| 图的Aα特征多项式系数的一个注记 |
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| 引用本文： | 柳顺义,覃忠美.图的Aα特征多项式系数的一个注记[J].浙江大学学报(理学版),2019,46(4):399-404. |
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| 作者姓名： | 柳顺义 覃忠美 |
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| 作者单位： | 长安大学 理学院, 陕西 西安 710064 |
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| 摘 要： | 设G是有n 个顶点的图,A(G)和(D)分别表示图G 的邻接矩阵和度矩阵?定义Aα ( G )= αD ( G )+( 1 -α ) A( G ),α ∈ 0,1 ]?图G 的Aα -特征多项式定义为矩阵Aα ( G ) 的特征多项式,即det( xIn - Aα ( G ) ), 其中,In 为n 阶单位矩阵?给出了图的Aα-特征多项式的第5 个系数的组合表达式。
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A note on the coefficients of the A α-characteristic polynomial of a graph |
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| LIU Shunyi,QIN Zhongmei.A note on the coefficients of the A α-characteristic polynomial of a graph[J].Journal of Zhejiang University(Sciences Edition),2019,46(4):399-404. |
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| Authors: | LIU Shunyi QIN Zhongmei |
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| Institution: | School of Science, Chang'an University, Xi'an 710064, China |
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| Abstract: | Let G be a graph on n vertices, and let A( G ) and D ( G ) denote the adjacency matrix and the degree matrix of
G, respectively. Define Aα ( G )= αD ( G )+( 1 -α ) A( G ) for any real α ∈ 0,1 ]. The Aα-characteristic polynomial of G is the characteristic polynomial of Aα ( G ), i.e., det( xIn - Aα ( G ) ), where I n is the identity matrix of size n. In this paper, we give a combinatorial expression for the fifth coefficient of the Aα-characteristic polynomial of a graph. |
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