The bondage number of $(n-3)$-regular graphs of order $n$

TL;DR

This paper determines the exact bondage number of $(n-3)$-regular graphs of order $n$, showing it equals $n-3$, which advances understanding of graph stability related to domination properties.

Contribution

The paper provides a precise calculation of the bondage number for a specific class of regular graphs, filling a gap in graph domination theory.

Findings

Bondage number of $(n-3)$-regular graphs is $n-3$

Exact value established for all such graphs

Enhances understanding of domination stability in regular graphs

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 of $G$. In this paper, we determine that the exact value of the bondage number of $(n-3)$-regular graph $G$ of order $n$ is $n-3$.