id	sid	eid	entity	type
cana-4368	1	1	1074	CARDINAL
cana-4368	1	2	32	CARDINAL
cana-4368	2	1	9s	CARDINAL
cana-4368	2	2	e.esakkiammal 1	DATE
cana-4368	2	3	k.thirusangu2	GPE
cana-4368	2	4	3 1,2	CARDINAL
cana-4368	3	1	chennai	GPE
cana-4368	3	2	india	GPE
cana-4368	4	1	3department	CARDINAL
cana-4368	4	2	r.v. govt.	ORG
cana-4368	5	1	chennai	GPE
cana-4368	5	2	india	GPE
cana-4368	6	1	1esakkiammal2682@gmail.com,2kthirusangu@gmail.com,3seetha0687@gmail.com	ORG
cana-4368	6	2	12-01-2025	CARDINAL
cana-4368	6	3	15-02-2025	CARDINAL
cana-4368	6	4	01-03-2025	CARDINAL
cana-4368	7	1	two	CARDINAL
cana-4368	8	1	two	CARDINAL
cana-4368	10	1	one	CARDINAL
cana-4368	12	1	one	CARDINAL
cana-4368	13	1	1	CARDINAL
cana-4368	14	1	1	CARDINAL
cana-4368	14	2	two	CARDINAL
cana-4368	16	1	m+1	CARDINAL
cana-4368	16	2	bipartite	NORP
cana-4368	16	3	𝑆𝑛	ORG
cana-4368	16	4	one	CARDINAL
cana-4368	16	5	2	CARDINAL
cana-4368	16	6	2,𝑚	CARDINAL
cana-4368	16	7	1	CARDINAL
cana-4368	18	1	the year 1967	DATE
cana-4368	18	2	rosa	ORG
cana-4368	18	3	graham	PERSON
cana-4368	18	4	1980[4	CARDINAL
cana-4368	19	1	8	CARDINAL
cana-4368	23	1	1074	CARDINAL
cana-4368	23	2	32	CARDINAL
cana-4368	24	1	9s	CARDINAL
cana-4368	24	2	2025) 1929	DATE
cana-4368	25	1	2	CARDINAL
cana-4368	25	2	2.1	CARDINAL
cana-4368	27	1	0	CARDINAL
cana-4368	27	2	1,3,5	CARDINAL
cana-4368	29	1	2𝑛	CARDINAL
cana-4368	30	1	1	CARDINAL
cana-4368	30	2	max	PERSON
cana-4368	30	3	𝑓(𝑣)/𝑣 ∈	PERSON
cana-4368	31	1	2.2.1	CARDINAL
cana-4368	31	2	𝐏𝐦	GPE
cana-4368	31	3	1	CARDINAL
cana-4368	31	4	{vi /0 ≤	PERSON
cana-4368	32	1	0	CARDINAL
cana-4368	32	2	1	CARDINAL
cana-4368	32	3	1	CARDINAL
cana-4368	32	4	6	CARDINAL
cana-4368	32	5	2	CARDINAL
cana-4368	32	6	5	CARDINAL
cana-4368	33	1	2.3.2.theorem	CARDINAL
cana-4368	33	2	1	CARDINAL
cana-4368	33	3	1	CARDINAL
cana-4368	33	4	1 3	DATE
cana-4368	33	5	1	CARDINAL
cana-4368	35	1	1	CARDINAL
cana-4368	36	1	0	CARDINAL
cana-4368	36	2	0 ≤	MONEY
cana-4368	37	1	3.3.1	CARDINAL
cana-4368	40	1	00001	DATE
cana-4368	41	1	1	CARDINAL
cana-4368	41	2	1	CARDINAL
cana-4368	41	3	1(mod	CARDINAL
cana-4368	44	1	6]2	CARDINAL
cana-4368	44	2	3	CARDINAL
cana-4368	46	1	2]2	CARDINAL
cana-4368	46	2	1	CARDINAL
cana-4368	46	3	1074	CARDINAL
cana-4368	46	4	32	CARDINAL
cana-4368	47	1	9s	CARDINAL
cana-4368	47	2	1930	DATE
cana-4368	52	1	5]2	CARDINAL
cana-4368	52	2	3	CARDINAL
cana-4368	53	1	1	CARDINAL
cana-4368	54	1	1	CARDINAL
cana-4368	54	2	1 3	DATE
cana-4368	54	3	1	CARDINAL
cana-4368	55	1	3.odd	CARDINAL
cana-4368	55	2	𝑷𝟏𝟎	ORG
cana-4368	58	1	𝑆𝑛 graph 𝑛 ≥ 1	ORG
cana-4368	59	1	𝑆𝑛 𝑉	ORG
cana-4368	59	2	0	CARDINAL
cana-4368	59	3	1	CARDINAL
cana-4368	60	1	3.3.4.theorem	CARDINAL
cana-4368	60	2	𝑆𝑛	ORG
cana-4368	60	3	1	CARDINAL
cana-4368	60	4	2𝑛	CARDINAL
cana-4368	62	1	1 ≤	CARDINAL
cana-4368	63	1	0	CARDINAL
cana-4368	63	2	𝑓(𝑣0	GPE
cana-4368	64	1	≠ 𝑓(𝑣𝑖	PERSON
cana-4368	64	2	1 ≤	CARDINAL
cana-4368	64	3	3.3.3	CARDINAL
cana-4368	65	1	1 ≤	MONEY
cana-4368	65	2	𝑓(𝑣𝑖)]2	ORG
cana-4368	66	1	2 2𝑖−1	CARDINAL
cana-4368	66	2	1	CARDINAL
cana-4368	66	3	2𝑖	CARDINAL
cana-4368	66	4	1	CARDINAL
cana-4368	66	5	1 2	DATE
cana-4368	66	6	1074	CARDINAL
cana-4368	66	7	32	CARDINAL
cana-4368	67	1	9s	CARDINAL
cana-4368	67	2	2025) 1931	DATE
cana-4368	67	3	1 7 31	DATE
cana-4368	68	1	1	CARDINAL
cana-4368	68	2	𝑓(𝑣𝑖)]2	ORG
cana-4368	68	3	1 3 5	DATE
cana-4368	69	1	2n	CARDINAL
cana-4368	70	1	1	CARDINAL
cana-4368	72	1	𝑆𝑛	ORG
cana-4368	72	2	2𝑛	CARDINAL
cana-4368	73	1	1	CARDINAL
cana-4368	73	2	1	CARDINAL
cana-4368	74	1	𝑷𝒎	PRODUCT
cana-4368	74	2	2	CARDINAL
cana-4368	75	1	one	CARDINAL
cana-4368	75	2	𝑛. 𝑉	PERSON
cana-4368	75	3	0 ≤	QUANTITY
cana-4368	75	4	0	CARDINAL
cana-4368	75	5	1	CARDINAL
cana-4368	75	6	6	CARDINAL
cana-4368	75	7	2(𝑚𝑜𝑑4	CARDINAL
cana-4368	75	8	2	CARDINAL
cana-4368	75	9	3(𝑚𝑜𝑑4	CARDINAL
cana-4368	75	10	5	CARDINAL
cana-4368	75	11	7	CARDINAL
cana-4368	75	12	3	CARDINAL
cana-4368	75	13	2(𝑚𝑜𝑑4	CARDINAL
cana-4368	75	14	4	CARDINAL
cana-4368	75	15	0	CARDINAL
cana-4368	76	1	3	CARDINAL
cana-4368	76	2	1	CARDINAL
cana-4368	77	1	22𝑖−2	CARDINAL
cana-4368	77	2	1	CARDINAL
cana-4368	77	3	𝑣𝑖3	ORG
cana-4368	77	4	22𝑖−5	CARDINAL
cana-4368	77	5	1	CARDINAL
cana-4368	77	6	22𝑖−6	CARDINAL
cana-4368	77	7	1	CARDINAL
cana-4368	77	8	5	CARDINAL
cana-4368	77	9	3	CARDINAL
cana-4368	77	10	one	CARDINAL
cana-4368	77	11	1074	CARDINAL
cana-4368	77	12	32	CARDINAL
cana-4368	79	1	9s	CARDINAL
cana-4368	79	2	2025) 1932	DATE
cana-4368	80	1	3.3.6.theorem	CARDINAL
cana-4368	80	2	one	CARDINAL
cana-4368	80	3	2	CARDINAL
cana-4368	82	1	2𝑛	CARDINAL
cana-4368	82	2	1	CARDINAL
cana-4368	83	1	one	CARDINAL
cana-4368	83	2	0 ≤	QUANTITY
cana-4368	83	3	1 ≤	QUANTITY
cana-4368	83	4	0 ≤	QUANTITY
cana-4368	86	1	0	CARDINAL
cana-4368	86	2	1 ≤	CARDINAL
cana-4368	86	3	0 ≤	QUANTITY
cana-4368	86	4	3.3.6	CARDINAL
cana-4368	87	1	1 ≤	MONEY
cana-4368	87	2	2𝑖	CARDINAL
cana-4368	88	1	1	CARDINAL
cana-4368	89	1	0	CARDINAL
cana-4368	90	1	1 2	DATE
cana-4368	90	2	1 7 31	DATE
cana-4368	91	1	1	CARDINAL
cana-4368	91	2	1 3 5	DATE
cana-4368	91	3	2𝑛	CARDINAL
cana-4368	92	1	1	CARDINAL
cana-4368	93	1	6]2	CARDINAL
cana-4368	94	1	3	CARDINAL
cana-4368	95	1	𝑓(𝑣22))]2	ORG
cana-4368	96	1	1	CARDINAL
cana-4368	96	2	31	CARDINAL
cana-4368	97	1	1	CARDINAL
cana-4368	97	2	15 63	CARDINAL
cana-4368	98	1	22𝑛−2	CARDINAL
cana-4368	98	2	1	CARDINAL
cana-4368	98	3	𝑓(𝑣𝑖2)]2	ORG
cana-4368	98	4	1 1 1 1 1 1 1	QUANTITY
cana-4368	98	5	1 ≤	QUANTITY
cana-4368	98	6	5 ≤	QUANTITY
cana-4368	100	1	1	CARDINAL
cana-4368	100	2	1074	CARDINAL
cana-4368	100	3	32	CARDINAL
cana-4368	101	1	9s	CARDINAL
cana-4368	101	2	1933	DATE
cana-4368	102	1	1 2	CARDINAL
cana-4368	102	2	1	CARDINAL
cana-4368	102	3	4=	CARDINAL
cana-4368	102	4	1=𝑣(5−2)(j−2	CARDINAL
cana-4368	102	5	6 3 3=𝑣(3−1)(j−3	DATE
cana-4368	103	1	0=𝑣(5−2)(j−1	DATE
cana-4368	103	2	3	CARDINAL
cana-4368	103	3	2(𝑚𝑜𝑑4	CARDINAL
cana-4368	105	1	2]2	CARDINAL
cana-4368	105	2	1	CARDINAL
cana-4368	106	1	𝑓(𝑣23))]2	PERSON
cana-4368	107	1	4]2	CARDINAL
cana-4368	108	1	3	CARDINAL
cana-4368	108	2	3	CARDINAL
cana-4368	108	3	15 63	CARDINAL
cana-4368	109	1	22𝑛−2	CARDINAL
cana-4368	109	2	1 7 31	DATE
cana-4368	109	3	127	CARDINAL
cana-4368	110	1	1	CARDINAL
cana-4368	110	2	𝑓(𝑣𝑖3)]2	ORG
cana-4368	110	3	3 3 3	DATE
cana-4368	110	4	1 ≤	QUANTITY
cana-4368	110	5	6 ≤	QUANTITY
cana-4368	112	1	3	CARDINAL
cana-4368	112	2	1 2	CARDINAL
cana-4368	112	3	6 3 3=𝑣(3−1)(j−4	DATE
cana-4368	113	1	𝑣(4−2)(j−2	PERSON
cana-4368	115	1	2	CARDINAL
cana-4368	115	2	7=	CARDINAL
cana-4368	115	3	7=	CARDINAL
cana-4368	115	4	1 3 3 3 3 3 3	TIME
cana-4368	115	5	1074	CARDINAL
cana-4368	115	6	32	CARDINAL
cana-4368	116	1	9s	CARDINAL
cana-4368	116	2	1934	DATE
cana-4368	116	3	1 ≤	MONEY
cana-4368	116	4	2	CARDINAL
cana-4368	116	5	31=𝑣(5−2)(j−2	CARDINAL
cana-4368	116	6	5	CARDINAL
cana-4368	116	7	0 3=𝑣(4−2)(j−1) 15=𝑣(5−2)(j−1	DATE
cana-4368	116	8	𝑓(𝑣𝑖2)]2	ORG
cana-4368	116	9	3	CARDINAL
cana-4368	116	10	1 ≤	QUANTITY
cana-4368	116	11	7 ≤	QUANTITY
cana-4368	118	1	1	CARDINAL
cana-4368	118	2	1 2	CARDINAL
cana-4368	118	3	2	CARDINAL
cana-4368	118	4	7=𝑣(4−2)(j−2	CARDINAL
cana-4368	119	1	5	CARDINAL
cana-4368	119	2	0=𝑣(3−1)(j−3) 3=𝑣(4−2)(j−1	DATE
cana-4368	119	3	3=	DATE
cana-4368	119	4	3	CARDINAL
cana-4368	119	5	1 2	CARDINAL
cana-4368	119	6	5	CARDINAL
cana-4368	119	7	15	CARDINAL
cana-4368	119	8	3	CARDINAL
cana-4368	119	9	4	CARDINAL
cana-4368	119	10	1	CARDINAL
cana-4368	119	11	𝑓(𝑣𝑖3)]2	ORG
cana-4368	119	12	3	CARDINAL
cana-4368	119	13	1 ≤	QUANTITY
cana-4368	119	14	8 ≤	QUANTITY
cana-4368	121	1	3	CARDINAL
cana-4368	121	2	1074	CARDINAL
cana-4368	121	3	32	CARDINAL
cana-4368	122	1	9s	CARDINAL
cana-4368	122	2	1935	DATE
cana-4368	123	1	1 2	CARDINAL
cana-4368	123	2	5	CARDINAL
cana-4368	123	3	0=𝑣(3−1)(j−4) 3=𝑣(4−2)(j−2	TIME
cana-4368	123	4	3=𝑣(5−2)(j−2	DATE
cana-4368	123	5	1 7 7=𝑣(3−1)(j−3	QUANTITY
cana-4368	123	6	4=𝑣(4−2)(j−1	CARDINAL
cana-4368	123	7	4=𝑣(5−2)(j−1	CARDINAL
cana-4368	123	8	3	CARDINAL
cana-4368	124	1	one	CARDINAL
cana-4368	125	1	2𝑛	CARDINAL
cana-4368	125	2	1	CARDINAL
cana-4368	125	3	5 odd	CARDINAL
cana-4368	125	4	𝑷𝟓	CARDINAL
cana-4368	125	5	3.3.7	CARDINAL
cana-4368	128	1	0	CARDINAL
cana-4368	128	2	1	CARDINAL
cana-4368	128	3	1	CARDINAL
cana-4368	128	4	6	CARDINAL
cana-4368	128	5	2	CARDINAL
cana-4368	128	6	5	CARDINAL
cana-4368	128	7	6	CARDINAL
cana-4368	128	8	2	CARDINAL
cana-4368	128	9	5	CARDINAL
cana-4368	128	10	1	CARDINAL
cana-4368	128	11	1074	CARDINAL
cana-4368	128	12	32	CARDINAL
cana-4368	129	1	9s	CARDINAL
cana-4368	129	2	2025) 1936 https://internationalpubls.com end	DATE
cana-4368	130	1	+ 1	DATE
cana-4368	131	1	3.3.8.theorem	CARDINAL
cana-4368	133	1	2𝑛	CARDINAL
cana-4368	136	1	0	CARDINAL
cana-4368	136	2	𝑓(𝑢	GPE
cana-4368	136	3	two	CARDINAL
cana-4368	136	4	3.3.7.hence	CARDINAL
cana-4368	138	1	1	CARDINAL
cana-4368	139	1	1 ≤	MONEY
cana-4368	139	2	1(𝑚𝑜𝑑 4	DATE
cana-4368	139	3	6]2	CARDINAL
cana-4368	139	4	3	CARDINAL
cana-4368	139	5	2(𝑚𝑜𝑑 4	DATE
cana-4368	141	1	2]2	CARDINAL
cana-4368	141	2	1	CARDINAL
cana-4368	142	1	3(𝑚𝑜𝑑 4	DATE
cana-4368	143	1	5]2	CARDINAL
cana-4368	143	2	3	CARDINAL
cana-4368	143	3	0(𝑚𝑜𝑑 4	DATE
cana-4368	145	1	1	CARDINAL
cana-4368	145	2	2 ≤	QUANTITY
cana-4368	145	3	1(𝑚𝑜𝑑 4	DATE
cana-4368	145	4	2 3	DATE
cana-4368	145	5	1	CARDINAL
cana-4368	145	6	1	CARDINAL
cana-4368	145	7	30	CARDINAL
cana-4368	146	1	2	CARDINAL
cana-4368	146	2	5	CARDINAL
cana-4368	146	3	2(𝑚𝑜𝑑 4	DATE
cana-4368	146	4	2 3	DATE
cana-4368	146	5	1074	CARDINAL
cana-4368	146	6	32	CARDINAL
cana-4368	147	1	9s	CARDINAL
cana-4368	147	2	2025) 1937	DATE
cana-4368	147	3	6	CARDINAL
cana-4368	147	4	6	CARDINAL
cana-4368	148	1	25	CARDINAL
cana-4368	149	1	7	CARDINAL
cana-4368	149	2	5	CARDINAL
cana-4368	149	3	3(𝑚𝑜𝑑 4	DATE
cana-4368	149	4	2 3	DATE
cana-4368	149	5	2	CARDINAL
cana-4368	149	6	2	CARDINAL
cana-4368	149	7	29	CARDINAL
cana-4368	150	1	3	CARDINAL
cana-4368	150	2	5	CARDINAL
cana-4368	150	3	0(𝑚𝑜𝑑 4	DATE
cana-4368	150	4	2 3	DATE
cana-4368	150	5	5	CARDINAL
cana-4368	150	6	5	CARDINAL
cana-4368	150	7	26	CARDINAL
cana-4368	150	8	122 506 2042 8186	QUANTITY
cana-4368	151	1	6	CARDINAL
cana-4368	151	2	5	CARDINAL
cana-4368	153	1	2𝑛	CARDINAL
cana-4368	154	1	3	CARDINAL
cana-4368	155	1	1	CARDINAL
cana-4368	155	2	k, & seethalakshmi	ORG
cana-4368	155	3	113(7	CARDINAL
cana-4368	155	4	93	CARDINAL
cana-4368	156	1	2	CARDINAL
cana-4368	156	2	k, & seethalakshmi s.	ORG
cana-4368	157	1	2017	CARDINAL
cana-4368	157	2	14(3	CARDINAL
cana-4368	157	3	601	CARDINAL
cana-4368	158	1	1074	CARDINAL
cana-4368	158	2	32	CARDINAL
cana-4368	159	1	9s	CARDINAL
cana-4368	159	2	1938	DATE
cana-4368	160	1	3	CARDINAL
cana-4368	160	2	gallian j.a	PERSON
cana-4368	162	1	combinatorics	ORG
cana-4368	162	2	2019	DATE
cana-4368	163	1	ds6	PERSON
cana-4368	164	1	4	CARDINAL
cana-4368	164	2	massachussetts	PERSON
cana-4368	164	3	1972	DATE
cana-4368	165	1	5	CARDINAL
cana-4368	165	2	kaneria v.j	PERSON
cana-4368	165	3	meera meghpara	PERSON
cana-4368	165	4	one	CARDINAL
cana-4368	165	5	applications.2015	ORG
cana-4368	165	6	3(1	CARDINAL
cana-4368	165	7	49	CARDINAL
cana-4368	166	1	6	CARDINAL
cana-4368	166	2	one	CARDINAL
cana-4368	168	1	2014	DATE
cana-4368	168	2	6(2	CARDINAL
cana-4368	169	1	1-10	CARDINAL
cana-4368	169	2	jgraphoc.2014.6201	ORG
cana-4368	170	1	7	CARDINAL
cana-4368	170	2	52(7	CARDINAL
cana-4368	170	3	474	CARDINAL
cana-4368	171	1	8	CARDINAL
cana-4368	172	1	journal of tianjin university science and technology	ORG
cana-4368	173	1	2021;54(10	CARDINAL
cana-4368	173	2	106	CARDINAL