Geodesic
On the diversity of balls in a~graph of a~given diameter
Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 127-128

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The diversity vectors for balls in connected graphs are asymptotically studied. Here for a graph, the $i$th component of the vector is equal to the number of different balls of radius $i$ in the graph. The asymptotic behavior of the number of graphs with a special (in particular with the local) diversity of balls is researched. The diversity of balls of large radii in a graph of a given diameter is described.
Keywords: graph, balls, radius of ball, the diversity vector for balls. 
@article{PDMA_2015_8_a47,
     author = {T. I. Fedoryaeva},
     title = {On the diversity of balls in a~graph of a~given diameter},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {127--128},
     publisher = {mathdoc},
     number = {8},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2015_8_a47/}
}
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T. I. Fedoryaeva. On the diversity of balls in a~graph of a~given diameter. Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 127-128. http://geodesic.mathdoc.fr/item/PDMA_2015_8_a47/