{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T10:17:06Z","timestamp":1773656226760,"version":"3.50.1"},"reference-count":39,"publisher":"EDP Sciences","issue":"4","license":[{"start":{"date-parts":[[2022,8,9]],"date-time":"2022-08-09T00:00:00Z","timestamp":1660003200000},"content-version":"vor","delay-in-days":39,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2022,7,11]]},"published-print":{"date-parts":[[2022,7]]},"abstract":"<jats:p>For a graph <jats:italic>G<\/jats:italic>, we denote by <jats:italic>N<\/jats:italic>(<jats:italic>G<\/jats:italic>) the number of non-empty subtrees of <jats:italic>G<\/jats:italic>. If <jats:italic>G<\/jats:italic> is connected, its Wiener index <jats:italic>W<\/jats:italic>(<jats:italic>G<\/jats:italic>) is the sum of distances between all unordered pairs of vertices of <jats:italic>G<\/jats:italic>. In this paper we establish some comparative results between <jats:italic>N<\/jats:italic> and <jats:italic>W<\/jats:italic>. It is shown that <jats:italic>N<\/jats:italic>(<jats:italic>G<\/jats:italic>) &gt;\u00a0<jats:italic>W<\/jats:italic>(<jats:italic>G<\/jats:italic>) if <jats:italic>G<\/jats:italic> is a graph of order <jats:italic>n<\/jats:italic> \u2265 7 and diameter 2 or 3. Also some graphs are constructed with large diameters and <jats:italic>N<\/jats:italic>\u00a0&gt; <jats:italic>W<\/jats:italic>. Moreover, for a tree <jats:italic>T\u00a0\u2247\u00a0S<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> of order <jats:italic>n<\/jats:italic>, we prove that <jats:italic>W<\/jats:italic>(<jats:italic>T<\/jats:italic>)\u00a0&gt;\u00a0<jats:italic>N<\/jats:italic>(<jats:italic>T<\/jats:italic>) if <jats:italic>T<\/jats:italic> is a starlike tree with maximum degree 3 or a tree with exactly two vertices of maximum degrees 3 one of which has two leaf neighbors, or a broom with <jats:italic>k<\/jats:italic>log<jats:sub>2<\/jats:sub>\u00a0<jats:italic>n<\/jats:italic> leaves. And a method is provided for constructing the graphs with <jats:italic>N<\/jats:italic>\u00a0&lt;\u00a0<jats:italic>W<\/jats:italic>. Finally several related open problems are proposed to the comparison between <jats:italic>N<\/jats:italic> and <jats:italic>W<\/jats:italic>.<\/jats:p>","DOI":"10.1051\/ro\/2022118","type":"journal-article","created":{"date-parts":[[2022,7,12]],"date-time":"2022-07-12T18:55:31Z","timestamp":1657652131000},"page":"2495-2511","source":"Crossref","is-referenced-by-count":6,"title":["Comparative results between the number of subtrees and Wiener index of graphs"],"prefix":"10.1051","volume":"56","author":[{"given":"Kexiang","family":"Xu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zuwen","family":"Luo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2022,8,9]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"P28","DOI":"10.37236\/3101","volume":"20","author":"Andriantiana","year":"2013","journal-title":"Electron. 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