Search: a059166 -id:a059166
|
| |
|
|
A095983
|
|
Number of 2-edge-connected labeled graphs on n nodes.
|
|
+10
38
|
|
|
|
0, 0, 0, 1, 10, 253, 11968, 1047613, 169181040, 51017714393, 29180467201536, 32121680070545657, 68867078000231169536, 290155435185687263172693, 2417761175748567327193407488, 40013922635723692336670167608181, 1318910073755307133701940625759574016
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
| |
| |
|
|
| |
|
|
A004110
|
|
Number of n-node unlabeled graphs without endpoints (i.e., no nodes of degree 1).
(Formerly M1504)
|
|
+10
33
|
|
|
|
1, 1, 1, 2, 5, 16, 78, 588, 8047, 205914, 10014882, 912908876, 154636289460, 48597794716736, 28412296651708628, 31024938435794151088, 63533059372622888758054, 244916078509480823407040988, 1783406527599529094009748567708
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
CROSSREFS
|
Cf. A059166 (n-node connected labeled graphs without endpoints), A059167 (n-node labeled graphs without endpoints), A004108 (n-node connected unlabeled graphs without endpoints), A006024 (number of labeled mating graphs with n nodes), A129584 (bi-point-determining graphs).
|
| |
|
|
| |
|
|
A059167
|
|
Number of n-node labeled graphs without endpoints.
|
|
+10
30
|
|
|
|
1, 1, 1, 2, 15, 314, 13757, 1142968, 178281041, 52610850316, 29702573255587, 32446427369694348, 69254848513798160815, 291053505824567573585744, 2421830049319361003822380177, 40050220743831370293688592267252, 1319550593412053164173947687592553185
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
FORMULA
|
a(n) = Sum_{i=0..n-1} binomial(n-1, i)*b(i+1)*a(n-i-1), n>0, a(0)=1, where b(n) is number of n-node connected labeled graphs without endpoints (Cf. A059166).
|
|
|
MATHEMATICA
|
b[n_] := If[n < 3, Boole[n == 1], n!*Sum[(-1)^(n - j) * SeriesCoefficient[1 + Log[Sum[2^(k*(k - 1)/2)*x^k/k!, {k, 0, j}]], {x, 0, j}] * j^(n - j)/(n - j)!, {j, 0, n}]]; a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, i] b[i + 1] a[n - i - 1], {i, 0, n - 1}]; Table[a@ n, {n, 0, 15}] (* Michael De Vlieger, Sep 19 2016, after Vaclav Kotesovec at A059166 *)
|
|
|
CROSSREFS
|
Cf. A059166 (n-node connected labeled graphs without endpoints), A004108 (n-node connected unlabeled graphs without endpoints), A004110 (n-node unlabeled graphs without endpoints).
|
| |
|
|
| |
|
|
A327071
|
|
Number of labeled simple connected graphs with n vertices and at least one bridge, or graphs with spanning edge-connectivity 1.
|
|
+10
27
|
|
|
|
0, 0, 1, 3, 28, 475, 14736, 818643, 82367552, 15278576679, 5316021393280, 3519977478407687, 4487518206535452672, 11116767463976825779115, 53887635281876408097483776, 513758302006787897939587736715, 9668884580476067306398361085853696
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
| |
| |
|
|
| |
|
|
A004108
|
|
Number of n-node unlabeled connected graphs without endpoints.
(Formerly M2910)
|
|
+10
24
|
|
|
|
1, 1, 0, 1, 3, 11, 61, 507, 7442, 197772, 9808209, 902884343, 153723152913, 48443147912137, 28363697921914475, 30996525982586676021, 63502034385272108655525, 244852545421597419740767106, 1783161611489937453151313949442, 24603891216883233547700609793901996
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
CROSSREFS
|
Cf. A059166 (n-node connected labeled graphs without endpoints), A059167 (n-node labeled graphs without endpoints), A004110 (Euler Transform, n-node unlabeled graphs without endpoints).
|
| |
|
|
| |
|
|
A245797
|
|
The number of labeled graphs of n vertices that have endpoints, where an endpoint is a vertex with degree 1.
|
|
+10
22
|
|
|
|
0, 1, 6, 49, 710, 19011, 954184, 90154415, 16108626420, 5481798833245, 3582369649269620, 4532127781040045649, 11177949079089720090800, 54050029251399545975868271, 514598463471970554205910304780, 9677402372862708729859372687791391
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
CROSSREFS
|
Cf. A001187, A006129, A059166, A059167, A100743, A136284, A327079, A327098, A327103, A327229, A327230.
|
| |
|
|
| |
|
|
A327227
|
|
Number of labeled simple graphs covering n vertices with at least one endpoint/leaf.
|
|
+10
22
|
|
|
|
0, 0, 1, 3, 31, 515, 15381, 834491, 83016613, 15330074139, 5324658838645, 3522941267488973, 4489497643961740521, 11119309286377621015089, 53893949089393110881259181, 513788884660608277842596504415, 9669175277199248753133328740702449
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
CROSSREFS
|
Cf. A001187, A006129, A059166, A059167, A100743, A136284, A327079, A327098, A327103, A327228, A327230.
|
| |
|
|
| |
|
|
A100743
|
|
Number of labeled n-vertex graphs without vertices of degree <=1.
|
|
+10
14
|
|
|
|
1, 0, 0, 1, 10, 253, 12068, 1052793, 169505868, 51046350021, 29184353055900, 32122563615242615, 68867440268165982320, 290155715157676330952559, 2417761590648159731258579164, 40013923822242935823157820555477, 1318910080336893719646370269435043184
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
| |
| |
|
|
| |
|
|
A327079
|
|
Number of labeled simple connected graphs covering n vertices with at least one bridge that is not an endpoint/leaf (non-spanning edge-connectivity 1).
|
|
+10
14
|
|
|
|
0, 0, 1, 0, 12, 180, 4200, 157920, 9673664, 1011129840, 190600639200, 67674822473280, 46325637863907072, 61746583700640860736, 161051184122415878112640, 824849999242893693424992000, 8317799170120961768715123118080
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
| |
| |
|
|
| |
|
|
A327369
|
|
Triangle read by rows where T(n,k) is the number of labeled simple graphs with n vertices and exactly k endpoints (vertices of degree 1).
|
|
+10
14
|
|
|
|
1, 1, 0, 1, 0, 1, 2, 0, 6, 0, 15, 12, 30, 4, 3, 314, 320, 260, 80, 50, 0, 13757, 10890, 5445, 1860, 735, 66, 15, 1142968, 640836, 228564, 64680, 16800, 2772, 532, 0, 178281041, 68362504, 17288852, 3666600, 702030, 115416, 17892, 1016, 105
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
| |
| |
|
Search completed in 0.015 seconds
|
