A class of generalized symplectic graphs based on totally isotropic subspaces in symplectic spaces over finite fields

Let F(q )be a finite field of order q and F-q((2 nu)) be a 2 nu-dimensional symplectic space. In the present paper, we study a class of generalized symplectic graphs Gamma based on m-dimensional totally isotropic subspaces in F-q((2 nu)). It is shown that Gamma is vertex -transitive, and it is a 5-Deza graph with diameter m + 1. Moreover, we determine the parameters concerning the first subconstituent Gamma(1) and it is shown that Gamma(1) is also a 5-Deza graph.