Authors: T.W. Haynes, M.A. Henning Title: Graphs with large semipared domination number Source: Discussiones Mathematicae Graph Theory Received 07.08.2017, Revised 24.03.2018, Accepted 03.04.2018, doi: 10.7151/dmgt.2143 Abstract: Let G be a graph with vertex set V and no isolated vertices. A subset S ⊆ V is a semipaired dominating set of G if every vertex in V \setminus 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 \semiP(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 \semiP(G) \le \frac{2}{3}n, and we characterize the extremal graphs achieving equality in the bound. Keywords: paired-domination, semipaired domination Links: PDF