{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T16:19:26Z","timestamp":1787501966047,"version":"build-2736575974"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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 chromatic number, and the number of edges.  To obtain the results we combine classical cycle index enumeration with recent results from analytic combinatorics.<\/jats:p>","DOI":"10.37236\/984","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:48:27Z","timestamp":1578700107000},"source":"Crossref","is-referenced-by-count":11,"title":["Enumeration and Asymptotic Properties of Unlabeled Outerplanar Graphs"],"prefix":"10.37236","volume":"14","author":[{"given":"Manuel","family":"Bodirsky","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"\u00c9ric","family":"Fusy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mihyun","family":"Kang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefan","family":"Vigerske","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2007,9,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r66\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r66\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:01:17Z","timestamp":1579302077000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1r66"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,9,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/984","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,9,14]]},"article-number":"R66"}}