A census of Cayley graphs
Given positive integers k and n , we present methods to construct all groups of order at most n that contain a Cayley set of size k , and to enumerate the Cayley sets of order k in a given group, up to the action of the automorphism group. We use these methods to generate complete lists of pairwise nonisomorphic 3-valent Cayley graphs with at most 5,000 vertices and 4-valent Cayley graphs with at most 1,025 vertices.
Authors
- Rhys J. Evans (ORCID: https://orcid.org/0000-0002-2837-582X)
- Primož Potočnik
Institutions
- The University of Sydney (AU)
- University of Ljubljana (SI)
- Institute of Mathematics (BY)
- Institute of Mathematics, Physics, and Mechanics (SI)
Publication Details
- Journal
- Journal of Symbolic Computation
- Published
- 2026-03-31
- DOI
- https://doi.org/10.1016/j.jsc.2026.102580
- Primary Topic
- Finite Group Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Javna Agencija za Raziskovalno Dejavnost RS