{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T20:56:14Z","timestamp":1761598574288,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,9,26]],"date-time":"2024-09-26T00:00:00Z","timestamp":1727308800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Let H be a graph of order n with m edges. Let di=d(vi) be the degree of the vertex vi. The extended adjacency matrix Aex(H) of H is an n\u00d7n matrix defined as Aex(H)=(bij), where bij=12didj+djdi, whenever vi and vj are adjacent and equal to zero otherwise. The largest eigenvalue of Aex(H) is called the extended adjacency spectral radius of H and the sum of the absolute values of its eigenvalues is called the extended adjacency energy of H. In this paper, we obtain some sharp upper and lower bounds for the extended adjacency spectral radius in terms of different graph parameters and characterize the extremal graphs attaining these bounds. We also obtain some new bounds for the extended adjacency energy of a graph and characterize the extremal graphs attaining these bounds. In both cases, we show our bounds are better than some already known bounds in the literature.<\/jats:p>","DOI":"10.3390\/info15100586","type":"journal-article","created":{"date-parts":[[2024,9,26]],"date-time":"2024-09-26T08:20:52Z","timestamp":1727338852000},"page":"586","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the Extended Adjacency Eigenvalues of a Graph"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2729-7396","authenticated-orcid":false,"given":"Alaa","family":"Altassan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2226-7828","authenticated-orcid":false,"given":"Hilal A.","family":"Ganie","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Kashmir, Srinagar 190001, India"}]},{"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 NE1 8ST, UK"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,26]]},"reference":[{"key":"ref_1","unstructured":"Cvetkovi\u0107, D.M., Doob, M., and Sachs, H. (1980). 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