

A294217


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


9



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, 1, 1044, 3843, 4869, 2166, 378, 41, 4, 1, 12346, 64455, 113622, 68774, 14306, 1095, 65, 4, 1, 274668, 1921532, 4605833, 3953162, 1141597, 104829, 3441, 100, 5, 1
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OFFSET

1,4


COMMENTS

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


LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..210 (first 20 rows)
Eric Weisstein's World of Mathematics, Minimum Vertex Degree


FORMULA

T(n, 0) = A000088(n1).
T(n, n2) = A004526(n) for n > 1.
T(n, n1) = 1.
T(n, k) = A263293(n, n1k).  Andrew Howroyd, Sep 03 2019


EXAMPLE

Triangle begins:
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, 1;
...


CROSSREFS

Row sums are A000088 (simple graphs on n nodes).
Columns k=0..2 are A000088(n1), A324693, A324670.
Cf. A263293 (triangle of nnode maximum vertex degree counts).
The labeled version is A327366.
Cf. A002494, A004110, A261919, A327227, A327230, A327335, A327372.
Sequence in context: A322038 A123521 A322115 * A123246 A122518 A346031
Adjacent sequences: A294214 A294215 A294216 * A294218 A294219 A294220


KEYWORD

nonn,tabl


AUTHOR

Eric W. Weisstein, Oct 25 2017


STATUS

approved



