A054760 -id:A054760 - cp's OEIS frontend

A184991 Irregular triangle C(n,g) counting the connected 9-regular simple graphs on 2n vertices with girth at least g.

1, 9, 88193, 113314233813

Offset: 5

Jason Kimberley, Feb 03 2012

The first column is for girth at least 3. The row length is incremented to g-2 when 2n reaches A054760(9,g).

			1;
 9;
 88193;
 113314233813;
 ?, 1;
 ?, 1;
 ?, 14;

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

Connected 9-regular simple graphs with girth at least g: this sequence (triangle); chosen g: A014381 (g=3), A181170 (g=4).
Connected 9-regular simple graphs with girth exactly g: A184990 (triangle); chosen g: A184983 (g=3).
Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth at least g: A185131 (k=3), A184941 (k=4), A184951 (k=5), A184961 (k=6), A184971 (k=7), A184981 (k=8), this sequence (k=9).

A185200 Square array O(k,g) containing the least nontrivial order of disconnected k-regular simple graphs with girth at least g.

Original entry on oeis.org

6, 8, 8, 10, 12, 10, 12, 16, 20, 12, 14, 20, 38, 28, 14, 16, 24, 60, 52, 48, 16, 18, 28, 80, 84, 134, 60, 18, 20, 32, 100, 124

Offset: 0

Jason Kimberley, Jan 25 2011

This array is twice A054760.

(A proof of the monotonicity with respect to girth appears in Holton & Sheehan)

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g

Cf. A185204 - A185207: the triangular arrays D(n,k) counting disconnected k-regular simple graphs with girth at least g on n vertices, for 4 <= g <= 7.

cp's OEIS Frontend

A184991 Irregular triangle C(n,g) counting the connected 9-regular simple graphs on 2n vertices with girth at least g.

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