Perfect domination sets in Cayley graphs

In this paper, we get some results related to perfect domination sets of Cayley graphs. We show that if a Cayley graph C(A,X) has a perfect dominating set S which is a normal subgroup of A and whose induced subgraph is F, then there exists an F-bundle projection p:C(A,X)→Km for some positive integer m. As an application, we show that for any positive integer n, the following are equivalent: (a) the hypercube Qn has a perfect total domination set, (b) n=2m for a positive integer m, (c) Qn is a 2n−log2n−1K2-bundle over the complete graph Kn and (d) Qn is a covering of the complete bipartite graph Kn,n.