Counting Power Domination Sets in Complete m-ary Trees

Authors

Hays Whitlatch, Gonzaga UniversityFollow
Katharine Shultis, Gonzaga UniversityFollow
Olivia Ramirez, Gonzaga UniversityFollow
Michele Ortiz, Gonzaga UniversityFollow
Sviatlana Kniahnitskaya, Gonzaga UniversityFollow

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.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Whitlatch, Hays; Shultis, Katharine; Ramirez, Olivia; Ortiz, Michele; and Kniahnitskaya, Sviatlana (2023) "Counting Power Domination Sets in Complete m-ary Trees," Theory and Applications of Graphs: Vol. 10: Iss. 1, Article 4.
DOI: 10.20429/tag.2023.100104
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol10/iss1/4