id	sid	eid	entity	type
ejpam-6048	1	1	european journal	ORG
ejpam-6048	1	2	2025	DATE
ejpam-6048	1	3	18	CARDINAL
ejpam-6048	1	4	3	CARDINAL
ejpam-6048	1	5	6048	CARDINAL
ejpam-6048	1	6	1307-5543	DATE
ejpam-6048	1	7	new york	GPE
ejpam-6048	1	8	s. abdulcarim1,∗	PERSON
ejpam-6048	1	9	susan c. dagondon2 1	PERSON
ejpam-6048	1	10	mindanao state university	ORG
ejpam-6048	1	11	9700	CARDINAL
ejpam-6048	1	12	marawi city	GPE
ejpam-6048	1	13	philippines 2 department	ORG
ejpam-6048	1	14	mindanao state university-iligan institute of technology	ORG
ejpam-6048	1	15	9200	CARDINAL
ejpam-6048	4	1	two	CARDINAL
ejpam-6048	4	2	one	CARDINAL
ejpam-6048	4	3	cartesian	NORP
ejpam-6048	4	4	g′	PERSON
ejpam-6048	4	5	h′	PERSON
ejpam-6048	5	1	g′	PERSON
ejpam-6048	5	2	h′	ORG
ejpam-6048	5	3	two	CARDINAL
ejpam-6048	7	1	2020	DATE
ejpam-6048	7	2	05c05	CARDINAL
ejpam-6048	7	3	05c76	CARDINAL
ejpam-6048	7	4	1	CARDINAL
ejpam-6048	10	1	x.	EVENT
ejpam-6048	10	2	two	CARDINAL
ejpam-6048	11	1	two	CARDINAL
ejpam-6048	11	2	∈	ORG
ejpam-6048	11	3	n(v	ORG
ejpam-6048	12	1	w ∈	PERSON
ejpam-6048	12	2	vw ∈	ORG
ejpam-6048	13	1	one	CARDINAL
ejpam-6048	13	2	one	CARDINAL
ejpam-6048	15	1	normalah.abdulcarim@msumain.edu.ph	ORG
ejpam-6048	15	2	susan.dagondon@g.msuiit.edu.ph	GPE
ejpam-6048	15	3	s. dagondon	PERSON
ejpam-6048	16	1	1	CARDINAL
ejpam-6048	16	2	2025	CARDINAL
ejpam-6048	17	1	s. dagondon / eur	PERSON
ejpam-6048	18	1	j. pure	PERSON
ejpam-6048	18	2	18	CARDINAL
ejpam-6048	18	3	3	CARDINAL
ejpam-6048	18	4	2025	CARDINAL
ejpam-6048	18	5	6048 2	CARDINAL
ejpam-6048	18	6	14	CARDINAL
ejpam-6048	22	1	2008	DATE
ejpam-6048	23	1	1	CARDINAL
ejpam-6048	24	1	2014	DATE
ejpam-6048	24	2	alwardi et al	PERSON
ejpam-6048	25	1	2	CARDINAL
ejpam-6048	26	1	the following year	DATE
ejpam-6048	26	2	2015	DATE
ejpam-6048	26	3	kulli	PERSON
ejpam-6048	27	1	3	CARDINAL
ejpam-6048	28	1	murthy	PERSON
ejpam-6048	29	1	4	CARDINAL
ejpam-6048	29	2	two	CARDINAL
ejpam-6048	30	1	2	CARDINAL
ejpam-6048	31	1	1	CARDINAL
ejpam-6048	32	1	5	CARDINAL
ejpam-6048	36	1	2	CARDINAL
ejpam-6048	37	1	6	CARDINAL
ejpam-6048	38	1	two	CARDINAL
ejpam-6048	38	2	d(x	ORG
ejpam-6048	38	3	d(x	ORG
ejpam-6048	38	4	1	CARDINAL
ejpam-6048	40	1	ω	CARDINAL
ejpam-6048	40	2	∈	ORG
ejpam-6048	41	1	d(u	PERSON
ejpam-6048	41	2	2n	CARDINAL
ejpam-6048	41	3	n ∈ n∗	ORG
ejpam-6048	41	4	g. corollary 1	PERSON
ejpam-6048	44	1	∈	ORG
ejpam-6048	44	2	2n	CARDINAL
ejpam-6048	44	3	n ∈ n∗	ORG
ejpam-6048	44	4	\a	WORK_OF_ART
ejpam-6048	45	1	ω	CARDINAL
ejpam-6048	45	2	∪a	CARDINAL
ejpam-6048	45	3	1	CARDINAL
ejpam-6048	48	1	n. abdulcarim	PERSON
ejpam-6048	48	2	s. dagondon / eur	PERSON
ejpam-6048	49	1	j. pure	PERSON
ejpam-6048	49	2	18	CARDINAL
ejpam-6048	49	3	3	CARDINAL
ejpam-6048	49	4	2025	CARDINAL
ejpam-6048	49	5	6048 3	CARDINAL
ejpam-6048	49	6	14	CARDINAL
ejpam-6048	49	7	2	CARDINAL
ejpam-6048	50	1	∈	ORG
ejpam-6048	50	2	u ∈ ω	ORG
ejpam-6048	50	3	∈	ORG
ejpam-6048	50	4	3	CARDINAL
ejpam-6048	51	1	8	CARDINAL
ejpam-6048	51	2	two	CARDINAL
ejpam-6048	52	1	∈ e(h	ORG
ejpam-6048	54	1	1	CARDINAL
ejpam-6048	54	2	1	CARDINAL
ejpam-6048	54	3	two	CARDINAL
ejpam-6048	55	1	1 2	CARDINAL
ejpam-6048	55	2	1	CARDINAL
ejpam-6048	55	3	4	CARDINAL
ejpam-6048	55	4	3	CARDINAL
ejpam-6048	55	5	2	CARDINAL
ejpam-6048	55	6	2	CARDINAL
ejpam-6048	55	7	2	CARDINAL
ejpam-6048	55	8	1	CARDINAL
ejpam-6048	55	9	3	CARDINAL
ejpam-6048	55	10	4	DATE
ejpam-6048	55	11	1	CARDINAL
ejpam-6048	55	12	4	CARDINAL
ejpam-6048	55	13	3	CARDINAL
ejpam-6048	55	14	1	CARDINAL
ejpam-6048	55	15	3	CARDINAL
ejpam-6048	55	16	4	CARDINAL
ejpam-6048	55	17	1	CARDINAL
ejpam-6048	55	18	3	CARDINAL
ejpam-6048	55	19	4	CARDINAL
ejpam-6048	55	20	2	CARDINAL
ejpam-6048	55	21	2	CARDINAL
ejpam-6048	55	22	1	CARDINAL
ejpam-6048	55	23	4	CARDINAL
ejpam-6048	56	1	5	CARDINAL
ejpam-6048	56	2	two	CARDINAL
ejpam-6048	56	3	one	CARDINAL
ejpam-6048	57	1	⋃ v∈v	PERSON
ejpam-6048	59	1	2	CARDINAL
ejpam-6048	59	2	2	CARDINAL
ejpam-6048	59	3	two	CARDINAL
ejpam-6048	59	4	s. dagondon / eur	PERSON
ejpam-6048	60	1	j. pure	PERSON
ejpam-6048	60	2	18	CARDINAL
ejpam-6048	60	3	3	CARDINAL
ejpam-6048	60	4	2025	CARDINAL
ejpam-6048	60	5	6048 4	DATE
ejpam-6048	60	6	4a 4b	MONEY
ejpam-6048	60	7	5a	CARDINAL
ejpam-6048	60	8	3b	CARDINAL
ejpam-6048	60	9	2b	CARDINAL
ejpam-6048	60	10	1b	CARDINAL
ejpam-6048	60	11	1	CARDINAL
ejpam-6048	60	12	c2 c3 c4 c5	PERSON
ejpam-6048	60	13	2	CARDINAL
ejpam-6048	60	14	two	CARDINAL
ejpam-6048	60	15	two	CARDINAL
ejpam-6048	60	16	5	CARDINAL
ejpam-6048	61	1	9	CARDINAL
ejpam-6048	61	2	n(x	GPE
ejpam-6048	61	3	xy ∈	PERSON
ejpam-6048	62	1	n(x	GPE
ejpam-6048	64	1	6	CARDINAL
ejpam-6048	65	1	4	CARDINAL
ejpam-6048	68	1	3	CARDINAL
ejpam-6048	68	2	3	CARDINAL
ejpam-6048	68	3	v1 v2 v3 v4v5 h :	PERSON
ejpam-6048	68	4	3	CARDINAL
ejpam-6048	68	5	2	CARDINAL
ejpam-6048	68	6	n. abdulcarim	PERSON
ejpam-6048	68	7	s. dagondon / eur	PERSON
ejpam-6048	69	1	j. pure	PERSON
ejpam-6048	69	2	18	CARDINAL
ejpam-6048	69	3	3	CARDINAL
ejpam-6048	69	4	2025	CARDINAL
ejpam-6048	69	5	6048 5	DATE
ejpam-6048	69	6	14	CARDINAL
ejpam-6048	70	1	2	CARDINAL
ejpam-6048	70	2	7	CARDINAL
ejpam-6048	71	1	4	CARDINAL
ejpam-6048	71	2	⊆	CARDINAL
ejpam-6048	71	3	two	CARDINAL
ejpam-6048	72	1	2	CARDINAL
ejpam-6048	74	1	1 5	CARDINAL
ejpam-6048	74	2	4	CARDINAL
ejpam-6048	74	3	8	CARDINAL
ejpam-6048	75	1	4	CARDINAL
ejpam-6048	76	1	ni(g, j	ORG
ejpam-6048	76	2	4	CARDINAL
ejpam-6048	77	1	3	CARDINAL
ejpam-6048	80	1	+ x3	PERSON
ejpam-6048	81	1	1	CARDINAL
ejpam-6048	82	1	4	CARDINAL
ejpam-6048	82	2	g1	ORG
ejpam-6048	82	3	two	CARDINAL
ejpam-6048	83	1	x)ni(g2	PERSON
ejpam-6048	84	1	2	CARDINAL
ejpam-6048	85	1	4	CARDINAL
ejpam-6048	88	1	3	CARDINAL
ejpam-6048	88	2	3.1	CARDINAL
ejpam-6048	89	1	2	CARDINAL
ejpam-6048	89	2	s. dagondon / eur	PERSON
ejpam-6048	90	1	j. pure	PERSON
ejpam-6048	90	2	18	CARDINAL
ejpam-6048	90	3	3	CARDINAL
ejpam-6048	90	4	2025	CARDINAL
ejpam-6048	90	5	6048 6	CARDINAL
ejpam-6048	90	6	14	CARDINAL
ejpam-6048	92	1	1	CARDINAL
ejpam-6048	92	2	ω1,∆1 and	CARDINAL
ejpam-6048	92	3	ω2,∆2	ORG
ejpam-6048	93	1	xi1	PERSON
ejpam-6048	93	2	xi2	GPE
ejpam-6048	93	3	yj2	ORG
ejpam-6048	93	4	∈	ORG
ejpam-6048	93	5	xi1	PERSON
ejpam-6048	93	6	xi2	GPE
ejpam-6048	93	7	yj2	ORG
ejpam-6048	95	1	y1y2 /∈ e(h	ORG
ejpam-6048	96	1	xi1	ORG
ejpam-6048	96	2	xi2 ∈	ORG
ejpam-6048	96	3	∈	ORG
ejpam-6048	96	4	yj2	ORG
ejpam-6048	97	1	xi1	ORG
ejpam-6048	97	2	yj1)(xi2	GPE
ejpam-6048	97	3	yj2	ORG
ejpam-6048	98	1	xi1	ORG
ejpam-6048	98	2	xi2 ∈	ORG
ejpam-6048	98	3	xi1	ORG
ejpam-6048	98	4	xi2	GPE
ejpam-6048	99	1	∈	ORG
ejpam-6048	99	2	∈	ORG
ejpam-6048	99	3	xi+1 ∈ ∆1	ORG
ejpam-6048	99	4	∈	ORG
ejpam-6048	99	5	∈	ORG
ejpam-6048	99	6	∈	ORG
ejpam-6048	99	7	xi+1 ∈ ∆1	ORG
ejpam-6048	99	8	yi+1 ∈	ORG
ejpam-6048	100	1	xi1 ∈ ω1	PERSON
ejpam-6048	100	2	∈	ORG
ejpam-6048	100	3	xi2 ∈ ∆1	ORG
ejpam-6048	100	4	xi1	PRODUCT
ejpam-6048	100	5	xi2	GPE
ejpam-6048	100	6	yj2	ORG
ejpam-6048	101	1	3	CARDINAL
ejpam-6048	101	2	2	CARDINAL
ejpam-6048	103	1	ω2,∆2	ORG
ejpam-6048	104	1	more than 2	CARDINAL
ejpam-6048	104	2	∈	ORG
ejpam-6048	106	1	∈	ORG
ejpam-6048	106	2	∈	ORG
ejpam-6048	107	1	∈	ORG
ejpam-6048	108	1	2	CARDINAL
ejpam-6048	108	2	∈	ORG
ejpam-6048	108	3	∈	ORG
ejpam-6048	108	4	∈	ORG
ejpam-6048	110	1	∈	ORG
ejpam-6048	110	2	∈	ORG
ejpam-6048	110	3	∈	ORG
ejpam-6048	110	4	∈	ORG
ejpam-6048	110	5	vi ∈	PERSON
ejpam-6048	110	6	∈	ORG
ejpam-6048	110	7	∈	ORG
ejpam-6048	112	1	∈	ORG
ejpam-6048	112	2	v2 ∈	PRODUCT
ejpam-6048	112	3	∈	ORG
ejpam-6048	112	4	u4 ∈ ∆1	ORG
ejpam-6048	112	5	∈	ORG
ejpam-6048	114	1	1	CARDINAL
ejpam-6048	115	1	1	CARDINAL
ejpam-6048	117	1	more than 2	CARDINAL
ejpam-6048	118	1	2	CARDINAL
ejpam-6048	119	1	4	CARDINAL
ejpam-6048	120	1	ω2,∆2	ORG
ejpam-6048	121	1	∈	ORG
ejpam-6048	121	2	∈	ORG
ejpam-6048	122	1	n. abdulcarim	PERSON
ejpam-6048	122	2	s. dagondon / eur	PERSON
ejpam-6048	123	1	j. pure	PERSON
ejpam-6048	123	2	18	CARDINAL
ejpam-6048	123	3	3	CARDINAL
ejpam-6048	123	4	2025	CARDINAL
ejpam-6048	123	5	6048 7	DATE
ejpam-6048	123	6	14	CARDINAL
ejpam-6048	124	1	3	CARDINAL
ejpam-6048	124	2	3	CARDINAL
ejpam-6048	125	1	∈	ORG
ejpam-6048	125	2	∈	ORG
ejpam-6048	127	1	∈	ORG
ejpam-6048	127	2	∈	ORG
ejpam-6048	127	3	ω2,∆2	ORG
ejpam-6048	128	1	∈	ORG
ejpam-6048	128	2	∈	ORG
ejpam-6048	129	1	∈	ORG
ejpam-6048	129	2	∈	ORG
ejpam-6048	136	1	⋃	DATE
ejpam-6048	138	1	̸ a.	PERSON
ejpam-6048	141	1	x4	PERSON
ejpam-6048	143	1	∈	ORG
ejpam-6048	144	1	x4	PERSON
ejpam-6048	145	1	y3y4 /∈ e(h	ORG
ejpam-6048	147	1	⋃	PERSON
ejpam-6048	147	2	4	CARDINAL
ejpam-6048	148	1	ω2,∆2	ORG
ejpam-6048	151	1	n. abdulcarim	PERSON
ejpam-6048	151	2	s. dagondon / eur	PERSON
ejpam-6048	152	1	j. pure	PERSON
ejpam-6048	152	2	18	CARDINAL
ejpam-6048	152	3	3	CARDINAL
ejpam-6048	152	4	2025	CARDINAL
ejpam-6048	152	5	6048 8	DATE
ejpam-6048	152	6	14	CARDINAL
ejpam-6048	153	1	ω2,∆2	ORG
ejpam-6048	154	1	theorems 3 and	ORG
ejpam-6048	154	2	4	DATE
ejpam-6048	154	3	∈	ORG
ejpam-6048	154	4	∈	ORG
ejpam-6048	155	1	3	CARDINAL
ejpam-6048	155	2	∈	ORG
ejpam-6048	155	3	∈	ORG
ejpam-6048	155	4	∈	ORG
ejpam-6048	156	1	|ω1||ω2|	ORG
ejpam-6048	156	2	∈	ORG
ejpam-6048	157	1	∈	ORG
ejpam-6048	158	1	ni(a	PERSON
ejpam-6048	170	1	5	CARDINAL
ejpam-6048	170	2	5	CARDINAL
ejpam-6048	171	1	1	CARDINAL
ejpam-6048	171	2	3	DATE
ejpam-6048	171	3	4	CARDINAL
ejpam-6048	171	4	n. abdulcarim	PERSON
ejpam-6048	171	5	s. dagondon / eur	PERSON
ejpam-6048	172	1	j. pure	PERSON
ejpam-6048	172	2	18	CARDINAL
ejpam-6048	172	3	3	CARDINAL
ejpam-6048	172	4	2025	CARDINAL
ejpam-6048	172	5	6048 9	DATE
ejpam-6048	173	1	1 2	CARDINAL
ejpam-6048	173	2	1	CARDINAL
ejpam-6048	173	3	3	CARDINAL
ejpam-6048	173	4	4	CARDINAL
ejpam-6048	173	5	2	CARDINAL
ejpam-6048	173	6	5	CARDINAL
ejpam-6048	173	7	6	CARDINAL
ejpam-6048	173	8	7	CARDINAL
ejpam-6048	173	9	1	CARDINAL
ejpam-6048	173	10	3	CARDINAL
ejpam-6048	173	11	4	CARDINAL
ejpam-6048	173	12	1	CARDINAL
ejpam-6048	173	13	3	CARDINAL
ejpam-6048	173	14	4	CARDINAL
ejpam-6048	173	15	2	CARDINAL
ejpam-6048	173	16	5	CARDINAL
ejpam-6048	173	17	6	CARDINAL
ejpam-6048	173	18	7	DATE
ejpam-6048	173	19	2	CARDINAL
ejpam-6048	173	20	5	CARDINAL
ejpam-6048	173	21	6	CARDINAL
ejpam-6048	173	22	7	DATE
ejpam-6048	173	23	2	CARDINAL
ejpam-6048	173	24	5	CARDINAL
ejpam-6048	173	25	6	CARDINAL
ejpam-6048	173	26	1	CARDINAL
ejpam-6048	173	27	3	CARDINAL
ejpam-6048	173	28	4	CARDINAL
ejpam-6048	173	29	2	CARDINAL
ejpam-6048	173	30	5	CARDINAL
ejpam-6048	173	31	6	CARDINAL
ejpam-6048	173	32	7	CARDINAL
ejpam-6048	173	33	2	CARDINAL
ejpam-6048	173	34	5	CARDINAL
ejpam-6048	173	35	6	CARDINAL
ejpam-6048	173	36	1	CARDINAL
ejpam-6048	173	37	3	CARDINAL
ejpam-6048	173	38	4	DATE
ejpam-6048	173	39	1	CARDINAL
ejpam-6048	173	40	3	CARDINAL
ejpam-6048	173	41	4	CARDINAL
ejpam-6048	173	42	5	CARDINAL
ejpam-6048	173	43	2	CARDINAL
ejpam-6048	173	44	5	DATE
ejpam-6048	173	45	6	DATE
ejpam-6048	173	46	7	CARDINAL
ejpam-6048	174	1	3	CARDINAL
ejpam-6048	174	2	1	CARDINAL
ejpam-6048	174	3	3	CARDINAL
ejpam-6048	174	4	4	CARDINAL
ejpam-6048	174	5	1	CARDINAL
ejpam-6048	174	6	3	CARDINAL
ejpam-6048	174	7	4	CARDINAL
ejpam-6048	174	8	1	CARDINAL
ejpam-6048	174	9	3	CARDINAL
ejpam-6048	174	10	4	CARDINAL
ejpam-6048	174	11	∈	ORG
ejpam-6048	174	12	2	CARDINAL
ejpam-6048	174	13	5	CARDINAL
ejpam-6048	174	14	6	CARDINAL
ejpam-6048	174	15	7	CARDINAL
ejpam-6048	174	16	2	CARDINAL
ejpam-6048	174	17	5	DATE
ejpam-6048	174	18	6	CARDINAL
ejpam-6048	174	19	7	DATE
ejpam-6048	174	20	2	CARDINAL
ejpam-6048	174	21	5	DATE
ejpam-6048	174	22	6	CARDINAL
ejpam-6048	174	23	7	DATE
ejpam-6048	174	24	∈	ORG
ejpam-6048	174	25	2	CARDINAL
ejpam-6048	174	26	5	CARDINAL
ejpam-6048	174	27	6	CARDINAL
ejpam-6048	174	28	2	CARDINAL
ejpam-6048	174	29	5	CARDINAL
ejpam-6048	174	30	6	CARDINAL
ejpam-6048	174	31	7	CARDINAL
ejpam-6048	174	32	2	CARDINAL
ejpam-6048	174	33	5	CARDINAL
ejpam-6048	174	34	6	CARDINAL
ejpam-6048	174	35	1	CARDINAL
ejpam-6048	174	36	3	CARDINAL
ejpam-6048	174	37	4	CARDINAL
ejpam-6048	174	38	1	CARDINAL
ejpam-6048	174	39	3	CARDINAL
ejpam-6048	174	40	4	DATE
ejpam-6048	174	41	1	CARDINAL
ejpam-6048	174	42	3	CARDINAL
ejpam-6048	174	43	4	CARDINAL
ejpam-6048	174	44	n. abdulcarim	PERSON
ejpam-6048	174	45	s. dagondon / eur	PERSON
ejpam-6048	175	1	j. pure	PERSON
ejpam-6048	175	2	18	CARDINAL
ejpam-6048	175	3	3	CARDINAL
ejpam-6048	175	4	2025	CARDINAL
ejpam-6048	175	5	6048 10	DATE
ejpam-6048	175	6	3	CARDINAL
ejpam-6048	175	7	3	CARDINAL
ejpam-6048	175	8	3	CARDINAL
ejpam-6048	175	9	4	CARDINAL
ejpam-6048	175	10	4	CARDINAL
ejpam-6048	175	11	x3(3)+3(4	CARDINAL
ejpam-6048	175	12	+ x3(3)+3(3	QUANTITY
ejpam-6048	177	1	+ 2x21 + x24	DATE
ejpam-6048	178	1	5	CARDINAL
ejpam-6048	178	2	g. proof	PERSON
ejpam-6048	181	1	(g)×v	CARDINAL
ejpam-6048	181	2	h)×v	ORG
ejpam-6048	182	1	β((g	GPE
ejpam-6048	184	1	g1	ORG
ejpam-6048	190	1	g1	ORG
ejpam-6048	190	2	one	CARDINAL
ejpam-6048	192	1	β((g	GPE
ejpam-6048	194	1	β(v	PERSON
ejpam-6048	196	1	g1	ORG
ejpam-6048	197	1	g1	ORG
ejpam-6048	197	2	h1)(g2	NORP
ejpam-6048	197	3	⇔	CARDINAL
ejpam-6048	197	4	h1h2	CARDINAL
ejpam-6048	199	1	g. therefore	PERSON
ejpam-6048	199	2	g. remark 3.	PERSON
ejpam-6048	201	1	3.2	CARDINAL
ejpam-6048	202	1	two	CARDINAL
ejpam-6048	205	1	ω2,∆2	ORG
ejpam-6048	206	1	ni(g ◦h	ORG
ejpam-6048	210	1	n. abdulcarim	PERSON
ejpam-6048	210	2	s. dagondon / eur	PERSON
ejpam-6048	211	1	j. pure	PERSON
ejpam-6048	211	2	18	CARDINAL
ejpam-6048	211	3	3	CARDINAL
ejpam-6048	211	4	2025	CARDINAL
ejpam-6048	211	5	6048 11	DATE
ejpam-6048	211	6	14	CARDINAL
ejpam-6048	213	1	ω2,∆2	ORG
ejpam-6048	214	1	1	CARDINAL
ejpam-6048	218	1	two	CARDINAL
ejpam-6048	218	2	ofh	ORG
ejpam-6048	218	3	|∆1|	GPE
ejpam-6048	218	4		GPE
ejpam-6048	218	5	j∈∆1 hj	PERSON
ejpam-6048	219	1	|∆1|	GPE
ejpam-6048	222	1	ni(g ◦h	ORG
ejpam-6048	225	1	|∆1|	GPE
ejpam-6048	227	1	6	CARDINAL
ejpam-6048	227	2	two	CARDINAL
ejpam-6048	227	3	2	CARDINAL
ejpam-6048	227	4	2	CARDINAL
ejpam-6048	228	1	1	CARDINAL
ejpam-6048	228	2	d2 2 a3 b3 c3	PRODUCT
ejpam-6048	228	3	3	CARDINAL
ejpam-6048	228	4	4	CARDINAL
ejpam-6048	228	5	5	CARDINAL
ejpam-6048	229	1	2	CARDINAL
ejpam-6048	229	2	6	CARDINAL
ejpam-6048	229	3	2),k1,3	CARDINAL
ejpam-6048	229	4	2	CARDINAL
ejpam-6048	229	5	n. abdulcarim	PERSON
ejpam-6048	229	6	s. dagondon / eur	PERSON
ejpam-6048	230	1	j. pure	PERSON
ejpam-6048	230	2	18	CARDINAL
ejpam-6048	230	3	3	CARDINAL
ejpam-6048	230	4	2025	CARDINAL
ejpam-6048	230	5	6048 12	CARDINAL
ejpam-6048	230	6	14	CARDINAL
ejpam-6048	230	7	1	CARDINAL
ejpam-6048	230	8	2	CARDINAL
ejpam-6048	230	9	3	CARDINAL
ejpam-6048	230	10	5	DATE
ejpam-6048	230	11	6	CARDINAL
ejpam-6048	232	1	1	CARDINAL
ejpam-6048	232	2	2	DATE
ejpam-6048	232	3	4	DATE
ejpam-6048	232	4	b3	GPE
ejpam-6048	232	5	a5	PERSON
ejpam-6048	232	6	c5	ORG
ejpam-6048	232	7	1	CARDINAL
ejpam-6048	232	8	2	DATE
ejpam-6048	232	9	4	DATE
ejpam-6048	232	10	b3	GPE
ejpam-6048	232	11	a5	PERSON
ejpam-6048	232	12	c5	GPE
ejpam-6048	232	13	1	CARDINAL
ejpam-6048	232	14	2	DATE
ejpam-6048	232	15	4	DATE
ejpam-6048	232	16	b3	GPE
ejpam-6048	232	17	c3	PERSON
ejpam-6048	232	18	1	CARDINAL
ejpam-6048	232	19	2	DATE
ejpam-6048	232	20	4	DATE
ejpam-6048	232	21	b3	GPE
ejpam-6048	232	22	c3	PERSON
ejpam-6048	232	23	1	CARDINAL
ejpam-6048	232	24	2	DATE
ejpam-6048	232	25	4	DATE
ejpam-6048	232	26	d3, a5	ORG
ejpam-6048	232	27	c5	ORG
ejpam-6048	232	28	1	CARDINAL
ejpam-6048	232	29	2	DATE
ejpam-6048	232	30	4	DATE
ejpam-6048	232	31	d3, a5	ORG
ejpam-6048	232	32	c5	GPE
ejpam-6048	232	33	1	CARDINAL
ejpam-6048	232	34	2	DATE
ejpam-6048	232	35	4	DATE
ejpam-6048	232	36	1	CARDINAL
ejpam-6048	232	37	2	DATE
ejpam-6048	232	38	4	DATE
ejpam-6048	232	39	3	CARDINAL
ejpam-6048	232	40	5	DATE
ejpam-6048	232	41	6	DATE
ejpam-6048	232	42	3	CARDINAL
ejpam-6048	232	43	5	DATE
ejpam-6048	232	44	6	DATE
ejpam-6048	232	45	3	CARDINAL
ejpam-6048	232	46	5	DATE
ejpam-6048	232	47	6	DATE
ejpam-6048	232	48	3	CARDINAL
ejpam-6048	232	49	5	DATE
ejpam-6048	232	50	6	DATE
ejpam-6048	232	51	3	CARDINAL
ejpam-6048	232	52	5	DATE
ejpam-6048	232	53	6	DATE
ejpam-6048	232	54	3	CARDINAL
ejpam-6048	232	55	5	DATE
ejpam-6048	232	56	6	DATE
ejpam-6048	232	57	3	CARDINAL
ejpam-6048	232	58	5	DATE
ejpam-6048	232	59	6	DATE
ejpam-6048	232	60	3	CARDINAL
ejpam-6048	232	61	5	DATE
ejpam-6048	232	62	6	DATE
ejpam-6048	233	1	6	CARDINAL
ejpam-6048	233	2	ni(g ◦h	ORG
ejpam-6048	236	1	|∆1|	GPE
ejpam-6048	238	1	2x3(x+	CARDINAL
ejpam-6048	238	2	2x3(x3	CARDINAL
ejpam-6048	238	3	2x6	CARDINAL
ejpam-6048	240	1	7	CARDINAL
ejpam-6048	241	1	1a	CARDINAL
ejpam-6048	241	2	1b	CARDINAL
ejpam-6048	241	3	6b	CARDINAL
ejpam-6048	241	4	1c	CARDINAL
ejpam-6048	241	5	2c	MONEY
ejpam-6048	241	6	6c	CARDINAL
ejpam-6048	241	7	1d	CARDINAL
ejpam-6048	241	8	2d	DATE
ejpam-6048	242	1	2	CARDINAL
ejpam-6048	242	2	7	CARDINAL
ejpam-6048	242	3	2	CARDINAL
ejpam-6048	242	4	2	CARDINAL
ejpam-6048	242	5	1d	CARDINAL
ejpam-6048	242	6	2d	DATE
ejpam-6048	242	7	4d	CARDINAL
ejpam-6048	242	8	3d	CARDINAL
ejpam-6048	242	9	5d	CARDINAL
ejpam-6048	242	10	6d	CARDINAL
ejpam-6048	242	11	1a	CARDINAL
ejpam-6048	242	12	2a	CARDINAL
ejpam-6048	242	13	4a	CARDINAL
ejpam-6048	242	14	1b	CARDINAL
ejpam-6048	242	15	2b	CARDINAL
ejpam-6048	242	16	4b	CARDINAL
ejpam-6048	242	17	1c	CARDINAL
ejpam-6048	242	18	2c	CARDINAL
ejpam-6048	242	19	4c	CARDINAL
ejpam-6048	242	20	1a	CARDINAL
ejpam-6048	242	21	2a	CARDINAL
ejpam-6048	242	22	4a	CARDINAL
ejpam-6048	242	23	1b	CARDINAL
ejpam-6048	242	24	2b	CARDINAL
ejpam-6048	242	25	4b	CARDINAL
ejpam-6048	242	26	3c	CARDINAL
ejpam-6048	242	27	5c	CARDINAL
ejpam-6048	242	28	6c	CARDINAL
ejpam-6048	242	29	1a	CARDINAL
ejpam-6048	242	30	2a	CARDINAL
ejpam-6048	242	31	4a	CARDINAL
ejpam-6048	242	32	3b	CARDINAL
ejpam-6048	242	33	5b	CARDINAL
ejpam-6048	242	34	6b	CARDINAL
ejpam-6048	242	35	1c	CARDINAL
ejpam-6048	242	36	2c	CARDINAL
ejpam-6048	242	37	4c	CARDINAL
ejpam-6048	242	38	1a	CARDINAL
ejpam-6048	242	39	2a	CARDINAL
ejpam-6048	242	40	4a	CARDINAL
ejpam-6048	242	41	3b	CARDINAL
ejpam-6048	242	42	5b	CARDINAL
ejpam-6048	242	43	6b	CARDINAL
ejpam-6048	242	44	3c	CARDINAL
ejpam-6048	242	45	5c	CARDINAL
ejpam-6048	242	46	6c	CARDINAL
ejpam-6048	242	47	3a	CARDINAL
ejpam-6048	242	48	5a	CARDINAL
ejpam-6048	242	49	6a	CARDINAL
ejpam-6048	242	50	1b	CARDINAL
ejpam-6048	242	51	2b	CARDINAL
ejpam-6048	242	52	4b	CARDINAL
ejpam-6048	242	53	1c	CARDINAL
ejpam-6048	242	54	2c	CARDINAL
ejpam-6048	242	55	4c	CARDINAL
ejpam-6048	242	56	3a	CARDINAL
ejpam-6048	242	57	5a	CARDINAL
ejpam-6048	242	58	6a	CARDINAL
ejpam-6048	242	59	1b	CARDINAL
ejpam-6048	242	60	2b	CARDINAL
ejpam-6048	242	61	4b	CARDINAL
ejpam-6048	242	62	3c	CARDINAL
ejpam-6048	242	63	5c	CARDINAL
ejpam-6048	242	64	6c	CARDINAL
ejpam-6048	242	65	3a	CARDINAL
ejpam-6048	242	66	5a	CARDINAL
ejpam-6048	242	67	6a	CARDINAL
ejpam-6048	242	68	3b	CARDINAL
ejpam-6048	242	69	5b	CARDINAL
ejpam-6048	242	70	6b	CARDINAL
ejpam-6048	242	71	1c	CARDINAL
ejpam-6048	242	72	2c	CARDINAL
ejpam-6048	242	73	4c	CARDINAL
ejpam-6048	242	74	3a	CARDINAL
ejpam-6048	242	75	5a	CARDINAL
ejpam-6048	242	76	6a	CARDINAL
ejpam-6048	242	77	3b	CARDINAL
ejpam-6048	242	78	5b	CARDINAL
ejpam-6048	242	79	6b	CARDINAL
ejpam-6048	242	80	3c	CARDINAL
ejpam-6048	242	81	5c	CARDINAL
ejpam-6048	242	82	6c	CARDINAL
ejpam-6048	243	1	6	CARDINAL
ejpam-6048	243	2	2	CARDINAL
ejpam-6048	247	1	s. dagondon / eur	PERSON
ejpam-6048	248	1	j. pure	PERSON
ejpam-6048	248	2	18	CARDINAL
ejpam-6048	248	3	3	CARDINAL
ejpam-6048	248	4	2025	CARDINAL
ejpam-6048	248	5	6048 13	DATE
ejpam-6048	248	6	14	CARDINAL
ejpam-6048	249	1	2x6	CARDINAL
ejpam-6048	250	1	+ 8x10	CARDINAL
ejpam-6048	251	1	7	CARDINAL
ejpam-6048	254	1	g ∼= h.	ORG
ejpam-6048	254	2	ω2,∆2	ORG
ejpam-6048	255	1	|∆1|	GPE
ejpam-6048	255	2	|∆1|	GPE
ejpam-6048	256	1	|∆1|	GPE
ejpam-6048	257	1	ni(g ◦h	ORG
ejpam-6048	264	1	7	CARDINAL
ejpam-6048	265	1	k1,4	GPE
ejpam-6048	265	2	8	CARDINAL
ejpam-6048	265	3	k1,4	PERSON
ejpam-6048	265	4	k1,4	ORG
ejpam-6048	265	5	1	CARDINAL
ejpam-6048	265	6	d2 e2 a2	PRODUCT
ejpam-6048	265	7	2	CARDINAL
ejpam-6048	265	8	b3 c3 d3 e3 a3	ORG
ejpam-6048	265	9	3 b4 c4 d4 e4	QUANTITY
ejpam-6048	265	10	4 b0 c0 d0 e0	QUANTITY
ejpam-6048	265	11	0	CARDINAL
ejpam-6048	266	1	k1,4	GPE
ejpam-6048	266	2	k1,4	ORG
ejpam-6048	266	3	8	CARDINAL
ejpam-6048	266	4	k1,4	GPE
ejpam-6048	266	5	k1,4	ORG
ejpam-6048	266	6	2	CARDINAL
ejpam-6048	266	7	k1,4	ORG
ejpam-6048	266	8	1	CARDINAL
ejpam-6048	266	9	4	CARDINAL
ejpam-6048	266	10	n. abdulcarim	PERSON
ejpam-6048	266	11	s. dagondon / eur	PERSON
ejpam-6048	267	1	j. pure	PERSON
ejpam-6048	267	2	18	CARDINAL
ejpam-6048	267	3	3	CARDINAL
ejpam-6048	267	4	2025	CARDINAL
ejpam-6048	267	5	6048 14	DATE
ejpam-6048	267	6	14	DATE
ejpam-6048	268	1	1	CARDINAL
ejpam-6048	268	2	4	CARDINAL
ejpam-6048	268	3	1	CARDINAL
ejpam-6048	268	4	4	CARDINAL
ejpam-6048	268	5	k1,4	GPE
ejpam-6048	269	1	x1(x+ x4)4	PERSON
ejpam-6048	271	1	x4(x+	PERSON
ejpam-6048	272	1	+ 4x3	DATE
ejpam-6048	273	1	+ 4x	CARDINAL
ejpam-6048	275	1	2x5 + 5x8	PERCENT
ejpam-6048	278	1	the department of science and technology	ORG
ejpam-6048	278	2	mindanao state university iligan institute of technology	ORG
ejpam-6048	278	3	mindanao	GPE
ejpam-6048	278	4	marawi city	GPE
ejpam-6048	279	1	1	CARDINAL
ejpam-6048	279	2	nowakowski	PERSON
ejpam-6048	281	1	astralasian journal of combinatorics	ORG
ejpam-6048	281	2	42:55–68, 2008	DATE
ejpam-6048	282	1	2	CARDINAL
ejpam-6048	282	2	a. alwardi	PERSON
ejpam-6048	282	3	shivaswamy	PERSON
ejpam-6048	284	1	european journal	ORG
ejpam-6048	284	2	6:13–24	DATE
ejpam-6048	284	3	2016	DATE
ejpam-6048	285	1	3	CARDINAL
ejpam-6048	285	2	kulli	PERSON
ejpam-6048	287	1	8:93–99	CARDINAL
ejpam-6048	287	2	2015	DATE
ejpam-6048	288	1	4	CARDINAL
ejpam-6048	288	2	puttaswamy k.b. murthy	PERSON
ejpam-6048	290	1	indian	NORP
ejpam-6048	290	2	1–7	CARDINAL
ejpam-6048	290	3	2014	DATE
ejpam-6048	291	1	5	CARDINAL
ejpam-6048	291	2	f. harary	PERSON
ejpam-6048	293	1	addison-wesley publishing company	ORG
ejpam-6048	293	2	1969	DATE
ejpam-6048	294	1	6	CARDINAL
ejpam-6048	294	2	r. diestel	PERSON
ejpam-6048	295	1	fifth	ORDINAL
ejpam-6048	296	1	2017	DATE
ejpam-6048	297	1	7	CARDINAL
ejpam-6048	297	2	s. dagondon.	PERSON
ejpam-6048	298	1	two	CARDINAL
ejpam-6048	299	1	european journal	ORG
ejpam-6048	299	2	1:64–81	GPE
ejpam-6048	299	3	2022	CARDINAL
ejpam-6048	300	1	8	CARDINAL
ejpam-6048	300	2	bondy	PERSON
ejpam-6048	300	3	murthy	PERSON
ejpam-6048	302	1	2007	DATE
ejpam-6048	303	1	9	CARDINAL
ejpam-6048	303	2	f. buckley	PERSON
ejpam-6048	303	3	f. harary	PERSON
ejpam-6048	305	1	addison-wesley	ORG
ejpam-6048	305	2	1990	DATE