Orthogonal graphs of odd characteristic and their automorphisms

The (isotropic) orthogonal graph O(2ν+δ,q) over Fq of odd characteristic, where ν⩾1 and δ=0,1 or 2 is introduced. When ν=1, O(2⋅1+δ,q) is a complete graph. When ν⩾2, O(2ν+δ,q) is strongly regular and its parameters are computed, as well as its chromatic number. The automorphism groups of orthogonal graphs are also determined.