All graphs with paired-domination number two less than their order

Włodzimierz Ulatowski
2013 Opuscula Mathematica  
Let G = (V, E) be a graph with no isolated vertices. A set S ⊆ V is a paired-dominating set of G if every vertex not in S is adjacent with some vertex in S and the subgraph induced by S contains a perfect matching. The paired-domination number γp(G) of G is defined to be the minimum cardinality of a paired-dominating set of G. Let G be a graph of order n. In [Paired-domination in graphs, Networks 32 (1998), 199-206] Haynes and Slater described graphs G with γp(G) = n and also graphs with γp(G)
more » ... graphs with γp(G) = n − 1. In this paper we show all graphs for which γp(G) = n − 2.
doi:10.7494/opmath.2013.33.4.763 fatcat:lzn2wsl7tnhkxco667qjzqnvi4