Geodesic
The diversity vector of balls of a~typical graph of small diameter
Diskretnyj analiz i issledovanie operacij, Tome 22 (2015) no. 6, pp. 43-54

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For ordinary connected graphs, the diversity vectors of balls ($i$th component of the vector is equal to the number of different balls of radius $i$) are studied asymptotically. The asymptotic behavior of the number of graphs of small diameter with full diversity of balls is investigated. The diversity vector of balls of a typical graph of the given small diameter is calculated. Asymptotically exact value of the number of labeled $n$-vertex graphs of diameter 3 is obtained. Ill. 2, bibliogr. 12.
Keywords: graph, metric ball, radius of ball, number of balls, diversity vector of balls, typical graph. 
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     author = {T. I. Fedoryaeva},
     title = {The diversity vector of balls of a~typical graph of small diameter},
     journal = {Diskretnyj analiz i issledovanie operacij},
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     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/DA_2015_22_6_a2/}
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T. I. Fedoryaeva. The diversity vector of balls of a~typical graph of small diameter. Diskretnyj analiz i issledovanie operacij, Tome 22 (2015) no. 6, pp. 43-54. http://geodesic.mathdoc.fr/item/DA_2015_22_6_a2/