{"title":"匹配扩展的光谱条件","authors":"","doi":"10.1016/j.amc.2024.128982","DOIUrl":null,"url":null,"abstract":"<div><p>A graph <em>G</em> is called <em>k</em>-extendable if for any matching <em>M</em> of size <em>k</em> in <em>G</em>, there exists a perfect matching of <em>G</em> containing <em>M</em>. Let <span><math><mi>D</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and <span><math><mi>A</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> be the degree diagonal matrix and the adjacency matrix of <em>G</em>, respectively. For <span><math><mn>0</mn><mo>≤</mo><mi>α</mi><mo><</mo><mn>1</mn></math></span>, the spectral radius of <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mi>α</mi><mi>D</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>+</mo><mo>(</mo><mn>1</mn><mo>−</mo><mi>α</mi><mo>)</mo><mi>A</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is called the <em>α</em>-spectral radius of <em>G</em>. In this paper, we give a sufficient condition for a graph <em>G</em> to be <em>k</em>-extendable in terms of the <em>α</em>-spectral radius of <em>G</em> and characterize the corresponding extremal graphs. Moreover, we determine the spectral and signless Laplacian spectral radius conditions for a balanced bipartite graph to be <em>k</em>-extendable.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Spectral conditions for matching extension\",\"authors\":\"\",\"doi\":\"10.1016/j.amc.2024.128982\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A graph <em>G</em> is called <em>k</em>-extendable if for any matching <em>M</em> of size <em>k</em> in <em>G</em>, there exists a perfect matching of <em>G</em> containing <em>M</em>. Let <span><math><mi>D</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and <span><math><mi>A</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> be the degree diagonal matrix and the adjacency matrix of <em>G</em>, respectively. For <span><math><mn>0</mn><mo>≤</mo><mi>α</mi><mo><</mo><mn>1</mn></math></span>, the spectral radius of <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mi>α</mi><mi>D</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>+</mo><mo>(</mo><mn>1</mn><mo>−</mo><mi>α</mi><mo>)</mo><mi>A</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is called the <em>α</em>-spectral radius of <em>G</em>. In this paper, we give a sufficient condition for a graph <em>G</em> to be <em>k</em>-extendable in terms of the <em>α</em>-spectral radius of <em>G</em> and characterize the corresponding extremal graphs. Moreover, we determine the spectral and signless Laplacian spectral radius conditions for a balanced bipartite graph to be <em>k</em>-extendable.</p></div>\",\"PeriodicalId\":55496,\"journal\":{\"name\":\"Applied Mathematics and Computation\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.5000,\"publicationDate\":\"2024-08-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics and Computation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0096300324004430\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300324004430","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A graph G is called k-extendable if for any matching M of size k in G, there exists a perfect matching of G containing M. Let and be the degree diagonal matrix and the adjacency matrix of G, respectively. For , the spectral radius of is called the α-spectral radius of G. In this paper, we give a sufficient condition for a graph G to be k-extendable in terms of the α-spectral radius of G and characterize the corresponding extremal graphs. Moreover, we determine the spectral and signless Laplacian spectral radius conditions for a balanced bipartite graph to be k-extendable.
期刊介绍:
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.