Open AccessGlobal Power domination of graphs
Author(s) -
R. Prabha,
B. Thenmozhi
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1770/1/012065
Subject(s) - dominating set , domination analysis , mathematics , algorithm , graph , computer science , discrete mathematics , vertex (graph theory)
Monitoring an electric power system with a minimum number of PMUs is related to the domination problem in graph theory. In this paper, we introduce a new graph invariant called global power domination number. A power dominating set S of a graph G = ( V, E ) is a global power dominating set if S is also a power dominating set of G ¯ . The global power domination number γ gp ( G ) is the minimum cardinality of a global power dominating set. In this paper, we initiate the study of global power domination problem and prove its NP-completeness. We also characterize the global power domination number for trees and compute the exact value of γ gp ( G ) for certain families of graph.