A set is a paired-dominating set if every vertex in has at least one neighbor in S and the subgraph induced by S contains a perfect matching. The paired-domination number of a graph G, denoted by , is the minimum cardinality of a paired-dominating set of G. A conjecture of Goddard and Henning says that if G is not the Petersen graph and is a connected graph of order n with minimum degree , then . In this paper, we confirm this conjecture for k-regular graphs with k >= 4.
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