Counting Power Domination Sets in Complete m-ary Trees
Combinatorics
2022-01-25 v1
Abstract
Motivated by the question of computing the probability of successful power domination by placing k monitors uniformly at random, in this paper we give a recursive formula to count the number of power domination sets of size k in a labeled complete m-ary tree. As a corollary we show that the desired probability can be computed in exponential with linear exponent time.
Cite
@article{arxiv.2201.09111,
title = {Counting Power Domination Sets in Complete m-ary Trees},
author = {Sviatlana Kniahnitskaya and Michele Ortiz and Olivia Ramirez and Katharine Shultis and Hays Whitlatch},
journal= {arXiv preprint arXiv:2201.09111},
year = {2022}
}