Eternal Domination in Trees
Combinatorics
2021-12-07 v1
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 -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 -eternal domination number.
Keywords
Cite
@article{arxiv.2112.03107,
title = {Eternal Domination in Trees},
author = {William F. Klostermeyer and Gary MacGillivray},
journal= {arXiv preprint arXiv:2112.03107},
year = {2021}
}