Symplectic graphs over finite local rings

This work is based on ideas of Meemark and Prinyasart (2011) [8] who introduced the symplectic graph G Sp R ( V ) , where V is a symplectic space over a finite commutative ring R . When R = Z p n and V = R 2 v , they proved that G Sp R ( V ) is an strongly regular graph when ν = 1 and Li, Wang and Guo (2012) [6] showed that it is a strictly Deza graph when ν ≥ 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.