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English version: Journal of Applied and Industrial Mathematics, 2017, 11:2, 296303 

Volume 24, No 2, 2017, P. 1831 UDC 519.175.3
Keywords: enumeration, labeled graph, outerplanar graph, bicyclic graph, tricyclic graph, asymptotics. DOI: 10.17377/daio.2017.24.544 Vitaly A. Voblyi ^{1} Received 10 May 2016 References[1] V. A. Voblyi, Asymptotic enumeration of graphs of some types, Cand. Sci. Dissertation, VTs AN SSSR, Moscow, 1985 [Russian].[2] V. A. Voblyi, A formula for the number of labeled connected graphs, Diskretn. Anal. Issled. Oper., 19, No. 4, 48–59, 2012 [Russian]. [3] V. A. Voblyi and A. K. Meleshko, Enumeration of labeled rose graphs, in Materialy XVI Mezhdunarodnogo nauchnotechnicheskogo seminara “Kombinatornye konfiguratsii i ikh prilozheniya” (Proc. XVI Int. Sci. Tech. Seminar “Combinatorial Configurations and Its Applications”), Kirovograd, Ukraine, Apr. 11–12, 2014, pp. 27–29, Kirovograd Natl. Tech. Univ., Kirovograd, 2014 [Russian]. [4] E. F. Dmitriev, Enumeration of labeled twocolored connected graphs with small cyclomatic number, Depos. Manuscr. Deposited in VINITI, No. 455985 [Russian]. [5] A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integraly i ryady: Elementarnye funktsii (Integrals and Series: Elementary Functions), Nauka, Moscow, 1981 [Russian]. [6] V. E. Stepanov, On some features of the structure of a random graph near a critical point, Teor. Veroyatn. Primen., 32, No. 4, 633–657, 1987 [Russian]. Translated in Theory Probab. Appl., 32, No. 4, 573–594, 1987. [7] F. Harary, Graph Theory, AddisonWesley, Reading, MA, USA, 1969. Translated under the title Teoriya grafov, Mir, Moscow, 1973 [Russian]. [8] F. Harary and E. M. Palmer, Graphical Enumeration, Acad. Press, New York, 1973. Translated under the title Perechislenie grafov, Mir, Moscow, 1977 [Russian]. [9] M. Bodirsky and M. Kang, Generating outerplanar graphs uniformly at random, Comb. Probab. Comput., 15, 333–343, 2006. [10] M. Bodirsky, O. Gimenez, M. Kang, and M. Noy, Enumeration and limit laws of seriesparallel graph, Eur. J. Comb., 28, 2091–2105, 2007. [11] G. W. Ford and G. E. Uhlenbeck, Combinatorial problems in the theory of graphs. IV, Proc. Natl. Acad. Sci. USA, 43, No. 1, 163–167, 1957. [12] D. E. Knuth and B. Pittel, A recurrence related to trees, Proc. Am. Math. Soc. 105, No. 2, 335–349, 1989. [13] R. C. Read, Some unusual enumeration problems, Ann. N. Y. Acad. Sci. 175, 314–326, 1970. [14] E. M. Wright, The number of connected sparsely edged graphs, J. Graph Theory, 1, No. 4, 317–330, 1977. [15] E. M. Wright, The number of connected sparsely edged graphs. II. Smooth graphs and blocks, J. Graph Theory, 2, No. 4, 299–305, 1978. 

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