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

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{KYB_2012__48_3_a11,
     author = {Mese\v{z}nikov, D\'avid},
     title = {A construction of large graphs of diameter two and given degree from {Abelian} lifts of dipoles},
     journal = {Kybernetika},
     pages = {518--521},
     publisher = {mathdoc},
     volume = {48},
     number = {3},
     year = {2012},
     mrnumber = {2975804},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_3_a11/}
}
TY  - JOUR
AU  - Mesežnikov, Dávid
TI  - A construction of large graphs of diameter two and given degree from Abelian lifts of dipoles
JO  - Kybernetika
PY  - 2012
SP  - 518
EP  - 521
VL  - 48
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KYB_2012__48_3_a11/
LA  - en
ID  - KYB_2012__48_3_a11
ER  - 
%0 Journal Article
%A Mesežnikov, Dávid
%T A construction of large graphs of diameter two and given degree from Abelian lifts of dipoles
%J Kybernetika
%D 2012
%P 518-521
%V 48
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2012__48_3_a11/
%G en
%F KYB_2012__48_3_a11
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/