Difference Matrices, Generalized Hadamard Matrices and Orthomorphism Graphs Of Groups

Abstract

Orthomorphism graphs of groups are defined and a correspondence, between cliques of orthomorphism graphs and difference matrices and generalized Hadamard matrices, is established. Some examples of orthomorphism graphs are given.
Also, for $\lambda =1$, known values and bounds for clique numbers of orthomorphism graphs of groups of small order are surveyed.