A note on connected power domination of certain classes of graphs

Abstract

The efficiency of monitoring the electrical power systems can be optimised with the use of Phasor Measurement Unit (PMU). A complete monitoring of the network can be effectively implemented through the power domination problem, downsizing the count of PMUs. In this paper, we present a detailed study on the Connected Power Domination (CPD) of a graph, a variant of power domination with an additional constraint of being connected. Tight upper bounds on the Connected Power Domination Number of a graph $G$, denoted $\gamma_{p,c}(G)$ are established and also the nature of the CPD set of unicyclic graphs is explored. Further, this study gives the exact $\gamma_{p,c}$-set for certain classes of graphs including, Grid graph, Join of graphs, Kragujevac tree and Honeycomb network.