## 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 γ_{pr2}(*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