Power domination in Mycielskian of spiders

Abstract

The power domination problem in graphs consists of finding a minimum set of vertices [Formula: see text] that monitors the entire graph G governed by two ‘monitoring rules’- domination and propagation. A set [Formula: see text] 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: see text], of G. In this paper, we study the power domination problem in Mycielskian of spiders. For a spider T, we have [Formula: see text] and [Formula: see text]. We characterize spiders, T, for which [Formula: see text] and [Formula: see text]

Keywords

• Power domination
• Mycielskian
• spider
• 05C78