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A005177 Number of connected regular graphs with n nodes.
(Formerly M0347)
1, 1, 1, 1, 2, 2, 5, 4, 17, 22, 167, 539, 18979, 389436, 50314796, 2942198440, 1698517036411, 442786966115560, 649978211591600286, 429712868499646474880, 2886054228478618211088773, 8835589045148342277771518309, 152929279364927228928021274993215, 1207932509391069805495173301992815105, 99162609848561525198669168640159162918815 (list; graph; refs; listen; history; text; internal format)



N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=0..24.

E. Friedman, Illustration of small graphs

Daniel R. Herber, Enhancements to the perfect matching approach for graph enumeration-based engineering challenges, Proceedings of the ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE 2020).

Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

Markus Meringer, GENREG: A program for Connected Regular Graphs

M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146. [Jason Kimberley, Sep 23 2009]

Peter Steinbach, Field Guide to Simple Graphs, Volume 1, Part 17 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)

Eric Weisstein's World of Mathematics, Regular Graph.


a(n) = sum of the n-th row of A068934.

a(n) = A165647(n) - A165648(n).

This sequence is the inverse Euler transformation of A165647.


Regular simple graphs of any degree: this sequence (connected), A068932 (disconnected), A005176 (not necessarily connected), A275420 (multisets).

Connected regular graphs of any degree with girth at least g: this sequence (g=3), A186724 (g=4), A186725 (g=5), A186726 (g=6), A186727 (g=7), A186728 (g=8), A186729 (g=9).

Connected regular simple graphs: this sequence (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), A014382 (k=10), A014384 (k=11). - Jason Kimberley, Nov 03 2011

Sequence in context: A054079 A210713 A283825 * A253600 A045537 A243941

Adjacent sequences:  A005174 A005175 A005176 * A005178 A005179 A005180




N. J. A. Sloane


More terms from David Wasserman, Mar 08 2002

a(15) from Giovanni Resta, Feb 05 2009

Terms are sums of the output from M. Meringer's genreg software. To complete a(16) it was run by Jason Kimberley, Sep 23 2009

a(0)=1 (due to the empty graph being vacuously connected and regular) inserted by Jason Kimberley, Apr 11 2012

a(17)-a(21) from Andrew Howroyd, Mar 10 2020

a(22)-a(24) from Andrew Howroyd, May 19 2020



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Last modified April 16 03:25 EDT 2021. Contains 343030 sequences. (Running on oeis4.)