{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T19:27:48Z","timestamp":1774466868950,"version":"3.50.1"},"reference-count":23,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2023,9]]},"abstract":"<jats:p>Let [Formula: see text] be vertices of a graph [Formula: see text] with degree of the vertices being [Formula: see text] and [Formula: see text] respectively. First, let us define the weight of the edge [Formula: see text] as twice the value of [Formula: see text] in [Formula: see text]. Let us define [Formula: see text], the harmonic index of the graph [Formula: see text], as the sum obtained by adding the weight assigned to every edge of [Formula: see text]. In this paper, for the class of trees, we shall obtain an upper bound for the harmonic index [Formula: see text] in terms of the edge-vertex domination number and the order of [Formula: see text]. Also, we shall ascertain that the equality is true by characterizing the collection of all extremal trees attaining this bound.<\/jats:p>","DOI":"10.1142\/s0219691323500145","type":"journal-article","created":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T14:22:50Z","timestamp":1677680570000},"source":"Crossref","is-referenced-by-count":2,"title":["On the computation of extremal trees of Harmonic index with given edge-vertex domination number"],"prefix":"10.1142","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8121-7233","authenticated-orcid":false,"given":"B.","family":"Senthilkumar","sequence":"first","affiliation":[{"name":"School of Arts Sciences Humanities and Education, SASTRA Deemed to be University, Thanjavur 613 401, India"}]},{"given":"H. Naresh","family":"Kumar","sequence":"additional","affiliation":[{"name":"School of Arts Sciences Humanities and Education, SASTRA Deemed to be University, Thanjavur 613 401, India"}]},{"given":"Y. B.","family":"Venkatakrishnan","sequence":"additional","affiliation":[{"name":"School of Arts Sciences Humanities and Education, SASTRA Deemed to be University, Thanjavur 613 401, India"}]},{"given":"S. P.","family":"Raja","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Vellore Institute of Technology, Vellore 632 014, Tamilnadu, India"}]}],"member":"219","published-online":{"date-parts":[[2023,3,30]]},"reference":[{"issue":"1","key":"S0219691323500145BIB001","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/050634943","volume":"29","author":"Andriulli F. P.","year":"2007","journal-title":"SIAM J. Sci. Comput."},{"key":"S0219691323500145BIB002","first-page":"1121","volume-title":"Proc. IEEE 10th Int. Conf. Signal Processing","author":"Aoun N. B.","year":"2010"},{"issue":"2","key":"S0219691323500145BIB003","doi-asserted-by":"crossref","first-page":"2250027","DOI":"10.1142\/S1793557122500279","volume":"15","author":"Azari M.","year":"2022","journal-title":"Asian-Euro. J. Math."},{"key":"S0219691323500145BIB004","doi-asserted-by":"crossref","first-page":"125122","DOI":"10.1016\/j.amc.2020.125122","volume":"375","author":"Bermudo S.","year":"2020","journal-title":"Appl. Math. Comput."},{"issue":"1743","key":"S0219691323500145BIB005","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1098\/rspa.1980.0044","volume":"370","author":"Berry M. V.","year":"1980","journal-title":"Proc. R. Soc. Lond., Ser. A"},{"key":"S0219691323500145BIB006","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.amc.2016.01.017","volume":"279","author":"Borovi\u00e1nin B.","year":"2016","journal-title":"Appl. Math. Comput."},{"key":"S0219691323500145BIB007","doi-asserted-by":"crossref","first-page":"2740","DOI":"10.1016\/j.dam.2013.04.003","volume":"161","author":"Deng H.","year":"2013","journal-title":"Discrete Appl. Math."},{"key":"S0219691323500145BIB008","first-page":"187","volume":"60","author":"Fajtlowicz S.","year":"1987","journal-title":"Congr. Numer."},{"key":"S0219691323500145BIB009","doi-asserted-by":"crossref","first-page":"1399","DOI":"10.1016\/j.ijepes.2011.06.020","volume":"33","author":"Ghaemi A. H.","year":"2011","journal-title":"Electr. Power Energy Syst."},{"issue":"3","key":"S0219691323500145BIB010","doi-asserted-by":"crossref","first-page":"84","DOI":"10.3390\/e18030084","volume":"18","author":"Guariglia E.","year":"2016","journal-title":"Entropy"},{"issue":"3","key":"S0219691323500145BIB011","doi-asserted-by":"crossref","first-page":"304","DOI":"10.3390\/e21030304","volume":"21","author":"Guariglia E.","year":"2019","journal-title":"Entropy"},{"issue":"1","key":"S0219691323500145BIB012","first-page":"5542054","volume":"2022","author":"Guariglia E.","year":"2022","journal-title":"J. Funct. Spaces"},{"key":"S0219691323500145BIB013","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/978-3-319-42105-6_16","volume-title":"Engineering Mathematics II","author":"Guariglia E.","year":"2016"},{"key":"S0219691323500145BIB014","volume-title":"Fundamentals of Domination in Graphs","author":"Haynes T. W.","year":"1998"},{"key":"S0219691323500145BIB015","volume-title":"Domination in Graphs: Advanced Topics","author":"Haynes T. W.","year":"1998"},{"key":"S0219691323500145BIB016","first-page":"31","volume":"9","author":"Hu X.","year":"2022","journal-title":"Discrete Math. Lett."},{"key":"S0219691323500145BIB017","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s12044-016-0267-6","volume":"126","author":"Krishnakumari B.","year":"2016","journal-title":"Proc. Indian Acad. Sci. (Math. Sci.)"},{"issue":"4","key":"S0219691323500145BIB019","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1109\/83.841935","volume":"9","author":"Park H.-W.","year":"2000","journal-title":"IEEE Trans. Image Process."},{"key":"S0219691323500145BIB021","doi-asserted-by":"crossref","first-page":"126946","DOI":"10.1016\/j.amc.2022.126946","volume":"421","author":"Sun X.","year":"2022","journal-title":"Appl. Math. Comput."},{"key":"S0219691323500145BIB022","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.ipl.2018.01.012","volume":"134","author":"Venkatakrishnan Y. B.","year":"2018","journal-title":"Inf. Process. Lett."},{"key":"S0219691323500145BIB023","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1016\/j.dam.2022.10.021","volume":"325","author":"Wang T.","year":"2023","journal-title":"Discrete Appl. Math."},{"issue":"6","key":"S0219691323500145BIB024","doi-asserted-by":"crossref","first-page":"2247","DOI":"10.1216\/rmj.2022.52.2247","volume":"52","author":"Zheng Y.","year":"2022","journal-title":"Rocky Mountain J. Math."},{"issue":"7","key":"S0219691323500145BIB025","doi-asserted-by":"crossref","first-page":"1696","DOI":"10.1109\/TSP.2019.2896246","volume":"67","author":"Zheng X.","year":"2019","journal-title":"IEEE Trans. Signal Process."}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691323500145","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,8]],"date-time":"2023-12-08T02:15:54Z","timestamp":1702001754000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219691323500145"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,30]]},"references-count":23,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2023,9]]}},"alternative-id":["10.1142\/S0219691323500145"],"URL":"https:\/\/doi.org\/10.1142\/s0219691323500145","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"value":"0219-6913","type":"print"},{"value":"1793-690X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,3,30]]},"article-number":"2350014"}}