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

#### Abstract

In this paper, we explore connected Cayley graphs on non-abelian groups of order 5*p*^{2}, 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.

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#### Full Text:

PDFDOI: http://dx.doi.org/10.5614/ejgta.2024.12.1.8

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