Global Accurate Power Domination in Graphs

Abstract

Consider a graph G = (V, E), a dominating set D is an accurate dominating set, if V–D has no 
dominating set of cardinality |D|. If D is an accurate dominating set of a graph G then it is 
said to be global accurate dominating set, if D is also an accurate dominating set of  ????J. A 
dominating set D is a power dominating set of a graph G if it monitors all vertices and edges 
in G. The parameter ????H(G) is the power domination number which is the smallest size of a 
power dominating set in G. The parameter ????HHH(G) is the global accurate power domination 
number which is the minimum cardinality of a global accurate power dominating set. In this 
paper, some bounds for ????HHH(G) are obtained and exact values of ????HHH(G) for some standard 
graphs are found, also a Nordhaus-Gaddum type result is established.