cp's OEIS Frontend

A003400 Number of asymmetric (not necessarily connected) graphs with n nodes.

%I A003400 M4575 #45 Jun 02 2025 16:32:29
%S A003400 1,0,0,0,0,8,152,3696,135004,7971848,805364776,144123121972
%N A003400 Number of asymmetric (not necessarily connected) graphs with n nodes.
%C A003400 Number of simple graphs g on n nodes with |Aut(g)| = 1.
%D A003400 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 220, Section P3.4.
%D A003400 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003400 Klaus Brockhaus, <a href="/A003400/a003400.gif">The 6-node asymmetric graphs</a>
%H A003400 Zoran Maksimovic, <a href="/A075095/a075095.pdf">Number of graphs on n nodes whose automorphism group orders are k, n<=11</a>
%H A003400 Yoav Spector, Moshe Schwartz, <a href="https://arxiv.org/abs/1808.05632">Study of potential Hamiltonians for quantum graphity</a>, arXiv:1808.05632 [cond-mat.stat-mech], 2018.
%H A003400 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 A003400 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphAutomorphism.html">Graph Automorphism</a>
%H A003400 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IdentityGraph.html">Identity Graph</a>
%F A003400 a(n) = A124059(n) + A275867(n).
%o A003400 (nauty) for n in {1..10}; do geng -q ${n} | countg -q -a1 | grep altogether | awk '{print $1}'; done # - _Sean A. Irvine_, Apr 22 2015
%Y A003400 Cf. A124059 (connected simple asymmetric graphs).
%Y A003400 Cf. A275867 (disconnected simple asymmetric graphs).
%Y A003400 Cf. A000088 (simple graphs).
%K A003400 nonn,nice,hard,more
%O A003400 1,6
%A A003400 _N. J. A. Sloane_
%E A003400 a(8) and a(9) from _Eric W. Weisstein_, Jun 09 2004
%E A003400 a(10) and a(11) from Zoran Maksimovic, _Vladeta Jovovic_, Jan 21 2005
%E A003400 a(12) from _Sean A. Irvine_, Apr 22 2015