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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^-5/2ρ^-n, where g≈0.00909941 and ρ^-1≈7.50360 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 obtainarXiv:math/0511422v2 fatcat:yzrumfzlzvbjtmqarpcvqf2qpq