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

[摘要] 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.

[学科分类] 离散数学和组合数学

[关键词] Cages;Girth;Moore Graphs;Perfect Dominating Sets