A census of Cayley graphs

Evans, Rhys J. (author), Potočnik, Primož (author)

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.

• Language: English
• Keywords: Cayley graphs, enumeration, cubic graphs, quartic graphs
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.11.2026
• Year: 2026
• Number of pages: 15 str.
• Numbering: Vol. 137, article no. 102580
• PID: 20.500.12556/RUL-181440
• UDC: 512:519.17
• ISSN on article: 0747-7171
• DOI: 10.1016/j.jsc.2026.102580
• COBISS.SI-ID: 274459395
• Publication date in RUL: 08.04.2026

Record is a part of a journal

• Title: Journal of symbolic computation
• Shortened title: J. symb. comput.
• Publisher: Elsevier
• ISSN: 0747-7171
• COBISS.SI-ID: 27496192

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: Cayleyevi grafi, preštevanje, kubični grafi, kvartični grafi

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P1-0294
• Name: Računsko intenzivne metode v teoretičnem računalništvu, diskretni matematiki, kombinatorični optimizaciji ter numerični analizi in algebri z uporabo v naravoslovju in družboslovju

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: J1-4351
• Name: Generiranje, analiza in katalogizacija simetričnih grafov