{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T02:49:28Z","timestamp":1774320568000,"version":"3.50.1"},"reference-count":37,"publisher":"EDP Sciences","issue":"3","license":[{"start":{"date-parts":[[2023,6,14]],"date-time":"2023-06-14T00:00:00Z","timestamp":1686700800000},"content-version":"vor","delay-in-days":44,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2023,5,19]]},"published-print":{"date-parts":[[2023,5]]},"abstract":"<jats:p>Let<jats:italic>G<\/jats:italic>be a connected graph of even order<jats:italic>n<\/jats:italic>. An odd [1,\u00a0<jats:italic>b<\/jats:italic>]-factor of<jats:italic>G<\/jats:italic>is a spanning subgraph<jats:italic>F<\/jats:italic>of<jats:italic>G<\/jats:italic>such that<jats:italic>d<\/jats:italic><jats:sub><jats:italic>F<\/jats:italic><\/jats:sub>(<jats:italic>v<\/jats:italic>) \u2208\u00a0{1,\u00a03,\u00a05,\u00a0\u22ef,<jats:italic>b<\/jats:italic>} for any<jats:italic>v<\/jats:italic>\u00a0\u2208\u00a0<jats:italic>V<\/jats:italic>(<jats:italic>G<\/jats:italic>), where<jats:italic>b<\/jats:italic>is positive odd integer. The distance matrix<jats:italic>\u018a<\/jats:italic>(<jats:italic>G<\/jats:italic>) of<jats:italic>G<\/jats:italic>is a symmetric real matrix with (<jats:italic>i<\/jats:italic>,\u00a0<jats:italic>j<\/jats:italic>)-entry being the distance between the vertices<jats:italic>v<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>and<jats:italic>v<\/jats:italic><jats:sub><jats:italic>j<\/jats:italic><\/jats:sub>. The distance signless Laplacian matrix<jats:italic>Q<\/jats:italic>(<jats:italic>G<\/jats:italic>) of<jats:italic>G<\/jats:italic>is defined by<jats:italic>Q<\/jats:italic>(<jats:italic>G<\/jats:italic>), where<jats:italic>Tr<\/jats:italic>(<jats:italic>G<\/jats:italic>) is the diagonal matrix of the vertex transmissions in<jats:italic>G<\/jats:italic>. The largest eigenvalue<jats:italic>\u03b7<\/jats:italic><jats:sub>1<\/jats:sub>(<jats:italic>G<\/jats:italic>) of<jats:italic>Q<\/jats:italic>(<jats:italic>G<\/jats:italic>) is called the distance signless Laplacian spectral radius of<jats:italic>G<\/jats:italic>. In this paper, we verify sharp upper bounds on the distance signless Laplacian spectral radius to guarantee the existence of an odd [1,\u00a0<jats:italic>b<\/jats:italic>]-factor in a graph; we provide some graphs to show that the bounds are optimal.<\/jats:p>","DOI":"10.1051\/ro\/2023069","type":"journal-article","created":{"date-parts":[[2023,5,24]],"date-time":"2023-05-24T08:02:04Z","timestamp":1684915324000},"page":"1343-1351","source":"Crossref","is-referenced-by-count":3,"title":["Characterizing an odd [1,\u00a0<i>b<\/i>]-factor on the distance signless Laplacian spectral radius"],"prefix":"10.1051","volume":"57","author":[{"given":"Sizhong","family":"Zhou","sequence":"first","affiliation":[]},{"given":"Hongxia","family":"Liu","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2023,6,14]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.laa.2004.08.014","volume":"395","author":"Brouwer","year":"2005","journal-title":"Linear Algebra App."},{"key":"R2","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1016\/j.laa.2020.06.004","volume":"614","author":"Suil","year":"2021","journal-title":"Linear Algebra App."},{"key":"R3","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1080\/03081087.2017.1323845","volume":"66","author":"Liu","year":"2018","journal-title":"Linear Multilinear Algebra"},{"key":"R4","unstructured":"Liu C. and Li J., Distance signless Laplacian spectral radius and perfect matchings in graphs and bipartite graphs. 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