cp's OEIS Frontend

A005177 Number of connected regular graphs with n nodes.

%I A005177 M0347 #57 Feb 16 2025 08:32:28
%S A005177 1,1,1,1,2,2,5,4,17,22,167,539,18979,389436,50314796,2942198440,
%T A005177 1698517036411,442786966115560,649978211591600286,
%U A005177 429712868499646474880,2886054228478618211088773,8835589045148342277771518309,152929279364927228928021274993215,1207932509391069805495173301992815105,99162609848561525198669168640159162918815
%N A005177 Number of connected regular graphs with n nodes.
%D A005177 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005177 E. Friedman, <a href="/A000088/a000088a.gif">Illustration of small graphs</a>
%H A005177 Daniel R. Herber, <a href="https://www.engr.colostate.edu/~drherber/files/Herber2020b.pdf">Enhancements to the perfect matching approach for graph enumeration-based engineering challenges</a>, Proceedings of the ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE 2020).
%H A005177 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_k-reg_girth_ge_g_index">Index of sequences counting connected k-regular simple graphs with girth at least g</a>
%H A005177 Markus Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">GENREG: A program for Connected Regular Graphs</a>
%H A005177 M. Meringer, <a href="http://dx.doi.org/10.1002/(SICI)1097-0118(199902)30:2&lt;137::AID-JGT7&gt;3.0.CO;2-G">Fast generation of regular graphs and construction of cages</a>, J. Graph Theory 30 (2) (1999) 137-146. [_Jason Kimberley_, Sep 23 2009]
%H A005177 Peter Steinbach, <a href="/A000088/a000088_17.pdf">Field Guide to Simple Graphs, Volume 1</a>, Part 17 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
%H A005177 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RegularGraph.html">Regular Graph.</a>
%F A005177 a(n) = sum of the n-th row of A068934.
%F A005177 a(n) = A165647(n) - A165648(n).
%F A005177 This sequence is the inverse Euler transformation of A165647.
%Y A005177 Regular simple graphs of any degree: this sequence (connected), A068932 (disconnected), A005176 (not necessarily connected), A275420 (multisets).
%Y A005177 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).
%Y A005177 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
%K A005177 nonn,nice,hard
%O A005177 0,5
%A A005177 _N. J. A. Sloane_
%E A005177 More terms from _David Wasserman_, Mar 08 2002
%E A005177 a(15) from _Giovanni Resta_, Feb 05 2009
%E A005177 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
%E A005177 a(0)=1 (due to the empty graph being vacuously connected and regular) inserted by _Jason Kimberley_, Apr 11 2012
%E A005177 a(17)-a(21) from _Andrew Howroyd_, Mar 10 2020
%E A005177 a(22)-a(24) from _Andrew Howroyd_, May 19 2020