The Transitive Graphs with at Most \(26\) Vertices

Brendan D. McKay1, Gordon F. Royle2
1 Computer Science Department Australian National University GPO Box 4, ACT 2601, Australia
2 Mathematics Department University of Western Australia Nedlands, Wa 6009, Australia

Abstract

We complete the construction of all the simple graphs with at most \(26\) vertices and transitive automorphism group. The transitive graphs with up to \(19\) vertices were earlier constructed by McKay , and the transitive graphs with \(24\) vertices by Praeger and Royle . Although most of the construction was done by computer, a substantial preparation was necessary. Some of this theory may be of independent interest.