{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T15:12:36Z","timestamp":1770909156354,"version":"3.50.1"},"reference-count":23,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,17]],"date-time":"2022-09-17T00:00:00Z","timestamp":1663372800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"SERB-DST","award":["CRG\/2020\/000109"],"award-info":[{"award-number":["CRG\/2020\/000109"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The reciprocal distance Laplacian matrix of a connected graph G is defined as RDL(G)=RT(G)\u2212RD(G), where RT(G) is the diagonal matrix of reciprocal distance degrees and RD(G) is the Harary matrix. Clearly, RDL(G) is a real symmetric matrix, and we denote its eigenvalues as \u03bb1(RDL(G))\u2265\u03bb2(RDL(G))\u2265\u2026\u2265\u03bbn(RDL(G)). The largest eigenvalue \u03bb1(RDL(G)) of RDL(G), denoted by \u03bb(G), is called the reciprocal distance Laplacian spectral radius. In this paper, we obtain several upper bounds for the sum of k largest reciprocal distance Laplacian eigenvalues of G in terms of various graph parameters, such as order n, maximum reciprocal distance degree RTmax, minimum reciprocal distance degree RTmin, and Harary index H(G) of G. We determine the extremal cases corresponding to these bounds. As a consequence, we obtain the upper bounds for reciprocal distance Laplacian spectral radius \u03bb(G) in terms of the parameters as mentioned above and characterize the extremal cases. Moreover, we attain several upper and lower bounds for reciprocal distance Laplacian spread RDLS(G)=\u03bb1(RDL(G))\u2212\u03bbn\u22121(RDL(G)) in terms of various graph parameters. We determine the extremal graphs in many cases.<\/jats:p>","DOI":"10.3390\/sym14091937","type":"journal-article","created":{"date-parts":[[2022,9,20]],"date-time":"2022-09-20T04:28:55Z","timestamp":1663648135000},"page":"1937","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["On the Sum and Spread of Reciprocal Distance Laplacian Eigenvalues of Graphs in Terms of Harary Index"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5966-8780","authenticated-orcid":false,"given":"Saleem","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Kashmir, Srinagar 190006, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shariefuddin","family":"Pirzada","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Kashmir, Srinagar 190006, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2817-3400","authenticated-orcid":false,"given":"Yilun","family":"Shang","sequence":"additional","affiliation":[{"name":"Department of Computer and Information Sciences, Northumbria University, Newcastle upon Tyne NE1 8ST, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,17]]},"reference":[{"key":"ref_1","unstructured":"Pirzada, S. 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