Power domination on permutation graphs

Abstract

For the purposes of monitoring power networks, power companies use devices known as phase measurement units (PMUs); these monitor the waveform of the various nodes in a network. The cost of these units makes it worthwhile to minimize the number required. When a power network is modeled by a graph, the question of precisely how many are necessary to observe a given network, and of where they should be placed, is known as the power domination problem. We will consider this problem as it relates to permutation graphs on cycles, and suggest upper bounds for the power domination numbers on such graphs.