Holt, Derek F. and Royle, Gordon (2020) A census of small transitive groups and vertex-transitive graphs. Journal of Symbolic Computation, 101 . pp. 51-60. doi:10.1016/j.jsc.2019.06.006 ISSN 0747-7171.

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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, 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 47 and then by completely determining which groups of order at most 47 are CI groups.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Journal of Symbolic Computation
Publisher:	Elsevier Science Ltd. / Academic Press Ltd.
ISSN:	0747-7171
Official Date:	November 2020
Dates:	Date Event November 2020 Published 27 June 2019 Available 19 June 2019 Accepted
Volume:	101
Page Range:	pp. 51-60
DOI:	10.1016/j.jsc.2019.06.006
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	21 June 2019
Date of first compliant Open Access:	27 December 2020
Related URLs:	Publisher
Open Access Version:	ArXiv

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