Power domination in Mycielskian of spiders

Abstract

The power domination problem in graphs consists of finding a minimum set of vertices (Formula presented.) that monitors the entire graph G governed by two ‘monitoring rules’- domination and propagation. A set (Formula presented.) is a power dominating set (PDS) if it can monitor all vertices of G. The minimum cardinality of a PDS of G is called the power domination number, (Formula presented.), of G. In this paper, we study the power domination problem in Mycielskian of spiders. For a spider T, we have (Formula presented.) and (Formula presented.). We characterize spiders, T, for which (Formula presented.) and (Formula presented.).