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A construction of small $$(q-1)$$-regular graphs of girth 8. (English) Zbl 1310.05152
Summary: 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.

##### MSC:
 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C35 Extremal problems in graph theory
##### Keywords:
cages; girth; Moore graphs; perfect dominating sets
GENREG
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