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

M. Abreu, G. Araujo-Pardo, C. Balbuena, D. Labbate

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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.


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Cages; Girth; Moore Graphs; Perfect Dominating Sets

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