GRAPHS WITH SEMITOTAL DOMINATION NUMBER HALF THEIR ORDER

Abstract In an isolate-free graph G , a subset S of vertices is a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S . The semitotal domination number of G , denoted by $\gamma _{t2}(G)$ , is the minimum cardinality of a semitotal dominating set in G . Goddard, Henning and McPillan [‘Semitotal domination in graphs’, Utilitas Math. 94 (2014), 67–81] characterised the trees and graphs of minimum degree 2 with semitotal domination number half their order. In this paper, we characterise all graphs whose semitotal domination number is half their order.