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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.
Khazaei et al. (Sat,) studied this question.
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