The Properties Of Generalized Unitary Graph And Its Subconstituent

In this paper, Let H be a Hermitian matrix over finite field Fq2,and M be the set of all subspaces of (m,0) with respect to H in Fq22v,We construct a graph with M denoted by generalized unitary graph, then we discuss some properties of it. Firstly, we prove that it is aregular graph and the number of vertices is (?),the degree is (?),the diameter is min{2m,v}.And the unitary group of degree n with H is a subgroup of Aut (GUm(2v +δ,q2)) .Secondly, when 1 < m < v, for a fixed vertex M of the graph, we discuss the properties of the subconstituent of the graphΓ1(M).Γ1(M) is a quasi-Deza graph with the union of (?) isomorphic connected components. Each connected component is a quasi - Deza graph, and the number of vertices is q2n-4m+1,the degree is qn-2m-1(qn2m+2 qn-2m+(-1)(n-2m),the diameter is 2. In the end, we prove that a strongly regular graph lies in each component.