A Census of Small Transitive Groups and Vertex-Transitive Graphs
Combinatorics
2018-11-26 v1
Abstract
We describe two similar but independently-coded computations used to construct a complete catalogue of the transitive groups of degree less than , thereby verifying, unifying and extending the catalogues previously available. From this list, we construct all the vertex-transitive graphs of order less than . We then present a variety of summary data regarding the transitive groups and vertex-transitive graphs, focussing on properties that seem to occur most frequently in the study of groups acting on graphs. We illustrate how such catalogues can be used, first by finding a complete list of the elusive groups of order at most and then by completely determining which groups of order at most are CI groups
Cite
@article{arxiv.1811.09015,
title = {A Census of Small Transitive Groups and Vertex-Transitive Graphs},
author = {Derek Holt and Gordon Royle},
journal= {arXiv preprint arXiv:1811.09015},
year = {2018}
}