Combinatorial Data

I make available some of my combinatorial 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.


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
012345
6789
10
21
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
012345
6789
10
22
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
012345
6789
10
21
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
000
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
012345
6789
10
21
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
012345
6789
10
22
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
144801051
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
012345
6789
10
21
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
012345
6789
10
21
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
012345
6789
10
20
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
000
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
012345
6789
10
21
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
012345
6789
10
20
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
000
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