The number of near regular graphs with chromatic number

Order 2

Size	Degree sequence	χ=2
1	1 1	1

Order 3

Size	Degree sequence	χ=2	χ=3
2	2 1 1	1	0

2 2 2

Order 4

Size	Degree sequence	χ=2	χ=3	χ=4
2	1 1 1 1	1	0	0
3	2 2 1 1	1	0	0
4	2 2 2 2	1	0	0
5	3 3 2 2	0	1	0
6	3 3 3 3	0	0	1

Order 5

Size	Degree sequence	χ=2	χ=3	χ=4	χ=5
3	2 1 1 1 1	1	0	0	0
4	2 2 2 1 1	1	1	0	0
5	2 2 2 2 2	0	1	0	0
6	3 3 2 2 2	1	1	0	0
7	3 3 3 3 2	0	1	0	0
8	4 3 3 3 3	0	1	0	0
9	4 4 4 3 3	0	0	1	0
10	4 4 4 4 4	0	0	0	1

Order 6

Size	Degree sequence	χ=2	χ=3	χ=4	χ=5	χ=6
3	1 1 1 1 1 1	1	0	0	0	0
4	2 2 1 1 1 1	2	0	0	0	0
5	2 2 2 2 1 1	2	1	0	0	0
6	2 2 2 2 2 2	1	1	0	0	0
7	3 3 2 2 2 2	1	3	0	0	0
8	3 3 3 3 2 2	1	3	0	0	0
9	3 3 3 3 3 3	1	1	0	0	0
10	4 4 3 3 3 3	0	3	0	0	0
11	4 4 4 4 3 3	0	1	1	0	0
12	4 4 4 4 4 4	0	1	0	0	0
13	5 5 4 4 4 4	0	0	1	0	0
14	5 5 5 5 4 4	0	0	0	1	0
15	5 5 5 5 5 5	0	0	0	0	1

Order 7

Size	Degree sequence	χ=2	χ=3	χ=4	χ=5	χ=6	χ=7
4	2 1 1 1 1 1 1	1	0	0	0	0	0
5	2 2 2 1 1 1 1	2	1	0	0	0	0
6	2 2 2 2 2 1 1	2	2	0	0	0	0
7	2 2 2 2 2 2 2	0	2	0	0	0	0
8	3 3 2 2 2 2 2	1	6	0	0	0	0
9	3 3 3 3 2 2 2	1	9	1	0	0	0
10	3 3 3 3 3 3 2	0	4	0	0	0	0
11	4 3 3 3 3 3 3	0	3	1	0	0	0
12	4 4 4 3 3 3 3	1	6	4	0	0	0
13	4 4 4 4 4 3 3	0	4	3	0	0	0
14	4 4 4 4 4 4 4	0	1	1	0	0	0
15	5 5 4 4 4 4 4	0	1	3	0	0	0
16	5 5 5 5 4 4 4	0	1	2	0	0	0
17	5 5 5 5 5 5 4	0	0	1	0	0	0
18	6 5 5 5 5 5 5	0	0	1	0	0	0
19	6 6 6 5 5 5 5	0	0	0	1	0	0
20	6 6 6 6 6 5 5	0	0	0	0	1	0
21	6 6 6 6 6 6 6	0	0	0	0	0	1

Order 8

Size	Degree sequence	χ=2	χ=3	χ=4	χ=5	χ=6	χ=7	χ=8
4	1 1 1 1 1 1 1 1	1	0	0	0	0	0	0
5	2 2 1 1 1 1 1 1	2	0	0	0	0	0	0
6	2 2 2 2 1 1 1 1	4	1	0	0	0	0	0
7	2 2 2 2 2 2 1 1	3	3	0	0	0	0	0
8	2 2 2 2 2 2 2 2	2	1	0	0	0	0	0
9	3 3 2 2 2 2 2 2	3	10	0	0	0	0	0
10	3 3 3 3 2 2 2 2	4	23	1	0	0	0	0
11	3 3 3 3 3 3 2 2	2	17	1	0	0	0	0
12	3 3 3 3 3 3 3 3	1	4	1	0	0	0	0
13	4 4 3 3 3 3 3 3	1	24	3	0	0	0	0
14	4 4 4 4 3 3 3 3	1	40	9	0	0	0	0
15	4 4 4 4 4 4 3 3	1	17	10	0	0	0	0
16	4 4 4 4 4 4 4 4	1	2	3	0	0	0	0
17	5 5 4 4 4 4 4 4	0	7	13	0	0	0	0
18	5 5 5 5 4 4 4 4	0	6	22	0	0	0	0
19	5 5 5 5 5 5 4 4	0	2	11	0	0	0	0
20	5 5 5 5 5 5 5 5	0	0	3	0	0	0	0
21	6 6 5 5 5 5 5 5	0	1	4	1	0	0	0
22	6 6 6 6 5 5 5 5	0	0	4	1	0	0	0
23	6 6 6 6 6 6 5 5	0	0	1	1	0	0	0
24	6 6 6 6 6 6 6 6	0	0	1	0	0	0	0
25	7 7 6 6 6 6 6 6	0	0	0	1	0	0	0
26	7 7 7 7 6 6 6 6	0	0	0	0	1	0	0
27	7 7 7 7 7 7 6 6	0	0	0	0	0	1	0
28	7 7 7 7 7 7 7 7	0	0	0	0	0	0	1

Order 9

Size	Degree sequence	χ=2	χ=3	χ=4	χ=5	χ=6	χ=7	χ=8	χ=9
5	2 1 1 1 1 1 1 1 1	1	0	0	0	0	0	0	0
6	2 2 2 1 1 1 1 1 1	3	1	0	0	0	0	0	0
7	2 2 2 2 2 1 1 1 1	4	3	0	0	0	0	0	0
8	2 2 2 2 2 2 2 1 1	3	5	0	0	0	0	0	0
9	2 2 2 2 2 2 2 2 2	0	4	0	0	0	0	0	0
10	3 3 2 2 2 2 2 2 2	4	16	0	0	0	0	0	0
11	3 3 3 3 2 2 2 2 2	4	55	1	0	0	0	0	0
12	3 3 3 3 3 3 2 2 2	3	63	2	0	0	0	0	0
13	3 3 3 3 3 3 3 3 2	0	19	1	0	0	0	0	0
14	4 3 3 3 3 3 3 3 3	0	26	2	0	0	0	0	0
15	4 4 4 3 3 3 3 3 3	1	167	10	0	0	0	0	0
16	4 4 4 4 4 3 3 3 3	1	244	40	1	0	0	0	0
17	4 4 4 4 4 4 4 3 3	0	93	33	0	0	0	0	0
18	4 4 4 4 4 4 4 4 4	0	10	6	0	0	0	0	0
19	5 5 4 4 4 4 4 4 4	0	48	77	1	0	0	0	0
20	5 5 5 5 4 4 4 4 4	1	67	215	3	0	0	0	0
21	5 5 5 5 5 5 4 4 4	0	30	142	6	0	0	0	0
22	5 5 5 5 5 5 5 5 4	0	4	21	3	0	0	0	0
23	6 5 5 5 5 5 5 5 5	0	2	14	4	0	0	0	0
24	6 6 6 5 5 5 5 5 5	0	4	46	18	0	0	0	0
25	6 6 6 6 6 5 5 5 5	0	2	34	24	0	0	0	0
26	6 6 6 6 6 6 6 5 5	0	1	9	10	0	0	0	0
27	6 6 6 6 6 6 6 6 6	0	1	1	2	0	0	0	0
28	7 7 6 6 6 6 6 6 6	0	0	3	5	0	0	0	0
29	7 7 7 7 6 6 6 6 6	0	0	1	6	0	0	0	0
30	7 7 7 7 7 7 6 6 6	0	0	1	2	1	0	0	0
31	7 7 7 7 7 7 7 7 6	0	0	0	1	0	0	0	0
32	8 7 7 7 7 7 7 7 7	0	0	0	1	0	0	0	0
33	8 8 8 7 7 7 7 7 7	0	0	0	0	1	0	0	0
34	8 8 8 8 8 7 7 7 7	0	0	0	0	0	1	0	0
35	8 8 8 8 8 8 8 7 7	0	0	0	0	0	0	1	0
36	8 8 8 8 8 8 8 8 8	0	0	0	0	0	0	0	1

Order 10

Size	Degree sequence	χ=2	χ=3	χ=4	χ=5	χ=6	χ=7	χ=8	χ=9	χ=10
5	1 1 1 1 1 1 1 1 1 1	1	0	0	0	0	0	0	0	0
6	2 2 1 1 1 1 1 1 1 1	2	0	0	0	0	0	0	0	0
7	2 2 2 2 1 1 1 1 1 1	5	1	0	0	0	0	0	0	0
8	2 2 2 2 2 2 1 1 1 1	7	4	0	0	0	0	0	0	0
9	2 2 2 2 2 2 2 2 1 1	5	6	0	0	0	0	0	0	0
10	2 2 2 2 2 2 2 2 2 2	2	3	0	0	0	0	0	0	0
11	3 3 2 2 2 2 2 2 2 2	6	26	0	0	0	0	0	0	0
12	3 3 3 3 2 2 2 2 2 2	18	113	2	0	0	0	0	0	0
13	3 3 3 3 3 3 2 2 2 2	16	194	4	0	0	0	0	0	0
14	3 3 3 3 3 3 3 3 2 2	6	110	4	0	0	0	0	0	0
15	3 3 3 3 3 3 3 3 3 3	2	17	2	0	0	0	0	0	0
16	4 4 3 3 3 3 3 3 3 3	5	279	18	0	0	0	0	0	0
17	4 4 4 4 3 3 3 3 3 3	7	1290	110	0	0	0	0	0	0
18	4 4 4 4 4 4 3 3 3 3	5	1608	304	1	0	0	0	0	0
19	4 4 4 4 4 4 4 4 3 3	2	501	216	1	0	0	0	0	0
20	4 4 4 4 4 4 4 4 4 4	1	28	30	1	0	0	0	0	0
21	5 5 4 4 4 4 4 4 4 4	1	409	598	2	0	0	0	0	0
22	5 5 5 5 4 4 4 4 4 4	1	989	2753	6	0	0	0	0	0
23	5 5 5 5 5 5 4 4 4 4	1	627	3107	14	0	0	0	0	0
24	5 5 5 5 5 5 5 5 4 4	1	115	882	12	0	0	0	0	0
25	5 5 5 5 5 5 5 5 5 5	1	6	50	3	0	0	0	0	0
26	6 6 5 5 5 5 5 5 5 5	0	31	647	42	0	0	0	0	0
27	6 6 6 6 5 5 5 5 5 5	0	41	1631	246	0	0	0	0	0
28	6 6 6 6 6 6 5 5 5 5	0	21	1041	345	0	0	0	0	0
29	6 6 6 6 6 6 6 6 5 5	0	5	184	113	0	0	0	0	0
30	6 6 6 6 6 6 6 6 6 6	0	1	9	11	0	0	0	0	0
31	7 7 6 6 6 6 6 6 6 6	0	1	44	75	0	0	0	0	0
32	7 7 7 7 6 6 6 6 6 6	0	1	51	162	0	0	0	0	0
33	7 7 7 7 7 7 6 6 6 6	0	1	24	105	3	0	0	0	0
34	7 7 7 7 7 7 7 7 6 6	0	0	6	25	1	0	0	0	0
35	7 7 7 7 7 7 7 7 7 7	0	0	1	3	1	0	0	0	0
36	8 8 7 7 7 7 7 7 7 7	0	0	1	8	2	0	0	0	0
37	8 8 8 8 7 7 7 7 7 7	0	0	1	6	4	0	0	0	0
38	8 8 8 8 8 8 7 7 7 7	0	0	0	4	2	0	0	0	0
39	8 8 8 8 8 8 8 8 7 7	0	0	0	1	1	0	0	0	0
40	8 8 8 8 8 8 8 8 8 8	0	0	0	1	0	0	0	0	0
41	9 9 8 8 8 8 8 8 8 8	0	0	0	0	1	0	0	0	0
42	9 9 9 9 8 8 8 8 8 8	0	0	0	0	0	1	0	0	0
43	9 9 9 9 9 9 8 8 8 8	0	0	0	0	0	0	1	0	0
44	9 9 9 9 9 9 9 9 8 8	0	0	0	0	0	0	0	1	0
45	9 9 9 9 9 9 9 9 9 9	0	0	0	0	0	0	0	0	1

Order 11

Size	Degree sequence	χ=2	χ=3	χ=4	χ=5	χ=6	χ=7	χ=8	χ=9	χ=10	χ=11
6	2 1 1 1 1 1 1 1 1 1 1	1	0	0	0	0	0	0	0	0	0
7	2 2 2 1 1 1 1 1 1 1 1	3	1	0	0	0	0	0	0	0	0
8	2 2 2 2 2 1 1 1 1 1 1	6	3	0	0	0	0	0	0	0	0
9	2 2 2 2 2 2 2 1 1 1 1	7	8	0	0	0	0	0	0	0	0
10	2 2 2 2 2 2 2 2 2 1 1	5	10	0	0	0	0	0	0	0	0
11	2 2 2 2 2 2 2 2 2 2 2	0	6	0	0	0	0	0	0	0	0
12	3 3 2 2 2 2 2 2 2 2 2	7	42	0	0	0	0	0	0	0	0
13	3 3 3 3 2 2 2 2 2 2 2	19	234	2	0	0	0	0	0	0	0
14	3 3 3 3 3 3 2 2 2 2 2	25	558	7	0	0	0	0	0	0	0
15	3 3 3 3 3 3 3 3 2 2 2	12	487	11	0	0	0	0	0	0	0
16	3 3 3 3 3 3 3 3 3 3 2	0	116	4	0	0	0	0	0	0	0
17	4 3 3 3 3 3 3 3 3 3 3	0	206	8	0	0	0	0	0	0	0
18	4 4 4 3 3 3 3 3 3 3 3	7	3135	105	0	0	0	0	0	0	0
19	4 4 4 4 4 3 3 3 3 3 3	7	11844	619	2	0	0	0	0	0	0
20	4 4 4 4 4 4 4 3 3 3 3	5	13143	1426	3	0	0	0	0	0	0
21	4 4 4 4 4 4 4 4 4 3 3	0	3859	863	2	0	0	0	0	0	0
22	4 4 4 4 4 4 4 4 4 4 4	0	188	77	1	0	0	0	0	0	0
23	5 5 4 4 4 4 4 4 4 4 4	0	4881	4104	6	0	0	0	0	0	0
24	5 5 5 5 4 4 4 4 4 4 4	1	19481	33459	29	0	0	0	0	0	0
25	5 5 5 5 5 5 4 4 4 4 4	1	20052	63728	76	1	0	0	0	0	0
26	5 5 5 5 5 5 5 5 4 4 4	0	5947	32142	67	0	0	0	0	0	0
27	5 5 5 5 5 5 5 5 5 5 4	0	394	3340	15	0	0	0	0	0	0
28	6 5 5 5 5 5 5 5 5 5 5	0	229	3483	37	0	0	0	0	0	0
29	6 6 6 5 5 5 5 5 5 5 5	0	1107	36247	802	0	0	0	0	0	0
30	6 6 6 6 6 5 5 5 5 5 5	1	1275	78054	4526	2	0	0	0	0	0
31	6 6 6 6 6 6 6 5 5 5 5	0	477	46251	6239	3	0	0	0	0	0
32	6 6 6 6 6 6 6 6 6 5 5	0	64	7064	1861	2	0	0	0	0	0
33	6 6 6 6 6 6 6 6 6 6 6	0	3	177	84	2	0	0	0	0	0
34	7 7 6 6 6 6 6 6 6 6 6	0	11	2481	2216	16	0	0	0	0	0
35	7 7 7 7 6 6 6 6 6 6 6	0	12	5438	9032	95	0	0	0	0	0
36	7 7 7 7 7 7 6 6 6 6 6	0	8	3244	9015	205	0	0	0	0	0
37	7 7 7 7 7 7 7 7 6 6 6	0	2	628	2475	142	0	0	0	0	0
38	7 7 7 7 7 7 7 7 7 7 6	0	0	36	155	23	0	0	0	0	0
39	8 7 7 7 7 7 7 7 7 7 7	0	0	14	83	23	0	0	0	0	0
40	8 8 8 7 7 7 7 7 7 7 7	0	1	30	349	130	0	0	0	0	0
41	8 8 8 8 8 7 7 7 7 7 7	0	0	24	355	211	0	0	0	0	0
42	8 8 8 8 8 8 8 7 7 7 7	0	0	9	132	114	0	0	0	0	0
43	8 8 8 8 8 8 8 8 8 7 7	0	0	2	23	24	0	0	0	0	0
44	8 8 8 8 8 8 8 8 8 8 8	0	0	0	3	3	0	0	0	0	0
45	9 9 8 8 8 8 8 8 8 8 8	0	0	1	4	10	0	0	0	0	0
46	9 9 9 9 8 8 8 8 8 8 8	0	0	0	4	10	1	0	0	0	0
47	9 9 9 9 9 9 8 8 8 8 8	0	0	0	1	7	1	0	0	0	0
48	9 9 9 9 9 9 9 9 8 8 8	0	0	0	1	2	1	0	0	0	0
49	9 9 9 9 9 9 9 9 9 9 8	0	0	0	0	1	0	0	0	0	0
50	10 9 9 9 9 9 9 9 9 9 9	0	0	0	0	1	0	0	0	0	0
51	10 10 10 9 9 9 9 9 9 9 9	0	0	0	0	0	1	0	0	0	0
52	10 10 10 10 10 9 9 9 9 9 9	0	0	0	0	0	0	1	0	0	0
53	10 10 10 10 10 10 10 9 9 9 9	0	0	0	0	0	0	0	1	0	0
54	10 10 10 10 10 10 10 10 10 9 9	0	0	0	0	0	0	0	0	1	0
55	10 10 10 10 10 10 10 10 10 10 10	0	0	0	0	0	0	0	0	0	1