Graphs With Large Semipaired Domination Number

摘要

Let G be a graph with vertex set V and no isolated vertices. A sub-set S ? V is a semipaired dominating set of G if every vertex in V S is adjacent to a vertex in S and S can be partitioned into two element subsets such that the vertices in each subset are at most distance two apart. The semipaired domination number γ_( pr 2)( G ) is the minimum cardinality of a semipaired dominating set of G . We show that if G is a connected graph G of order n ≥ 3, then γ pr 2 ( G ) ≤ 2 3 n , and we characterize the extremal graphs achieving equality in the bound.