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We show that the only non\u2010trivial finite 3\u2010graphs homogeneous in the sense of Fra\u00efss\u00e9 are those associated with the projective planes over GF(2) and GF(3), and with the projective lines over GF(5) and GF(9). To exclude other possibilities we use the classification of doubly transitive finite permutation groups.<\/jats:p>","DOI":"10.1002\/malq.19950410302","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T17:47:19Z","timestamp":1180201639000},"page":"287-306","source":"Crossref","is-referenced-by-count":9,"title":["Finite Homogeneous 3\u2010Graphs"],"prefix":"10.1002","volume":"41","author":[{"given":"Alistair H.","family":"Lachlan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Allyson","family":"Tripp","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511600739"},{"key":"e_1_2_1_3_2","volume-title":"Theory of Groups of Finite Order","author":"Burnside W.","year":"1955"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/13.1.1"},{"key":"e_1_2_1_5_2","first-page":"65","volume-title":"Logic Colloquium '85","author":"Cherlin G.","year":"1987"},{"key":"e_1_2_1_6_2","unstructured":"Cherlin G. 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