Abstract
We obtain an explicit formula for the number of labeled connected outerplanar k-cyclic n-vertex bridgeless graphs. We find asymptotics for the number of those graphs for a large number of vertices and fixed k. As a consequence, we prove that, for k fixed, almost all labeled connected outerplanar k-cyclic graphs have bridges.
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The author is grateful to the referees for their remarks and suggestions on the improvement of the exposition of the results of the article.
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Russian Text © The Author(s), 2020, published in Diskretnyi Analiz i Issledovanie Operatsii, 2020, Vol. 27, No. 1, pp. 5–16.
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Voblyi, V.A. On the Number of Labeled Outerplanar k-Cyclic Bridgeless Graphs. J. Appl. Ind. Math. 14, 205–211 (2020). https://doi.org/10.1134/S1990478920010196
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DOI: https://doi.org/10.1134/S1990478920010196