On the Bondage Number of Block Graphs

Abstract

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 $b(G)\le \mathrm{\Delta }(G)$ for any block graph $G$, and we characterize all block graphs with $b(G)=\mathrm{\Delta }(G).$