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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,14

COMMENTS

Since the nontrivial 10-regular graph with the least number of vertices is K_11, there are no disconnected 10-regular graphs with less than 22 vertices. Thus for n<22 this sequence also counts the number of all 10-regular graphs on n 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. 131-135 of Probl\`{e}mes combinatoires et th\'{e}orie des graphes (Orsay, 9-13 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), 137-146.

LINKS

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

Jason Kimberley, Index of sequences counting connected k-regular 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 10-regular; since it is acyclic, it has infinite girth. [From Jason Kimberley, Feb 10 2011]

CROSSREFS

10-regular 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: A180476 A003399 A180359 * A035308 A212925 A185277

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

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Last modified August 1 00:45 EDT 2014. Contains 245104 sequences.