs-2009	215	42	cbaann	cbaann	PROPN
iajs-2009	215	43			PROPN
iajs-2009	215	44	,	,	PUNCT
iajs-2009	215	45	}	}	PUNCT
iajs-2009	215	46	,	,	PUNCT
iajs-2009	215	47	,	,	PUNCT
iajs-2009	215	48	0	0	NUM
iajs-2009	215	49	{	{	PUNCT
iajs-2009	215	50	)	)	PUNCT
iajs-2009	215	51	(	(	PUNCT
iajs-2009	215	52	cabann	cabann	VERB
iajs-2009	215	53			PROPN
iajs-2009	215	54	ˑand	ˑand	NOUN
iajs-2009	215	55	}	}	PUNCT
iajs-2009	215	56	,	,	PUNCT
iajs-2009	215	57	{	{	PUNCT
iajs-2009	215	58	)	)	PUNCT
iajs-2009	215	59	(	(	PUNCT
iajs-2009	215	60	bacann	bacann	PROPN
iajs-2009	215	61			PROPN
iajs-2009	215	62	,	,	PUNCT
iajs-2009	215	63	ˑ	ˑ	NOUN
iajs-2009	215	64	then	then	ADV
iajs-2009	215	65	𝐸	𝐸	PROPN
iajs-2009	215	66			PROPN
iajs-2009	215	67	𝑋	𝑋	NOUN
iajs-2009	215	68	0	0	NUM
iajs-2009	215	69	𝑎	𝑎	NOUN
iajs-2009	215	70	,	,	PUNCT
iajs-2009	215	71	0	0	NUM
iajs-2009	215	72	𝑏	𝑏	NOUN
iajs-2009	215	73	,	,	PUNCT
iajs-2009	215	74	𝑎	𝑎	NOUN
iajs-2009	215	75	𝑏	𝑏	NOUN
iajs-2009	215	76	.	.	PUNCT
iajs-2009	216	1	ˑtheˑ	ˑtheˑ	PROPN
iajs-2009	216	2	followingˑ	followingˑ	NOUN
iajs-2009	216	3	figure	figure	NOUN
iajs-2009	216	4	showsˑ	showsˑ	VERB
iajs-2009	216	5	the	the	DET
iajs-2009	216	6	graph	graph	NOUN
iajs-2009	216	7	ω	ω	NUM
iajs-2009	216	8	𝑋	𝑋	PROPN
iajs-2009	216	9	ˑ	ˑ	NOUN
iajs-2009	216	10	and	and	CCONJ
iajs-2009	216	11			PROPN
iajs-2009	216	12	𝑋	𝑋	PROPN
iajs-2009	216	13	.	.	PUNCT
iajs-2009	217	1			PROPN
iajs-2009	217	2	0ˑ	0ˑ	NOUN
iajs-2009	217	3	aˑ	aˑ	ADP
iajs-2009	217	4	bˑ	bˑ	ADP
iajs-2009	217	5	c	c	PROPN
iajs-2009	217	6	0ˑ	0ˑ	NOUN
iajs-2009	217	7	0	0	NUM
iajs-2009	217	8	aˑˑ	aˑˑ	PROPN
iajs-2009	217	9	b	b	NOUN
iajs-2009	217	10	cˑ	cˑ	NOUN
iajs-2009	217	11	aˑ	aˑ	ADP
iajs-2009	217	12	0	0	NUM
iajs-2009	217	13	0ˑˑ	0ˑˑ	NOUN
iajs-2009	217	14	a	a	DET
iajs-2009	217	15	cˑ	cˑ	NOUN
iajs-2009	217	16	bˑ	bˑ	ADP
iajs-2009	217	17	0	0	NUM
iajs-2009	217	18	0ˑˑ	0ˑˑ	NOUN
iajs-2009	217	19	0	0	PUNCT
iajs-2009	218	1	c	c	NOUN
iajs-2009	218	2	cˑ	cˑ	NOUN
iajs-2009	218	3	0	0	NUM
iajs-2009	218	4	aˑ	aˑ	ADP
iajs-2009	218	5	bˑ	bˑ	PROPN
iajs-2009	218	6	0	0	NUM
iajs-2009	218	7			PROPN
iajs-2009	218	8	0	0	NUM
iajs-2009	218	9	aˑ	aˑ	ADP
iajs-2009	218	10	b	b	NOUN
iajs-2009	218	11	c	c	NOUN
iajs-2009	218	12	0	0	NUM
iajs-2009	218	13	0	0	NUM
iajs-2009	219	1	0ˑ	0ˑ	NOUN
iajs-2009	219	2	0	0	NUM
iajs-2009	219	3	0	0	NUM
iajs-2009	220	1	a	a	DET
iajs-2009	220	2	0	0	NUM
iajs-2009	220	3	0ˑ	0ˑ	NOUN
iajs-2009	220	4	0	0	PUNCT
iajs-2009	221	1	a	a	DET
iajs-2009	221	2	b	b	NOUN
iajs-2009	221	3	0	0	NUM
iajs-2009	221	4	0ˑ	0ˑ	NOUN
iajs-2009	221	5	0	0	NUM
iajs-2009	221	6	b	b	X
iajs-2009	221	7	c	c	NOUN
iajs-2009	221	8	0	0	PUNCT
iajs-2009	222	1	a	a	DET
iajs-2009	222	2	b	b	PROPN
iajs-2009	222	3	c	c	NOUN
iajs-2009	222	4	mathematics	mathematic	NOUN
iajs-2009	222	5	|	|	ADV
iajs-2009	222	6	168	168	NUM
iajs-2009	222	7	ibn	ibn	PROPN
iajs-2009	222	8	al	al	PROPN
iajs-2009	222	9	-	-	PUNCT
iajs-2009	222	10	haitham	haitham	PROPN
iajs-2009	222	11	jour	jour	X
iajs-2009	222	12	.	.	PROPN
iajs-2009	222	13	for	for	ADP
iajs-2009	222	14	pure	pure	ADJ
iajs-2009	222	15	&	&	CCONJ
iajs-2009	222	16	appl	appl	PROPN
iajs-2009	222	17	.	.	PUNCT
iajs-2009	223	1	sci	sci	PROPN
iajs-2009	223	2	.	.	PROPN
iajs-2009	223	3	ihjpas	ihjpas	PROPN
iajs-2009	223	4	https://doi.org/10.30526/31.3.2009	https://doi.org/10.30526/31.3.2009	PROPN
iajs-2009	223	5	vol	vol	NOUN
iajs-2009	223	6	.	.	PROPN
iajs-2009	224	1	31	31	NUM
iajs-2009	225	1	(	(	PUNCT
iajs-2009	225	2	3	3	NUM
iajs-2009	225	3	)	)	SYM
iajs-2009	225	4	2018	2018	NUM
iajs-2009	225	5	figure	figure	NOUN
iajs-2009	225	6	3	3	NUM
iajs-2009	225	7	.	.	PUNCT
iajs-2009	226	1	the	the	DET
iajs-2009	226	2	graphsˑω	graphsˑω	NOUN
iajs-2009	226	3	𝑋	𝑋	VERB
iajs-2009	226	4	and	and	PROPN
iajs-2009	226	5	𝑋	𝑋	PROPN
iajs-2009	226	6	ˑ	ˑ	PROPN
iajs-2009	226	7	example	example	NOUN
iajs-2009	226	8	ˑ27ˑ.ˑlet	ˑ27ˑ.ˑlet	NOUN
iajs-2009	226	9	ˑ	ˑ	NOUN
iajs-2009	226	10	}	}	PUNCT
iajs-2009	226	11	,	,	PUNCT
iajs-2009	226	12	,	,	PUNCT
iajs-2009	226	13	,	,	PUNCT
iajs-2009	226	14	,	,	PUNCT
iajs-2009	226	15	0	0	NUM
iajs-2009	226	16	{	{	PUNCT
iajs-2009	226	17	dcbax	dcbax	NOUN
iajs-2009	226	18			PROPN
iajs-2009	226	19	beˑaˑ	beˑaˑ	NOUN
iajs-2009	226	20	setˑ	setˑ	PROPN
iajs-2009	226	21	in	in	ADP
iajs-2009	226	22	example	example	NOUN
iajs-2009	226	23	18	18	NUM
iajs-2009	226	24	.	.	PUNCT
iajs-2009	226	25	thenˑ	thenˑ	PROPN
iajs-2009	226	26	theˑ	theˑ	PROPN
iajs-2009	226	27	set	set	VERB
iajs-2009	226	28	ofˑˑ	ofˑˑ	ADJ
iajs-2009	226	29	vertices	vertex	NOUN
iajs-2009	226	30	ˑof	ˑof	NUM
iajs-2009	226	31	ˑ	ˑ	PROPN
iajs-2009	226	32	𝑋	𝑋	PROPN
iajs-2009	226	33	ˑ	ˑ	PROPN
iajs-2009	226	34	is	be	AUX
iajs-2009	226	35	ˑ	ˑ	NOUN
iajs-2009	226	36	]	]	PUNCT
iajs-2009	226	37	}	}	PUNCT
iajs-2009	226	38	[	[	X
iajs-2009	226	39	]	]	X
iajs-2009	226	40	,	,	PUNCT
iajs-2009	226	41	[	[	X
iajs-2009	226	42	]	]	X
iajs-2009	226	43	,	,	PUNCT
iajs-2009	226	44	[	[	X
iajs-2009	226	45	]	]	X
iajs-2009	226	46	,	,	PUNCT
iajs-2009	226	47	0	0	NUM
iajs-2009	226	48	{	{	PUNCT
iajs-2009	226	49	[	[	PUNCT
iajs-2009	226	50	dca	dca	PROPN
iajs-2009	226	51	ˑand	ˑand	CCONJ
iajs-2009	226	52	ˑthe	ˑthe	DET
iajs-2009	226	53	set	set	NOUN
iajs-2009	226	54	of	of	ADP
iajs-2009	226	55	edges	edge	NOUN
iajs-2009	226	56	is	be	AUX
iajs-2009	226	57	}	}	PUNCT
iajs-2009	226	58	]	]	PUNCT
iajs-2009	226	59	,	,	PUNCT
iajs-2009	226	60	[	[	X
iajs-2009	226	61	]	]	X
iajs-2009	226	62	[	[	X
iajs-2009	226	63	]	]	X
iajs-2009	226	64	,	,	PUNCT
iajs-2009	226	65	[	[	X
iajs-2009	226	66	]	]	X
iajs-2009	226	67	[	[	X
iajs-2009	226	68	]	]	X
iajs-2009	226	69	,	,	PUNCT
iajs-2009	226	70	[	[	X
iajs-2009	226	71	]	]	X
iajs-2009	226	72	[	[	X
iajs-2009	226	73	]	]	X
iajs-2009	226	74	,	,	PUNCT
iajs-2009	226	75	[	[	X
iajs-2009	226	76	]	]	X
iajs-2009	226	77	0	0	NUM
iajs-2009	226	78	{	{	PUNCT
iajs-2009	226	79	[	[	PUNCT
iajs-2009	226	80	dcdacad	dcdacad	ADJ
iajs-2009	226	81			VERB
iajs-2009	226	82	the	the	DET
iajs-2009	226	83	figure	figure	NOUN
iajs-2009	226	84	(	(	PUNCT
iajs-2009	226	85	4	4	NUM
iajs-2009	226	86	)	)	PUNCT
iajs-2009	226	87	shows	show	VERB
iajs-2009	226	88	ˑthe	ˑthe	DET
iajs-2009	226	89	graph	graph	NOUN
iajs-2009	226	90	of	of	ADP
iajs-2009	226	91	ˑequivalence	ˑequivalence	NOUN
iajs-2009	226	92	classes	class	NOUN
iajs-2009	226	93	ˑ	ˑ	PROPN
iajs-2009	226	94	𝑋	𝑋	PROPN
iajs-2009	226	95	.	.	PUNCT
iajs-2009	227	1	figure	figure	VERB
iajs-2009	227	2	4	4	NUM
iajs-2009	227	3	.	.	PUNCT
iajs-2009	228	1	the	the	DET
iajs-2009	228	2	graph	graph	NOUN
iajs-2009	228	3	𝑋	𝑋	PROPN
iajs-2009	228	4	lemma	lemma	PROPN
iajs-2009	228	5	28	28	NUM
iajs-2009	228	6	.	.	PUNCT
iajs-2009	229	1	with	with	ADP
iajs-2009	229	2	ˑnotations	ˑnotation	NOUN
iajs-2009	229	3	asˑ	asˑ	VERB
iajs-2009	229	4	before	before	ADV
iajs-2009	229	5	.	.	PUNCT
iajs-2009	230	1	1	1	X
iajs-2009	230	2	)	)	PUNCT
iajs-2009	230	3	ˑ	ˑ	PROPN
iajs-2009	230	4	𝑋	𝑋	PROPN
iajs-2009	230	5	is	be	AUX
iajs-2009	230	6	ˑa	ˑa	ADP
iajs-2009	230	7	sub	sub	NOUN
iajs-2009	230	8	graphˑ	graphˑ	NOUN
iajs-2009	230	9	of	of	ADP
iajs-2009	230	10	ω	ω	PROPN
iajs-2009	230	11	𝑋	𝑋	NOUN
iajs-2009	230	12	;	;	PUNCT
iajs-2009	230	13	2	2	X
iajs-2009	230	14	)	)	PUNCT
iajs-2009	230	15	for	for	ADP
iajs-2009	230	16	all	all	DET
iajs-2009	230	17	ˑ	ˑ	NOUN
iajs-2009	230	18	xx	xx	PROPN
iajs-2009	230	19	,	,	PUNCT
iajs-2009	230	20	weˑ	weˑ	PROPN
iajs-2009	230	21	have	have	VERB
iajs-2009	230	22	)	)	PUNCT
iajs-2009	230	23	(	(	PUNCT
iajs-2009	230	24	)	)	PUNCT
iajs-2009	230	25	(	(	PUNCT
iajs-2009	230	26	xannxn	xannxn	PROPN
iajs-2009	230	27			PROPN
iajs-2009	230	28	.	.	PUNCT
iajs-2009	231	1	proof.ˑ	proof.ˑ	PROPN
iajs-2009	231	2	straightforward	straightforward	ADJ
iajs-2009	231	3	.	.	PUNCT
iajs-2009	232	1	theorem29.ˑ	theorem29.ˑ	VERB
iajs-2009	232	2	let	let	VERB
iajs-2009	232	3			PROPN
iajs-2009	232	4	𝑋	𝑋	PROPN
iajs-2009	232	5	be	be	AUX
iajs-2009	232	6	theˑ	theˑ	NOUN
iajs-2009	232	7	graphˑ	graphˑ	ADJ
iajs-2009	232	8	ofˑ	ofˑ	NOUN
iajs-2009	232	9	equivalence	equivalence	NOUN
iajs-2009	232	10	ˑclassesˑˑ	ˑclassesˑˑ	NOUN
iajs-2009	232	11	of	of	ADP
iajs-2009	232	12	x	x	PROPN
iajs-2009	232	13	.ˑ	.ˑ	PROPN
iajs-2009	232	14	for	for	ADP
iajs-2009	232	15	ˑany	ˑany	ADJ
iajs-2009	232	16	distinct	distinct	ADJ
iajs-2009	232	17	ˑvertices	ˑvertice	NOUN
iajs-2009	232	18	𝑥ˑ	𝑥ˑ	ADP
iajs-2009	232	19	,	,	PUNCT
iajs-2009	232	20	𝑦	𝑦	NOUN
iajs-2009	232	21	ˑ	ˑ	ADJ
iajs-2009	232	22	𝑋	𝑋	PROPN
iajs-2009	232	23	ˑ	ˑ	NOUN
iajs-2009	232	24	,	,	PUNCT
iajs-2009	232	25	if	if	SCONJ
iajs-2009	232	26	ˑ	ˑ	PRON
iajs-2009	232	27	]	]	X
iajs-2009	233	1	[	[	X
iajs-2009	233	2	]	]	X
iajs-2009	233	3	[	[	PUNCT
iajs-2009	233	4	yandx	yandx	NOUN
iajs-2009	233	5	ˑˑconnected	ˑˑconnecte	VERB
iajs-2009	233	6	ˑby	ˑby	ADV
iajs-2009	233	7	ˑanˑ	ˑanˑ	PROPN
iajs-2009	233	8	edgeˑ,ˑ	edgeˑ,ˑ	PROPN
iajs-2009	233	9	thenˑ	thenˑ	NOUN
iajs-2009	233	10	)	)	PUNCT
iajs-2009	233	11	(	(	PUNCT
iajs-2009	233	12	)	)	PUNCT
iajs-2009	233	13	(	(	PUNCT
iajs-2009	233	14	yannxann	yannxann	PROPN
iajs-2009	233	15			PROPN
iajs-2009	233	16	.	.	PUNCT
iajs-2009	234	1	proof.ˑ	proof.ˑ	PROPN
iajs-2009	234	2	suppose	suppose	VERB
iajs-2009	234	3	that	that	SCONJ
iajs-2009	234	4	ˑ	ˑ	NOUN
iajs-2009	234	5	)	)	PUNCT
iajs-2009	234	6	(	(	PUNCT
iajs-2009	234	7	)	)	PUNCT
iajs-2009	234	8	(	(	PUNCT
iajs-2009	234	9	yannxann	yannxann	PROPN
iajs-2009	234	10			PROPN
iajs-2009	234	11	,	,	PUNCT
iajs-2009	234	12	thenˑ	thenˑ	PROPN
iajs-2009	234	13	yx	yx	X
iajs-2009	234	14	~	~	PUNCT
iajs-2009	234	15	.	.	PUNCT
iajs-2009	235	1	henceˑ	henceˑ	PROPN
iajs-2009	235	2	]	]	PUNCT
iajs-2009	236	1	[	[	X
iajs-2009	236	2	]	]	X
iajs-2009	236	3	[	[	PUNCT
iajs-2009	236	4	yx	yx	X
iajs-2009	236	5			NUM
iajs-2009	236	6	this	this	DET
iajs-2009	236	7	isˑ	isˑ	NOUN
iajs-2009	236	8	a	a	DET
iajs-2009	236	9	contradictionˑ.	contradictionˑ.	ADJ
iajs-2009	236	10	thereforeˑ	thereforeˑ	NOUN
iajs-2009	236	11	)	)	PUNCT
iajs-2009	236	12	(	(	PUNCT
iajs-2009	236	13	)	)	PUNCT
iajs-2009	236	14	(	(	PUNCT
iajs-2009	236	15	yannxann	yannxann	PROPN
iajs-2009	236	16			PROPN
iajs-2009	236	17	.	.	PUNCT
iajs-2009	237	1	the	the	DET
iajs-2009	237	2	ˑconverse	ˑconverse	NOUN
iajs-2009	237	3	of	of	ADP
iajs-2009	237	4	thisˑ	thisˑ	NOUN
iajs-2009	237	5	theorem	theorem	VERB
iajs-2009	237	6	is	be	AUX
iajs-2009	237	7	ˑnot	ˑnot	ADV
iajs-2009	237	8	true	true	ADJ
iajs-2009	237	9	.	.	PUNCT
iajs-2009	238	1	in	in	ADP
iajs-2009	238	2	exampleˑ27	exampleˑ27	NOUN
iajs-2009	238	3	,	,	PUNCT
iajs-2009	238	4	we	we	PRON
iajs-2009	238	5	haveˑ	haveˑ	VERB
iajs-2009	238	6	the	the	DET
iajs-2009	238	7	verticesˑ	verticesˑ	NOUN
iajs-2009	238	8	]	]	X
iajs-2009	239	1	[	[	X
iajs-2009	239	2	,	,	PUNCT
iajs-2009	239	3	]	]	X
iajs-2009	239	4	0	0	NUM
iajs-2009	239	5	[	[	PUNCT
iajs-2009	239	6	c	c	NOUN
iajs-2009	239	7	and	and	CCONJ
iajs-2009	239	8	ˑ	ˑ	NOUN
iajs-2009	239	9	)	)	PUNCT
iajs-2009	239	10	(	(	PUNCT
iajs-2009	239	11	)	)	PUNCT
iajs-2009	239	12	0	0	NUM
iajs-2009	239	13	(	(	PUNCT
iajs-2009	239	14	cannann	cannann	PROPN
iajs-2009	239	15			PROPN
iajs-2009	239	16	but	but	CCONJ
iajs-2009	239	17	noˑ	noˑ	PROPN
iajs-2009	239	18	edge	edge	NOUN
iajs-2009	239	19	jointˑ	jointˑ	NOUN
iajs-2009	239	20	between	between	ADP
iajs-2009	239	21	themˑ.	themˑ.	NOUN
iajs-2009	239	22	theorem30	theorem30	NOUN
iajs-2009	239	23	.	.	PUNCT
iajs-2009	240	1	ˑlet	ˑlet	NOUN
iajs-2009	240	2	x	x	PUNCT
iajs-2009	240	3	as	as	SCONJ
iajs-2009	240	4	ˑmentioned	ˑmentione	VERB
iajs-2009	240	5	above	above	ADV
iajs-2009	240	6	.	.	PUNCT
iajs-2009	241	1	if	if	SCONJ
iajs-2009	241	2	ω	ω	PROPN
iajs-2009	241	3	𝑋	𝑋	PROPN
iajs-2009	241	4	is	be	AUX
iajs-2009	241	5	a	a	DET
iajs-2009	241	6	ˑcomplete	ˑcomplete	ADJ
iajs-2009	241	7	graph	graph	NOUN
iajs-2009	241	8	,	,	PUNCT
iajs-2009	241	9	ˑthen	ˑthen	ADV
iajs-2009	241	10	ω	ω	PROPN
iajs-2009	241	11	𝑋	𝑋	NOUN
iajs-2009	241	12			PUNCT
iajs-2009	241	13	𝑋	𝑋	PROPN
iajs-2009	241	14	.	.	PUNCT
iajs-2009	242	1	but	but	CCONJ
iajs-2009	242	2	theˑ	theˑ	NOUN
iajs-2009	242	3	convers	convers	PROPN
iajs-2009	242	4	is	be	AUX
iajs-2009	242	5	notˑ	notˑ	VERB
iajs-2009	242	6	true	true	ADJ
iajs-2009	242	7	.	.	PUNCT
iajs-2009	243	1	proof.ˑ	proof.ˑ	PROPN
iajs-2009	243	2	suppose	suppose	VERB
iajs-2009	243	3	that	that	SCONJ
iajs-2009	243	4	ˑv	ˑv	PROPN
iajs-2009	243	5	ω	ω	NUM
iajs-2009	243	6	𝑋	𝑋	PROPN
iajs-2009	243	7	𝑥	𝑥	PROPN
iajs-2009	243	8	,	,	PUNCT
iajs-2009	243	9	𝑥	𝑥	X
iajs-2009	243	10	,	,	PUNCT
iajs-2009	243	11	…	…	PUNCT
iajs-2009	243	12	,	,	PUNCT
iajs-2009	243	13	𝑥	𝑥	X
iajs-2009	243	14	.	.	PUNCT
iajs-2009	244	1	if	if	SCONJ
iajs-2009	244	2	ω	ω	NOUN
iajs-2009	244	3	𝑋	𝑋	PROPN
iajs-2009	244	4	ˑ	ˑ	PROPN
iajs-2009	244	5	is	be	AUX
iajs-2009	244	6	the	the	DET
iajs-2009	244	7	completeˑ	completeˑ	NOUN
iajs-2009	244	8	graph	graph	NOUN
iajs-2009	244	9	,	,	PUNCT
iajs-2009	244	10	then	then	ADV
iajs-2009	244	11	ˑevery	ˑevery	PROPN
iajs-2009	244	12	pair	pair	NOUN
iajs-2009	244	13	of	of	ADP
iajs-2009	244	14	ˑits	ˑit	NOUN
iajs-2009	244	15	verticesˑ	verticesˑ	NOUN
iajs-2009	244	16	are	be	AUX
iajs-2009	244	17	adjacent.ˑ	adjacent.ˑ	PRON
iajs-2009	244	18	thus	thus	ADV
iajs-2009	244	19	nixxxxn	nixxxxn	VERB
iajs-2009	244	20	i	i	PRON
iajs-2009	244	21	,	,	PUNCT
iajs-2009	244	22	...	...	PUNCT
iajs-2009	244	23	,	,	PUNCT
iajs-2009	244	24	2	2	NUM
iajs-2009	244	25	}	}	PUNCT
iajs-2009	244	26	,	,	PUNCT
iajs-2009	244	27	,	,	PUNCT
iajs-2009	244	28	...	...	PUNCT
iajs-2009	244	29	,	,	PUNCT
iajs-2009	244	30	,	,	PUNCT
iajs-2009	244	31	{	{	PUNCT
iajs-2009	244	32	)	)	PUNCT
iajs-2009	244	33	(	(	PUNCT
iajs-2009	244	34	321	321	NUM
iajs-2009	244	35			NUM
iajs-2009	244	36	nixxxxn	nixxxxn	VERB
iajs-2009	244	37	i	i	PRON
iajs-2009	244	38	,	,	PUNCT
iajs-2009	244	39	...	...	PUNCT
iajs-2009	244	40	,	,	PUNCT
iajs-2009	244	41	3,1	3,1	NUM
iajs-2009	244	42	}	}	PUNCT
iajs-2009	244	43	,	,	PUNCT
iajs-2009	244	44	,	,	PUNCT
iajs-2009	244	45	...	...	PUNCT
iajs-2009	244	46	,	,	PUNCT
iajs-2009	244	47	,	,	PUNCT
iajs-2009	244	48	{	{	PUNCT
iajs-2009	244	49	)	)	PUNCT
iajs-2009	244	50	(	(	PUNCT
iajs-2009	244	51	312	312	NUM
iajs-2009	244	52			NUM
iajs-2009	244	53	,	,	PUNCT
iajs-2009	244	54	…	…	PUNCT
iajs-2009	244	55	,	,	PUNCT
iajs-2009	244	56	}	}	PUNCT
iajs-2009	244	57	,	,	PUNCT
iajs-2009	244	58	...	...	PUNCT
iajs-2009	244	59	,	,	PUNCT
iajs-2009	244	60	,	,	PUNCT
iajs-2009	244	61	{	{	PUNCT
iajs-2009	244	62	)	)	PUNCT
iajs-2009	244	63	(	(	PUNCT
iajs-2009	244	64	121	121	NUM
iajs-2009	244	65			PROPN
iajs-2009	244	66	nn	nn	PROPN
iajs-2009	244	67	xxxxn	xxxxn	PROPN
iajs-2009	244	68	.	.	PUNCT
iajs-2009	245	1	then	then	ADV
iajs-2009	245	2	,	,	PUNCT
iajs-2009	245	3	)	)	PUNCT
iajs-2009	245	4	(	(	PUNCT
iajs-2009	245	5	)	)	PUNCT
iajs-2009	245	6	(	(	PUNCT
iajs-2009	245	7	)	)	PUNCT
iajs-2009	245	8	,	,	PUNCT
iajs-2009	245	9	...	...	PUNCT
iajs-2009	245	10	,	,	PUNCT
iajs-2009	245	11	(	(	PUNCT
iajs-2009	245	12	)	)	PUNCT
iajs-2009	245	13	(	(	PUNCT
iajs-2009	245	14	)	)	PUNCT
iajs-2009	245	15	,	,	PUNCT
iajs-2009	245	16	(	(	PUNCT
iajs-2009	245	17	)	)	PUNCT
iajs-2009	245	18	(	(	PUNCT
iajs-2009	245	19	2211	2211	NUM
iajs-2009	245	20	nn	nn	NUM
iajs-2009	245	21	xnxannxnxannxnxann	xnxannxnxannxnxann	PROPN
iajs-2009	245	22			NOUN
iajs-2009	245	23	,	,	PUNCT
iajs-2009	245	24	thus	thus	ADV
iajs-2009	245	25	)	)	PUNCT
iajs-2009	245	26	(	(	PUNCT
iajs-2009	245	27	...	...	PUNCT
iajs-2009	245	28	)	)	PUNCT
iajs-2009	245	29	(	(	PUNCT
iajs-2009	245	30	)	)	PUNCT
iajs-2009	245	31	(	(	PUNCT
iajs-2009	245	32	21	21	NUM
iajs-2009	245	33	nxannxannxann	nxannxannxann	NOUN
iajs-2009	245	34			PROPN
iajs-2009	245	35	mathematics	mathematic	NOUN
iajs-2009	245	36	|	|	ADV
iajs-2009	245	37	169	169	NUM
iajs-2009	245	38	ibn	ibn	PROPN
iajs-2009	245	39	al	al	PROPN
iajs-2009	245	40	-	-	PUNCT
iajs-2009	245	41	haitham	haitham	PROPN
iajs-2009	245	42	jour	jour	X
iajs-2009	245	43	.	.	PROPN
iajs-2009	246	1	for	for	ADP
iajs-2009	246	2	pure	pure	ADJ
iajs-2009	246	3	&	&	CCONJ
iajs-2009	246	4	appl	appl	PROPN
iajs-2009	246	5	.	.	PUNCT
iajs-2009	247	1	sci	sci	PROPN
iajs-2009	247	2	.	.	PROPN
iajs-2009	247	3	ihjpas	ihjpas	PROPN
iajs-2009	247	4	https://doi.org/10.30526/31.3.2009	https://doi.org/10.30526/31.3.2009	PROPN
iajs-2009	247	5	vol	vol	NOUN
iajs-2009	247	6	.	.	PROPN
iajs-2009	248	1	31	31	NUM
iajs-2009	249	1	(	(	PUNCT
iajs-2009	249	2	3	3	NUM
iajs-2009	249	3	)	)	PUNCT
iajs-2009	249	4	2018	2018	NUM
iajs-2009	249	5	thereforeˑˑ	thereforeˑˑ	ADJ
iajs-2009	249	6	everyˑ	everyˑ	NOUN
iajs-2009	249	7	vertex	vertex	NOUN
iajs-2009	249	8	of	of	ADP
iajs-2009	249	9	ˑω	ˑω	ADP
iajs-2009	249	10	𝑋	𝑋	PROPN
iajs-2009	249	11	isˑˑ	isˑˑ	PROPN
iajs-2009	249	12	a	a	DET
iajs-2009	249	13	equivalenceˑ	equivalenceˑ	ADJ
iajs-2009	249	14	classˑ	classˑ	NOUN
iajs-2009	249	15	of	of	ADP
iajs-2009	249	16	ˑˑ	ˑˑ	PROPN
iajs-2009	249	17	𝑋	𝑋	PROPN
iajs-2009	249	18	,	,	PUNCT
iajs-2009	249	19	thusˑ	thusˑ	VERB
iajs-2009	249	20	theˑ	theˑ	NOUN
iajs-2009	249	21	vertices	vertex	NOUN
iajs-2009	249	22	of	of	ADP
iajs-2009	249	23	ˑˑ	ˑˑ	PROPN
iajs-2009	249	24	𝑋	𝑋	PROPN
iajs-2009	249	25	ˑ	ˑ	NOUN
iajs-2009	249	26	are	be	AUX
iajs-2009	249	27	distinctˑ	distinctˑ	ADJ
iajs-2009	249	28	and	and	CCONJ
iajs-2009	249	29	ˑthe	ˑthe	DET
iajs-2009	249	30	sameˑ	sameˑ	ADJ
iajs-2009	249	31	number	number	NOUN
iajs-2009	249	32	of	of	ADP
iajs-2009	249	33	ˑvertices	ˑvertice	NOUN
iajs-2009	249	34	of	of	ADP
iajs-2009	249	35	ˑ	ˑ	PROPN
iajs-2009	249	36	ω	ω	NOUN
iajs-2009	249	37	𝑋	𝑋	PROPN
iajs-2009	249	38	ˑ	ˑ	NOUN
iajs-2009	249	39	,	,	PUNCT
iajs-2009	249	40	thenˑ	thenˑ	VERB
iajs-2009	249	41	there	there	PRON
iajs-2009	249	42	existˑ	existˑ	VERB
iajs-2009	249	43	an	an	DET
iajs-2009	249	44	isomorphic	isomorphic	ADJ
iajs-2009	249	45	ˑ	ˑ	PROPN
iajs-2009	249	46	𝑓	𝑓	PROPN
iajs-2009	249	47	:	:	PUNCT
iajs-2009	249	48	ω	ω	PROPN
iajs-2009	249	49	𝑋	𝑋	PROPN
iajs-2009	249	50	→	→	SYM
iajs-2009	249	51			PROPN
iajs-2009	249	52	𝑋	𝑋	PROPN
iajs-2009	249	53	ˑ	ˑ	ADP
iajs-2009	249	54	such	such	ADJ
iajs-2009	249	55	thatˑ	thatˑ	NOUN
iajs-2009	249	56	]	]	X
iajs-2009	249	57	[	[	X
iajs-2009	249	58	)	)	PUNCT
iajs-2009	249	59	(	(	PUNCT
iajs-2009	249	60	ii	ii	NOUN
iajs-2009	249	61	xxf	xxf	PROPN
iajs-2009	249	62			PROPN
iajs-2009	249	63	for	for	ADP
iajs-2009	249	64	ˑeachˑˑ	ˑeachˑˑ	PROPN
iajs-2009	249	65	}	}	PUNCT
iajs-2009	249	66	,	,	PUNCT
iajs-2009	249	67	...	...	PUNCT
iajs-2009	249	68	,	,	PUNCT
iajs-2009	249	69	2,1	2,1	NUM
iajs-2009	249	70	{	{	PUNCT
iajs-2009	249	71	ni	ni	ADJ
iajs-2009	249	72	ˑand	ˑand	NOUN
iajs-2009	249	73	theˑˑ	theˑˑ	NOUN
iajs-2009	249	74	mapping	mapping	NOUN
iajs-2009	249	75	of	of	ADP
iajs-2009	249	76	ˑedges	ˑedge	NOUN
iajs-2009	249	77	ˑ𝑓	ˑ𝑓	NOUN
iajs-2009	249	78	:	:	PUNCT
iajs-2009	249	79	𝐸	𝐸	PROPN
iajs-2009	249	80	ω	ω	NOUN
iajs-2009	249	81	𝑋	𝑋	PROPN
iajs-2009	249	82	→	→	SYM
iajs-2009	249	83	𝐸	𝐸	PROPN
iajs-2009	249	84			PROPN
iajs-2009	249	85	𝑋	𝑋	NOUN
iajs-2009	249	86	,	,	PUNCT
iajs-2009	249	87	ˑwhich	ˑwhich	NOUN
iajs-2009	249	88	sendsˑ	sendsˑ	NOUN
iajs-2009	249	89	theˑ	theˑ	NOUN
iajs-2009	249	90	edge	edge	VERB
iajs-2009	249	91	ji	ji	PROPN
iajs-2009	249	92	xx	xx	NUM
iajs-2009	249	93			VERB
iajs-2009	249	94	in	in	ADP
iajs-2009	249	95	ˑ𝐸	ˑ𝐸	PROPN
iajs-2009	249	96	ω	ω	PROPN
iajs-2009	249	97	𝑋	𝑋	PROPN
iajs-2009	249	98	ˑ	ˑ	NOUN
iajs-2009	249	99	toˑ	toˑ	ADP
iajs-2009	249	100	the	the	DET
iajs-2009	249	101	edge	edge	NOUN
iajs-2009	249	102	ˑ	ˑ	NOUN
iajs-2009	249	103	]	]	X
iajs-2009	249	104	[	[	X
iajs-2009	249	105	]	]	X
iajs-2009	249	106	[	[	PUNCT
iajs-2009	249	107	ji	ji	NOUN
iajs-2009	249	108	xx	xx	NUM
iajs-2009	249	109			PROPN
iajs-2009	249	110	inˑ	inˑ	NOUN
iajs-2009	249	111	𝐸	𝐸	PROPN
iajs-2009	249	112			PROPN
iajs-2009	249	113	𝑋	𝑋	NOUN
iajs-2009	249	114	is	be	AUX
iajs-2009	249	115	ˑa	ˑa	ADJ
iajs-2009	249	116	well-ˑˑdefined	well-ˑˑdefined	ADJ
iajs-2009	249	117	ˑbijection	ˑbijection	NOUN
iajs-2009	249	118	.	.	PUNCT
iajs-2009	250	1	the	the	DET
iajs-2009	250	2	converseˑ	converseˑ	NOUN
iajs-2009	250	3	of	of	ADP
iajs-2009	250	4	this	this	DET
iajs-2009	250	5	theoremˑ	theoremˑ	NOUN
iajs-2009	250	6	is	be	AUX
iajs-2009	250	7	false	false	ADJ
iajs-2009	250	8	asˑ	asˑ	NOUN
iajs-2009	250	9	illustrated	illustrate	VERB
iajs-2009	250	10	inˑ	inˑ	PROPN
iajs-2009	250	11	example31	example31	PROPN
iajs-2009	250	12	,	,	PUNCT
iajs-2009	250	13	ˑwe	ˑwe	PROPN
iajs-2009	250	14	have	have	AUX
iajs-2009	250	15	exampleˑˑ31.ˑˑlet	exampleˑˑ31.ˑˑlet	VERB
iajs-2009	250	16	}	}	PUNCT
iajs-2009	250	17	,	,	PUNCT
iajs-2009	250	18	,	,	PUNCT
iajs-2009	250	19	,	,	PUNCT
iajs-2009	250	20	0	0	NUM
iajs-2009	250	21	{	{	PUNCT
iajs-2009	250	22	cbax	cbax	PROPN
iajs-2009	250	23			PROPN
iajs-2009	250	24	beˑˑaˑ	beˑˑaˑ	NOUN
iajs-2009	250	25	set	set	NOUN
iajs-2009	250	26	.	.	PUNCT
iajs-2009	251	1	define	define	VERB
iajs-2009	251	2			PROPN
iajs-2009	251	3	-ˑoperation	-ˑoperation	PROPN
iajs-2009	251	4	and	and	CCONJ
iajs-2009	251	5			PROPN
iajs-2009	251	6	-ˑoperationˑ	-ˑoperationˑ	PROPN
iajs-2009	251	7	by	by	ADP
iajs-2009	251	8	ˑthe	ˑthe	DET
iajs-2009	251	9	ˑfollowing	ˑfollowe	VERB
iajs-2009	251	10	ˑˑtablesˑ	ˑˑtablesˑ	ADV
iajs-2009	251	11	thenˑˑ	thenˑˑ	ADP
iajs-2009	251	12	)	)	PUNCT
iajs-2009	251	13	0	0	NUM
iajs-2009	251	14	,	,	PUNCT
iajs-2009	251	15	,	,	PUNCT
iajs-2009	251	16	,	,	PUNCT
iajs-2009	251	17	(	(	PUNCT
iajs-2009	251	18	x	x	VERB
iajs-2009	251	19	is	be	AUX
iajs-2009	251	20	a	a	DET
iajs-2009	251	21	ˑku	ˑku	NOUN
iajs-2009	251	22	-	-	PUNCT
iajs-2009	251	23	semigroup	semigroup	NOUN
iajs-2009	251	24	.	.	PUNCT
iajs-2009	252	1	ˑ	ˑ	NOUN
iajs-2009	252	2	we	we	PRON
iajs-2009	252	3	ˑdetermine	ˑdetermine	VERB
iajs-2009	252	4	the	the	DET
iajs-2009	252	5	ˑgraph	ˑgraph	PROPN
iajs-2009	252	6	ω	ω	NOUN
iajs-2009	252	7	𝑋	𝑋	PROPN
iajs-2009	252	8	ˑ	ˑ	PROPN
iajs-2009	252	9	as	as	SCONJ
iajs-2009	252	10	follows	follow	VERB
iajs-2009	252	11	:	:	PUNCT
iajs-2009	252	12	ˑv	ˑv	PROPN
iajs-2009	252	13	ω	ω	NUM
iajs-2009	252	14	𝑋	𝑋	PROPN
iajs-2009	252	15	0	0	NUM
iajs-2009	252	16	,	,	PUNCT
iajs-2009	252	17	𝑎	𝑎	NOUN
iajs-2009	252	18	,	,	PUNCT
iajs-2009	252	19	𝑏	𝑏	NOUN
iajs-2009	252	20	,	,	PUNCT
iajs-2009	252	21	𝑐	𝑐	NOUN
iajs-2009	252	22	and	and	CCONJ
iajs-2009	252	23	ˑˑ	ˑˑ	NOUN
iajs-2009	252	24	e	e	PROPN
iajs-2009	252	25	ω	ω	PROPN
iajs-2009	253	1	𝑋	𝑋	PROPN
iajs-2009	253	2	0	0	NUM
iajs-2009	253	3	𝑎	𝑎	NOUN
iajs-2009	253	4	,	,	PUNCT
iajs-2009	253	5	𝑎	𝑎	PROPN
iajs-2009	253	6	𝑏	𝑏	NOUN
iajs-2009	253	7	,	,	PUNCT
iajs-2009	253	8	𝑎	𝑎	PROPN
iajs-2009	253	9	𝑐	𝑐	NOUN
iajs-2009	253	10	,	,	PUNCT
iajs-2009	253	11	𝑏	𝑏	PROPN
iajs-2009	253	12	𝑐	𝑐	PROPN
iajs-2009	253	13	.	.	PUNCT
iajs-2009	254	1	ˑthe	ˑthe	DET
iajs-2009	254	2	set	set	VERB
iajs-2009	254	3	ˑof	ˑof	NUM
iajs-2009	254	4	verticesˑ	verticesˑ	NOUN
iajs-2009	254	5	of	of	ADP
iajs-2009	254	6			PROPN
iajs-2009	254	7	𝑋	𝑋	PROPN
iajs-2009	254	8	is	be	AUX
iajs-2009	254	9	]	]	PUNCT
iajs-2009	254	10	}	}	PUNCT
iajs-2009	254	11	[	[	X
iajs-2009	254	12	]	]	X
iajs-2009	254	13	,	,	PUNCT
iajs-2009	254	14	[	[	X
iajs-2009	254	15	]	]	X
iajs-2009	254	16	,	,	PUNCT
iajs-2009	254	17	[	[	X
iajs-2009	254	18	]	]	X
iajs-2009	254	19	,	,	PUNCT
iajs-2009	254	20	0	0	NUM
iajs-2009	254	21	{	{	PUNCT
iajs-2009	254	22	[	[	PUNCT
iajs-2009	254	23	cba	cba	NOUN
iajs-2009	254	24	,	,	PUNCT
iajs-2009	254	25	sinceˑ	sinceˑ	NOUN
iajs-2009	254	26	}	}	PUNCT
iajs-2009	254	27	,	,	PUNCT
iajs-2009	254	28	{	{	PUNCT
iajs-2009	254	29	)	)	PUNCT
iajs-2009	254	30	0	0	NUM
iajs-2009	254	31	(	(	PUNCT
iajs-2009	254	32	aann	aann	NOUN
iajs-2009	254	33			NUM
iajs-2009	254	34	}	}	PUNCT
iajs-2009	254	35	,	,	PUNCT
iajs-2009	254	36	,	,	PUNCT
iajs-2009	254	37	0	0	NUM
iajs-2009	254	38	{	{	PUNCT
iajs-2009	254	39	)	)	PUNCT
iajs-2009	254	40	(	(	PUNCT
iajs-2009	254	41	cbaann	cbaann	PROPN
iajs-2009	254	42			PROPN
iajs-2009	254	43	,	,	PUNCT
iajs-2009	254	44	}	}	PUNCT
iajs-2009	254	45	,	,	PUNCT
iajs-2009	254	46	{	{	PUNCT
iajs-2009	254	47	)	)	PUNCT
iajs-2009	254	48	(	(	PUNCT
iajs-2009	254	49	cabann	cabann	PROPN
iajs-2009	254	50			PROPN
iajs-2009	254	51	and	and	CCONJ
iajs-2009	254	52	ˑ	ˑ	NOUN
iajs-2009	254	53	}	}	PUNCT
iajs-2009	254	54	,	,	PUNCT
iajs-2009	254	55	{	{	PUNCT
iajs-2009	254	56	)	)	PUNCT
iajs-2009	254	57	(	(	PUNCT
iajs-2009	254	58	bacann	bacann	PROPN
iajs-2009	254	59			PROPN
iajs-2009	254	60	,	,	PUNCT
iajs-2009	254	61	ˑ	ˑ	NOUN
iajs-2009	254	62	then	then	ADV
iajs-2009	254	63	eˑ	eˑ	PROPN
iajs-2009	254	64			PROPN
iajs-2009	254	65	𝑋	𝑋	PROPN
iajs-2009	254	66	0	0	NUM
iajs-2009	254	67	𝑎	𝑎	NOUN
iajs-2009	254	68	,	,	PUNCT
iajs-2009	254	69	𝑎	𝑎	NOUN
iajs-2009	254	70	𝑏	𝑏	NOUN
iajs-2009	254	71	,	,	PUNCT
iajs-2009	254	72	𝑎	𝑎	NOUN
iajs-2009	254	73	ˑ	ˑ	NOUN
iajs-2009	254	74	𝑐	𝑐	NOUN
iajs-2009	254	75	,	,	PUNCT
iajs-2009	254	76	𝑏	𝑏	DET
iajs-2009	254	77	ˑ	ˑ	PROPN
iajs-2009	254	78	𝑐	𝑐	NOUN
iajs-2009	254	79	.	.	PUNCT
iajs-2009	255	1	ˑ	ˑ	PRON
iajs-2009	255	2	theˑ	theˑ	NOUN
iajs-2009	255	3	followingˑ	followingˑ	NOUN
iajs-2009	255	4	figure	figure	NOUN
iajs-2009	255	5	showsˑ	showsˑ	VERB
iajs-2009	255	6	the	the	DET
iajs-2009	255	7	graph	graph	NOUN
iajs-2009	255	8	ω	ω	NUM
iajs-2009	255	9	𝑋	𝑋	PROPN
iajs-2009	255	10	ˑ	ˑ	NOUN
iajs-2009	255	11	and	and	CCONJ
iajs-2009	255	12			PROPN
iajs-2009	255	13	𝑋	𝑋	PROPN
iajs-2009	255	14	.	.	PUNCT
iajs-2009	256	1	figure	figure	NOUN
iajs-2009	256	2	5	5	NUM
iajs-2009	256	3	.	.	PUNCT
iajs-2009	257	1	the	the	DET
iajs-2009	257	2	graphsˑω	graphsˑω	NOUN
iajs-2009	257	3	𝑋	𝑋	VERB
iajs-2009	257	4	and	and	ADJ
iajs-2009	257	5	𝑋	𝑋	NOUN
iajs-2009	257	6	ˑin	ˑin	NOUN
iajs-2009	257	7	above	above	ADP
iajs-2009	257	8	figure	figure	NOUN
iajs-2009	257	9	ω	ω	PROPN
iajs-2009	257	10	𝑋	𝑋	PROPN
iajs-2009	257	11			PUNCT
iajs-2009	257	12	𝑋	𝑋	PROPN
iajs-2009	257	13	ˑ	ˑ	PROPN
iajs-2009	257	14	,	,	PUNCT
iajs-2009	257	15	butˑ	butˑ	PROPN
iajs-2009	257	16	ω	ω	PROPN
iajs-2009	257	17	𝑋	𝑋	PROPN
iajs-2009	257	18	is	be	AUX
iajs-2009	257	19	not	not	PART
iajs-2009	257	20	aˑ	aˑ	ADP
iajs-2009	257	21	complete	complete	ADJ
iajs-2009	257	22	graphˑ.	graphˑ.	NOUN
iajs-2009	257	23	theorem	theorem	VERB
iajs-2009	257	24	32.ˑif	32.ˑif	PROPN
iajs-2009	257	25	ω	ω	PROPN
iajs-2009	257	26	𝑋	𝑋	PROPN
iajs-2009	257	27	is	be	AUX
iajs-2009	257	28	aˑ	aˑ	ADP
iajs-2009	257	29	star	star	NOUN
iajs-2009	257	30	graph,ˑ	graph,ˑ	X
iajs-2009	257	31	then	then	ADV
iajs-2009	257	32			PROPN
iajs-2009	257	33	𝑋	𝑋	PROPN
iajs-2009	257	34	is	be	AUX
iajs-2009	257	35	ˑan	ˑan	ADJ
iajs-2009	257	36	edge	edge	NOUN
iajs-2009	257	37	.	.	PUNCT
iajs-2009	258	1	proof.ˑ	proof.ˑ	PROPN
iajs-2009	258	2	suppose	suppose	VERB
iajs-2009	258	3	that	that	SCONJ
iajs-2009	258	4	ˑω	ˑω	ADP
iajs-2009	258	5	𝑋	𝑋	PROPN
iajs-2009	258	6	is	be	AUX
iajs-2009	258	7	a	a	DET
iajs-2009	258	8	starˑ	starˑ	NOUN
iajs-2009	258	9	graph	graph	NOUN
iajs-2009	258	10	with	with	ADP
iajs-2009	258	11	vertexˑ	vertexˑ	NOUN
iajs-2009	258	12	set	set	VERB
iajs-2009	258	13	v	v	NUM
iajs-2009	258	14	ω	ω	NOUN
iajs-2009	258	15	𝑋	𝑋	PROPN
iajs-2009	258	16	𝑥	𝑥	PROPN
iajs-2009	258	17	,	,	PUNCT
iajs-2009	258	18	𝑥	𝑥	X
iajs-2009	258	19	,	,	PUNCT
iajs-2009	258	20	…	…	PUNCT
iajs-2009	258	21	,	,	PUNCT
iajs-2009	259	1	𝑥	𝑥	X
iajs-2009	259	2	.	.	PUNCT
iajs-2009	259	3	thisˑ	thisˑ	NOUN
iajs-2009	259	4	set	set	VERB
iajs-2009	259	5	can	can	AUX
iajs-2009	259	6	be	be	AUX
iajs-2009	259	7	splitˑ	splitˑ	ADJ
iajs-2009	259	8	into	into	ADP
iajs-2009	259	9	two	two	NUM
iajs-2009	259	10	ˑsets	ˑset	NOUN
iajs-2009	259	11	}	}	PUNCT
iajs-2009	259	12	{	{	PUNCT
iajs-2009	259	13	11	11	NUM
iajs-2009	259	14	xv	xv	NOUN
iajs-2009	259	15			PROPN
iajs-2009	259	16	andˑ	andˑ	ADJ
iajs-2009	259	17	}	}	PUNCT
iajs-2009	259	18	,	,	PUNCT
iajs-2009	259	19	...	...	PUNCT
iajs-2009	259	20	,	,	PUNCT
iajs-2009	259	21	{	{	PUNCT
iajs-2009	259	22	22	22	NUM
iajs-2009	259	23	nxxv	nxxv	ADJ
iajs-2009	259	24			NUM
iajs-2009	259	25	such	such	ADJ
iajs-2009	259	26	thatˑ	thatˑ	NOUN
iajs-2009	259	27	the	the	DET
iajs-2009	259	28	vertex	vertex	NOUN
iajs-2009	259	29	ˑof	ˑof	PROPN
iajs-2009	259	30	1v	1v	NUM
iajs-2009	259	31	is	be	AUX
iajs-2009	259	32	joinedˑ	joinedˑ	VERB
iajs-2009	259	33	to	to	ADP
iajs-2009	259	34	each	each	DET
iajs-2009	259	35	vertex	vertex	NOUN
iajs-2009	259	36	ˑof	ˑof	PROPN
iajs-2009	259	37	2v	2v	PROPN
iajs-2009	259	38	by	by	ADP
iajs-2009	259	39	exactlyˑ	exactlyˑ	PROPN
iajs-2009	259	40	one	one	NUM
iajs-2009	259	41	edge	edge	NOUN
iajs-2009	259	42	.	.	PUNCT
iajs-2009	260	1	thusˑ	thusˑ	VERB
iajs-2009	260	2	,	,	PUNCT
iajs-2009	260	3	the	the	DET
iajs-2009	260	4	set	set	NOUN
iajs-2009	260	5	of	of	ADP
iajs-2009	260	6	ˑedges	ˑedge	NOUN
iajs-2009	260	7	is	be	AUX
iajs-2009	260	8	𝐸	𝐸	PROPN
iajs-2009	260	9	ω	ω	NUM
iajs-2009	260	10	𝑋	𝑋	NOUN
iajs-2009	260	11	𝑥	𝑥	X
iajs-2009	260	12	𝑥	𝑥	NOUN
iajs-2009	260	13	,	,	PUNCT
iajs-2009	260	14	𝑥	𝑥	PROPN
iajs-2009	260	15	𝑥	𝑥	X
iajs-2009	260	16	,	,	PUNCT
iajs-2009	260	17	…	…	PUNCT
iajs-2009	260	18	,	,	PUNCT
iajs-2009	260	19	𝑥	𝑥	PRON
iajs-2009	261	1	𝑥	𝑥	X
iajs-2009	261	2	,	,	PUNCT
iajs-2009	261	3	so	so	ADV
iajs-2009	261	4	2321	2321	NUM
iajs-2009	261	5	}	}	PUNCT
iajs-2009	261	6	,	,	PUNCT
iajs-2009	261	7	...	...	PUNCT
iajs-2009	261	8	,	,	PUNCT
iajs-2009	261	9	,	,	PUNCT
iajs-2009	261	10	{	{	PUNCT
iajs-2009	261	11	)	)	PUNCT
iajs-2009	261	12	(	(	PUNCT
iajs-2009	261	13	vxxxxn	vxxxxn	VERB
iajs-2009	261	14	n	n	PRON
iajs-2009	261	15			NUM
iajs-2009	261	16	and	and	CCONJ
iajs-2009	261	17	1312	1312	NUM
iajs-2009	261	18	)	)	PUNCT
iajs-2009	261	19	(	(	PUNCT
iajs-2009	261	20	...	...	PUNCT
iajs-2009	261	21	)	)	PUNCT
iajs-2009	261	22	(	(	PUNCT
iajs-2009	261	23	}	}	PUNCT
iajs-2009	261	24	{	{	PUNCT
iajs-2009	261	25	)	)	PUNCT
iajs-2009	261	26	(	(	PUNCT
iajs-2009	261	27	vxnxnxxn	vxnxnxxn	VERB
iajs-2009	261	28	n	n	X
iajs-2009	261	29			PROPN
iajs-2009	261	30	,	,	PUNCT
iajs-2009	261	31	ˑthen	ˑthen	ADV
iajs-2009	261	32	21	21	NUM
iajs-2009	261	33	)	)	PUNCT
iajs-2009	261	34	(	(	PUNCT
iajs-2009	261	35	vxann	vxann	PROPN
iajs-2009	261	36			PROPN
iajs-2009	261	37	and	and	CCONJ
iajs-2009	261	38	132	132	NUM
iajs-2009	261	39	)	)	PUNCT
iajs-2009	261	40	(	(	PUNCT
iajs-2009	261	41	...	...	PUNCT
iajs-2009	261	42	)	)	PUNCT
iajs-2009	261	43	(	(	PUNCT
iajs-2009	261	44	)	)	PUNCT
iajs-2009	261	45	(	(	PUNCT
iajs-2009	261	46	vxannxannxann	vxannxannxann	PROPN
iajs-2009	261	47	n	n	PROPN
iajs-2009	261	48			PROPN
iajs-2009	261	49	.	.	PUNCT
iajs-2009	262	1	ˑthen	ˑthen	ADV
iajs-2009	262	2	thereˑ	thereˑ	NOUN
iajs-2009	262	3	are	be	AUX
iajs-2009	262	4	two	two	NUM
iajs-2009	262	5	distinctˑ	distinctˑ	ADJ
iajs-2009	262	6	equivalence	equivalence	NOUN
iajs-2009	262	7	classesˑ	classesˑ	NOUN
iajs-2009	262	8	]	]	X
iajs-2009	262	9	[	[	PUNCT
iajs-2009	262	10	1x	1x	NOUN
iajs-2009	262	11	and	and	CCONJ
iajs-2009	262	12	]	]	X
iajs-2009	262	13	[	[	PUNCT
iajs-2009	262	14	2x	2x	NUM
iajs-2009	262	15	in	in	ADP
iajs-2009	262	16			PROPN
iajs-2009	262	17	𝑋	𝑋	PROPN
iajs-2009	262	18	,	,	PUNCT
iajs-2009	262	19	whichˑ	whichˑ	ADJ
iajs-2009	262	20	are	be	AUX
iajs-2009	262	21	adjacent.ˑ	adjacent.ˑ	PRON
iajs-2009	262	22	thus	thus	ADV
iajs-2009	262	23			PROPN
iajs-2009	262	24	𝑋	𝑋	PROPN
iajs-2009	262	25	is	be	AUX
iajs-2009	262	26	ˑan	ˑan	PROPN
iajs-2009	262	27	edge	edge	NOUN
iajs-2009	262	28	.	.	PUNCT
iajs-2009	263	1	lemma	lemma	PROPN
iajs-2009	263	2	33	33	NUM
iajs-2009	263	3	.	.	PUNCT
iajs-2009	264	1	let	let	VERB
iajs-2009	264	2	g	g	NOUN
iajs-2009	264	3	and	and	CCONJ
iajs-2009	264	4	h	h	NOUN
iajs-2009	264	5	be	be	VERB
iajs-2009	264	6	two	two	NUM
iajs-2009	264	7	graphs	graph	NOUN
iajs-2009	264	8	and	and	CCONJ
iajs-2009	264	9	hg	hg	X
iajs-2009	264	10			PROPN
iajs-2009	264	11	.	.	PUNCT
iajs-2009	265	1	ˑifˑˑ	ˑifˑˑ	VERB
iajs-2009	265	2	yxf	yxf	NOUN
iajs-2009	265	3			PROPN
iajs-2009	265	4	)	)	PUNCT
iajs-2009	265	5	(	(	PUNCT
iajs-2009	265	6	,	,	PUNCT
iajs-2009	265	7	ˑˑthenˑˑ	ˑˑthenˑˑ	NOUN
iajs-2009	265	8	)	)	PUNCT
iajs-2009	265	9	(	(	PUNCT
iajs-2009	265	10	)	)	PUNCT
iajs-2009	265	11	)	)	PUNCT
iajs-2009	265	12	(	(	PUNCT
iajs-2009	265	13	(	(	PUNCT
iajs-2009	265	14	ynxnf	ynxnf	NOUN
iajs-2009	265	15			PROPN
iajs-2009	265	16	ˑfor	ˑfor	ADP
iajs-2009	265	17	allˑ	allˑ	ADV
iajs-2009	265	18	)	)	PUNCT
iajs-2009	265	19	(	(	PUNCT
iajs-2009	265	20	)	)	PUNCT
iajs-2009	265	21	(	(	PUNCT
iajs-2009	265	22	hvyandgvx	hvyandgvx	X
iajs-2009	265	23			NUM
iajs-2009	265	24	ˑ.	ˑ.	PROPN
iajs-2009	265	25			PROPN
iajs-2009	266	1	ˑ	ˑ	ADV
iajs-2009	266	2	0	0	NUM
iajs-2009	266	3	aˑ	aˑ	ADP
iajs-2009	266	4	bˑ	bˑ	PROPN
iajs-2009	266	5	c	c	PROPN
iajs-2009	266	6	0ˑ	0ˑ	ADJ
iajs-2009	266	7	0ˑ	0ˑ	NOUN
iajs-2009	266	8	aˑ	aˑ	AUX
iajs-2009	266	9	bˑ	bˑ	PART
iajs-2009	266	10	cˑ	cˑ	VERB
iajs-2009	266	11	a	a	DET
iajs-2009	266	12	0ˑ	0ˑ	ADJ
iajs-2009	266	13	0ˑ	0ˑ	NOUN
iajs-2009	266	14	aˑ	aˑ	ADP
iajs-2009	266	15	c	c	NOUN
iajs-2009	266	16	b	b	NOUN
iajs-2009	266	17	0ˑ	0ˑ	ADJ
iajs-2009	266	18	0ˑ	0ˑ	ADJ
iajs-2009	266	19	0ˑ	0ˑ	NOUN
iajs-2009	267	1	c	c	X
iajs-2009	267	2	cˑ	cˑ	VERB
iajs-2009	267	3	0ˑ	0ˑ	NOUN
iajs-2009	267	4	aˑ	aˑ	ADP
iajs-2009	267	5	bˑ	bˑ	PROPN
iajs-2009	267	6	0	0	NUM
iajs-2009	268	1			PROPN
iajs-2009	268	2	0	0	NUM
iajs-2009	268	3	aˑˑ	aˑˑ	PROPN
iajs-2009	268	4	b	b	NOUN
iajs-2009	268	5	cˑ	cˑ	NOUN
iajs-2009	268	6	0ˑ	0ˑ	NOUN
iajs-2009	268	7	0	0	NUM
iajs-2009	268	8	0ˑˑ	0ˑˑ	NOUN
iajs-2009	268	9	0	0	PUNCT
iajs-2009	269	1	0ˑ	0ˑ	NOUN
iajs-2009	269	2	a	a	DET
iajs-2009	269	3	0ˑ	0ˑ	NOUN
iajs-2009	269	4	aˑˑ	aˑˑ	ADJ
iajs-2009	269	5	0ˑ	0ˑ	NOUN
iajs-2009	269	6	c	c	PROPN
iajs-2009	269	7	b	b	SYM
iajs-2009	269	8	0	0	NUM
iajs-2009	269	9	0ˑˑ	0ˑˑ	NOUN
iajs-2009	269	10	b	b	PROPN
iajs-2009	269	11	0	0	NUM
iajs-2009	269	12	cˑ	cˑ	NOUN
iajs-2009	269	13	0	0	NUM
iajs-2009	269	14	cˑ	cˑ	NOUN
iajs-2009	269	15	0ˑ	0ˑ	PROPN
iajs-2009	269	16	c	c	PROPN
iajs-2009	269	17	mathematics	mathematic	NOUN
iajs-2009	269	18	|	|	ADV
iajs-2009	269	19	170	170	NUM
iajs-2009	269	20	ibn	ibn	PROPN
iajs-2009	269	21	al	al	PROPN
iajs-2009	269	22	-	-	PUNCT
iajs-2009	269	23	haitham	haitham	PROPN
iajs-2009	269	24	jour	jour	X
iajs-2009	269	25	.	.	PROPN
iajs-2009	270	1	for	for	ADP
iajs-2009	270	2	pure	pure	ADJ
iajs-2009	270	3	&	&	CCONJ
iajs-2009	270	4	appl	appl	PROPN
iajs-2009	270	5	.	.	PUNCT
iajs-2009	271	1	sci	sci	PROPN
iajs-2009	271	2	.	.	PROPN
iajs-2009	271	3	ihjpas	ihjpas	PROPN
iajs-2009	271	4	https://doi.org/10.30526/31.3.2009	https://doi.org/10.30526/31.3.2009	PROPN
iajs-2009	271	5	vol	vol	NOUN
iajs-2009	271	6	.	.	PROPN
iajs-2009	272	1	31	31	NUM
iajs-2009	273	1	(	(	PUNCT
iajs-2009	273	2	3	3	NUM
iajs-2009	273	3	)	)	SYM
iajs-2009	273	4	2018	2018	NUM
iajs-2009	273	5	proof	proof	NOUN
iajs-2009	273	6	.	.	PUNCT
iajs-2009	274	1	let	let	VERB
iajs-2009	274	2	hgf	hgf	NOUN
iajs-2009	274	3			NOUN
iajs-2009	274	4	:	:	PUNCT
iajs-2009	274	5	be	be	AUX
iajs-2009	274	6	a	a	DET
iajs-2009	274	7	graph	graph	NOUN
iajs-2009	274	8	isomorphism	isomorphism	NOUN
iajs-2009	274	9	,	,	PUNCT
iajs-2009	274	10	)	)	PUNCT
iajs-2009	274	11	(	(	PUNCT
iajs-2009	274	12	gvx	gvx	PROPN
iajs-2009	274	13	and	and	CCONJ
iajs-2009	274	14	)	)	PUNCT
iajs-2009	274	15	(	(	PUNCT
iajs-2009	274	16	)	)	PUNCT
iajs-2009	274	17	(	(	PUNCT
iajs-2009	274	18	hvyxf	hvyxf	VERB
iajs-2009	274	19			X
iajs-2009	274	20	.	.	PUNCT
iajs-2009	275	1	then	then	ADV
iajs-2009	275	2	)	)	PUNCT
iajs-2009	275	3	(	(	PUNCT
iajs-2009	275	4	)	)	PUNCT
iajs-2009	275	5	}	}	PUNCT
iajs-2009	275	6	(:	(:	NOUN
iajs-2009	275	7	)	)	PUNCT
iajs-2009	275	8	(	(	PUNCT
iajs-2009	275	9	{	{	PUNCT
iajs-2009	275	10	)	)	PUNCT
iajs-2009	275	11	}	}	PUNCT
iajs-2009	275	12	(	(	PUNCT
iajs-2009	275	13	)	)	PUNCT
iajs-2009	275	14	(:	(:	NOUN
iajs-2009	275	15	)	)	PUNCT
iajs-2009	275	16	(	(	PUNCT
iajs-2009	275	17	{	{	PUNCT
iajs-2009	275	18	}	}	PUNCT
iajs-2009	275	19	:)	:)	INTJ
iajs-2009	275	20	(	(	PUNCT
iajs-2009	275	21	{	{	PUNCT
iajs-2009	275	22	)	)	PUNCT
iajs-2009	275	23	)	)	PUNCT
iajs-2009	275	24	(	(	PUNCT
iajs-2009	275	25	(	(	PUNCT
iajs-2009	275	26	ynzfyzfzfxfzfzxzfxnf	ynzfyzfzfxfzfzxzfxnf	ADJ
iajs-2009	275	27			NOUN
iajs-2009	275	28	.	.	PUNCT
iajs-2009	276	1	theorem	theorem	VERB
iajs-2009	276	2	34	34	NUM
iajs-2009	276	3	.	.	PUNCT
iajs-2009	277	1	ˑlet	ˑlet	NOUN
iajs-2009	277	2	x	x	PUNCT
iajs-2009	277	3	and	and	CCONJ
iajs-2009	277	4	y	y	PROPN
iajs-2009	277	5	be	be	VERB
iajs-2009	277	6	two	two	NUM
iajs-2009	277	7	ku	ku	NOUN
iajs-2009	277	8	-	-	PUNCT
iajs-2009	277	9	semigroups	semigroup	NOUN
iajs-2009	277	10	.	.	PUNCT
iajs-2009	278	1	if	if	SCONJ
iajs-2009	278	2	ˑω	ˑω	ADP
iajs-2009	278	3	𝑋	𝑋	PROPN
iajs-2009	278	4			PROPN
iajs-2009	278	5	ω	ω	X
iajs-2009	278	6	𝑌	𝑌	PROPN
iajs-2009	278	7	ˑ	ˑ	NOUN
iajs-2009	278	8	,	,	PUNCT
iajs-2009	278	9	ˑthen	ˑthen	SCONJ
iajs-2009	278	10			PROPN
iajs-2009	278	11	𝑋	𝑋	PROPN
iajs-2009	278	12			PUNCT
iajs-2009	278	13	𝑌	𝑌	PROPN
iajs-2009	278	14	.	.	PUNCT
iajs-2009	279	1	proof.ˑ	proof.ˑ	PROPN
iajs-2009	279	2	supposeˑ	supposeˑ	NOUN
iajs-2009	279	3	that	that	SCONJ
iajs-2009	279	4	ˑ𝑉	ˑ𝑉	PROPN
iajs-2009	279	5	ω	ω	NOUN
iajs-2009	279	6	𝑋	𝑋	PROPN
iajs-2009	279	7	𝑥	𝑥	PROPN
iajs-2009	279	8	,	,	PUNCT
iajs-2009	279	9	𝑥	𝑥	X
iajs-2009	279	10	,	,	PUNCT
iajs-2009	279	11	…	…	PUNCT
iajs-2009	279	12	,	,	PUNCT
iajs-2009	279	13	𝑥	𝑥	PRON
iajs-2009	279	14	ˑ	ˑ	NOUN
iajs-2009	279	15	and	and	CCONJ
iajs-2009	279	16	ˑ𝑉	ˑ𝑉	PROPN
iajs-2009	280	1	ω	ω	PROPN
iajs-2009	280	2	𝑌	𝑌	PROPN
iajs-2009	280	3	𝑦	𝑦	PROPN
iajs-2009	280	4	,	,	PUNCT
iajs-2009	280	5	𝑦	𝑦	PRON
iajs-2009	280	6	,	,	PUNCT
iajs-2009	280	7	…	…	PUNCT
iajs-2009	280	8	,	,	PUNCT
iajs-2009	280	9	𝑦	𝑦	PRON
iajs-2009	280	10	ˑ	ˑ	PRON
iajs-2009	280	11	such	such	ADJ
iajs-2009	280	12	thatˑ	thatˑ	NOUN
iajs-2009	280	13	the	the	DET
iajs-2009	280	14	isomorphismˑ	isomorphismˑ	NOUN
iajs-2009	280	15	𝑓	𝑓	X
iajs-2009	280	16	:	:	PUNCT
iajs-2009	280	17	ω	ω	PROPN
iajs-2009	280	18	𝑋	𝑋	PROPN
iajs-2009	280	19	→	→	SYM
iajs-2009	280	20	ω	ω	NUM
iajs-2009	280	21	𝑌	𝑌	PROPN
iajs-2009	280	22	ˑ	ˑ	PROPN
iajs-2009	280	23	satisfies	satisfy	VERB
iajs-2009	280	24	ˑ	ˑ	PROPN
iajs-2009	280	25	ii	ii	VERB
iajs-2009	280	26	yxf	yxf	NOUN
iajs-2009	280	27			NUM
iajs-2009	280	28	)	)	PUNCT
iajs-2009	280	29	(	(	PUNCT
iajs-2009	280	30	for	for	ADP
iajs-2009	280	31	eachˑ	eachˑ	ADJ
iajs-2009	280	32	}	}	PUNCT
iajs-2009	280	33	,	,	PUNCT
iajs-2009	280	34	...	...	PUNCT
iajs-2009	280	35	,	,	PUNCT
iajs-2009	280	36	2,1	2,1	NUM
iajs-2009	280	37	{	{	PUNCT
iajs-2009	280	38	ni	ni	NOUN
iajs-2009	280	39	.	.	PUNCT
iajs-2009	281	1	ˑbyˑ	ˑbyˑ	PROPN
iajs-2009	281	2	lemmaˑ	lemmaˑ	VERB
iajs-2009	281	3	33	33	NUM
iajs-2009	281	4	,	,	PUNCT
iajs-2009	281	5	)	)	PUNCT
iajs-2009	281	6	(	(	PUNCT
iajs-2009	281	7	)	)	PUNCT
iajs-2009	281	8	)	)	PUNCT
iajs-2009	281	9	(	(	PUNCT
iajs-2009	281	10	(	(	PUNCT
iajs-2009	281	11	ii	ii	X
iajs-2009	281	12	ynxnf	ynxnf	NOUN
iajs-2009	281	13			PROPN
iajs-2009	281	14	for	for	ADP
iajs-2009	281	15	eachˑ	eachˑ	ADJ
iajs-2009	281	16	i	i	PRON
iajs-2009	281	17	,	,	PUNCT
iajs-2009	281	18	thenˑ	thenˑ	PROPN
iajs-2009	281	19	)	)	PUNCT
iajs-2009	281	20	(	(	PUNCT
iajs-2009	281	21	)	)	PUNCT
iajs-2009	281	22	)	)	PUNCT
iajs-2009	282	1	(	(	PUNCT
iajs-2009	282	2	(	(	PUNCT
iajs-2009	282	3	ii	ii	NOUN
iajs-2009	282	4	yannxannf	yannxannf	NOUN
iajs-2009	282	5			PROPN
iajs-2009	282	6	and	and	CCONJ
iajs-2009	282	7	the	the	DET
iajs-2009	282	8	mapping	mapping	NOUN
iajs-2009	282	9	ofˑ	ofˑ	PRON
iajs-2009	282	10	edges	edge	NOUN
iajs-2009	282	11	ˑ𝑓	ˑ𝑓	NOUN
iajs-2009	282	12	:	:	PUNCT
iajs-2009	282	13	𝐸	𝐸	PROPN
iajs-2009	282	14			PROPN
iajs-2009	282	15	𝑋	𝑋	PROPN
iajs-2009	282	16	→	→	SYM
iajs-2009	282	17	𝐸	𝐸	PROPN
iajs-2009	282	18			PROPN
iajs-2009	282	19	𝑌	𝑌	PROPN
iajs-2009	282	20	,	,	PUNCT
iajs-2009	282	21	which	which	PRON
iajs-2009	282	22	sendsˑ	sendsˑ	VERB
iajs-2009	282	23	the	the	DET
iajs-2009	282	24	edge	edge	NOUN
iajs-2009	282	25	ˑ	ˑ	NOUN
iajs-2009	282	26	]	]	X
iajs-2009	283	1	[	[	X
iajs-2009	283	2	]	]	X
iajs-2009	283	3	[	[	PUNCT
iajs-2009	283	4	ji	ji	NOUN
iajs-2009	283	5	xx	xx	NUM
iajs-2009	283	6			PROPN
iajs-2009	283	7	in	in	ADP
iajs-2009	283	8			PROPN
iajs-2009	283	9	𝑋	𝑋	PROPN
iajs-2009	283	10	to	to	ADP
iajs-2009	283	11	the	the	DET
iajs-2009	283	12	edge	edge	NOUN
iajs-2009	283	13	]	]	X
iajs-2009	283	14	[	[	X
iajs-2009	283	15	]	]	X
iajs-2009	283	16	[	[	PUNCT
iajs-2009	283	17	ji	ji	X
iajs-2009	283	18	yy	yy	PROPN
iajs-2009	283	19			PROPN
iajs-2009	283	20	in	in	ADP
iajs-2009	283	21			PROPN
iajs-2009	283	22	𝑌	𝑌	PROPN
iajs-2009	283	23	is	be	AUX
iajs-2009	283	24	aˑ	aˑ	ADP
iajs-2009	283	25	well-ˑdefined	well-ˑdefined	ADJ
iajs-2009	283	26	ˑbijection	ˑbijection	NOUN
iajs-2009	283	27	.	.	PUNCT
iajs-2009	284	1	ˑthus	ˑthu	NOUN
iajs-2009	284	2			PROPN
iajs-2009	284	3	𝑋	𝑋	PROPN
iajs-2009	284	4	ˑ	ˑ	NOUN
iajs-2009	284	5	𝑌	𝑌	PROPN
iajs-2009	284	6	.	.	PUNCT
iajs-2009	285	1	theˑ	theˑ	NOUN
iajs-2009	285	2	converseˑ	converseˑ	NOUN
iajs-2009	285	3	of	of	ADP
iajs-2009	285	4	this	this	DET
iajs-2009	285	5	theoremˑ	theoremˑ	NOUN
iajs-2009	285	6	is	be	AUX
iajs-2009	285	7	not	not	PART
iajs-2009	285	8	true	true	ADJ
iajs-2009	285	9	.	.	PUNCT
iajs-2009	286	1	inˑ	inˑ	PROPN
iajs-2009	286	2	examples	example	NOUN
iajs-2009	286	3	27	27	NUM
iajs-2009	286	4	and	and	CCONJ
iajs-2009	286	5	31	31	NUM
iajs-2009	286	6	,	,	PUNCT
iajs-2009	286	7	we	we	PRON
iajs-2009	286	8	have	have	VERB
iajs-2009	286	9			PROPN
iajs-2009	286	10	𝑋	𝑋	NOUN
iajs-2009	286	11			PUNCT
iajs-2009	286	12	𝑌	𝑌	PROPN
iajs-2009	286	13	ˑ	ˑ	PROPN
iajs-2009	286	14	but	but	CCONJ
iajs-2009	286	15	ω	ω	NUM
iajs-2009	286	16	𝑋	𝑋	PROPN
iajs-2009	286	17	ω	ω	PROPN
iajs-2009	286	18	𝑌	𝑌	PROPN
iajs-2009	286	19	.	.	PUNCT
iajs-2009	287	1	references	reference	NOUN
iajs-2009	287	2	1	1	NUM
iajs-2009	287	3	.	.	PUNCT
iajs-2009	287	4	prabpayak	prabpayak	NOUN
iajs-2009	287	5	.	.	PUNCT
iajs-2009	288	1	c.	c.	PROPN
iajs-2009	288	2	;	;	PUNCT
iajs-2009	288	3	leerawat	leerawat	NOUN
iajs-2009	288	4	.	.	PUNCT
iajs-2009	289	1	u.	u.	VERB
iajs-2009	289	2	on	on	ADP
iajs-2009	289	3	ideals	ideal	NOUN
iajs-2009	289	4	and	and	CCONJ
iajs-2009	289	5	congruence	congruence	NOUN
iajs-2009	289	6	in	in	ADP
iajs-2009	289	7	ku	ku	PROPN
iajs-2009	289	8	-	-	PUNCT
iajs-2009	289	9	algebras	algebras	PROPN
iajs-2009	289	10	.	.	PUNCT
iajs-2009	290	1	scientia	scientia	PROPN
iajs-2009	290	2	magna	magna	PROPN
iajs-2009	290	3	journal	journal	PROPN
iajs-2009	290	4	.	.	PUNCT
iajs-2009	291	1	2009	2009	NUM
iajs-2009	291	2	,	,	PUNCT
iajs-2009	291	3	5	5	NUM
iajs-2009	291	4	,	,	PUNCT
iajs-2009	291	5	1	1	NUM
iajs-2009	291	6	,	,	PUNCT
iajs-2009	291	7	54	54	NUM
iajs-2009	291	8	-	-	SYM
iajs-2009	291	9	57	57	NUM
iajs-2009	291	10	.	.	X
iajs-2009	292	1	2	2	NUM
iajs-2009	292	2	.	.	X
iajs-2009	292	3	prabpayak	prabpayak	NOUN
iajs-2009	292	4	.	.	PUNCT
iajs-2009	293	1	c.	c.	PROPN
iajs-2009	293	2	;	;	PUNCT
iajs-2009	293	3	leerawat	leerawat	NOUN
iajs-2009	293	4	.	.	PUNCT
iajs-2009	294	1	u.	u.	PROPN
iajs-2009	294	2	on	on	ADP
iajs-2009	294	3	isomorphisms	isomorphism	NOUN
iajs-2009	294	4	of	of	ADP
iajs-2009	294	5	ku	ku	PROPN
iajs-2009	294	6	-	-	PUNCT
iajs-2009	294	7	algebras	algebras	PROPN
iajs-2009	294	8	.	.	PUNCT
iajs-2009	295	1	scientiamagna	scientiamagna	PROPN
iajs-2009	295	2	journal	journal	PROPN
iajs-2009	295	3	.	.	PUNCT
iajs-2009	296	1	2009	2009	NUM
iajs-2009	296	2	,	,	PUNCT
iajs-2009	296	3	5	5	NUM
iajs-2009	296	4	,	,	PUNCT
iajs-2009	296	5	3	3	NUM
iajs-2009	296	6	,	,	PUNCT
iajs-2009	296	7	25	25	NUM
iajs-2009	296	8	-	-	SYM
iajs-2009	296	9	31	31	NUM
iajs-2009	296	10	.	.	PUNCT
iajs-2009	297	1	3	3	X
iajs-2009	297	2	.	.	X
iajs-2009	297	3	fatema	fatema	PROPN
iajs-2009	297	4	.	.	PUNCT
iajs-2009	298	1	f.	f.	PROPN
iajs-2009	298	2	kareem	kareem	PROPN
iajs-2009	298	3	;	;	PUNCT
iajs-2009	298	4	elaf	elaf	PROPN
iajs-2009	298	5	.	.	PUNCT
iajs-2009	299	1	r.	r.	PROPN
iajs-2009	299	2	h.	h.	PROPN
iajs-2009	299	3	on	on	ADP
iajs-2009	299	4	ku	ku	PROPN
iajs-2009	299	5	-	-	PUNCT
iajs-2009	299	6	semigroups	semigroup	NOUN
iajs-2009	299	7	.	.	PUNCT
iajs-2009	300	1	int	int	NOUN
iajs-2009	300	2	.	.	PUNCT
iajs-2009	301	1	j.sc	j.sc	NOUN
iajs-2009	301	2	.	.	PUNCT
iajs-2009	302	1	nat	nat	PROPN
iajs-2009	302	2	.	.	PUNCT
iajs-2009	303	1	2017	2017	NUM
iajs-2009	303	2	,	,	PUNCT
iajs-2009	303	3	8(4	8(4	NUM
iajs-2009	303	4	)	)	PUNCT
iajs-2009	304	1	,	,	PUNCT
iajs-2009	304	2	1	1	NUM
iajs-2009	304	3	4	4	NUM
iajs-2009	304	4	.	.	PUNCT
iajs-2009	304	5	beck	beck	PROPN
iajs-2009	304	6	,	,	PUNCT
iajs-2009	304	7	i.	i.	PROPN
iajs-2009	304	8	coloring	coloring	PROPN
iajs-2009	304	9	of	of	ADP
iajs-2009	304	10	commutative	commutative	ADJ
iajs-2009	304	11	rings	ring	NOUN
iajs-2009	304	12	.	.	PUNCT
iajs-2009	305	1	j.	j.	PROPN
iajs-2009	305	2	algebra.1988	algebra.1988	PROPN
iajs-2009	305	3	,	,	PUNCT
iajs-2009	305	4	116	116	NUM
iajs-2009	305	5	,	,	PUNCT
iajs-2009	305	6	208	208	NUM
iajs-2009	305	7	-	-	SYM
iajs-2009	305	8	226	226	NUM
iajs-2009	305	9	.	.	PUNCT
iajs-2009	306	1	5	5	NUM
iajs-2009	306	2	.	.	X
iajs-2009	306	3	akbari	akbari	PROPN
iajs-2009	306	4	.	.	PUNCT
iajs-2009	307	1	s.	s.	PROPN
iajs-2009	307	2	;	;	PUNCT
iajs-2009	307	3	kiani	kiani	PROPN
iajs-2009	307	4	.	.	PUNCT
iajs-2009	308	1	d.	d.	PROPN
iajs-2009	308	2	;	;	PUNCT
iajs-2009	308	3	mohammadi	mohammadi	NOUN
iajs-2009	308	4	.	.	PUNCT
iajs-2009	309	1	f.	f.	PROPN
iajs-2009	309	2	;	;	PUNCT
iajs-2009	309	3	moradi	moradi	NOUN
iajs-2009	309	4	.	.	PUNCT
iajs-2009	310	1	s.	s.	PROPN
iajs-2009	310	2	the	the	DET
iajs-2009	310	3	total	total	ADJ
iajs-2009	310	4	graph	graph	NOUN
iajs-2009	310	5	and	and	CCONJ
iajs-2009	310	6	regular	regular	ADJ
iajs-2009	310	7	graph	graph	NOUN
iajs-2009	310	8	of	of	ADP
iajs-2009	310	9	a	a	DET
iajs-2009	310	10	commutative	commutative	ADJ
iajs-2009	310	11	ring	ring	NOUN
iajs-2009	310	12	.	.	PUNCT
iajs-2009	311	1	j.	j.	PROPN
iajs-2009	311	2	pure	pure	PROPN
iajs-2009	311	3	appl	appl	PROPN
iajs-2009	311	4	.	.	PUNCT
iajs-2009	312	1	algebra	algebra	PROPN
iajs-2009	312	2	.	.	PUNCT
iajs-2009	313	1	2009	2009	NUM
iajs-2009	313	2	,	,	PUNCT
iajs-2009	313	3	213	213	NUM
iajs-2009	313	4	,	,	PUNCT
iajs-2009	313	5	2224	2224	NUM
iajs-2009	313	6	-	-	SYM
iajs-2009	313	7	2228	2228	NUM
iajs-2009	313	8	.	.	PUNCT
iajs-2009	314	1	6	6	NUM
iajs-2009	314	2	.	.	X
iajs-2009	314	3	anderson	anderson	PROPN
iajs-2009	314	4	.	.	PROPN
iajs-2009	314	5	,	,	PUNCT
iajs-2009	314	6	d.	d.	PROPN
iajs-2009	314	7	f.	f.	PROPN
iajs-2009	314	8	;	;	PUNCT
iajs-2009	314	9	badawi	badawi	PROPN
iajs-2009	314	10	.	.	PUNCT
iajs-2009	315	1	a.	a.	NOUN
iajs-2009	316	1	the	the	DET
iajs-2009	316	2	total	total	ADJ
iajs-2009	316	3	graph	graph	NOUN
iajs-2009	316	4	of	of	ADP
iajs-2009	316	5	a	a	DET
iajs-2009	316	6	commutative	commutative	ADJ
iajs-2009	316	7	ring	ring	NOUN
iajs-2009	316	8	.	.	PUNCT
iajs-2009	317	1	j.	j.	PROPN
iajs-2009	317	2	algebra	algebra	PROPN
iajs-2009	317	3	.	.	PUNCT
iajs-2009	318	1	2008	2008	NUM
iajs-2009	318	2	,	,	PUNCT
iajs-2009	318	3	320	320	NUM
iajs-2009	318	4	,	,	PUNCT
iajs-2009	318	5	2706	2706	NUM
iajs-2009	318	6	-	-	SYM
iajs-2009	318	7	2719	2719	NUM
iajs-2009	318	8	.	.	PUNCT
iajs-2009	319	1	7	7	X
iajs-2009	319	2	.	.	NUM
iajs-2009	319	3	behboodi	behboodi	NOUN
iajs-2009	319	4	.	.	PUNCT
iajs-2009	320	1	m.	m.	NOUN
iajs-2009	320	2	;	;	PUNCT
iajs-2009	320	3	rakeei	rakeei	NOUN
iajs-2009	320	4	.	.	PUNCT
iajs-2009	321	1	z.	z.	PROPN
iajs-2009	322	1	the	the	DET
iajs-2009	322	2	annihilating	annihilate	VERB
iajs-2009	322	3	-	-	PUNCT
iajs-2009	322	4	ideal	ideal	ADJ
iajs-2009	322	5	graph	graph	NOUN
iajs-2009	322	6	of	of	ADP
iajs-2009	322	7	commutative	commutative	ADJ
iajs-2009	322	8	rings	ring	NOUN
iajs-2009	322	9	ii	ii	PROPN
iajs-2009	322	10	,	,	PUNCT
iajs-2009	322	11	journal	journal	NOUN
iajs-2009	322	12	of	of	ADP
iajs-2009	322	13	algebra	algebra	NOUN
iajs-2009	322	14	and	and	CCONJ
iajs-2009	322	15	its	its	PRON
iajs-2009	322	16	application	application	NOUN
iajs-2009	322	17	.	.	PUNCT
iajs-2009	323	1	2008	2008	NUM
iajs-2009	323	2	,	,	PUNCT
iajs-2009	323	3	10	10	NUM
iajs-2009	323	4	,	,	PUNCT
iajs-2009	323	5	4	4	NUM
iajs-2009	323	6	,	,	PUNCT
iajs-2009	323	7	741	741	NUM
iajs-2009	323	8	-	-	SYM
iajs-2009	323	9	753	753	NUM
iajs-2009	323	10	.	.	NOUN
iajs-2009	324	1	8	8	NUM
iajs-2009	324	2	.	.	X
iajs-2009	325	1	demeyer	demeyer	PROPN
iajs-2009	325	2	.	.	PUNCT
iajs-2009	326	1	f.	f.	PROPN
iajs-2009	326	2	;	;	PUNCT
iajs-2009	326	3	mckenzie	mckenzie	PROPN
iajs-2009	326	4	.	.	PUNCT
iajs-2009	327	1	t.	t.	PROPN
iajs-2009	327	2	;	;	PUNCT
iajs-2009	327	3	schneider	schneider	PROPN
iajs-2009	327	4	.	.	PUNCT
iajs-2009	328	1	k.	k.	PROPN
iajs-2009	329	1	the	the	DET
iajs-2009	329	2	zero	zero	NUM
iajs-2009	329	3	-	-	PUNCT
iajs-2009	329	4	divisor	divisor	NOUN
iajs-2009	329	5	graph	graph	NOUN
iajs-2009	329	6	of	of	ADP
iajs-2009	329	7	a	a	DET
iajs-2009	329	8	commutative	commutative	ADJ
iajs-2009	329	9	semigroup	semigroup	NOUN
iajs-2009	329	10	.	.	PUNCT
iajs-2009	330	1	semigroup	semigroup	PROPN
iajs-2009	330	2	forum	forum	PROPN
iajs-2009	330	3	.	.	PUNCT
iajs-2009	331	1	2002	2002	NUM
iajs-2009	331	2	,	,	PUNCT
iajs-2009	331	3	65	65	NUM
iajs-2009	331	4	,	,	PUNCT
iajs-2009	331	5	206	206	NUM
iajs-2009	331	6	-	-	SYM
iajs-2009	331	7	214	214	NUM
iajs-2009	331	8	.	.	PUNCT
iajs-2009	332	1	9	9	X
iajs-2009	332	2	.	.	X
iajs-2009	332	3	mulay	mulay	NOUN
iajs-2009	332	4	.	.	PUNCT
iajs-2009	333	1	s.	s.	PROPN
iajs-2009	333	2	b.	b.	PROPN
iajs-2009	333	3	cycles	cycles	PROPN
iajs-2009	333	4	and	and	CCONJ
iajs-2009	333	5	symmetries	symmetry	NOUN
iajs-2009	333	6	of	of	ADP
iajs-2009	333	7	zerodivisors	zerodivisors	PROPN
iajs-2009	333	8	.	.	PUNCT
iajs-2009	334	1	comm	comm	NOUN
iajs-2009	334	2	.	.	PUNCT
iajs-2009	335	1	algebra	algebra	PROPN
iajs-2009	335	2	.	.	PUNCT
iajs-2009	336	1	2002	2002	NUM
iajs-2009	336	2	,	,	PUNCT
iajs-2009	336	3	7	7	NUM
iajs-2009	336	4	,	,	PUNCT
iajs-2009	336	5	30	30	NUM
iajs-2009	336	6	,	,	PUNCT
iajs-2009	336	7	3533	3533	NUM
iajs-2009	336	8	-	-	SYM
iajs-2009	336	9	3558	3558	NUM
iajs-2009	336	10	.	.	PUNCT
iajs-2009	337	1	10	10	NUM
iajs-2009	337	2	.	.	PUNCT
iajs-2009	338	1	weber	weber	PROPN
iajs-2009	338	2	.	.	PUNCT
iajs-2009	339	1	d.	d.	PROPN
iajs-2009	339	2	zero	zero	NUM
iajs-2009	339	3	-	-	PUNCT
iajs-2009	339	4	divisor	divisor	NOUN
iajs-2009	339	5	graphs	graph	NOUN
iajs-2009	339	6	and	and	CCONJ
iajs-2009	339	7	lattices	lattice	NOUN
iajs-2009	339	8	of	of	ADP
iajs-2009	339	9	finite	finite	PROPN
iajs-2009	339	10	commutative	commutative	ADJ
iajs-2009	339	11	rings	ring	NOUN
iajs-2009	339	12	.	.	PUNCT
iajs-2009	340	1	rose	rose	PROPN
iajs-2009	340	2	-	-	PUNCT
iajs-2009	340	3	hulman	hulman	NOUN
iajs-2009	340	4	undergraduate	undergraduate	NOUN
iajs-2009	340	5	math	math	NOUN
iajs-2009	340	6	.	.	PUNCT
iajs-2009	341	1	j.	j.	PROPN
iajs-2009	341	2	2011	2011	NUM
iajs-2009	341	3	,	,	PUNCT
iajs-2009	341	4	1	1	NUM
iajs-2009	341	5	,	,	PUNCT
iajs-2009	341	6	12	12	NUM
iajs-2009	341	7	,	,	PUNCT
iajs-2009	341	8	57	57	NUM
iajs-2009	341	9	-	-	SYM
iajs-2009	341	10	70	70	NUM
iajs-2009	341	11	.	.	PUNCT
iajs-2009	341	12	11	11	NUM
iajs-2009	341	13	.	.	PUNCT
iajs-2009	342	1	jun	jun	PROPN
iajs-2009	342	2	.	.	PUNCT
iajs-2009	343	1	y.	y.	PROPN
iajs-2009	343	2	b	b	PROPN
iajs-2009	343	3	;	;	PUNCT
iajs-2009	343	4	lee	lee	PROPN
iajs-2009	343	5	.	.	PUNCT
iajs-2009	344	1	k.j	k.j	PROPN
iajs-2009	344	2	.	.	PROPN
iajs-2009	344	3	graphs	graph	NOUN
iajs-2009	344	4	based	base	VERB
iajs-2009	344	5	on	on	ADP
iajs-2009	344	6	bck\bci	bck\bci	NOUN
iajs-2009	344	7	-	-	PUNCT
iajs-2009	344	8	algebra	algebra	NOUN
iajs-2009	344	9	.	.	PUNCT
iajs-2009	345	1	int	int	NOUN
iajs-2009	345	2	.	.	PUNCT
iajs-2009	346	1	j.	j.	PROPN
iajs-2009	346	2	math.math	math.math	PROPN
iajs-2009	346	3	.	.	PUNCT
iajs-2009	347	1	sci	sci	PROPN
iajs-2009	347	2	.	.	PROPN
iajs-2009	347	3	2011	2011	NUM
iajs-2009	347	4	,	,	PUNCT
iajs-2009	347	5	1	1	NUM
iajs-2009	347	6	article	article	NOUN
iajs-2009	347	7	,	,	PUNCT
iajs-2009	347	8	1	1	NUM
iajs-2009	347	9	-	-	SYM
iajs-2009	347	10	8	8	NUM
iajs-2009	347	11	.	.	PUNCT
iajs-2009	347	12	12	12	NUM
iajs-2009	347	13	.	.	PUNCT
iajs-2009	348	1	zahiri	zahiri	PROPN
iajs-2009	348	2	.	.	PUNCT
iajs-2009	349	1	o.	o.	PROPN
iajs-2009	349	2	;	;	PUNCT
iajs-2009	349	3	borzooei	borzooei	PROPN
iajs-2009	349	4	.	.	PUNCT
iajs-2009	350	1	r.	r.	PROPN
iajs-2009	350	2	graph	graph	NOUN
iajs-2009	350	3	of	of	ADP
iajs-2009	350	4	bci	bci	NOUN
iajs-2009	350	5	-	-	PUNCT
iajs-2009	350	6	algebras	algebra	NOUN
iajs-2009	350	7	.	.	PUNCT
iajs-2009	351	1	int	int	NOUN
iajs-2009	351	2	.	.	PUNCT
iajs-2009	352	1	j.	j.	PROPN
iajs-2009	352	2	math	math	PROPN
iajs-2009	352	3	.	.	PUNCT
iajs-2009	353	1	math	math	NOUN
iajs-2009	353	2	.	.	PUNCT
iajs-2009	354	1	sci	sci	PROPN
iajs-2009	354	2	.	.	PROPN
iajs-2009	354	3	2012	2012	NUM
iajs-2009	354	4	,	,	PUNCT
iajs-2009	354	5	1	1	NUM
iajs-2009	354	6	article	article	NOUN
iajs-2009	354	7	1	1	NUM
iajs-2009	354	8	-	-	SYM
iajs-2009	354	9	12	12	NUM
iajs-2009	354	10	.	.	PUNCT
iajs-2009	354	11	13	13	NUM
iajs-2009	354	12	.	.	PUNCT
iajs-2009	354	13	mostafa	mostafa	PROPN
iajs-2009	354	14	.	.	PUNCT
iajs-2009	355	1	s.	s.	PROPN
iajs-2009	355	2	m.	m.	PROPN
iajs-2009	355	3	;	;	PUNCT
iajs-2009	355	4	kareem	kareem	PROPN
iajs-2009	355	5	.	.	PUNCT
iajs-2009	356	1	f.f	f.f	PROPN
iajs-2009	356	2	.	.	PROPN
iajs-2009	356	3	graph	graph	NOUN
iajs-2009	356	4	of	of	ADP
iajs-2009	356	5	equivalence	equivalence	NOUN
iajs-2009	356	6	classes	class	NOUN
iajs-2009	356	7	of	of	ADP
iajs-2009	356	8	a	a	DET
iajs-2009	356	9	commutative	commutative	ADJ
iajs-2009	356	10	isalgebra	isalgebra	NOUN
iajs-2009	356	11	.	.	PUNCT
iajs-2009	357	1	bulletin	bulletin	NOUN
iajs-2009	357	2	of	of	ADP
iajs-2009	357	3	mathematics	mathematic	NOUN
iajs-2009	357	4	and	and	CCONJ
iajs-2009	357	5	statistics	statistic	NOUN
iajs-2009	357	6	research	research	NOUN
iajs-2009	357	7	.	.	PUNCT
iajs-2009	358	1	2016	2016	NUM
iajs-2009	358	2	,	,	PUNCT
iajs-2009	358	3	4	4	NUM
iajs-2009	358	4	,	,	PUNCT
iajs-2009	358	5	2	2	NUM
iajs-2009	358	6	,	,	PUNCT
iajs-2009	358	7	92	92	NUM
iajs-2009	358	8	-	-	SYM
iajs-2009	358	9	101	101	NUM
iajs-2009	358	10	.	.	PUNCT
iajs-2009	359	1	14	14	NUM
iajs-2009	359	2	.	.	PUNCT
iajs-2009	360	1	mostafa	mostafa	PROPN
iajs-2009	360	2	.	.	PUNCT
iajs-2009	361	1	s.	s.	PROPN
iajs-2009	361	2	m.	m.	PROPN
iajs-2009	361	3	;	;	PUNCT
iajs-2009	361	4	abd	abd	NOUN
iajs-2009	361	5	-	-	PUNCT
iajs-2009	361	6	elnaby	elnaby	NOUN
iajs-2009	361	7	.	.	PUNCT
iajs-2009	362	1	m.	m.	NOUN
iajs-2009	362	2	a.	a.	PROPN
iajs-2009	362	3	;	;	PUNCT
iajs-2009	362	4	yousef	yousef	PROPN
iajs-2009	362	5	.	.	PUNCT
iajs-2009	362	6	m.	m.	PROPN
iajs-2009	362	7	m.	m.	PROPN
iajs-2009	362	8	m.	m.	NOUN
iajs-2009	362	9	fuzzy	fuzzy	ADJ
iajs-2009	362	10	ideals	ideal	NOUN
iajs-2009	362	11	of	of	ADP
iajs-2009	362	12	ku	ku	PROPN
iajs-2009	362	13	-	-	PUNCT
iajs-2009	362	14	algebras	algebras	PROPN
iajs-2009	362	15	.	.	PUNCT
iajs-2009	363	1	international	international	PROPN
iajs-2009	363	2	mathematical	mathematical	PROPN
iajs-2009	363	3	forum	forum	PROPN
iajs-2009	363	4	.	.	PUNCT
iajs-2009	364	1	2011	2011	NUM
iajs-2009	364	2	,	,	PUNCT
iajs-2009	364	3	6	6	NUM
iajs-2009	364	4	,	,	PUNCT
iajs-2009	364	5	63	63	NUM
iajs-2009	364	6	,	,	PUNCT
iajs-2009	364	7	3139	3139	NUM
iajs-2009	364	8	-	-	SYM
iajs-2009	364	9	3149	3149	NUM
iajs-2009	364	10	.	.	PUNCT
iajs-2009	365	1	15	15	NUM
iajs-2009	365	2	.	.	X
iajs-2009	365	3	mostafa	mostafa	PROPN
iajs-2009	365	4	.	.	PUNCT
iajs-2009	366	1	s.	s.	PROPN
iajs-2009	366	2	m.	m.	PROPN
iajs-2009	366	3	;	;	PUNCT
iajs-2009	366	4	radwan	radwan	PROPN
iajs-2009	366	5	.	.	PUNCT
iajs-2009	367	1	a.	a.	PROPN
iajs-2009	367	2	e.	e.	PROPN
iajs-2009	367	3	;	;	PUNCT
iajs-2009	367	4	ibrahem	ibrahem	NOUN
iajs-2009	367	5	.	.	PUNCT
iajs-2009	368	1	f.	f.	PROPN
iajs-2009	368	2	a.	a.	PROPN
iajs-2009	368	3	;	;	PUNCT
iajs-2009	368	4	kareem	kareem	PROPN
iajs-2009	368	5	.	.	PUNCT
iajs-2009	369	1	f.	f.	PROPN
iajs-2009	369	2	f.	f.	PROPN
iajs-2009	370	1	the	the	DET
iajs-2009	370	2	graph	graph	NOUN
iajs-2009	370	3	of	of	ADP
iajs-2009	370	4	a	a	DET
iajs-2009	370	5	commutative	commutative	ADJ
iajs-2009	370	6	ku	ku	NOUN
iajs-2009	370	7	-	-	PUNCT
iajs-2009	370	8	algebra	algebra	PROPN
iajs-2009	370	9	.	.	PUNCT
iajs-2009	371	1	algebra	algebra	NOUN
iajs-2009	371	2	letters	letter	NOUN
iajs-2009	371	3	1	1	NUM
iajs-2009	371	4	.	.	NOUN
iajs-2009	371	5	2015	2015	NUM
iajs-2009	371	6	,	,	PUNCT
iajs-2009	371	7	1	1	NUM
iajs-2009	371	8	,	,	PUNCT
iajs-2009	371	9	1	1	NUM
iajs-2009	371	10	-	-	SYM
iajs-2009	371	11	18	18	NUM
iajs-2009	371	12	.	.	PUNCT
iajs-2009	372	1	16	16	NUM
iajs-2009	372	2	.	.	PUNCT
iajs-2009	373	1	wilson	wilson	PROPN
iajs-2009	373	2	,	,	PUNCT
iajs-2009	373	3	r.j	r.j	PROPN
iajs-2009	373	4	.	.	PROPN
iajs-2009	373	5	introduction	introduction	NOUN
iajs-2009	373	6	to	to	AUX
iajs-2009	373	7	graph	graph	NOUN
iajs-2009	373	8	theory	theory	NOUN
iajs-2009	373	9	.	.	PUNCT
iajs-2009	374	1	oliver	oliver	PROPN
iajs-2009	374	2	and	and	CCONJ
iajs-2009	374	3	boyed	boyed	ADJ
iajs-2009	374	4	,	,	PUNCT
iajs-2009	374	5	edinburgh	edinburgh	PROPN
iajs-2009	374	6	.	.	PROPN
iajs-2009	374	7	1972	1972	NUM
iajs-2009	374	8	.	.	PUNCT