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English version: Journal of Applied and Industrial Mathematics, 2017, 11:2, 204214 

Volume 24, No 2, 2017, P. 6886 UDC 519.1+519.175
Keywords: graph, labeled graph, shortest path, graph diameter, number of graphs, ordinary graph. DOI: 10.17377/daio.2017.24.534 Tatiana I. Fedoryaeva ^{1,2} Received 29 March 2016 References[1] V. A. Emelichev, O. I. Melnikov, V. I. Sarvanov, and R. I. Tyshkevich, Lektsii po teorii grafov, Nauka, Moscow, 1990 [Russian]. Translated under the title Lectures on Graph Theory, B. I. Wissenschaftsverlag, Mannheim, 1994.[2] T. I. Fedoryaeva, The diversity vector of balls of a typical graph of small diameter, Diskretn. Anal. Issled. Oper., 22, No. 6, 43–54, 2015 [Russian]. [3] F. Harary, Graph Theory, AddisonWesley, Reading, MA, USA, 1969. Translated under the title Teoriya grafov, Mir, Moscow, 1973 [Russian]. [4] S. V. Yablonskii, Vvedenie v diskretnuyu matematiku (Introduction to Discrete Mathematics), Nauka, Moscow, 1986 [Russian]. [5] Z. Füredi and Y. Kim, The number of graphs of given diameter, 2012 (Cornell Univ. Libr. ePrint Archive, arXiv:1204.4580). [6] Y. Kim, Problems in extremal combinatorics, Ph. D. Thesis, Univ. Ill. UrbanaChampaign, Urbana, Champaign, 2011. [7] J. W. Moon and L. Moser, Almost all (0,1) matrices are primitive, Stud. Sci. Math. Hung., 1, 153–156, 1966. [8] I. Tomescu, An asymptotic formula for the number of graphs having small diameter, Discrete Math., 156, No. 1–3, 219–228, 1996. [9] I. Tomescu, Almost all graphs and hhypergraphs have small diameter, Aus?tralas. J. Comb., 31, 313–323, 2005. 

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