POWER DOMINATION ON SEMI-STRONG PRODUCT OF GRAPHS

Résumé

An electrical power system can be monitored efficiently by placing the measurement device called Phase Measurement Unit (PMU) in the power network which can be effectively done by identifying the locations where the devices have to be placed, giving rise to the power domination (PD) concept in graphs. A set of vertices S ⊆ V that monitors every vertex in the graph G= (V,E) according to the rules of power domination is called as the power dominating set (PD-set). The power domination number (PD-number) of a graph G denoted by γ_p(G), is the minimum number of vertices that are required to power dominate the entire graph. In this paper, we investigate the bounds for the semi-strong product (SSP) of two general graphs in terms of the power domination number, γ_p(G). Also, we establish the exact bounds for certain graphs based on their orders and PD-numbers.