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 $q\ge 16$, which are the smallest known so far whenever $q-1$ is not a prime power or a prime power plus one itself.

8 pages, 2 figures