{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T21:34:34Z","timestamp":1769981674499,"version":"3.49.0"},"reference-count":11,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":5575,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1991,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We define two two\u2010variable polynomials for rooted trees and one two\u2010variable polynomial for unrooted trees, all of which are based on the coranknullity formulation of the Tutte polynomial of a graph or matroid. For the rooted polynomials, we show that the polynomial completely determines the rooted tree, i.e., rooted trees <jats:italic>T<\/jats:italic><jats:sub>1<\/jats:sub> and <jats:italic>T<\/jats:italic><jats:sub>2<\/jats:sub> are isomorphic if and only if <jats:italic>f<\/jats:italic>(<jats:italic>T<\/jats:italic><jats:sub>1<\/jats:sub>) = <jats:italic>f<\/jats:italic>(<jats:italic>T<\/jats:italic><jats:sub>2<\/jats:sub>). The corresponding question is open in the unrooted case, although we can reconstruct the degree sequence, number of subtrees of size <jats:italic>k<\/jats:italic> for all <jats:italic>k<\/jats:italic>, and the number of paths of length <jats:italic>k<\/jats:italic> for all <jats:italic>k<\/jats:italic> from the (unrooted) polynomial. The key difference between these three polynomials and the standard Tutte polynomial is the rank function used; we use pruning and branching ranks to define the polynomials. We also give a subtree expansion of the polynomials and a deletion\u2010contraction recursion they satisfy.<\/jats:p>","DOI":"10.1002\/jgt.3190150308","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T07:17:01Z","timestamp":1181287021000},"page":"317-331","source":"Crossref","is-referenced-by-count":23,"title":["Tutte polynomials for trees"],"prefix":"10.1002","volume":"15","author":[{"given":"Sharad","family":"Chaudhary","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gary","family":"Gordon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.2307\/1967597"},{"key":"e_1_2_1_3_2","volume-title":"Theory of Matroids, Advanced Theory","author":"Bj\u00f6rner A."},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"T.Brylawski The Tutte polynomial part I: General theory.Matroid Theory and Its Applications.Proceedings of Third International Mathematical Summer Centre (C. I. M. E.)1980. Ligouri Naples Italy (1982)125\u2013276.","DOI":"10.1007\/978-3-642-11110-5_3"},{"key":"e_1_2_1_5_2","volume-title":"Theory of Matroids, Advanced Theory","author":"Brylawski T."},{"key":"e_1_2_1_6_2","unstructured":"G.Gordon A Tutte polynomial for partially ordered sets. Submitted."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.2307\/2047815"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-9763-6"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1954-010-9"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.2307\/1967604"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1932-05460-X"},{"key":"e_1_2_1_12_2","first-page":"277","article-title":"The lattice of all subtrees of a tree","volume":"27","author":"Zelinka B.","year":"1977","journal-title":"Math. Slovaca"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190150308","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190150308","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T21:47:28Z","timestamp":1698011248000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190150308"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,7]]},"references-count":11,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1991,7]]}},"alternative-id":["10.1002\/jgt.3190150308"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190150308","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,7]]}}}