Orthogonal graphs over Galois rings of odd characteristic

Assume that ν is a positive integer and δ = 0 , 1 or 2. In this paper we introduce the orthogonal graph Γ 2 ν + δ over a Galois ring of odd characteristic and prove that it is arc transitive. Moreover, we compute its parameters as a quasi-strongly regular graph. In particular, we show that Γ 2 + δ is a strongly regular graph and Γ 2 ν + 1 is a strictly Deza graph when ν ≥ 2 .