Eternal Domination in Trees

William F. Klostermeyer; Gary MacGillivray

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arXiv · 2112.03107

Eternal Domination in Trees

William F. Klostermeyer·Gary MacGillivray

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Abstract

Mobile guards on the vertices of a graph are used to defend the graph against an infinite sequence of attacks on vertices. A guard must move from a neighboring vertex to an attacked vertex (we assume attacks happen only at vertices containing no guard). More than one guard is allowed to move in response to an attack. The $m$-eternal domination number is the minimum number of guards needed to defend the graph. We characterize the trees achieving several upper and lower bounds on the $m$-eternal domination number.

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William F. Klostermeyer, Gary MacGillivray. 2021-12-06. Eternal Domination in Trees. https://arxiv.org/abs/2112.03107

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