Orthogonal graphs over Galois rings of odd characteristic

Abstract

Assume that $\nu$ is a positive integer and $\delta=0, 1$ or $2$. In this paper we introduce the orthogonal graph $\Gamma^{2\nu+\delta}$ 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 $\Gamma^{2+\delta}$ is a strongly regular graph and $\Gamma^{2\nu+1}$ is a strictly Deza graph when $\nu\geq 2$.