Deza graphs based on symplectic spaces

AbstractLet Fq2ν be the 2ν-dimensional symplectic space over a finite field Fq. For 0≤s≤ν−1 and ν≥2, let W0 be a fixed subspace of type (ν+s,s) in Fq2ν, and let X be the set of the 1-dimensional subspaces in Fq2ν not contained in W0. Denote by Γ the graph with the vertex set X, in which two vertices P and Q are adjacent if P+Q is non-isotropic. Note that Γ is a subgraph of the symplectic graph Sp(2ν,q). In this paper, we determine an equitable partition of X and compute its quotient matrix. Moreover, we show that Γ is a strictly Deza graph, compute its parameters and spectra. Finally, we prove that the (fractional) chromatic number of Γ is qν