Abstract
An independent perfect dominating set in a graph Γ with vertex set V(Γ) is a subset S of V(Γ) such that S is an independent set and every vertex in V(Γ)∖S is adjacent to exactly one vertex in S. In this paper, we first give a necessary and sufficient condition for the existence of independent perfect dominating sets in semi-Cayley graphs of finite groups. Further, we obtain a necessary and sufficient condition for Cayley graphs to have independent perfect dominating sets on two classes non-abelian groups.
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