Homometric sets in diameter-two and outerplanar graphs

Abstract

We improve the best previously-known lower bound on the size of largest homometric sets in sparse diameter-two graphs. Along with the proof, we provide a method for constructing the desired homometric sets. We also study outerplanar graphs and show how to construct homometric sets in a given outerplanar graph of the size at least clogn, where n is the number of vertices in the graph, and c a positive fixed constant.