Symplectic graphs over finite local rings

This work is based on ideas of Meemark and Prinyasart (2011) [8] who introduced the symplectic graph g(SPR(V)), where V is a symplectic space over a finite commutative ring R. When R = Z(pn) and V = R-2v, they proved that g(SPR(V)) is an strongly regular graph when v = 1 and Li, Wang and Guo (2012) [6] showed that it is a strictly Deza graph when v >= 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. (C) 2013 Elsevier Ltd. All rights reserved.