Semitotal domination of some known trees

Abstract

Let G = (V, E) be a graph without isolated vertices with vertex set V of order n = |V | and edge set E of size m = |E|. A vertex of a graph G is said to dominate itself and all its neighbors. A semitotal dominating set in G is a set of S such that S is a dominating set of G and each vertex in the S is within 2-distance from the another vertex of S. The semitotal domination number, denoted by γt2(G), is the minimum cardinality of a semitotal dominating set of G. This graph parameter was introduced by Goddard, Henning and McPillan in 2014 as a generalization of the domination number and the total domination number parameters. In this paper, we examine semitotal domination number of some known trees such as comet, double comet, complete k-ary tree, binomial tree, banana tree and Et p graphs.