Paired Eternal Domination in Grid Graphs and k-Trees
Date
2023-09-19
Authors
Penner, Georgia
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Abstract
We explore the paired eternal domination number on two different classes of graphs. The paired eternal domination problem is a variation on eternal domination where guards must remain paired after every move. We first consider grid graphs, finding exact values for 2xn grids. We also find bounds on the paired eternal domination number, but not tight bounds, for larger grid graphs, in particular 3xn and 4xn grids. For a restricted subset of k-trees with small maximum degree, we extend a prior result on trees to these k-trees, allowing the use of a previously invented algorithm to determine the paired eternal domination number of these graphs.
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Keywords
Graph theory, Dominating sets, Eternal domination, Paired domination