Graphs With Large Semipaired Domination Number

Abstract

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 γpr2(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 γpr2(G)≤23n${\gamma _{{\rm{pr}}2}}(G) \le {2 \over 3}n$, and we characterize the extremal graphs achieving equality in the bound.

Keywords

• paired-domination
• semipaired domination
• 05c69