Symplectic graphs overfinite commutative rings

Abstract

This work is based on ideas ofMeemark and Prinyasart [12] who introduced the symplectic graph GSpR(V ), where V is a symplectic space over a finite commutative ring R. When R = Zpn and V = R2 , they proved that GSpR(V ) is a strongly regular graph when ν = 1 and Li,Wang and Guo [10] showed that it is strictly Deza graphwhen ν ≥ 2. In this dissertation,we study symplectic graphs over finite commutative rings. We can classify if our graph is a strongly regular graph or a Deza graph. We also show that it is arc transitive, and determine chromatic numbers and automorphism groups. Moreover, we apply the combinatorial technique presented in [12] to prove similar results on subconstituents of symplectic graphs over finite local rings.