

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. [From 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 Probl\`{e}mes combinatoires et th\'{e}orie 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. [From 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 A034995 A109464
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



