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

We investigate the generalized bilinear forms graph Γ d over a residue class ring Z p s . The graph Γ d 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 Γ d and its complement are maximum cliques. The graph Γ d is useful for error-correcting codes. We show that there is a largest independent set of Γ d which is a linear MRD code over Z p s .