{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T11:20:15Z","timestamp":1761218415767,"version":"3.41.2"},"reference-count":32,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100001843","name":"Science and Engineering Research Board","doi-asserted-by":"publisher","award":["MTR\/2017\/000084"],"award-info":[{"award-number":["MTR\/2017\/000084"]}],"id":[{"id":"10.13039\/501100001843","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2022,8]]},"abstract":"<jats:p> Let [Formula: see text] be a simple graph with [Formula: see text] vertices, [Formula: see text] edges having Laplacian eigenvalues [Formula: see text]. The Laplacian energy LE[Formula: see text] is defined as LE[Formula: see text], where [Formula: see text] is the average degree of [Formula: see text]. Radenkovi\u0107 and Gutman conjectured that among all trees of order [Formula: see text], the path graph [Formula: see text] has the smallest Laplacian energy. Let [Formula: see text] be the family of trees of order [Formula: see text] having diameter [Formula: see text]. In this paper, we show that Laplacian energy of any tree [Formula: see text] is greater than the Laplacian energy of [Formula: see text], thereby proving the conjecture for all trees of diameter [Formula: see text]. We also show the truth of conjecture for all trees with number of non-pendent vertices at most [Formula: see text]. Further, we give some sufficient conditions for the conjecture to hold for a tree of order [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830922500094","type":"journal-article","created":{"date-parts":[[2021,9,7]],"date-time":"2021-09-07T03:19:11Z","timestamp":1630984751000},"source":"Crossref","is-referenced-by-count":3,"title":["On a conjecture of Laplacian energy of trees"],"prefix":"10.1142","volume":"14","author":[{"given":"Hilal A.","family":"Ganie","sequence":"first","affiliation":[{"name":"Department of School Education, JK Government Kashmir, India"}]},{"given":"Bilal A.","family":"Rather","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Kashmir, Srinagar, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1137-517X","authenticated-orcid":false,"given":"S.","family":"Pirzada","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Kashmir, Srinagar, India"}]}],"member":"219","published-online":{"date-parts":[[2021,9,6]]},"reference":[{"key":"S1793830922500094BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2008.06.008"},{"key":"S1793830922500094BIB002","series-title":"Spectra of Graphs: Theory and Application","volume-title":"An Introduction to the Theory of Graph Spectra","volume":"75","author":"Cvetkovi\u0107 D. 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