| 循环图及其补图的拉普拉斯矩阵的谱 |
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| 引用本文： | 杜先云,任秋道.循环图及其补图的拉普拉斯矩阵的谱[J].四川理工学院学报(自然科学版),2009,22(2). |
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| 作者姓名： | 杜先云 任秋道 |
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| 作者单位： | 绵阳师范学院数学与信息科学系,四川,绵阳,621000 |
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| 摘 要： | 文章利用循环矩阵的性质,获得循环图G(n;±S)=(V,E)的特征值λr=sum from j=1 to n ajω(j-1)r,r=0,1,…,n-1。其中ω=cos2π/n+isin2π/n。并且循环图及其补图的拉普拉斯矩阵的谱sum from j=1 to n aj-sum from j=1 to n ajω(j-1)r,n-sum from j=1 to n ajω(j-1)r。
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| 关 键 词： | 邻接矩阵 拉普拉斯矩阵 特征值 循环图 |
Laplacian Spectra of Circulant Graph and Its Complement |
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| DU Xian-yun,REN Qiu-dao.Laplacian Spectra of Circulant Graph and Its Complement[J].Journal of Sichuan University of Science & Engineering:Natural Science Editton,2009,22(2). |
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| Authors: | DU Xian-yun REN Qiu-dao |
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| Institution: | Department of Mathematics and Information Science;Mianyang Normal University;Mianyang 621000;China |
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| Abstract: | With the characteristics of a circulant matrix,the paper obtains that the spectra of a circulant graphG(n;±S)=(V,E) are λr=sum from j=1 to n ajω(j-1)r,r=0,1,…,n-1,for ω=cos2π/n+isin2π/n.And that the Laplacian spectra of circulant graph and its complement are sum from j=1 to n aj-sum from j=1 to n ajω(j-1)r,n-sum from j=1 to n ajω(j-1)r. |
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| Keywords: | adjacent matrix Laplacian matrix eigenvalue circulant graph |
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