Trees with Unique Minimum Locating-Dominating Sets.

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Lane, Stephen M
locating-domination; locating-dominating set; Discrete Mathematics and Combinatorics; Mathematics; Physical Sciences and Mathematics
thesis / dissertation description
A set S of vertices in a graph G = (V, E) is a locating-dominating set if S is a dominating set of G, and every pair of distinct vertices {u, v} in V - S is located with respect to S, that is, if the set of neighbors of u that are in S is not equal to the set of neighbors of v that are in S. We give a construction of trees that have unique minimum locating-dominating sets.