Data

Chromatic Numbers of Small Graphs

• Chromatic numbers of simple graphs on 7 or fewer vertices.

• 	$n = 1$	2	3	4	5	6	7
  $\chi = 1$	0	0	0	0	0	0	0
  2	1	1	3	5	17	44	182
  3	0	1	2	12	64	475	5036
  4	0	0	1	3	26	282	5009
  5	0	0	0	1	4	46	809
  6	0	0	0	0	1	5	74
  7	0	0	0	0	0	1	6
  8	0	0	0	0	0	0	1
  Total:	1	2	6	21	112	853	11117

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• Chromatic numbers of $k$-regular simple graphs on 10 or fewer vertices.

• 	$\chi = 1$	2	3	4	5	6	7	8	9
  $k = 1$	0	0	0	0	0	0	0	0	0
  2	5	6	4	2	1	0	0	0	0
  3	0	13	22	42	6	2	0	0	0
  4	0	0	4	40	53	11	1	0	0
  5	0	0	0	2	3	13	3	1	0
  6	0	0	0	0	1	0	1	0	0
  7	0	0	0	0	0	1	0	0	0
  8	0	0	0	0	0	0	1	0	0
  9	0	0	0	0	0	0	0	1	0
  10	0	0	0	0	0	0	0	0	1
  Total:	5	19	30	86	64	27	6	2	1

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• Chromatic numbers of connected $k$-regular simple graphs on 10 or fewer vertices.

• 	$\chi = 1$	2	3	4	5	6	7	8	9
  $k = 1$	0	0	0	0	0	0	0	0	0
  2	1	4	4	2	1	0	0	0	0
  3	0	4	22	42	6	2	0	0	0
  4	0	0	1	40	53	11	1	0	0
  5	0	0	0	1	3	13	3	1	0
  6	0	0	0	0	1	0	1	0	0
  7	0	0	0	0	0	1	0	0	0
  8	0	0	0	0	0	0	1	0	0
  9	0	0	0	0	0	0	0	1	0
  10	0	0	0	0	0	0	0	0	1
  Total:	1	8	27	85	64	27	6	2	1

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Chromatic Indices of Small Graphs

• Chromatic numbers of connected simple graphs of order 9 or less and size 10 or less.

• 	$n = 2$	3	4	5	6	7	8	9
  $\chi = 2$	0	1	2	1	2	1	2	1
  3	0	1	4	8	26	58	162	254
  4	0	0	0	10	45	193	435	538
  5	0	0	0	2	21	80	187	215
  6	0	0	0	0	0	18	39	59
  7	0	0	0	0	0	0	9	13
  8	0	0	0	0	0	0	0	4
  9	0	0	0	0	0	0	0	0
  Total:	0	2	6	21	94	350	834	1084

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• Chromatic numbers of simple graphs of order 9 or less and size 10 or less.

• 	$n = 2$	3	4	5	6	7	8	9
  $\chi = 2$	0	1	3	5	10	15	26	37
  3	0	1	5	14	46	123	350	772
  4	0	0	0	10	55	258	749	1476
  5	0	0	0	2	23	104	305	568
  6	0	0	0	0	0	18	57	125
  7	0	0	0	0	0	0	9	22
  8	0	0	0	0	0	0	0	4
  9	0	0	0	0	0	0	0	0
  Total:	0	2	8	31	134	518	1496	3004

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