{"title":"图组成的距离谱","authors":"Indulal Gopalapillai","doi":"10.26493/1855-3974.103.E09","DOIUrl":null,"url":null,"abstract":"The D -eigenvalues μ 1 , μ 2 , ..., μ p of a graph G are the eigenvalues of its distance matrix D and form the distance spectrum or the D -spectrum. In this paper we obtain the D -spectrum of the cartesian product if two distance regular graphs. The D -spectrum of the lexicographic product G [ H ] of two graphs G and H when H is regular is also obtained. The D -eigenvalues of the Hamming graphs Ham( d, n ) of diameter d and order n d and those of the C 4 nanotori, T k , m , C 4 , are determined.","PeriodicalId":49239,"journal":{"name":"Ars Mathematica Contemporanea","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2009-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"28","resultStr":"{\"title\":\"Distance spectrum of graph compositions\",\"authors\":\"Indulal Gopalapillai\",\"doi\":\"10.26493/1855-3974.103.E09\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The D -eigenvalues μ 1 , μ 2 , ..., μ p of a graph G are the eigenvalues of its distance matrix D and form the distance spectrum or the D -spectrum. In this paper we obtain the D -spectrum of the cartesian product if two distance regular graphs. The D -spectrum of the lexicographic product G [ H ] of two graphs G and H when H is regular is also obtained. The D -eigenvalues of the Hamming graphs Ham( d, n ) of diameter d and order n d and those of the C 4 nanotori, T k , m , C 4 , are determined.\",\"PeriodicalId\":49239,\"journal\":{\"name\":\"Ars Mathematica Contemporanea\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2009-06-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"28\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ars Mathematica Contemporanea\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.26493/1855-3974.103.E09\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ars Mathematica Contemporanea","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.26493/1855-3974.103.E09","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
The D -eigenvalues μ 1 , μ 2 , ..., μ p of a graph G are the eigenvalues of its distance matrix D and form the distance spectrum or the D -spectrum. In this paper we obtain the D -spectrum of the cartesian product if two distance regular graphs. The D -spectrum of the lexicographic product G [ H ] of two graphs G and H when H is regular is also obtained. The D -eigenvalues of the Hamming graphs Ham( d, n ) of diameter d and order n d and those of the C 4 nanotori, T k , m , C 4 , are determined.
期刊介绍：
Ars mathematica contemporanea will publish high-quality articles in contemporary mathematics that arise from the discrete and concrete mathematics paradigm. It will favor themes that combine at least two different fields of mathematics. In particular, we welcome papers intersecting discrete mathematics with other branches of mathematics, such as algebra, geometry, topology, theoretical computer science, and combinatorics. The name of the journal was chosen carefully. Symmetry is certainly a theme that is quite welcome to the journal, as it is through symmetry that mathematics comes closest to art.
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