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