Power Domination And Related Variants In Graphs: A Survey And Future Directions

Abstract

Power domination is a major extension of the classical domination in graphs inspired by the problem of monitoring an electric power system by "phasor measurement units". In comparison with the classical domination, power domination includes some propagation rules that enable a small number of measuring units to observe the entire power network. There are many different variations and extensions of power domination, such as power edge domination, equitable power edge domination, etc., that were proposed to meet specific requirements of the power system and related structures. The goal of this article is to present a working survey on power domination, which would give a reader a comprehensive understanding of this concept and its variations. We focus our analysis on the results related to the power domination on graphs, including product of graphs, and power monitoring networks and propose a number of open problems on domination in graphs in general.