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A014381 Number of connected regular graphs of degree 9 with 2n nodes. 15
1, 0, 0, 0, 0, 1, 9, 88193, 113314233813 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

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

LINKS

Table of n, a(n) for n=0..8.

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.

FORMULA

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

EXAMPLE

The null graph on 0 vertices is vacuously connected and 9-regular; 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).

9-regular simple graphs: this sequence (connected), A185293 (disconnected).

Connected 9-regular simple graphs with girth at least g: this sequence (g=3), A181170 (g=4).

Connected 9-regular 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

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Last modified November 27 04:47 EST 2014. Contains 250155 sequences.