GENERALIZED ORTHOGONAL GRAPHS OF CHARACTERISTIC A POWER OF 2

Let R be a finite local ring of characteristic a power of 2 with the residue field k. In this paper, we define a generalized orthogonal graph on a module of rank at least 2 over R. Then we study its graph properties via the same graph over k. The number of vertices and the valency of each vertex in this graph over R are computed. We also prove that this graph is arc transitive and find its diameter. Moreover, the first subconstituent of this orthogonal graph is considered. We show that it is a generalized strongly regular graph.