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 $\nu \ge 2$.

arXiv comment10 pages