Symplectic graphs over finite local rings

This work is based on ideas of Meemark and Prinyasart (2011) [8] who introduced the symplectic graph GSpR(V), where VV is a symplectic space over a finite commutative ring RR. When R=ZpnR=Zpn and V=R2vV=R2v, they proved that GSpR(V) is an strongly regular graph when ν=1ν=1 and Li, Wang and Guo (2012) [6] showed that it is a strictly Deza graph when ν≥2ν≥2. In this paper, we study symplectic graphs over finite local rings. We can classify if our graph is a strongly regular graph or a strictly Deza graph. We also show that it is arc transitive. Moreover, we apply the combinatorial technique presented in Meemark and Prinyasart (2011) [8] to prove similar results on subconstituents of symplectic graphs.