Geodesic
Exact upper estimates of the number of different balls of given radius for the graphs with fixed number of vertexes and diameter
Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 6, pp. 74-92

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For the $n$-vertex usual connected graphs with diameter $d$ the exact upper estimates of the number of different balls of given radius are obtained from investigation of the location of the centers of distinct balls. Ill. 5, bibl. 7.
Keywords: graph, diameter of the graph, metric ball, radius of the ball, number of balls, estimates. 
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     author = {T. I. Fedoryaeva},
     title = {Exact upper estimates of the number of different balls of given radius for the graphs with fixed number of vertexes and diameter},
     journal = {Diskretnyj analiz i issledovanie operacij},
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T. I. Fedoryaeva. Exact upper estimates of the number of different balls of given radius for the graphs with fixed number of vertexes and diameter. Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 6, pp. 74-92. http://geodesic.mathdoc.fr/item/DA_2009_16_6_a6/