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.
