| 图多项式以及图的不同特征根个数 |
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| 引用本文： | 刘儒英.图多项式以及图的不同特征根个数[J].青海师范大学学报(自然科学版),1989(3). |
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| 作者姓名： | 刘儒英 |
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| 作者单位： | 青海师范大学 |
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| 摘 要： | 设G是具有邻接矩阵A的简单图,P(x)是有理系数多项式,如果P(A)是某个图的邻接矩阵,我们记这个图为P(G)。我们考虑这样的问题:给一个图G,什么样的多项式P(x)给出一个图P(G)?这个图是什么样的图?当G是星图时,本文对上述问题给出完全的回答。然后,还导出一个连通正则图的不同特征根个数的新的下界。
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| 关 键 词： | 图多项式 星图 图的谱 |
POLYNOMIALS ON GRAPH AND THE NUMBER OF DISTINCT EIGENVALUES OF GRAPHS |
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| Liu Ruying.POLYNOMIALS ON GRAPH AND THE NUMBER OF DISTINCT EIGENVALUES OF GRAPHS[J].Journal of Qinghai Normal University(Natural Science Edition),1989(3). |
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| Authors: | Liu Ruying |
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| Institution: | Department of Mathematics |
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| Abstract: | Let G be a simple graph with adjacency matrrx A. and p(x) a polynomral with rational coefficients. If p ( A ) is the adjacency matrix of a graph, we denote that graph by p(G). We consider the question. Given a graph G, which polynomials p(x) give rise to a graph p(G) and what are those graphs? We give a complete answer if G is a Star graph. We then derive a new lower bound for the number of distinct eigenvalues of a regular connected graph. |
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| Keywords: | Polynomials on graph Star graph Spectra of graphs |
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