Abstract
The inflation G I of a graph G with n( G) vertices and m( G) edges is obtained from G by replacing every vertex of degree d of G by a clique K d . 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 if the subgraph induced by S contains a perfect matching. The paired domination number γ p( G) is the minimum cardinality of a paired dominating set of G. In this paper, we show that if a graph G has a minimum degree δ( G)⩾2, then n( G)⩽ γ p ( G I )⩽4 m( G)/[ δ( G)+1], and the equality γ p(G I) = n(G) holds if and only if G has a perfect matching. In addition, we present a linear time algorithm to compute a minimum paired-dominating set for an inflation tree.
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