A124059 Number of connected asymmetric graphs with n nodes.

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

Offset

1,6

Comments

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

Links

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

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

Formula

Inverse WEIGH transform of A003400 (see Transforms link).

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

Crossrefs

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.

Sequence in context: A061899 A134492 A067421 * A275867 A052764 A341957

Adjacent sequences: A124056 A124057 A124058 * A124060 A124061 A124062

Keyword

hard,more,nonn

Author

Franklin T. Adams-Watters, Nov 03 2006

Extensions

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

Status

approved