Bondage Numbers of Mycielski Graphs

Abstract

The bondage number \(b(G)\) of a nonempty graph \(G\) is the smallest number of edges, removal of which from \(G\) results in a graph with domination number greater than that of \(G\). In this paper, we study the bondage number of Mycielski graphs. First, we present some properties of dominating sets and give sharp upper bounds for bondage numbers of Mycielski graphs. Second, we obtain a characterization of Mycielski graphs of trees bondage numbers of which are 1. Finally, we calculate the exact values for bondage numbers of Mycielski graphs underlying graphs of which are complete graphs, paths, cycles, complete \(t\)-partite graphs, etc.