{"title":"通过连续分数求循环 koken 图谱和特征空间以及 2oken 的一般方法","authors":"M.A. Reyes , C. Dalfó , M.A. Fiol , A. Messegué","doi":"10.1016/j.dam.2024.09.031","DOIUrl":null,"url":null,"abstract":"<div><div>The <span><math><mi>k</mi></math></span>-token graph <span><math><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> of a graph <span><math><mi>G</mi></math></span> is the graph whose vertices are the <span><math><mi>k</mi></math></span>-subsets of vertices from <span><math><mi>G</mi></math></span>, two of which being adjacent whenever their symmetric difference is a pair of adjacent vertices in <span><math><mi>G</mi></math></span>. In this paper, we propose a general method to find the spectrum and eigenspaces of the <span><math><mi>k</mi></math></span>-token graph <span><math><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> of a cycle <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. The method is based on the theory of lift graphs and the recently introduced theory of over-lifts. In the case of <span><math><mrow><mi>k</mi><mo>=</mo><mn>2</mn></mrow></math></span>, we use continuous fractions to derive the spectrum and eigenspaces of the 2-token graph of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"360 ","pages":"Pages 353-365"},"PeriodicalIF":1.0000,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A general method to find the spectrum and eigenspaces of the k-token graph of a cycle, and 2-token through continuous fractions\",\"authors\":\"M.A. Reyes , C. Dalfó , M.A. Fiol , A. Messegué\",\"doi\":\"10.1016/j.dam.2024.09.031\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The <span><math><mi>k</mi></math></span>-token graph <span><math><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> of a graph <span><math><mi>G</mi></math></span> is the graph whose vertices are the <span><math><mi>k</mi></math></span>-subsets of vertices from <span><math><mi>G</mi></math></span>, two of which being adjacent whenever their symmetric difference is a pair of adjacent vertices in <span><math><mi>G</mi></math></span>. In this paper, we propose a general method to find the spectrum and eigenspaces of the <span><math><mi>k</mi></math></span>-token graph <span><math><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> of a cycle <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. The method is based on the theory of lift graphs and the recently introduced theory of over-lifts. In the case of <span><math><mrow><mi>k</mi><mo>=</mo><mn>2</mn></mrow></math></span>, we use continuous fractions to derive the spectrum and eigenspaces of the 2-token graph of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>.</div></div>\",\"PeriodicalId\":50573,\"journal\":{\"name\":\"Discrete Applied Mathematics\",\"volume\":\"360 \",\"pages\":\"Pages 353-365\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-10-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0166218X24004219\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166218X24004219","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
图 G 的 k 标记图 Fk(G) 是指其顶点是来自 G 的 k 个顶点子集的图，只要其中两个顶点的对称差是 G 中的一对相邻顶点，那么这两个顶点就是相邻的。本文提出了一种求循环 Cn 的 k 标记图 Fk(Cn) 的谱和特征空间的一般方法。该方法基于提升图理论和最近引入的过提升理论。在 k=2 的情况下，我们使用连续分数来推导 Cn 的 2oken 图的谱和特征空间。
A general method to find the spectrum and eigenspaces of the k-token graph of a cycle, and 2-token through continuous fractions
The -token graph of a graph is the graph whose vertices are the -subsets of vertices from , two of which being adjacent whenever their symmetric difference is a pair of adjacent vertices in . In this paper, we propose a general method to find the spectrum and eigenspaces of the -token graph of a cycle . The method is based on the theory of lift graphs and the recently introduced theory of over-lifts. In the case of , we use continuous fractions to derive the spectrum and eigenspaces of the 2-token graph of .
期刊介绍：
The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal.
Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.
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