Work

A census of Cayley graphs

Year: 2026

Type: article

Abstract: 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.

Source: Journal of Symbolic Computation

DOI: 10.1016/j.jsc.2026.102580

Authors: Rhys J. Evans, Primož Potočnik

Institutions: The University of Sydney, University of Ljubljana, Institute of Mathematics, Physics, and Mechanics

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,160

Funder: Javna Agencija za Raziskovalno Dejavnost RS