A construction of small (q-1)-regular graphs of girth 8

preprint2015arXivOpen access

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.

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A construction of small (q-1)-regular graphs of girth 8

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