

A014382


Number of connected regular graphs of degree 10 with n nodes.


13



1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 10, 540, 805579, 2585136741, 9799685588961
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OFFSET

0,14


COMMENTS

Since the nontrivial 10regular graph with the least number of vertices is K_11, there are no disconnected 10regular graphs with less than 22 vertices. Thus for n<22 this sequence also gives the number of all 10regular graphs on n 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.
M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137146.


LINKS

Table of n, a(n) for n=0..17.
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.


EXAMPLE

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


CROSSREFS

10regular simple graphs: this sequence (connected), A185203 (disconnected).
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), A014381 (k=9), this sequence (k=10), A014384 (k=11).
Sequence in context: A003399 A180359 A289200 * A035308 A212925 A273032
Adjacent sequences: A014379 A014380 A014381 * A014383 A014384 A014385


KEYWORD

nonn,hard,more


AUTHOR

N. J. A. Sloane


EXTENSIONS

Using the symmetry of A051031, a(16) and a(17) from Jason Kimberley, Sep 25 2009 and Jan 03 2011


STATUS

approved



