On the Equality of Accurate Power Domination and Power Domination Numbers of Some Graphs

Abstract

The power domination number of a graph G, denoted  refers to the minimum size of a power dominating set within G. The accurate power domination number, represented by  is the smallest cardinality of a power dominating set D such that no other subset of V(G)∖D of the same size can also serve as a power dominating set. This paper focuses on identifying graphs for which . In particular, it characterizes all trees that meet this equality condition and also explores a comparison between the accurate power domination number and power domination number across various corona graphs.