A Construction of Small $(q-1)$-Regular Graphs of Girth 8

Abstract

In this note we construct a new infinite family of $(q-1)$-regular graphs of girth 8 and order $2q(q-1)^2$ for all prime powers $q\geq 16$, which are the smallest known so far whenever $q-1$ is not a prime power or a prime power plus one itself.

A corrigendum was added May 18, 2021.