{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:17:26Z","timestamp":1753885046432,"version":"3.41.2"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2025,2]]},"abstract":"<jats:p> Let [Formula: see text] be a simple connected graph. The modified first Zagreb index is denoted by [Formula: see text] is defined as [Formula: see text]. We present a lower bound for [Formula: see text] in terms of order and total domination number for trees and characterize the extremal trees attaining the bound. <\/jats:p>","DOI":"10.1142\/s1793830924500307","type":"journal-article","created":{"date-parts":[[2024,3,28]],"date-time":"2024-03-28T12:30:44Z","timestamp":1711629044000},"source":"Crossref","is-referenced-by-count":0,"title":["Modified Zagreb index and total domination in trees"],"prefix":"10.1142","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1717-239X","authenticated-orcid":false,"given":"H. Naresh","family":"Kumar","sequence":"first","affiliation":[{"name":"School of Arts Sciences Humanities & Education, SASTRA Deemed to be University, Thanjavur 613401, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8121-7233","authenticated-orcid":false,"given":"B.","family":"Senthilkumar","sequence":"additional","affiliation":[{"name":"School of Arts Sciences Humanities & Education, SASTRA Deemed to be University, Thanjavur 613401, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2782-6315","authenticated-orcid":false,"given":"S.","family":"Balachandran","sequence":"additional","affiliation":[{"name":"School of Arts Sciences Humanities & Education, SASTRA Deemed to be University, Thanjavur 613401, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4560-2040","authenticated-orcid":false,"given":"Y. B.","family":"Venkatakrishnan","sequence":"additional","affiliation":[{"name":"School of Arts Sciences Humanities & Education, SASTRA Deemed to be University, Thanjavur 613401, India"},{"name":"Directorate of Online & Distance Education, SASTRA Deemed to be University, Thanjavur 613401, India"}]}],"member":"219","published-online":{"date-parts":[[2024,4,18]]},"reference":[{"key":"S1793830924500307BIB001","first-page":"125122","volume":"375","author":"Bermudo S.","year":"2020","journal-title":"Appl. Math. Comput."},{"key":"S1793830924500307BIB002","first-page":"208","volume":"279","author":"Borovi\u0107anin B.","year":"2016","journal-title":"Appl. Math. Comput."},{"key":"S1793830924500307BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s11464-015-0431-9"},{"key":"S1793830924500307BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(97)00067-X"},{"key":"S1793830924500307BIB005","first-page":"422","volume":"275","author":"Deng H.","year":"2016","journal-title":"Appl. Math. Comput."},{"key":"S1793830924500307BIB006","first-page":"2163","volume":"8","author":"Dhanalakshmi K.","year":"2021","journal-title":"Eur. J. Mol. Clin. Med."},{"key":"S1793830924500307BIB007","first-page":"637","volume":"24","author":"Elumalai S.","year":"2022","journal-title":"Math. Rep."},{"key":"S1793830924500307BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/0009-2614(72)85099-1"},{"key":"S1793830924500307BIB009","doi-asserted-by":"publisher","DOI":"10.1063\/1.430994"},{"key":"S1793830924500307BIB010","first-page":"83","volume":"50","author":"Gutman I.","year":"2004","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"S1793830924500307BIB011","first-page":"659","volume":"65","author":"Hao J.","year":"2011","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"S1793830924500307BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-6525-6"},{"key":"S1793830924500307BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2009.08.015"},{"key":"S1793830924500307BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/s10878-014-9802-5"},{"key":"S1793830924500307BIB015","first-page":"13","volume":"8","author":"Milovanovi\u0107 I.","year":"2023","journal-title":"Commun. Combin. Optim."},{"key":"S1793830924500307BIB016","first-page":"641","volume":"72","author":"Xu K.","year":"2014","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"S1793830924500307BIB017","first-page":"127131","volume":"427","author":"Yang J.","year":"2021","journal-title":"Appl. Math. Comput."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830924500307","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T04:31:17Z","timestamp":1738038677000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830924500307"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,18]]},"references-count":17,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2025,2]]}},"alternative-id":["10.1142\/S1793830924500307"],"URL":"https:\/\/doi.org\/10.1142\/s1793830924500307","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2024,4,18]]},"article-number":"2450030"}}