Symplectic graphs over finite commutative rings

Let V be a symplectic space over a finite commutative ring R and let G Sp R ( V ) be the symplectic graph over R . In this work, we show that it is arc transitive and determine the chromatic number. Moreover, if R is a finite local ring, we obtain its automorphism group, and the chromatic number and the automorphism group of each subconstituent.