Abstract
A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S and the subgraph induced by S contains a perfect matching. The minimum cardinality of a paired-dominating set of G is the paired-domination number of G , denoted by γ p r ( G ) . In this work, we present several upper bounds on the paired-domination number in terms of the maximum degree, minimum degree, girth and order.
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