{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:13:05Z","timestamp":1760148785697,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,10]],"date-time":"2023-06-10T00:00:00Z","timestamp":1686355200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Let G=(V,E) be a simple connected graph with vertex set V and edge set E, respectively. The term \u201canti-reciprocal eigenvalue property\u201c refers to a non-singular graph G for which, \u22121\u03bb\u2208\u03c3(G), whenever \u03bb\u2208\u03c3(G), \u2200\u03bb\u2208\u03c3(G). Here, \u03c3(G) is the multiset of all eigenvalues of A(G). Moreover, if multiplicities of eigenvalues and their negative reciprocals are equal, then that graph is said to have strong anti-reciprocal eigenvalue properties, and the graph is referred to as a strong anti-reciprocal graph (or (\u2212SR) graph). In this article, a new family of graphs Fn(k,j) is introduced and the energy of F5(k,k2)k\u22652 is calculated. Furthermore, with the help of F5(k,k2), some families of (\u2212SR) graphs are constructed.<\/jats:p>","DOI":"10.3390\/sym15061240","type":"journal-article","created":{"date-parts":[[2023,6,12]],"date-time":"2023-06-12T01:28:21Z","timestamp":1686533301000},"page":"1240","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Spectral Characterization of Graphs with Respect to the Anti-Reciprocal Eigenvalue Property"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7859-5409","authenticated-orcid":false,"given":"Hao","family":"Guan","sequence":"first","affiliation":[{"name":"Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China"},{"name":"School of Computer Science of Information Technology, Qiannan Normal University for Nationalities, Duyun 558000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1470-7624","authenticated-orcid":false,"given":"Aysha","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Prince Sattam Bin Abdulaziz University, Al-Kharj 11991, Saudi Arabia"}]},{"given":"Sadia","family":"Akhter","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan"}]},{"given":"Saira","family":"Hameed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,10]]},"reference":[{"key":"ref_1","unstructured":"Cvetkovic, D.M., Doob, M., and Sachs, H. 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