Power domination in generalized Mycielskian of spiders - Sreethu, K; Varghese, Seema (MATHEMATICA SCANDINAVICA, 2024)
The power domination problem in the graph was introduced to model the monitoring problem in electric networks. It is to find a set of vertices with minimum cardinality, called a power dominating set (PDS), that monitors the whole set V after applying the rules, domination and propagation. In this paper, we discuss the power domination problem in generalized Mycielskian of spiders. We characterize spiders with γ _P(μ _m(T))= 1. If γ _P(μ _m(T)) eq 1 and m is even then γ _P(μ _m(T))=m2 +1. We also show that if m is odd and γ _P(μ _m(T)) eq 1 , then m+12 ceil ≤ γ _P(μ _m(T))≤ m2 ceil +1.