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This article is cited in 1 scientific paper (total in 1 paper)
Enumeration of labeled outerplanar bicyclic and tricyclic graphs
V. A. Voblyi, A. K. Meleshko Bauman Moscow State University, 5 Bld. 1 Vtoraya Baumanskaya St., 105005 Moscow, Russia
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 $n$. Tab. 1, illustr. 4, bibliogr. 15.
Keywords:
enumeration, labeled graph, outerplanar graph, bicyclic graph, tricyclic graph, asymptotics.
Received: 10.05.2016 Revised: 11.10.2016
Citation:
V. A. Voblyi, A. K. Meleshko, “Enumeration of labeled outerplanar bicyclic and tricyclic graphs”, Diskretn. Anal. Issled. Oper., 24:2 (2017), 18–31; J. Appl. Industr. Math., 11:2 (2017), 296–303
Linking options:
https://www.mathnet.ru/eng/da867 https://www.mathnet.ru/eng/da/v24/i2/p18
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Abstract page: | 275 | Full-text PDF : | 58 | References: | 47 | First page: | 10 |
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