5 papers
Optimal Sensor Placement in Power Grids: Power Domination, Set Covering, and the Neighborhoods of Zero Forcing Forts
Logan A. Smith, Illya V. Hicks
To monitor electrical activity throughout the power grid and mitigate outages, sensors known as phasor measurement units can installed. Due to implementation costs, it is desirable…
An integer program and new lower bounds for computing the strong rainbow connection numbers of graphs
Logan A. Smith, David T. Mildebrath, Illya V. Hicks
We present an integer programming model to compute the strong rainbow connection number, , of any simple graph . We introduce several enhancements to the proposed model,…
A Polynomial Time Algorithm for Computing the Strong Rainbow Connection Numbers of Odd Cacti
Logan A. Smith, David T. Mildebrath, Illya V. Hicks
We consider the problem of computing the strong rainbow connection number for cactus graphs in which all cycles have odd length. We present a formula to calculate $src…
Power domination throttling
Boris Brimkov, Joshua Carlson, Illya V. Hicks +2
A power dominating set of a graph is a set that colors every vertex of according to the following rules: in the first timestep, every vertex in be…
Connected power domination in graphs
Boris Brimkov, Derek Mikesell, Logan Smith
The study of power domination in graphs arises from the problem of placing a minimum number of measurement devices in an electrical network while monitoring the entire network. A p…