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 $Γ^{2ν+δ}$ 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 $Γ^{2ν+1}$ is a strictly Deza graph when $ν\geq 2$.

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