cp's OEIS Frontend

A294217 Triangle read by rows: T(n,k) is the number of graphs with n vertices and minimum vertex degree k, (0 <= k < n).

%I A294217 #25 Feb 16 2025 08:33:51
%S A294217 1,1,1,2,1,1,4,4,2,1,11,12,8,2,1,34,60,43,15,3,1,156,378,360,121,25,3,
%T A294217 1,1044,3843,4869,2166,378,41,4,1,12346,64455,113622,68774,14306,1095,
%U A294217 65,4,1,274668,1921532,4605833,3953162,1141597,104829,3441,100,5,1
%N A294217 Triangle read by rows: T(n,k) is the number of graphs with n vertices and minimum vertex degree k, (0 <= k < n).
%C A294217 Terms may be computed without generating each graph by enumerating the number of graphs by degree sequence. A PARI program showing this technique for graphs with labeled vertices is given in A327366. Burnside's lemma can be used to extend this method to the unlabeled case. - _Andrew Howroyd_, Mar 10 2020
%H A294217 Andrew Howroyd, <a href="/A294217/b294217.txt">Table of n, a(n) for n = 1..210</a> (first 20 rows)
%H A294217 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimumVertexDegree.html">Minimum Vertex Degree</a>
%F A294217 T(n, 0) = A000088(n-1).
%F A294217 T(n, n-2) = A004526(n) for n > 1.
%F A294217 T(n, n-1) = 1.
%F A294217 T(n, k) = A263293(n, n-1-k). - _Andrew Howroyd_, Sep 03 2019
%e A294217 Triangle begins:
%e A294217     1;
%e A294217     1,   1;
%e A294217     2,   1,   1;
%e A294217     4,   4,   2,   1;
%e A294217    11,  12,   8,   2,  1;
%e A294217    34,  60,  43,  15,  3, 1;
%e A294217   156, 378, 360, 121, 25, 3, 1;
%e A294217   ...
%Y A294217 Row sums are A000088 (simple graphs on n nodes).
%Y A294217 Columns k=0..2 are A000088(n-1), A324693, A324670.
%Y A294217 Cf. A263293 (triangle of n-node maximum vertex degree counts).
%Y A294217 The labeled version is A327366.
%Y A294217 Cf. A002494, A004110, A261919, A327227, A327230, A327335, A327372.
%K A294217 nonn,tabl
%O A294217 1,4
%A A294217 _Eric W. Weisstein_, Oct 25 2017