New results about the bondage number of a graph Original Research Article

The bondage number b(G) of a nonempty graph G was first introduced by Fink, Jacobson, Kinch and Roberts [3]. Among other results they showed that b(G)⩽2 if G is a tree. In this paper we present a characterization of those trees having bondage number 1. Further on we present the first lower bounds for the bondage number and some new sharp upper bounds.