{"title":"DL-integral and DQ-integral n-Cayley graphs","authors":"Lantao Zou, Yongjiang Wu, Lihua Feng","doi":"10.1016/j.amc.2024.129178","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we derive a decomposition formula for spectra of the distance Laplacian matrix <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>L</mi></mrow></msup></math></span> and distance signless Laplacian matrix <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>Q</mi></mrow></msup></math></span> of <em>n</em>-Cayley graphs by using group representation theory. Besides, we compute the <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>L</mi></mrow></msup></math></span> and <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>Q</mi></mrow></msup></math></span> spectra of the <em>n</em>-gonal <em>n</em>-cone graph and the <em>n</em>-sunlet graph. Finally, we present some examples of <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>L</mi></mrow></msup></math></span>-integral graphs and <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>Q</mi></mrow></msup></math></span>-integral graphs.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"489 ","pages":""},"PeriodicalIF":3.5000,"publicationDate":"2024-11-06","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/S0096300324006398","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we derive a decomposition formula for spectra of the distance Laplacian matrix and distance signless Laplacian matrix of n-Cayley graphs by using group representation theory. Besides, we compute the and spectra of the n-gonal n-cone graph and the n-sunlet graph. Finally, we present some examples of -integral graphs and -integral graphs.
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.