Abstract
An independent perfect domination set in a graph \(\varGamma \) is an independent set S of \(V(\varGamma )\) such that every vertex of \(V(\varGamma )\setminus S\) 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 domination sets in Semi-Cayley graph SC(G; R, R, T) over finite group G. Further, we obtain a necessary and sufficient condition for Cayley graphs on two class non-abelian groups to have independent perfect domination sets.
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