Orthogonal graphs over finite commutative rings of odd characteristic

Let (V, beta) 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. 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. Moreover, we work on subconstituents of the graph. (C) 2016 Elsevier Inc. All rights reserved.