A275867 -id:A275867 - cp's OEIS frontend

A124059 Number of connected asymmetric graphs with n nodes.

1, 0, 0, 0, 0, 8, 144, 3552, 131452, 7840396, 797524380, 143325597564

Offset: 1

Franklin T. Adams-Watters, Nov 03 2006

A graph possessing only a single automorphism is called an identity or asymmetric graph, |Aut(g)|=1. - Travis Hoppe, Apr 27 2014

C. O. Aguilar and B. Gharesifard, Graph Controllability Classes for the Laplacian Leader-Follower Dynamics, 2014. See Table 1.
Ernesto Estrada, Communicability cosine distance: similarity and symmetry in graphs/networks, hal-04169459 [math], 2023. See p. 22.
N. J. A. Sloane, Transforms
Yoav Spector, Moshe Schwartz, Study of potential Hamiltonians for quantum graphity, arXiv:1808.05632 [cond-mat.stat-mech], 2018.
Eric Weisstein's World of Mathematics, Graph Automorphism
Eric Weisstein's World of Mathematics, Identity Graph
Myung-Gon Yoon, Peter Rowlinson, Dragos Cvetkovic, and Zoran Stanic, Controllability of multi-agent dynamical systems with a broadcasting control signal, Asian J. Control 16 (4) (2014) 1066-1072, Table 1

Cf. A003400 (not-necessarily connected simple asymmetric graphs).
Cf. A275867 (disconnected simple asymmetric graphs).
Cf. Values of |Aut(g)| for simple connected graphs, A124059, A241454, A241455, A241456, A241457, A241458, A241459, A241460, A241461, A241462, A241463, A241464, A241465, A241466, A241467, A241468, A241469, A241470, A241471.

Inverse WEIGH transform of A003400 (see Transforms link).

a(n) = A003400(n) - A275867(n).

a(12) from Alois P. Heinz, Jun 11 2018

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

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

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

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).

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

Cf. A124059 (connected simple asymmetric graphs).
Cf. A275867 (disconnected simple asymmetric graphs).
Cf. A000088 (simple graphs).

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

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

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

cp's OEIS Frontend

A124059 Number of connected asymmetric graphs with n nodes.

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