Abstract
The class of outerplanar graphs is used for testing the average complexity of algorithms on graphs. A random labeled outerplanar graph can be generated by a polynomial algorithm based on the results of an enumeration of such graphs. By a bicyclic (tricyclic) graph we mean a connected graph with cyclomatic number 2 (respectively, 3). We find explicit formulas for the number of labeled connected outerplanar bicyclic and tricyclic graphs with n vertices and also obtain asymptotics for the number of these graphs for large n. Moreover, we obtain explicit formulas for the number of labeled outerplanar bicyclic and tricyclic n-vertex blocks and deduce the corresponding asymptotics for large n.
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Original Russian Text © V.A. Voblyi, A.K. Meleshko, 2017, published in Diskretnyi Analiz i Issledovanie Operatsii, 2017, Vol. 24, No. 2, pp. 18–31.
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Voblyi, V.A., Meleshko, A.K. Enumeration of labeled outerplanar bicyclic and tricyclic graphs. J. Appl. Ind. Math. 11, 296–303 (2017). https://doi.org/10.1134/S1990478917020168
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DOI: https://doi.org/10.1134/S1990478917020168