A003400 Number of asymmetric (not necessarily connected) graphs with n nodes. (Formerly M4575)

1, 0, 0, 0, 0, 8, 152, 3696, 135004, 7971848, 805364776, 144123121972

Offset

1,6

Comments

Number of simple graphs g on n nodes with |Aut(g)| = 1.

References

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 220, Section P3.4.

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

Links

Table of n, a(n) for n=1..12.

Klaus Brockhaus, The 6-node asymmetric graphs

Zoran Maksimovic, Number of graphs on n nodes whose automorphism group orders are k, n<=11

Yoav Spector, Moshe Schwartz, Study of potential Hamiltonians for quantum graphity, arXiv:1808.05632 [cond-mat.stat-mech], 2018.

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, Graph Automorphism

Eric Weisstein's World of Mathematics, Identity Graph

Formula

a(n) = A124059(n) + A275867(n).

Prog

(nauty/bash) for n in {1..10}; do geng -q ${n} | countg -q -a1 | grep altogether | awk '{print $1}'; done # - Sean A. Irvine, Apr 22 2015

Crossrefs

Cf. A124059 (connected simple asymmetric graphs).

Cf. A275867 (disconnected simple asymmetric graphs).

Cf. A000088 (simple graphs).

Sequence in context: A221732 A249931 A123770 * A360338 A059510 A264708

Adjacent sequences: A003397 A003398 A003399 * A003401 A003402 A003403

Keyword

nonn,nice,hard,more

Author

N. J. A. Sloane

Extensions

a(8) and a(9) from Eric W. Weisstein, Jun 09 2004

a(10) and a(11) from Zoran Maksimovic, Vladeta Jovovic, Jan 21 2005

a(12) from Sean A. Irvine, Apr 22 2015

Status

approved