A124059 Number of connected asymmetric graphs with n nodes.

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

Offset: 1

Author

Franklin T. Adams-Watters, Nov 03 2006

Keywords

• hard
• more
• nonn

Comments

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

Links

• 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

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.

Formula

Inverse WEIGH transform of A003400 (see Transforms link).

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

Extensions

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