Bounds on the paired domination number of graphs with minimum degree at least three

Abstract

A set S of vertices in a graph G is a paired dominating set if every vertex of G is adjacent to a vertex in S and the subgraph induced by S contains a perfect matching (not necessarily as an induced subgraph). The minimum cardinality of a paired dominating set of G is the paired domination number γpr(G) of G. In this paper, we show that if G is a graph of order n and δ(G)≥3, then γpr(G)≤1903730000n<0.634567n.