Disjoint homometric sets in graphs - Albertson, Michael O. (Ars mathematica contemporanea, 2011)
Two subsets of vertices in a graph are called homometric if the multisets of distances determined by them are the same. Let ?$h(n)$? denote the largest number ?$h$? such that any connected graph of ?$n$? vertices contains two disjoint homometric subsets of size ?$h$?. It is shown that ?$\frac{c \log n}{\log\log n} 3$?.
Keywords: Golumb ruler; graph distances; graph theory; homometric subsets; homometrične podmnožice; ravninski grafi; razdalje v grafih; teorija grafov