On the bondage, strong and weak bondage numbers in Complementary Prism Graphs

Abstract

Let G = (V (G), E(G)) be a simple undirected graph of order n, and let S subset of (G). If every vertex in V (G) - S is adjacent to at least one vertex in S, then the set S is called a dominating set. The domination number of G is the minimum cardinality taken over all sets of S, and it is denoted by gamma(G). Recently, the effect of one or more edges deletion on the domination number has been examined in many papers. Let F subset of E(G). The bondage number b(G) of G is the minimum cardinality taken over all sets of F such that gamma(G - F) > gamma(G). In the literature, a lot of domination and bondage parameters have been defined depending on different properties. In this paper, we investigate the bondage, strong and weak bondage numbers of complementary prism graphs of some well-known graph families.