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arXiv · 2304.11795

Fractional eternal domination: securely distributing resources across a network

Fnu Devvrit·Aaron Krim-Yee·Nithish Kumar·Gary MacGillivray·Ben Seamone·Virgélot Virgile·AnQi Xu
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Abstract

This paper initiates the study of fractional eternal domination in graphs, a natural relaxation of the well-studied eternal domination problem. We study the connections to flows and linear programming in order to obtain results on the complexity of determining the fractional eternal domination number of a graph $G$, which we denote $\gamma_{\,\textit{f}}^{\infty}(G)$. We study the behaviour of $\gamma_{\,\textit{f}}^{\infty}(G)$ as it relates to other domination parameters. We also determine bounds on, and in some cases exact values for, $\gamma_{\,\textit{f}}^{\infty}(G)$ when $G$ is a member of one of a variety of important graph classes, including trees, split graphs, strongly chordal graphs, Kneser graphs, abelian Cayley graphs, and graph products.

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Fnu Devvrit, Aaron Krim-Yee, Nithish Kumar, Gary MacGillivray, Ben Seamone, Virgélot Virgile, AnQi Xu. 2023-04-24. Fractional eternal domination: securely distributing resources across a network. https://arxiv.org/abs/2304.11795

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