Bilinear forms graphs over residue class rings

We investigate the bilinear forms graph Γ over the residue class ring modulo ps (where p is a prime number and s is a positive integer). First, we prove that the bilinear forms graph Γ is a connected vertex transitive graph. When p>2, Γ is distance-regular if and only if s=1. Next, we completely determine the valency of a vertex, the clique number, the independence number and the chromatic number of the bilinear forms graph Γ, respectively. Finally, we show that both Γ and the complement of Γ are not cores and their cores are complete.