Graph Data

I make available some of my graph data. The following tables depict graph counts related to graph connectivity (some of them now listed also in www.oeis.org). Every data file provided contains a compressed list of the first 20 MB of the smallest graphs in question (in graph6 format without graph6 header). Some data files exceed the given numbers. Since there is no standard definition of (edge-)connectivity for K0 and K1, these two graphs (n<2) are excluded.

Dr. Jens M. Schmidt, Jan 18 2021 (Homepage)

simple non-isomorphic n-vertex graphs of edge-connectivity k

data
OEIS
 data
OEIS
 data
OEIS
 data
OEIS
 data
OEIS
 data
OEIS
 data
OEIS
 data
OEIS		 data
OEIS		 data
OEIS		 data
OEIS
n\k
 0 1 2 3 4 5
 6 7 8 9
 10
2 1
 1
 0
 0
 0
 0
 0
 0
 0
 0
 0
3
 2
 1
 1
 0
 0
 0
 0
 0
 0
 0
 0
4
 5
 3
 2
 1
 0
 0
 0
 0
 0
 0
 0
5
 13
 10
 8
 2
 1
 0
 0
 0
 0
 0
 0
6
 44
 52
 41
 15
 3
 1
 0
 0
 0
 0
 0
7
 191
 351
 352
 121
 25
 3
 1
 0
 0
 0
 0
8
 1229
 3714
 4820
 2159
 378
 41
 4
 1
 0
 0
 0
9
 13588
 63638
 113256
 68715
 14306
 1095
 65
 4
 1
 0
 0
10
 288597
 1912203
 4602039
 3952378
 1141575
 104829
 3441
 100
 5
 1
 0
11
 12297299
 103882478
 325754696
 389968005
 164245876
 21981199
 857365
 10790
 150
 5
 1
12

40348545658
 65161587084
 39637942895
 8077770931
 487560158
 7772555
 36095
 225
 6
13





466534106494
 12294282710
 77299066
 124046
 327
14







348666442245
 835008556
 448757
15









9714022948


k-edge-connected simple non-isomorphic n-vertex graphs

data
OEIS
 data
OEIS
 data
OEIS
 data
OEIS		 data
OEIS		 data
OEIS		 data
OEIS		 data
OEIS		 data
OEIS		 data
OEIS		 data
OEIS
n\k
 0 1 2 3 4 5
 6 7 8 9
 10
2 2
 1
 0
 0
 0
 0
 0
 0
 0
 0
 0
3
 4
 2
 1
 0
 0
 0
 0
 0
 0
 0
 0
4
 11
 6
 3
 1
 0
 0
 0
 0
 0
 0
 0
5
 34
 21
 11
 3
 1
 0
 0
 0
 0
 0
 0
6
 156
 112
 60
 19
 4
 1
 0
 0
 0
 0
 0
7
 1044
 853
 502
 150
 29
 4
 1
 0
 0
 0
 0
8
 12346
 11117
 7403
 2583
 424
 46
 5
 1
 0
 0
 0
9
 274668
 261080
 197442
 84186
 15471
 1165
 70
 5
 1
 0
 0
10
 12005168
 11716571
 9804368
 5202329
 1249951
 108376
 3547
 106
 6
 1
 0
11
 1018997864
 1006700565
 902818087
 577063391
 187095386
 22849510
 868311
 10946
 156
 6
 1
12




8573139971
 495369040
 7808882
 36327
 232
 7
13





478905812650
 12371706156
 77423446
 124380
 334
14







349501900040
 835457795
 449239
15









9715703918


non-isomorphic minimally k-edge-connected n-vertex graphs

OEIS
 OEIS
 OEIS
 OEIS OEIS OEIS OEIS OEIS OEIS OEIS OEIS
n\k
 0 1 2 3 4 5
 6 7 8 9
 10
2 1
 1
 0
 0
 0
 0
 0
 0
 0
 0
 0
3
 1
 1
 1
 0
 0
 0
 0
 0
 0
 0
 0
4
 1
 2
 1
 1
 0 0 0
 0
 0
 0
 0
5
 1
 3
 3
 1
 1
 0
 0
 0
 0
 0
 0
6
 1
 6
 4
 4
 1
 1
 0
 0
 0
 0
 0
7
 1
 11
 11
 8
 5
 1
 1
 0
 0
 0
 0
8
 1
 23
 23
 34
 17
 7
 1
 1
 0
 0
 0
9
 1
 47
 63
 118
 114
 32
 9
 1
 1
 0
 0
10
 1
 106
 159
 613
 940
 483
 71
 12
 1
 1
 0
11
 1
 235
 459
 3240
 11275
 10877 2516
 167
 15
 1
 1
12
 1
 551
 1331
 20207
 167504
 386198
 176323
 15891
 375
 20
 1
13
 1
 1301
 4083
 135217



116394
 1107
 25
14
 1
 3159
 12750
 989373





2498
15
 1
 7741
 41142









simple non-isomorphic n-vertex graphs of connectivity k

data
OEIS
 data
OEIS
 data
OEIS
 data
OEIS
 data
OEIS
 data
OEIS		 data
OEIS		 data
OEIS		 data
OEIS		 data
OEIS		 data
OEIS
n\k
 0 1 2 3 4 5
 6 7 8 9
 10
2 1
 1
 0
 0
 0
 0
 0
 0
 0
 0
 0
3
 2
 1
 1
 0
 0
 0
 0
 0
 0
 0
 0
4
 5
 3
 2
 1
 0
 0
 0
 0
 0
 0
 0
5
 13
 11
 7
 2
 1
 0
 0
 0
 0
 0
 0
6
 44
 56
 39
 13
 3
 1
 0
 0
 0
 0
 0
7
 191
 385
 332
 111
 21
 3
 1
 0
 0
 0
 0
8
 1229
 3994
 4735
 2004
 345
 34
 4
 1
 0
 0
 0
9
 13588
 67014
 113176
 66410
 13429
 992
 54
 4
 1
 0
 0
10
 288597
 1973029
 4629463
 3902344
 1109105
 99419
 3124
 81
 5
 1
 0
11
 12297299
 105731474
 327695586
 388624106
 162318088
 21500415
 820956
 9813
 121
 5
 1
12



39460518399
 8004834513
 479476753
 7499483
 32960
 179
 6
13








113778
 257
14









413672
15












k-connected simple non-isomorphic n-vertex graphs

data
OEIS
 data
OEIS
 data
OEIS
 data
OEIS
 data
OEIS
 data
OEIS
 data
OEIS		 data
OEIS		 data
OEIS		 data
OEIS		 data
OEIS
n\k
 0 1 2 3 4 5
 6 7 8 9
 10
2 2
 1
 0
 0
 0
 0
 0
 0
 0
 0
 0
3
 4
 2
 1
 0
 0
 0
 0
 0
 0
 0
 0
4
 11
 6
 3
 1
 0
 0
 0
 0
 0
 0
 0
5
 34
 21
 10
 3
 1
 0
 0
 0
 0
 0
 0
6
 156
 112
 56
 17
 4
 1
 0
 0
 0
 0
 0
7
 1044
 853
 468
 136
 25
 4
 1
 0
 0
 0
 0
8
 12346
 11117
 7123
 2388
 384
 39
 5
 1
 0
 0
 0
9
 274668
 261080
 194066
 80890
 14480 1051
 59
 5
 1
 0
 0
10
 12005168 11716571 9743542
 5114079
 1211735
 102630
 3211
 87
 6
 1
 0
11
 1018997864 1006700565
 900969091
 573273505
 184649399
 22331311
 830896
 9940
 127
 6
 1
12





487009382
7532629
 33146
 186
 7
13







75146405
114042
 264
14









414048
15












non-isomorphic minimally k-connected n-vertex graphs

OEIS
 OEIS
 OEIS
 OEIS OEIS OEIS OEIS OEIS OEIS OEIS OEIS
n\k
 0 1 2 3 4 5
 6 7 8 9
 10
2 1
 1
 0
 0
 0
 0
 0
 0
 0
 0
 0
3
 1
 1
 1
 0
 0
 0
 0
 0
 0
 0
 0
4
 1
 2
 1
 1
 0
 0
 0
 0
 0
 0
 0
5
 1
 3
 2
 1
 1
 0
 0
 0
 0
 0
 0
6
 1
 6
 3
 3
 1
 1
 0
 0
 0
 0
 0
7
 1
 11
 6
 5
 5
 1
 1
 0
 0
 0
 0
8
 1
 23
 12
 18
 13
 5
 1
 1
 0
 0
 0
9
 1
 47
 28
 57
 83
 26
 7
 1
 1
 0
 0
10
 1
 106
 68
 285
 704
 397
 57
 10
 1
 1
 0
11
 1
 235
 184
 1513
 8738
 9240
 2206
 133
 11
 1
 1
12
 1
 551
 526
 9824
 136391
 346234
 162374
 14370
 320
 15
 1
13
 1
 1301
 1602
 69536
 2503248
 15088613
 16601226
 3210677
 108300
 908
 19
14
 1
 3159
 5075
 540622
 51882628



912344
 2186
15
 1
 7741
 16711
 4494676









simple non-isomorphic n-vertex graphs of essential connectivity k
(if there is no edge-separating separator, of connectivity k)












n\k
 0 1 2 3 4 5
 6 7 8 9
 10
2 1
 1
 0
 0
 0
 0
 0
 0
 0
 0
 0
3
 2
 1
 1
 0
 0
 0
 0
 0
 0
 0
 0
4
 5
 3
 2
 1
 0
 0
 0
 0
 0
 0
 0
5
 13
 11
 7
 2
 1
 0
 0
 0
 0
 0
 0
6
 41
 51
 47
 13
 3
 1
 0
 0
 0
 0
 0
7
 148
 274
 373
 224
 21
 3
 1
 0
 0
 0
 0
8
 674
 1843
 3886
 4188
 1716
 23
 4
 1
 0
 0
 0
9
 4049
 16746
 55686
 101795
 77227
 19106
 54
 4
 1
 0
 0
10
 35253
 228518
 1210838
 3559572
 4575227
 2095596
 300077
 81
 5
 1
 0
11
 509217
 5406817
 42394810
 187473868
 385705441
 310868016
 80490925
 6148643
 121
 5
 1
12










13










14










15












simple non-isomorphic n-vertex graphs of essential connectivity k and connectivity k-1












n\k
 0 1 2 3 4 5
 6 7 8 9
 10
2 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
3
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
4
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
5
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
6
 0
 3
 8
 0
 0
 0
 0
 0
 0
 0
 0
7
 0
 21
 102
 83
 0
 0
 0
 0
 0
 0
 0
8
 0
 147
 1278
 1853
 689
 0
 0
 0 0 0
 0
9
 0
 1147
 19430
 49533
 32150
 5316
 0
 0
 0
 0
 0
10
 0
 11930
 416657
 1820699
 2001196
 604126
 43941
 0
 0
 0
 0
11
 0
 185711
 13631965
 97836754
 176314350
 90997449
 12725569
 391331
 0
 0
 0
12






302186106
 3781740
 0
 0
13








39480557
 0
14










15












simple non-isomorphic n-vertex graphs of cyclic connectivity k
(if there is no cycle-separating separator, of essential connectivity k)












n\k
 0 1 2 3 4 5
 6 7 8 9
 10
2 1
 1
 0
 0
 0
 0
 0
 0
 0
 0
 0
3
 2
 1
 1
 0
 0
 0
 0
 0
 0
 0
 0
4
 5
 3
 2
 1
 0
 0
 0
 0
 0
 0
 0
5
 13
 11
 7
 2
 1
 0
 0
 0
 0
 0
 0
6
 41
 51
 47
 13
 3
 1
 0
 0
 0
 0
 0
7
 148
 274
 373
 224
 21
 3
 1
 0
 0
 0
 0
8
 674
 1825
 3904
 4188
 1716
 34
 4
 1
 0
 0
 0
9
 4043
 16117
 55070
 103046
 77227
 19106
 54
 4
 1
 0
 0
10
 35044
 206844
 1122868
 3535451
 4709201
 2095596
 300077
 81
 5
 1
 0
11
 499874








1
12










13










14










15












simple non-isomorphic n-vertex graphs of cyclic connectivity k and connectivity k-1












n\k
 0 1 2 3 4 5
 6 7 8 9
 10
2 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
3
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
4
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
5
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
6
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
7
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
8
 0
 6 18
 0
 0
 0
 0
 0 0 0
 0
9
 0
 99 977 1862
 0
 0
 0
 0
 0
 0
 0
10
 0
 1450 35358 168092
 148829 0
 0
 0
 0
 0
 0
11
 0
 21493 1167941
 11542327
 25628220
 10543887
 0
 0
 0
 0
 0
12






0
 0
 0
 0
13







0
 0
 0
14








0
 0
15









0