Theoretical Computer Science ( IF 0.747 ) Pub Date : 2021-02-22 , DOI: 10.1016/j.tcs.2021.02.006
Xiaomeng Wang; Shou-Jun Xu; Xianyue Li

An independent perfect dominating set in a graph Γ with vertex set $V\left(\mathrm{\Gamma }\right)$ is a subset S of $V\left(\mathrm{\Gamma }\right)$ such that S is an independent set and every vertex in $V\left(\mathrm{\Gamma }\right)\setminus S$ 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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