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Res."],"accepted":{"date-parts":[[2025,7,6]]},"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p>A fractional matching of <jats:italic>G<\/jats:italic> is a function <jats:italic>f<\/jats:italic> : <jats:italic>E<\/jats:italic>(<jats:italic>G<\/jats:italic>) \u2192 [0, 1] such that \u2211<jats:italic>e\u2208E<jats:sub>G<\/jats:sub><\/jats:italic>(<jats:italic>v<jats:sub>i<\/jats:sub><\/jats:italic>) <jats:italic>f<\/jats:italic>(<jats:italic>e<\/jats:italic>) \u2264 1 for any <jats:italic>v<jats:sub>i<\/jats:sub><\/jats:italic> <jats:italic>\u2208<\/jats:italic> <jats:italic>V<\/jats:italic> (<jats:italic>G<\/jats:italic>), where <jats:italic>E<jats:sub>G<\/jats:sub><\/jats:italic>(<jats:italic>v<jats:sub>i<\/jats:sub><\/jats:italic>) = {<jats:italic>e<\/jats:italic> : <jats:italic>e<\/jats:italic> <jats:italic>\u2208<\/jats:italic> <jats:italic>E<\/jats:italic>(<jats:italic>G<\/jats:italic>) and <jats:italic>e<\/jats:italic> is incident with <jats:italic>v<jats:sub>i<\/jats:sub><\/jats:italic>}. Let <jats:italic>\u03b1<jats:sub>f<\/jats:sub><\/jats:italic> (<jats:italic>G<\/jats:italic>) denote the fractional matching number of <jats:italic>G<\/jats:italic>, which is defined as <jats:italic>\u03b1<jats:sub>f<\/jats:sub><\/jats:italic> (<jats:italic>G<\/jats:italic>) = max{\u2211<jats:italic>e\u2208E<\/jats:italic>(<jats:italic>G<\/jats:italic>) <jats:italic>f<\/jats:italic>(<jats:italic>e<\/jats:italic>) : <jats:italic>f<\/jats:italic> is a fractional matching of <jats:italic>G<\/jats:italic>}. Let {<jats:italic>G<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>G<\/jats:italic><jats:sub>2<\/jats:sub>, <jats:italic>G<\/jats:italic><jats:sub>3<\/jats:sub>, . . .} be a set of graphs, a {<jats:italic>G<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>G<\/jats:italic><jats:sub>2<\/jats:sub>, <jats:italic>G<\/jats:italic><jats:sub>3<\/jats:sub>, . . .}-factor of a graph <jats:italic>G<\/jats:italic> is a spanning subgraph of <jats:italic>G<\/jats:italic> such that each component of which is isomorphic to one of {<jats:italic>G<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>G<\/jats:italic><jats:sub>2<\/jats:sub>, <jats:italic>G<\/jats:italic><jats:sub>3<\/jats:sub>, . . .}. In this paper, we first establish a sharp upper bound for the distance spectral radius to guarantee that <jats:italic>\u03b1<jats:sub>f<\/jats:sub><\/jats:italic> (<jats:italic>G<\/jats:italic>) &gt; <jats:italic>n\u2212k<\/jats:italic>\/2 in a graph <jats:italic>G<\/jats:italic> of order <jats:italic>n<\/jats:italic> with given minimum degree, where 0 <jats:italic>&lt; k &lt; n<\/jats:italic> is an integer. Then we give a sharp upper bound on the distance spectral radius of a graph <jats:italic>G<\/jats:italic> with given minimum degree <jats:italic>\u03b4<\/jats:italic> to ensure that <jats:italic>G<\/jats:italic> has a {<jats:italic>K<\/jats:italic><jats:sub>2<\/jats:sub>, {<jats:italic>C<jats:sub>k<\/jats:sub>}}<\/jats:italic>-factor, where 3 \u2264 <jats:italic>k &lt;<\/jats:italic> +<jats:italic>\u221e<\/jats:italic> is an integer. Moreover, we obtain a sharp upper bound on the distance spectral radius for the existence of a {<jats:italic>K<\/jats:italic><jats:sub>1,1<\/jats:sub>, <jats:italic>K<\/jats:italic><jats:sub>1,2<\/jats:sub>, . . . , <jats:italic>K<\/jats:italic><jats:sub>1,k<\/jats:sub>}-factor with 2 \u2264 <jats:italic>k &lt;<\/jats:italic> +<jats:italic>\u221e<\/jats:italic> in a graph <jats:italic>G<\/jats:italic> with given minimum degree.<\/jats:p>","DOI":"10.1051\/ro\/2025097","type":"journal-article","created":{"date-parts":[[2025,7,10]],"date-time":"2025-07-10T08:04:06Z","timestamp":1752134646000},"page":"2451-2461","source":"Crossref","is-referenced-by-count":1,"title":["On the distance spectral radius, fractional matching and factors of graphs with given minimum degree"],"prefix":"10.1051","volume":"59","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"}]},{"given":"Ligong","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2025,9,5]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0012-365X(82)90048-6","volume":"42","author":"Amahashi","year":"1982","journal-title":"Discrete Math."},{"key":"R2","doi-asserted-by":"crossref","unstructured":"Berman A. and Plemmons R.J., Nonnegative Matrices in the Mathematical Sciences. 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