{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:24:06Z","timestamp":1753885446452,"version":"3.41.2"},"reference-count":37,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071411"],"award-info":[{"award-number":["12071411"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012579","name":"Natural Science Foundation of Qinghai","doi-asserted-by":"publisher","award":["2021-ZJ-703"],"award-info":[{"award-number":["2021-ZJ-703"]}],"id":[{"id":"10.13039\/501100012579","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,7]]},"abstract":"<jats:p> Let [Formula: see text] and [Formula: see text] be the adjacency matrix and the diagonal matrix of vertex degrees of a graph [Formula: see text], respectively. For any real [Formula: see text], Nikiforov defined the matrix [Formula: see text] as [Formula: see text]. Let [Formula: see text] be complement of [Formula: see text]. Define [Formula: see text] where [Formula: see text] and [Formula: see text] are the identity matrix and the all-ones matrix, respectively. Since [Formula: see text] is the Seidel matrix of [Formula: see text], this new matrix is the generalization of Seidel matrix. Further, [Formula: see text] is a subset of universal adjacency matrices defined by Haemers and Omidi. In this paper, [Formula: see text]-eigenvalues and [Formula: see text]-energy of [Formula: see text] respectively, are investigated, which not only extends Seidel matrix but also enriches the theory of universal adjacency matrices. <\/jats:p>","DOI":"10.1142\/s1793830922501269","type":"journal-article","created":{"date-parts":[[2022,6,24]],"date-time":"2022-06-24T07:39:45Z","timestamp":1656056385000},"source":"Crossref","is-referenced-by-count":0,"title":["On the S\u03b1-matrix of graphs"],"prefix":"10.1142","volume":"15","author":[{"given":"Zhen","family":"Lin","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, The State Key Laboratory of Tibetan Intelligent, Information Processing and Application, Qinghai Normal University, Xining 810008, Qinghai, P. R. China"},{"name":"Academy of Plateau Science and Sustainability, People\u2019s Government of Qinghai Province and Beijing, Normal University, P. R. 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