20.500.12556/RUL-181440 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. Cayley graphs enumeration cubic graphs quartic graphs Cayleyevi grafi preštevanje kubični grafi kvartični grafi true false true Angleški jezik Slovenski jezik Članek v reviji 2026-04-08 08:50:12 2026-04-08 08:50:14 2026-04-21 10:52:43 0000-00-00 00:00:00 2026 0 0 15 str. article no. 102580 Vol. 137 Nov.-Dec. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-11-01 512:519.17 0747-7171 10.1016/j.jsc.2026.102580 274459395 1-s2.0-S0747717126000283-main.pdf 1-s2.0-S0747717126000283-main.pdf 1 7A13EDCE13118EB0BF341B7A6BC7A7B4 b75ccf5d936ec43e3ab06518f449153d1643fd54d4094d87d8b2fd5faf9b2283 517d46b0-3317-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=231890 https://www.sciencedirect.com/science/article/pii/S0747717126000283 1 0144591b-3317-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=231889 https://zenodo.org/records/15775470 Cubic Cayley graphs on up to 5000 vertices 0 fe49fb87-3d5e-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=232814 https://zenodo.org/records/15775678 Quartic Cayley graphs on up to 1025 vertices 0 112909fe-3d5f-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=232815 Fakulteta za matematiko in fiziko 0 0 0