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Enumeration of Unlabeled Outerplanar Graphs

Manuel Bodirsky·Eric Fusy·Mihyun Kang·Stefan Vigerske
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Abstract

We determine the exact and asymptotic number of unlabeled outerplanar graphs. The exact number g_n of unlabeled outerplanar graphs on n vertices can be computed in polynomial time, and g_n is asymptotically $g n^{-5/2}ρ^{-n}$, where $g\approx0.00909941$ and $ρ^{-1}\approx7.50360$ can be approximated. Using our enumerative results we investigate several statistical properties of random unlabeled outerplanar graphs on n vertices, for instance concerning connectedness, chromatic number, and the number of edges. To obtain the results we combine classical cycle index enumeration with recent results from analytic combinatorics.

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Manuel Bodirsky, Eric Fusy, Mihyun Kang, Stefan Vigerske. 2006-01-25. Enumeration of Unlabeled Outerplanar Graphs. https://arxiv.org/abs/math/0511422

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