On the Bondage Number of Block Graphs

Let \(\gamma(G)\) be the domination number of a graph \(G\). The bondage number \(b(G)\) of a nonempty graph \(G\) is the minimum cardinality among all sets of edges \(X\) for which \(\gamma(G – X) > \gamma(G)\).

In this paper we show that \(b(G) \leq \Delta(G)\) for any block graph \(G\), and we characterize all block graphs with \(b(G) = \Delta(G).\)