A census of small transitive groups and vertex-transitive graphs

D. Holt; Gordon Royle

doi:10.1016/j.jsc.2019.06.006

A census of small transitive groups and vertex-transitive graphs

D. Holt, Gordon Royle

Mathematics and Statistics

Research output: Contribution to journal › Article

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Abstract

We describe two similar but independently-coded computations used to construct a complete catalogue of the transitive groups of degree less than 48, thereby verifying, unifying and extending the catalogues previously available. From this list, we construct all the vertex-transitive graphs of order less than 48. We then present a variety of summary data regarding the transitive groups and vertex-transitive graphs, focusing 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 47 and then by completely determining which groups of order at most 47 are CI groups.

Original language	English
Journal	Journal of Symbolic Computation
DOIs	https://doi.org/10.1016/j.jsc.2019.06.006
Publication status	E-pub ahead of print - 27 Jun 2019

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Holt, D., & Royle, G. (2019). A census of small transitive groups and vertex-transitive graphs. Journal of Symbolic Computation. https://doi.org/10.1016/j.jsc.2019.06.006

Holt, D. ; Royle, Gordon. / A census of small transitive groups and vertex-transitive graphs. In: Journal of Symbolic Computation. 2019.

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Holt, D & Royle, G 2019, 'A census of small transitive groups and vertex-transitive graphs' Journal of Symbolic Computation. https://doi.org/10.1016/j.jsc.2019.06.006

A census of small transitive groups and vertex-transitive graphs. / Holt, D.; Royle, Gordon.

In: Journal of Symbolic Computation, 27.06.2019.

Research output: Contribution to journal › Article

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