Eternal Paired Domination in Trees
Date
2022-06-29
Authors
Moss, Elena
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Abstract
There are a wide variety of problems in graph domination. We discuss eternal paired domination in trees, a variation which requires guards stationed at the vertices of a dominating set to be able to defend against any sequence of attacks, while the guards remain adjacent to a “buddy” at all times. We have found an algorithm to obtain such a decomposition and proved that it is minimum. The eternal paired domination number of any non-trivial tree T is 2γ(T), where γ(T) is the domination number of T. Finally, we provide a counterexample in split graphs to demonstrate that this strategy cannot generalize to all chordal graphs.
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Keywords
graph theory, eternal domination, dynamic dominating sets, trees, stars