A184983 Number of connected 8-regular simple graphs on n vertices with girth exactly 3.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 6, 94, 10786, 3459386, 1470293676, 733351105934

Offset

0,12

Links

Table of n, a(n) for n=0..16.

Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth exactly g

Formula

a(n) = A014378(n) - A181154(n).

Example

a(0)=0 because even though the null graph (on zero vertices) is vacuously 8-regular and connected, since it is acyclic, it has infinite girth.
The a(9)=1 complete graph on 9 vertices is 8-regular; it has 36 edges and 84 triangles.

Mathematica

A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {_, _}][[All, 2]]];
A014378 = A@014378;
A181154 = A@181154;
a[n_] := A014378[[n + 1]] - A181154[[n + 1]];
a /@ Range[0, 16] (* Jean-François Alcover, Jan 27 2020 *)

Crossrefs

Connected 8-regular simple graphs with girth at least g: A014378 (g=3), A181154 (g=4).

Connected 8-regular simple graphs with girth exactly g: this sequence (g=3).

Sequence in context: A321073 A198257 A296820 * A184980 A184981 A014378

Adjacent sequences: A184980 A184981 A184982 * A184984 A184985 A184986

Keyword

nonn,hard,more

Author

Jason Kimberley, Feb 28 2011

Status

approved