Orthogonal Graphs Over Finite Commutative Rings of Odd Characteristic

Abstract

Let (V β)be an orthogonal space over a finite commutative ring R of odd characteristic. We determine the structure of V when R is a finite local ring. We define a graph for V called an orthogonal graph. We show that our graph is vertex and arc transitive and determine the chromatic number of the graph. Moreover, if R is a finite local ring, we can classify if it is a strongly regular or quasi-strongly regular graph and we obtain its automorphism group.