A census of small transitive groups and vertex-transitive graphs. (November 2020)

• Record Type: Journal Article
• Authors: Holt, Derek; Royle, Gordon
• Is Part Of: Journal of symbolic computation. Volume 101(2020)
• Page Start: 51
• Page End: 60
• Publication Date: 2020-11
• Subjects: Transitive permutation group -- Vertex-transitive graph -- Computer enumeration -- Cayley graph -- Elusive group -- CI-group; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.06.006
• Languages: English
• ISSNs: 0747-7171

Abstract

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.