English

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}
}
R2 v1 2026-06-24T08:58:44.257Z