{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:39:32Z","timestamp":1740155972512,"version":"3.37.3"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"crossref","award":["11671135"],"award-info":[{"award-number":["11671135"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2019,12]]},"abstract":"<jats:p> For a real number [Formula: see text], the [Formula: see text]-matrix of a graph [Formula: see text] is defined to be [Formula: see text] where [Formula: see text] and [Formula: see text] are the adjacency matrix and degree diagonal matrix of [Formula: see text], respectively. The [Formula: see text]-spectral radius of [Formula: see text], denoted by [Formula: see text], is the largest eigenvalue of [Formula: see text]. In this paper, we consider the upper bound of the [Formula: see text]-spectral radius [Formula: see text], also we give some upper bounds for the second largest eigenvalue of [Formula: see text]-matrix. <\/jats:p>","DOI":"10.1142\/s1793830919500708","type":"journal-article","created":{"date-parts":[[2019,9,27]],"date-time":"2019-09-27T03:13:48Z","timestamp":1569554028000},"page":"1950070","source":"Crossref","is-referenced-by-count":2,"title":["Some spectral properties of A\u03b1-matrix"],"prefix":"10.1142","volume":"11","author":[{"given":"Shuang","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Mathematics, East China University of Science and Technology, Shanghai, P. R. China"}]},{"given":"Yan","family":"Zhu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, East China University of Science and Technology, Shanghai, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2019,12,19]]},"reference":[{"key":"S1793830919500708BIB001","series-title":"Graduate Texts in Mathematics","volume-title":"Graph Theory","author":"Bondy J.","year":"1984"},{"key":"S1793830919500708BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84882-981-7"},{"key":"S1793830919500708BIB003","first-page":"81","volume":"23","author":"Chen Y.","year":"2019","journal-title":"Oper. Res. Trans."},{"volume-title":"Spectra of Graphs-Theory and Application","year":"1980","author":"Cvetkovic D.","key":"S1793830919500708BIB004"},{"key":"S1793830919500708BIB005","volume-title":"Matrix Analysis","author":"Horn R.","year":"2013","edition":"2"},{"key":"S1793830919500708BIB006","doi-asserted-by":"publisher","DOI":"10.2298\/AADM1701081N"},{"key":"S1793830919500708BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2017.01.029"},{"key":"S1793830919500708BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2016.12.042"},{"key":"S1793830919500708BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2018.03.036"},{"key":"S1793830919500708BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(88)90147-4"},{"volume-title":"Matrix Iterative Analysis","year":"2009","author":"Varga R.","key":"S1793830919500708BIB011"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830919500708","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,20]],"date-time":"2019-12-20T01:44:00Z","timestamp":1576806240000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830919500708"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12]]},"references-count":11,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["10.1142\/S1793830919500708"],"URL":"https:\/\/doi.org\/10.1142\/s1793830919500708","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2019,12]]}}}