English

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 GG on nn vertices with no isolated vertices is at most 2n/32n/3. Moreover, the equality is achieved if and only if every non-leaf vertex of GG is a support vertex with one or two leaf neighbors. Our result answers an open question of Beaton and Brown.

Keywords

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}
}