Tetravalent non-normal Cayley graphs of order 5p^2

Khazaei, Soghra
Sharifi, Hesam (Department of Mathematics, Faculty of Science, Shahed University, Tehran, Iran.)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 12, No 1 (2024): Electronic Journal of Graph Theory and Applications

In this paper, we explore connected Cayley graphs on non-abelian groups of order 5p2, where p is a prime greater than 5, and Sylow p-subgroup is cyclic with respect to tetravalent sets that encompass elements with different orders. We prove that these graphs are normal; however, they are not normal edge-transitive, arc-transitive, nor half-transitive. Additionally, we establish that the group is a 5-CI-group.