Geodesic
On graphs with given diameter, number of vertices, and local diversity of balls
Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 1, pp. 65-74

Voir la notice de l'article provenant de la source Math-Net.Ru

The $n$-vertex graphs with diameter $d$ and local $t$-diversity of balls, i.e. graphs having $n$ different balls of radius $i$ for every $i\leq t$, in connection with the characterization problem of the diversity vectors of balls of usual connected graphs are studied. For such graphs there exists a lower bound for the number of vertices, defined by the parameters $d$ and $t$. All graphs of the minimal possible order with diameter $d$ and local $t$-diversity of balls (full diversity of balls) are explicitly described up to isomorphism. Moreover, the diversity vector of balls is calculated for any such graph. Ill. 4, bibl. 8.
Keywords: graph, diameter of the graph, metric ball, radius of the ball, number of balls, diversity vector of balls. 
T. I. Fedoryaeva. On graphs with given diameter, number of vertices, and local diversity of balls. Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 1, pp. 65-74. http://geodesic.mathdoc.fr/item/DA_2010_17_1_a3/
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