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Independent perfect domination sets in Cayley graphs

In this paper, we show that a Cayley graph for an abelian group has an independent perfect domination set if and only if it is a covering graph of a complete graph. As an application, we show that the hypercube Qn has an independent perfect domination set if and only if Qn is a regular covering of the complete graph Kn+1 if and only if n = 2m − 1 for some natural number m. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 213–219, 2001