{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T13:28:10Z","timestamp":1740144490700,"version":"3.37.3"},"reference-count":19,"publisher":"EDP Sciences","issue":"5","license":[{"start":{"date-parts":[[2024,10,21]],"date-time":"2024-10-21T00:00:00Z","timestamp":1729468800000},"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":["12001434"],"award-info":[{"award-number":["12001434"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271439"],"award-info":[{"award-number":["12271439"]}],"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":[[2024,9,11]]},"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:p>Let <jats:italic>D<\/jats:italic>(<jats:italic>G<\/jats:italic>) be the distance matrix of a strongly connected digraph <jats:italic>G<\/jats:italic>, <jats:italic>Tr<\/jats:italic>(<jats:italic>G<\/jats:italic>) be the diagonal matrix with vertex transmissions of <jats:italic>G<\/jats:italic> as diagonal entries. The generalized distance matrix <jats:italic>D<jats:sub>\u03b2<\/jats:sub><\/jats:italic>(<jats:italic>G<\/jats:italic>) of the strongly connected digraph <jats:italic>G<\/jats:italic> is defined as <jats:italic>D<jats:sub>\u03b2<\/jats:sub><\/jats:italic>(<jats:italic>G<\/jats:italic>) = <jats:italic>\u03b2Tr<\/jats:italic>(<jats:italic>G<\/jats:italic>)+(1\u2212<jats:italic>\u03b2<\/jats:italic>)<jats:italic>D<\/jats:italic>(<jats:italic>G<\/jats:italic>), for any real 0 \u2264 <jats:italic>\u03b2<\/jats:italic> \u2264 1. The generalized distance spectral radius of <jats:italic>G<\/jats:italic> is the spectral radius of <jats:italic>D<jats:sub>\u03b2<\/jats:sub><\/jats:italic>(<jats:italic>G<\/jats:italic>). Let <jats:italic>\u03bc<\/jats:italic>1<jats:italic>\u03b2<\/jats:italic>(<jats:italic>G<\/jats:italic>),<jats:italic>\u03bc<\/jats:italic>2<jats:italic>\u03b2<\/jats:italic>(<jats:italic>G<\/jats:italic>),...,<jats:italic>\u03bcn\u03b2<\/jats:italic>(<jats:italic>G<\/jats:italic>) be the eigenvalues of <jats:italic>D<jats:sub>\u03b2<\/jats:sub><\/jats:italic>(<jats:italic>G<\/jats:italic>), the generalized distance energy of the digraph <jats:italic>G<\/jats:italic> is <jats:italic>ED\u03b2<\/jats:italic>(<jats:italic>G<\/jats:italic>)=\u03a3<jats:italic>i<\/jats:italic>=1<jats:italic>n<\/jats:italic>|<jats:italic>\u03bci\u03b2<\/jats:italic>(<jats:italic>G<\/jats:italic>)\u2212<jats:italic>\u03b2W<\/jats:italic>(<jats:italic>G<\/jats:italic>)<jats:italic>n<\/jats:italic>|, where <jats:italic>W<\/jats:italic> (<jats:italic>G<\/jats:italic>) is the sum of distances between all ordered pairs of vertices of <jats:italic>G<\/jats:italic>. In this paper, we obtain some sharp upper and lower bounds for the generalized distance spectral radius of <jats:italic>G<\/jats:italic> and characterize the extremal digraphs. Moreover, we also give some lower bounds on the generalized distance energy of digraphs.<\/jats:p>","DOI":"10.1051\/ro\/2024181","type":"journal-article","created":{"date-parts":[[2024,9,14]],"date-time":"2024-09-14T18:45:22Z","timestamp":1726339522000},"page":"4575-4588","source":"Crossref","is-referenced-by-count":0,"title":["Sharp bounds on the generalized distance spectral radius and generalized distance energy of strongly connected digraphs"],"prefix":"10.1051","volume":"58","author":[{"given":"Zengzhao","family":"Xu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weige","family":"Xi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2024,10,21]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/j.laa.2014.06.010","volume":"458","author":"Aouchiche","year":"2014","journal-title":"Linear Algebra Appl."},{"key":"R2","doi-asserted-by":"crossref","first-page":"2659","DOI":"10.1016\/j.laa.2013.07.023","volume":"439","author":"Chen","year":"2013","journal-title":"Linear Algebra Appl."},{"key":"R3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.laa.2018.10.014","volume":"563","author":"Cui","year":"2019","journal-title":"Linear Algebra Appl."},{"key":"R4","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/j.laa.2019.09.027","volume":"584","author":"Diaz","year":"2020","journal-title":"Linear Algebra Appl."},{"key":"R5","doi-asserted-by":"crossref","unstructured":"Horn R.A. and Johnson C.R., Matrix Analysis. Cambridge University Press, New York (1985).","DOI":"10.1017\/CBO9780511810817"},{"key":"R6","first-page":"218","volume":"293","author":"Li","year":"2017","journal-title":"Appl. Math. Comput."},{"key":"R7","doi-asserted-by":"crossref","first-page":"438","DOI":"10.13001\/1081-3810.1982","volume":"32","author":"Li","year":"2017","journal-title":"Electron. J. Linear Algebra"},{"key":"R8","doi-asserted-by":"crossref","first-page":"2537","DOI":"10.1016\/j.dam.2013.04.011","volume":"161","author":"Lin","year":"2013","journal-title":"Discrete Appl. Math."},{"key":"R9","doi-asserted-by":"crossref","first-page":"1750","DOI":"10.1080\/03081087.2014.972393","volume":"63","author":"Lin","year":"2015","journal-title":"Linear Multilinear Algebra"},{"key":"R10","first-page":"124","volume":"280","author":"Monsalve","year":"2016","journal-title":"Appl. Math. Comput."},{"key":"R11","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1080\/03081080701482943","volume":"56","author":"Pe\u00f1a","year":"2008","journal-title":"Linear Multilinear Algebra"},{"key":"R12","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1142\/S0129054115500203","volume":"26","author":"Qi","year":"2015","journal-title":"Int. J. Found. Comput. Sci."},{"key":"R13","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.2298\/FIL2104289X","volume":"35","author":"Xi","year":"2021","journal-title":"Filomat"},{"key":"R14","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1007\/s13226-017-0233-8","volume":"48","author":"Xi","year":"2017","journal-title":"Indian J. Pure Appl. Math."},{"key":"R15","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.laa.2019.07.010","volume":"581","author":"Xi","year":"2019","journal-title":"Linear Algebra Appl."},{"key":"R16","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/j.laa.2019.04.038","volume":"577","author":"Xi","year":"2019","journal-title":"Linear Algebra Appl."},{"key":"R17","doi-asserted-by":"crossref","first-page":"2547","DOI":"10.1080\/03081087.2019.1682496","volume":"69","author":"Xi","year":"2021","journal-title":"Linear Multilinear Algebra"},{"key":"R18","first-page":"124737","volume":"366","author":"Yang","year":"2020","journal-title":"Appl. Math. Comput."},{"key":"R19","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.dam.2021.08.008","volume":"304","author":"Zhang","year":"2021","journal-title":"Discrete Appl. Math."}],"container-title":["RAIRO - Operations Research"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2024181\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,21]],"date-time":"2024-10-21T07:58:18Z","timestamp":1729497498000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2024181"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9]]},"references-count":19,"journal-issue":{"issue":"5"},"alternative-id":["ro240142"],"URL":"https:\/\/doi.org\/10.1051\/ro\/2024181","relation":{},"ISSN":["0399-0559","2804-7303"],"issn-type":[{"type":"print","value":"0399-0559"},{"type":"electronic","value":"2804-7303"}],"subject":[],"published":{"date-parts":[[2024,9]]}}}