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arXiv · 2208.07484

Generalized Bondage Number: The $k$-synchronous bondage number of a graph

Rey Anaya·Alvaro Belmonte·Nathan Shank·Elise Sinani·Bryan Walker
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Abstract

We investigate a generalization of the bondage number of a graph called the \textit{$k\,$-synchronous bondage number}. The $k\,$-synchronous bondage number of a graph is the smallest number of edges that, when removed, increases the dominating number by $k$. In this paper, we discuss the 2-synchronous bondage number and then generalize to $k\,$-synchronous bondage number. We present $k\,$-synchronous bondage number for several graph classes and give bounds for general graphs. We propose this characteristic as a metric of the connectivity of a simple graph with possible uses in the field of network design and optimization.

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Rey Anaya, Alvaro Belmonte, Nathan Shank, Elise Sinani, Bryan Walker. 2022-08-16. Generalized Bondage Number: The $k$-synchronous bondage number of a graph. https://arxiv.org/abs/2208.07484

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