The Bondage Number of $(n-3)$-Regular Graphs of Order $n$

Abstract

Let $G=(V,E)$ be a graph. A subset $D\subseteq V$ is a dominating set if every vertex not in $D$ is adjacent to a vertex in $D$. The domination number of $G$ is the smallest cardinality of a dominating set of $G$. The bondage number of a nonempty graph $G$ is the smallest number of edges whose removal from $G$ results in a graph with larger domination number than $G$. In this paper, we determine that the exact value of the bondage number of an $(n-3)$-regular graph $G$ of order $n$ is $n-3$.