Physical Sciences and Mathematics Commons^™

Optimization Approaches For Open-Locating Dominating Sets, Daniel Blair Sweigart

Dissertations, Theses, and Masters Projects

An Open Locating-Dominating Set (OLD set) is a subset of vertices in a graph such that every vertex in the graph has a neighbor in the OLD set and every vertex has a unique set of neighbors in the OLD set. This can also represent where sensors, capable of detecting an event occurrence at an adjacent vertex, could be placed such that one could always identify the location of an event by the specific vertices that indicated an event occurred in their neighborhood. By the open neighborhood construct, which differentiates OLD sets from identifying codes, a vertex is not able …