Geodesic
A construction of large graphs of diameter two and given degree from Abelian lifts of dipoles
Kybernetika, Tome 48 (2012) no. 3, pp. 518-521.

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For any $d\ge 11$ 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.
Classification : 05C12, 05C35
Keywords: the degree-diameter problem; voltage assignment and lift; dipole 
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     author = {Mese\v{z}nikov, D\'avid},
     title = {A construction of large graphs of diameter two and given degree from {Abelian} lifts of dipoles},
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Mesežnikov, Dávid. A construction of large graphs of diameter two and given degree from Abelian lifts of dipoles. Kybernetika, Tome 48 (2012) no. 3, pp. 518-521. http://geodesic.mathdoc.fr/item/KYB_2012__48_3_a11/