Semitotal Domination Numbers of Grids, Tori and Cylinders

Abstract

Let G be a graph with no isolated vertex. A set 5 of vertices in G is a semitotal dominating set of G if it is a dominating set of G and every vertex in 5 is within distance 2 of another vertex of 5. The semitotal domination number, 712(G), is the minimum cardinality of a semitotal dominating set of G. Let GOH denote the Cartesian product of graphs G and if. In this paper, we determine the exact values of 7∗{PmOPn) ( for 2 < m < 4 ), 7t^CJDCn), 7t2(PJJCn) ( for m = 2,4 ) and yt2(CmOPn) ( for m = 3,4 ). Exact values of •yt2(CzDCn) and iti{PzQCn) for some n are given. Moreover, bounds on semitotal domination number of the graph PsDPn are provided. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.