Generalized bilinear forms graphs and MRD codes over a residue class ring

We investigate the generalized bilinear forms graph Γd over a residue class ring Zps. The graph Γd is a connected vertex-transitive graph, and we completely determine its independence number, clique number, chromatic number and maximum cliques. We also prove that cores of both Γd and its complement are maximum cliques. The graph Γd is useful for error-correcting codes. We show that there is a largest independent set of Γd which is a linear MRD code over Zps.