Semitotal domination number of some graph operations

Abstract

A semitotal dominating set S (abbreviated semi-TD-set) of graph G = (V, E) is a subset such that S is a dominating set and each vertex in the S is within 2 distance from the another vertex of S. The semitotal domination number, denoted by γ t2 (G), is the minimum cardinality taken over all semitotal dominating sets of G. In this paper, we examine the semitotal domination number of graphs obtained by some graph operations such as corona, join, modular product, and lexicographic product.