Geodesic
On the description problem of the diversity vectors of balls
Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 1, pp. 44-52

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The diversity vectors of balls are studied (the $i$th component of the vector is equal to the number of different balls of radius $i$) for ordinary connected graphs. The description problem of the diversity vectors of balls is solved for graphs with a small diameter. Ill. 3, bibliogr. 11.
Keywords: graph, metric ball, radius of ball, the number of balls, the diversity vector of balls. 
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A. A. Evdokimov; T. I. Fedoryaeva. On the description problem of the diversity vectors of balls. Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 1, pp. 44-52. http://geodesic.mathdoc.fr/item/DA_2014_21_1_a3/