On the domination, strong and weak domination in transformation graph Gxy

Abstract

Let G = (V(G)}E(G)) be a simple undirected graph of order n and size m, and x, y9 z be three variables taking value + or The transformation graph of (7, is a simple graph hav ing V(G) U E(G) as the vertex set. If an expression has n variables, and each variable can have the value + or the number of different combinations of values of the variables is 2n. Thus, we obtain eight kinds of transformation graphs. A set S C V(G) is a dominating set if every vertex in V(G)-S is adjacent to at least one vertex in S. The minimum cardinality taken over all dominating sets of G is called the domination number of G and is denoted by 7(G), There are several types of domination parameters depending upon the nature of dominating sets. In this paper, we investigate the domination number, the strong domination number and the weak domination number of the transformation graph. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.