

A014381


Number of connected regular graphs of degree 9 with 2n nodes.


15




OFFSET

0,7


COMMENTS

Since the nontrivial 9regular graph with the least number of vertices is K_10, there are no disconnected 9regular graphs with less than 20 vertices. Thus for n<20 this sequence also gives the number of all 9regular graphs on 2n vertices.  Jason Kimberley, Sep 25 2009


REFERENCES

CRC Handbook of Combinatorial Designs, 1996, p. 648.
I. A. Faradzev, Constructive enumeration of combinatorial objects, pp. 131135 of Problèmes combinatoires et théorie des graphes (Orsay, 913 Juillet 1976). Colloq. Internat. du C.N.R.S., No. 260, Centre Nat. Recherche Scient., Paris, 1978.


LINKS

Table of n, a(n) for n=0..8.
Jason Kimberley, Index of sequences counting connected kregular simple graphs with girth at least g
M. Meringer, Tables of Regular Graphs
Eric Weisstein's World of Mathematics, Regular Graph.


FORMULA

a(n) = A184993(n) + A181170(n).


EXAMPLE

The null graph on 0 vertices is vacuously connected and 9regular; since it is acyclic, it has infinite girth.  Jason Kimberley, Feb 10 2011


CROSSREFS

Connected regular simple graphs A005177 (any degree), A068934 (triangular array), specified degree k: A002851 (k=3), A006820 (k=4), A006821 (k=5), A006822 (k=6), A014377 (k=7), A014378 (k=8), this sequence (k=9), A014382 (k=10), A014384 (k=11).
9regular simple graphs: this sequence (connected), A185293 (disconnected).
Connected 9regular simple graphs with girth at least g: this sequence (g=3), A181170 (g=4).
Connected 9regular simple graphs with girth exactly g: A184993 (g=3).
Sequence in context: A058456 * A184991 A184993 A185293 A281360 A034995
Adjacent sequences: A014378 A014379 A014380 * A014382 A014383 A014384


KEYWORD

nonn,more,hard


AUTHOR

N. J. A. Sloane


EXTENSIONS

a(8) appended using the symmetry of A051031 by Jason Kimberley, Sep 25 2009


STATUS

approved



