On the average order of a dominating set of a forest
Combinatorics
2022-08-23 v1
Abstract
We show that the average order of a dominating set of a forest graph on vertices with no isolated vertices is at most . Moreover, the equality is achieved if and only if every non-leaf vertex of is a support vertex with one or two leaf neighbors. Our result answers an open question of Beaton and Brown.
Cite
@article{arxiv.2104.00600,
title = {On the average order of a dominating set of a forest},
author = {Aysel Erey},
journal= {arXiv preprint arXiv:2104.00600},
year = {2022}
}