A003400 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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

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).

KEYWORD

nonn,nice,hard,more

AUTHOR

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