A counterexample to a conjecture on the bondage number of a graph

Abstract The bondage number b(G) of a nonempty graph G was first introduced by Fink, Jacobson, Kinch and Roberts in [3]. They generalized a former approach to domination-critical graphs. In their publication they conjectured that b(G)⩽Δ(G)+1 for any nonempty graph G. In this note we present a counterexample for the conjecture.