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A construction of large graphs of diameter two and given degree from Abelian lifts of dipoles

Dávid Mesežnikov — 2012

Kybernetika

For any $d \geq 11$ we construct graphs of degree $d$ , diameter $2$ , and order $\frac{8}{25} d^{2} + O (d)$ , obtained as lifts of dipoles with voltages in cyclic groups. For Cayley Abelian graphs of diameter two a slightly better result of $\frac{9}{25} d^{2} + O (d)$ has been known [3] but it applies only to special values of degrees $d$ depending on prime powers.

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