Enumeration of Unlabeled Outerplanar Graphs [article]

Manuel Bodirsky, Stefan Vigerske
2006 arXiv   pre-print
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 obtain
more » ... the results we combine classical cycle index enumeration with recent results from analytic combinatorics.
arXiv:math/0511422v2 fatcat:yzrumfzlzvbjtmqarpcvqf2qpq