BONDAGE AND STRONG-WEAK BONDAGE NUMBERS OF TRANSFORMATION GRAPHS $G^{xyz}$

Abstract

Let G(V (G),E(G)) be a simple undirected graph. A dominating set of G is a subset D ⊆ V (G) such that every vertex in V (G) −D is adjacent to at least one vertex in D. The minimum cardinality taken over all dominating sets of G is called the domination number of G and also is denoted by (G). There are a lot of vulnerability parameters depending upon dominating set. These parameters are strong and weak domination numbers, reinforcement number, bondage number, strong and weak bondage numbers, etc. The bondage parameters are important in these parameters. The bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater than (G). In this paper, the bondage parameters have been examined of transformation graphs, then exact values and upper bounds have been obtained.