Enumeration of Unlabeled Outerplanar Graphs
  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, chromatic number, and the number of edges. To obtain the results we combine classical cycle index enumeration with recent results from analytic combinatorics. 
Manuel Bodirsky (1), Eric Fusy (2), Mihyun Kang (1), and Stefan   Vigerske (1) ((1) Humboldt University Berlin, (2) INRIA Ro...