An independent perfect dominating set in a graph Γ with vertex set $V(\mathrm{\Gamma })$ is a subset S of $V(\mathrm{\Gamma })$ such that S is an independent set and every vertex in $V(\mathrm{\Gamma })\setminus S$ 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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半凯利图中的独立理想控制集

带有顶点集的图Γ中的独立理想控制集 $V（\mathrm{\Gamma }）$是其子集小号的$V（\mathrm{\Gamma }）$这样S是一个独立的集合，并且每个顶点$V（\mathrm{\Gamma }）\setminus \mathrm{小号}$与S中的一个顶点正好相邻。在本文中，我们首先为有限群的半Cayley图中存在独立的理想控制集提供了充要条件。此外，我们为Cayley图获得了在两类非阿贝尔群上具有独立的理想控制集的必要和充分条件。