Semitotal domination in rooted product graphs

Abstract

A semitotal dominating set of a nontrivial connected graph G is a dominating set D of G such that every vertex in D is within distance two of another vertex in D. The semitotal domination number of G is the minimum cardinality among all semitotal dominating sets of G. In this article, we investigate the semitotal domination number of rooted product graphs. We derive exact formulas for this parameter and show that it can be expressed in terms of several domination parameters of the factor graphs. Furthermore, we characterize the graph families for which each of the obtained expressions is attained.