Journal of Applied and Industrial Mathematics, 2017, 11:2, 296-303
Volume 24, No 2, 2017, P. 18-31
Keywords: enumeration, labeled graph, outerplanar graph, bicyclic graph, tricyclic graph, asymptotics.
Received 10 May 2016
References V. A. Voblyi, Asymptotic enumeration of graphs of some types, Cand. Sci. Dissertation, VTs AN SSSR, Moscow, 1985 [Russian].
 V. A. Voblyi, A formula for the number of labeled connected graphs, Diskretn. Anal. Issled. Oper., 19, No. 4, 48–59, 2012 [Russian].
 V. A. Voblyi and A. K. Meleshko, Enumeration of labeled rose graphs, in Materialy XVI Mezhdunarodnogo nauchno-technicheskogo 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].
 E. F. Dmitriev, Enumeration of labeled two-colored connected graphs with small cyclomatic number, Depos. Manuscr. Deposited in VINITI, No. 4559-85 [Russian].
 A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integraly i ryady: Elementarnye funktsii (Integrals and Series: Elementary Functions), Nauka, Moscow, 1981 [Russian].
 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.
 F. Harary, Graph Theory, Addison-Wesley, Reading, MA, USA, 1969. Translated under the title Teoriya grafov, Mir, Moscow, 1973 [Russian].
 F. Harary and E. M. Palmer, Graphical Enumeration, Acad. Press, New York, 1973. Translated under the title Perechislenie grafov, Mir, Moscow, 1977 [Russian].
 M. Bodirsky and M. Kang, Generating outerplanar graphs uniformly at random, Comb. Probab. Comput., 15, 333–343, 2006.
 M. Bodirsky, O. Gimenez, M. Kang, and M. Noy, Enumeration and limit laws of series-parallel graph, Eur. J. Comb., 28, 2091–2105, 2007.
 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.
 D. E. Knuth and B. Pittel, A recurrence related to trees, Proc. Am. Math. Soc. 105, No. 2, 335–349, 1989.
 R. C. Read, Some unusual enumeration problems, Ann. N. Y. Acad. Sci. 175, 314–326, 1970.
 E. M. Wright, The number of connected sparsely edged graphs, J. Graph Theory, 1, No. 4, 317–330, 1977.
 E. M. Wright, The number of connected sparsely edged graphs. II. Smooth graphs and blocks, J. Graph Theory, 2, No. 4, 299–305, 1978.
|© Sobolev Institute of Mathematics, 2015|