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.

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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. 
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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/

[1] Evdokimov A. A., “Lokalno izometricheskie vlozheniya grafov i svoistvo prodolzheniya metriki”, Sib. zhurn. issled. operatsii, 1:1 (1994), 5–12 | MR | Zbl

[2] Evdokimov A. A., “Vlozheniya v klasse parametricheskikh otobrazhenii ogranichennogo iskazheniya”, Uch. zap. Kazansk. gos. un-ta, 151, no. 2, 2009, 72–79

[3] Emelichev V. A., Melnikov O. I., Sarvanov V. I., Tyshkevich R. I., Lektsii po teorii grafov, Nauka, M., 1990, 383 pp. | MR | Zbl

[4] Rychkov K. L., “O dostatochnykh usloviyakh suschestvovaniya grafa s zadannym raznoobraziem sharov”, Diskret. analiz i issled. operatsii. Ser. 1, 13:1 (2006), 99–108 | MR

[5] Fedoryaeva T. I., “O raznoobrazii metricheskikh sharov v grafakh”, Problemy teoreticheskoi kibernetiki, Tez. dokl. XIV Mezhdunar. konf. (Penza, 23–28 maya 2005 g.), Izd-vo mekh.-mat. f-ta MGU, M., 2005, 159

[6] Fedoryaeva T. I., “Raznoobrazie sharov v metricheskikh prostranstvakh derevev”, Diskret. analiz i issled. operatsii. Ser. 1, 12:3 (2005), 74–84 | MR

[7] Fedoryaeva T. I., “Vektory raznoobraziya sharov i svoistva ikh komponent”, Tr. VII Mezhdunar. konf. “Diskretnye modeli v teorii upravlyayuschikh sistem” (Moskva, 4–6 marta 2006 g.), Izd-vo MGU, M., 2006, 374–378

[8] Fedoryaeva T. I., “Vektory raznoobraziya sharov dlya grafov i otsenki ikh komponent”, Diskret. analiz i issled. operatsii. Ser. 1, 14:2 (2007), 47–67 | MR