{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T08:04:45Z","timestamp":1750320285524},"reference-count":0,"publisher":"Combinatorial Press","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ars Comb."],"published-print":{"date-parts":[[2024,6,30]]},"abstract":"<jats:p>Let \\( G=(V,E) \\) be a simple connected graph with vertex set \\( G \\) and edge set \\( E \\). The harmonic index of graph \\( G \\) is the value \\( H(G)=\\sum_{uv\\in E(G)} \\frac{2}{d_u+d_v} \\), where \\( d_x \\) refers to the degree of \\( x \\). We obtain an upper bound for the harmonic index of trees in terms of order and the total domination number, and we characterize the extremal trees for this bound.<\/jats:p>","DOI":"10.61091\/ars159-15","type":"journal-article","created":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T05:14:41Z","timestamp":1720588481000},"page":"179-186","source":"Crossref","is-referenced-by-count":1,"title":["Sharp Upper Bound for Harmonic Index of Trees with Given Total Domination Number"],"prefix":"10.61091","volume":"159","author":[{"given":"Roslan","family":"Hasni","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Special Interest Group on Modeling and Data Analytics (SIGMDA) Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fateme","family":"Movahedi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hailiza","family":"Kamarulhaili","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad Hadi","family":"Akhbari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"School of Mathematical Science, Universiti Sains Malaysia, 11800 USM Penang, Malaysia, 11800 USM Penang, Malaysia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Mathematics, Estahban Branch Islamic Azad University, Estahban, Iran","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"39747","published-online":{"date-parts":[[2024,6,30]]},"container-title":["Ars Combinatoria"],"original-title":[],"deposited":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T05:14:56Z","timestamp":1720588496000},"score":1,"resource":{"primary":{"URL":"https:\/\/combinatorialpress.com\/ars-articles\/volume-159\/sharp-upper-bound-for-harmonic-index-of-trees-with-given-total-domination-number\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,6,30]]},"published-print":{"date-parts":[[2024,6,30]]}},"URL":"https:\/\/doi.org\/10.61091\/ars159-15","relation":{},"ISSN":["0381-7032","2817-5204"],"issn-type":[{"value":"0381-7032","type":"print"},{"value":"2817-5204","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,30]]}}}