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

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

2011-09-19

arxiv.org/abs/1109.3931v1

Mathematics

Combinatorics

6 pages

Scientific paper

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 $n-3$.

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