generalized orthogonal graphs ofcharacteristic 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.