Power domination in Mycielskians of n-spiders

Abstract

The power domination problem in graphs was introduced to model the monitoring problem in electric networks. It is to find a set of vertices, S ⊆ V ( G ) , of a graph G, called the power dominating set, that monitors V(G) by application of two rules, namely, domination and propagation. In this article, we discuss the power domination problem in the Mycielskians of n-spiders. We show that the power domination number of the Mycielskians of n-spiders is bounded above by n and also characterize the Mycielskians of n-spiders with γ P = 1 and γ P = n .