Geodesic
GRAPHS RELATED TO DIAMETER AND CENTER
Acta mathematica Universitatis Comenianae, Tome 66 (1997) no. 1 
F. Gliviak; P. Kys. GRAPHS RELATED TO DIAMETER AND CENTER. Acta mathematica Universitatis Comenianae, Tome 66 (1997) no. 1. http://geodesic.mathdoc.fr/item/AMUC_1997_66_1_a1/
@article{AMUC_1997_66_1_a1,
     author = {F. Gliviak and P. Kys},
     title = {GRAPHS {RELATED} {TO} {DIAMETER} {AND} {CENTER}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {1997},
     volume = {66},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_1997_66_1_a1/}
}
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Voir la notice de l'article provenant de la source Comenius University

A graph is said to be an $L$-graph if all its paths of diametral length contain a central vertex of $G$. Using an earlier result we show that any graph can be embedded to an $L$-graph of radius a and diameter $b$, where $a\le b\le 2a$. We show that the known bounds of the number of edges and the maximum degree of the graphs of diameter $d\ge 2$ are sharp for $L$-graphs, too. Then we estimate the minimum degree of $L$-graphs. Finally we estimate the number of central vertices in $L$-graphs; all bounds are best possible.