Enumeration and Asymptotic Properties of Unlabeled Outerplanar Graphs

Manuel Bodirsky, Éric Fusy, Mihyun Kang, Stefan Vigerske
2007 Electronic Journal of Combinatorics  
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 $g\, n^{-5/2}\rho^{-n}$, where $g\approx0.00909941$ and $\rho^{-1}\approx7.50360$ can be approximated. Using our enumerative results we investigate several statistical properties of random unlabeled outerplanar graphs on $n$ vertices, for instance concerning connectedness, the
more » ... atic number, and the number of edges. To obtain the results we combine classical cycle index enumeration with recent results from analytic combinatorics.
doi:10.37236/984 fatcat:jd7sgnqbi5g7zpayq7yoboc7vi