{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:22:37Z","timestamp":1753885357089,"version":"3.41.2"},"reference-count":29,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2022,7]]},"abstract":"<jats:p> Let [Formula: see text] be a connected graph of order [Formula: see text] and let [Formula: see text] be the reciprocal distance matrix (also called Harary matrix) of the graph [Formula: see text]. Let [Formula: see text] be the eigenvalues of the reciprocal distance matrix [Formula: see text] of the connected graph [Formula: see text] called the reciprocal distance eigenvalues of [Formula: see text]. The Harary energy [Formula: see text] of a connected graph [Formula: see text] is defined as sum of the absolute values of the reciprocal distance eigenvalues of [Formula: see text], that is, [Formula: see text] In this paper, we establish some new lower and upper bounds for [Formula: see text] in terms of different graph parameters associated with the structure of the graph [Formula: see text]. We characterize the extremal graphs attaining these bounds. We also obtain a relation between the Harary energy and the sum of [Formula: see text] largest adjacency eigenvalues of a connected graph. <\/jats:p>","DOI":"10.1142\/s1793830921501494","type":"journal-article","created":{"date-parts":[[2021,6,19]],"date-time":"2021-06-19T11:32:01Z","timestamp":1624102321000},"source":"Crossref","is-referenced-by-count":1,"title":["Bounds and extremal graphs for Harary energy"],"prefix":"10.1142","volume":"14","author":[{"given":"A.","family":"Alhevaz","sequence":"first","affiliation":[{"name":"Faculty of Mathematical Sciences, Shahrood University of Technology, 316-3619995161, Shahrood, Iran"}]},{"given":"M.","family":"Baghipur","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Hormozgan, 3995, Bandar Abbas, Iran"}]},{"given":"H. A.","family":"Ganie","sequence":"additional","affiliation":[{"name":"Department of School Education JK Government, Kashmir, India"}]},{"given":"K. 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