{"title":"关于秩4图的谱性质","authors":"Jianxuan Luo","doi":"10.4236/am.2023.1411045","DOIUrl":null,"url":null,"abstract":"Let G be a graph and A(G) the adjacency matrix of G. The spectrum of G is the eigenvalues together with their multiplicities of A(G). Chang et al. (2011) characterized the structures of all graphs with rank 4. Monsalve and Rada (2021) gave the bound of spectral radius of all graphs with rank 4. Based on these results as above, we further investigate the spectral properties of graphs with rank 4. And we give the expressions of the spectral radius and energy of all graphs with rank 4. In particular, we show that some graphs with rank 4 are determined by their spectra.","PeriodicalId":64940,"journal":{"name":"应用数学(英文)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Spectral Properties of Graphs with Rank 4\",\"authors\":\"Jianxuan Luo\",\"doi\":\"10.4236/am.2023.1411045\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let G be a graph and A(G) the adjacency matrix of G. The spectrum of G is the eigenvalues together with their multiplicities of A(G). Chang et al. (2011) characterized the structures of all graphs with rank 4. Monsalve and Rada (2021) gave the bound of spectral radius of all graphs with rank 4. Based on these results as above, we further investigate the spectral properties of graphs with rank 4. And we give the expressions of the spectral radius and energy of all graphs with rank 4. In particular, we show that some graphs with rank 4 are determined by their spectra.\",\"PeriodicalId\":64940,\"journal\":{\"name\":\"应用数学(英文)\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"应用数学(英文)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4236/am.2023.1411045\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"应用数学(英文)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4236/am.2023.1411045","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
设G为图，a (G)为G的邻接矩阵，G的谱是a (G)的特征值及其复数。Chang et al.(2011)对所有4级图的结构进行了表征。Monsalve和Rada(2021)给出了所有4阶图的谱半径界。在上述结果的基础上，我们进一步研究了4阶图的谱性质。并给出了所有4阶图的谱半径和能量的表达式。特别地，我们证明了一些阶数为4的图是由它们的谱决定的。
Let G be a graph and A(G) the adjacency matrix of G. The spectrum of G is the eigenvalues together with their multiplicities of A(G). Chang et al. (2011) characterized the structures of all graphs with rank 4. Monsalve and Rada (2021) gave the bound of spectral radius of all graphs with rank 4. Based on these results as above, we further investigate the spectral properties of graphs with rank 4. And we give the expressions of the spectral radius and energy of all graphs with rank 4. In particular, we show that some graphs with rank 4 are determined by their spectra.
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