{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T13:28:56Z","timestamp":1740144536100,"version":"3.37.3"},"reference-count":12,"publisher":"EDP Sciences","issue":"5","license":[{"start":{"date-parts":[[2022,10,21]],"date-time":"2022-10-21T00:00:00Z","timestamp":1666310400000},"content-version":"vor","delay-in-days":50,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771172,12061039"],"award-info":[{"award-number":["11771172,12061039"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2022,10,4]]},"published-print":{"date-parts":[[2022,9]]},"abstract":"<jats:p><jats:italic>G<\/jats:italic> is a simple connected graph with adjacency matrix <jats:italic>A<\/jats:italic>(<jats:italic>G<\/jats:italic>) and degree diagonal matrix <jats:italic>D<\/jats:italic>(<jats:italic>G<\/jats:italic>). The signless Laplacian matrix of <jats:italic>G<\/jats:italic> is defined as <jats:italic>Q<\/jats:italic>(<jats:italic>G<\/jats:italic>)\u00a0=\u00a0<jats:italic>D<\/jats:italic>(<jats:italic>G<\/jats:italic>)\u00a0+\u00a0<jats:italic>A<\/jats:italic>(<jats:italic>G<\/jats:italic>). In 2017, Nikiforov [1] defined the matrix <jats:italic>A<jats:sub>\u03b1<\/jats:sub><\/jats:italic>(<jats:italic>G<\/jats:italic>)\u00a0=\u00a0<jats:italic>\u03b1 D<\/jats:italic>(<jats:italic>G<\/jats:italic>)\u00a0+\u00a0(<jats:italic>1<\/jats:italic>\u00a0\u2212\u00a0<jats:italic>\u03b1<\/jats:italic>)<jats:italic>A<\/jats:italic>(<jats:italic>G<\/jats:italic>) for <jats:italic>\u03b1<\/jats:italic>\u00a0\u2208\u00a0[0,1]. The <jats:italic>A<jats:sub>\u03b1<\/jats:sub><\/jats:italic>-spectral radius of <jats:italic>G<\/jats:italic> is the maximum eigenvalue of <jats:italic>A<jats:sub>\u03b1<\/jats:sub><\/jats:italic> (<jats:italic>G<\/jats:italic>). In 2019, Liu <jats:italic>et al.<\/jats:italic> [2] defined the matrix <jats:italic>\u0398<jats:sub>k<\/jats:sub><\/jats:italic>(<jats:italic>G<\/jats:italic>) as <jats:italic>\u0398<jats:sub>k<\/jats:sub><\/jats:italic> (<jats:italic>G<\/jats:italic>)\u00a0=\u00a0<jats:italic>kD<\/jats:italic>(<jats:italic>G<\/jats:italic>)\u00a0+\u00a0<jats:italic>A<\/jats:italic>(<jats:italic>G<\/jats:italic>), for <jats:italic>k<\/jats:italic>\u00a0\u2208\u00a0\u211d. In this paper, we present a new type of lower bound for the <jats:italic>A<jats:sub>\u03b1<\/jats:sub><\/jats:italic>-spectral radius of a graph after vertex deletion. Furthermore, we deduce some corollaries on <jats:italic>\u0398<jats:sub>k<\/jats:sub><\/jats:italic> (<jats:italic>G<\/jats:italic>), <jats:italic>A<\/jats:italic>(<jats:italic>G<\/jats:italic>), <jats:italic>Q<\/jats:italic>(<jats:italic>G<\/jats:italic>) matrices.<\/jats:p>","DOI":"10.1051\/ro\/2022176","type":"journal-article","created":{"date-parts":[[2022,10,4]],"date-time":"2022-10-04T18:57:02Z","timestamp":1664909822000},"page":"3635-3642","source":"Crossref","is-referenced-by-count":0,"title":["A bound for the <i>A<sub>\u03b1<\/sub><\/i>-spectral radius of a connected graph after vertex deletion"],"prefix":"10.1051","volume":"56","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5720-7681","authenticated-orcid":false,"given":"Chunxiang","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1359-3234","authenticated-orcid":false,"given":"Tao","family":"She","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2022,10,21]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"81","DOI":"10.2298\/AADM1701081N","volume":"11","author":"Nikiforov","year":"2017","journal-title":"Appl. Anal. Discrete Math."},{"key":"R2","doi-asserted-by":"crossref","first-page":"1718","DOI":"10.1016\/j.disc.2019.02.016","volume":"342","author":"Liu","year":"2019","journal-title":"Discrete Math."},{"key":"R3","unstructured":"West D.B., Introduction to Graph Theory. 2nd edn. (2001)."},{"key":"R4","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1016\/j.laa.2017.01.029","volume":"520","author":"Nikiforov","year":"2017","journal-title":"Linear Algebra Appl."},{"key":"R5","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.laa.2016.12.042","volume":"519","author":"Nikiforov","year":"2017","journal-title":"Linear Algebra Appl."},{"key":"R6","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.laa.2018.03.036","volume":"550","author":"Nikiforov","year":"2018","journal-title":"Linear Algebra Appl."},{"key":"R7","doi-asserted-by":"crossref","unstructured":"Lin H., Huang X. and Xue J., A Note on the A\u03b1-spectral Radius of Graphs (2018).","DOI":"10.1016\/j.laa.2018.08.008"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"Li D., Chen Y. and Meng J., The A\u03b1-spectral radius of trees and unicyclic graphs with given degree sequence. Appl. Math. Comput. 363 (2019).","DOI":"10.1016\/j.amc.2019.124622"},{"key":"R9","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.laa.2019.12.039","volume":"590","author":"Wang","year":"2020","journal-title":"Linear Algebra Appl."},{"key":"R10","doi-asserted-by":"crossref","first-page":"2559","DOI":"10.1016\/j.disc.2019.05.017","volume":"342","author":"Guo","year":"2019","journal-title":"Discrete Math."},{"key":"R11","doi-asserted-by":"crossref","unstructured":"Sun S. and Das K.C., A conjecture on the spectral radius of graphs. Linear Algebra Appl. (2019) 588.","DOI":"10.1016\/j.laa.2019.11.028"},{"key":"R12","doi-asserted-by":"crossref","unstructured":"Zhai M., Lin H. and Shu J., Spectral Extrema of Graphs with Fixed Size: Cycles and Complete Bipartite Graphs (2021).","DOI":"10.1016\/j.ejc.2021.103322"}],"container-title":["RAIRO - Operations Research"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2022176\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,21]],"date-time":"2022-10-21T08:03:07Z","timestamp":1666339387000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2022176"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9]]},"references-count":12,"journal-issue":{"issue":"5"},"alternative-id":["ro220144"],"URL":"https:\/\/doi.org\/10.1051\/ro\/2022176","relation":{},"ISSN":["0399-0559","2804-7303"],"issn-type":[{"type":"print","value":"0399-0559"},{"type":"electronic","value":"2804-7303"}],"subject":[],"published":{"date-parts":[[2022,9]]}}}