Eternal Distance-2 Domination in Trees
Abstract
We consider the eternal distance-2 domination problem, recently proposed by Cox, Meger, and Messinger, on trees. We show that finding a minimum eternal distance-2 dominating set of a tree is linear time in the order of the graph by providing a fast algorithm. Additionally, we characterise when trees have an eternal distance-2 domination number equal to their domination number or their distance-2 domination number, along with characterizing which trees are eternal distance-2 domination critical. We conclude by providing general upper and lower bounds for the eternal distance-k domination number of a graph, as well as constructing an infinite family of trees which meet said upper bound and another which meets the given lower bound.
Keywords
Cite
@article{arxiv.2308.00054,
title = {Eternal Distance-2 Domination in Trees},
author = {Alexander Clow and Christopher M van Bommel},
journal= {arXiv preprint arXiv:2308.00054},
year = {2023}
}
Comments
13 pages, 4 figures