Pentavalent 2-regular core-free Cayley graphs

A Cayley graph F = Cay(G, S) is said to be 2-regular core-free if G is core-free in some X <= Aut F and Aut F acts regularly on the set of 2-arcs of F. In this paper, we classify the pentavalent 2-regular core-free Cayley graphs. As a byproduct, we provide another proof of one of the results by Du et al. (2017) [6] regarding pentavalent symmetric graphs over nonabelian simple groups. Namely, we prove that the pentavalent 2-regular Cayley graphs over non-abelian simple groups are normal. Furthermore, we construct a pentavalent core-free 2-transitive Cayley graph Cay(G, S) such that Aut(G, S) is transitive but not 2-transitive on S. This answers a question posed by Li in 2008. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.