On symplectic graphs modulo pnpn

In this work, we study a family of regular graphs using the 2ν×2ν2ν×2ν symplectic group modulo pnpn, where pp is a prime and nn and νν are positive integers. We find that this graph is strongly regular only when ν=1ν=1. In addition, we define the symplectic graphs of a symplectic space VV over a commutative ring RR and show that it is vertex transitive and edge transitive when RR has stable range one, which is the case for ZpnZpn.