On the average order of a dominating set of a forest

Aysel Erey

Published 2021-04-01Version 1

We show that the average order of a dominating set of a forest graph $G$ on $n$ vertices with no isolated vertices is at most $2n/3$. Moreover, the equality is achieved if and only if every non-leaf vertex of $G$ is a support vertex with one or two leaf neighbors. Our result answers an open question of Beaton and Brown.