Graphs with large paired-domination number
In this paper, we continue the study of paired-domination in graphs introduced by Haynes and Slater (1998) Networks 32: 199 - 206. A paired-dominating set of a graph G with no isolated vertex is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number of G, denoted by gamma(pr)( G), is the minimum cardinality of a paired-dominating set of G. Let G be a connected graph of order n with minimum degree at least two. Haynes and Slater ( 1998) Networks 32: 199 - 206, showed that if n >= 6, then gamma(pr)( G)  = 14, we show that gamma(pr)( G) <= 2( n - 1)/3 and we characterize the ( infinite family of) graphs that achieve equality in this bound.
paired-domination bounds minimum degree two