Representations of graphs modulo n

A graph is said to be representable modulo n if its vertices can be labelled with distinct integers between 0 and n - 1 inclusive such that two vertices are adjacent if and only if their labels are relatively prime to n. The representation number of graph G is the smallest n representing G. We review known results and investigate representation numbers for several new classes. In particular, we relate the representation number of the disjoint union of complete graphs to the existence of complete families of mutually orthogonal Latin squares.

• Type: Journal
• Year: 2000
• Where: DM
• Authors: Anthony B. Evans, Garth Isaak, Darren A. Narayan
• Keywords: Distinct Integers, DM 2000, Representable Modulo, Representation Number