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English version: Journal of Applied and Industrial Mathematics, 2016, 10:2, 302-310 |
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Volume 23, No 2, 2016, P. 5-20 UDC 519.175.3
Keywords: enumeration, labeled graph, block, cactus, asymptotics. DOI: 10.17377/daio.2016.23.501 Vitali A. Voblyi 1 Received 13 July 2015 References[1] G. N. Bagaev and E. F. Dmitriev, The number of connected labeled bipartite graphs, Dokl. Akad. Nauk BSSR, 28, No. 12, 1061–1063, 1984.[2] V. A. Voblyi, Wright and Stepanov–Wright coefficients, Mat. Zametki, 42, No. 6, 854–862, 1987. Translated in Math. Notes Acad. Sci. USSR, 42, No. 6, 969–974, 1987. [3] V. A. Voblyi, On enumeration of labelled connected graphs by the number of cutpoints, Diskretn. Mat., 20, No. 1, 52–63, 2008. Translated in Discrete Math. Appl., 18, No. 1, 57–69, 2008. [4] V. A. Voblyi, A formula for the number of labeled connected graphs, Diskretn. Anal. Issled. Oper., 19, No. 4, 48–59, 2012. [5] V. A. Voblyi, Enumeration of labeled connected bicyclic and tricyclic graphs without bridges, Mat. Zametki, 91, No. 2, 308–311, 2012. Translated in Math. Notes, 91, No. 1, 293–297, 2012. [6] V. A. Voblyi, Enumeration of labeled bicyclic and tricyclic Eulerian graphs, Mat. Zametki, 92, No. 5, 678–683, 2012. Translated in Math. Notes, 92, No. 5–6, 619–623, 2012. [7] V. A. Voblyi, Enumeration of labeled Eulerian cacti, in Materialy XI Mezhdunarodnogo seminara “Diskretnaya matematika i ee prilozheniya” (Proc. XI Int. Seminar “Discrete Math. and Its Applications”), Moscow, Russia, Jan. 18–23, 2012, pp. 275–277, Izd. Mekh.-Mat. Fak. MGU, Moscow, 2012. [8] V. A. Voblyi, Enumeration of labeled geodetic planar graphs, Mat. Zametki, 97, No. 3, 336–341, 2015. Translated in Math. Notes, 97, No. 3, 321–325, 2015. [9] V. A. Voblyi and A. K. Meleshko, The number of labeled block-cactus graphs, Diskretn. Anal. Issled. Oper., 21, No. 2, 24–32, 2014. Translated in J. Appl. Indust. Math., 8, No. 3, 422427, 2014. [10] I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley & Sons, New York, 1983. Translated under the title Perechislitel’naya kombinatorika, Nauka, Moscow, 1990. [11] A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integraly i ryady. T. 3: Elementarnye funktsii (Integrals and Series. Vol. 3: Elementary Functions), Nauka, Moscow, 1981. [12] F. Harary, Graph Theory, Addison-Wesley, Reading, MA, USA, 1969. Translated under the title Teoriya grafov, Mir, Moscow, 1973. [13] F. Harary and E. M. Palmer, Graphical Enumeration, Acad. Press, New York, 1973. Translated under the title Perechislenie grafov, Mir, Moscow, 1977. [14] J. Riordan, Combinatorial Identities, John Wiley & Sons, New York, 1968. Translated under the title Kombinatornye tozhdestva, Nauka, Moscow, 1982. [15] M. Drmota, É. Fusy, M. Kang, V. Kraus, and J. Rué, Asymptotic study of subcritical graph classes, 2010 (Cornell Univ. Libr. e-Print Archive, arXiv:1003.4699). [16] L. Fleisher, Building chain and cactus representations of all minimum cuts from Hao–Orlin in the same asymptotic run time, J. Algorithms, 33, No. 1, 51–72, 1999. [17] G. W. Ford and G. E. Uhlenbeck, Combinatorial problems in the theory graphs. I, Proc. Natl. Acad. Sci. USA, 42, No. 3, 122–128, 1956. [18] G. W. Ford and G. E. Uhlenbeck, Combinatorial problems in the theory graphs. III, Proc. Natl. Acad. Sci. USA, 42, No. 8, 529–535, 1956. [19] P. Leroux, Enumerative problems inspired by Mayer’s theory of cluster integrals, Electron. J. Comb., 11, No. R32, 1–28, 2004. [20] F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, eds., NIST Handbook of Mathematical Functions, Cambridge Univ. Press, New York, 2010. [21] R. Vicente, D. Saad, and Y. Kabashima, Error-correcting code on a cactus: A solvable model, Europhys. Lett., 51, No. 6, 698–704, 2000. [22] E. M. Wright, The number of connected sparsely edged graphs. III. Asymptotic results, J. Graph Theory, 4, No. 4, 393–407, 1980. |
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