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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)



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. - Jason Kimberley, Sep 25 2009


CRC Handbook of Combinatorial Designs, 1996, p. 648.

I. A. Faradzev, Constructive enumeration of combinatorial objects, pp. 131-135 of Problèmes combinatoires et théorie 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.


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.


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


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 A273032

Adjacent sequences:  A014379 A014380 A014381 * A014383 A014384 A014385




N. J. A. Sloane


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



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Last modified January 22 15:32 EST 2017. Contains 281133 sequences.