Eigenvalues of graphs
Eigenvalues of graphs
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DOI：
10.1017/cbo9780511529993.004
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
Michael Doob;L. Beineke;Robin J. Wilson;P. Cameron
中科院分区：
文献类型：
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作者：
Michael Doob;L. Beineke;Robin J. Wilson;P. Cameron
本章概述了图的性质与其邻接矩阵的谱之间的一些关系。首先，我们给出一些工作的例子，并用它们来说明必要的矩阵理论背景。其次，图的特征值与路径结构有关。然后，我们研究通过图标号的特征值的建设。边界的特征值（从上面和下面）的影响也进行了探讨。最后，我们研究的问题，是否一个图是由它的谱。此外，我们还注意到图与其他矩阵之间的一些关系，这些关系与邻接矩阵有关。
This chapter gives a survey of some of the relationships between the properties of a graph and the spectrum of its adjacency matrix. First we give some working examples and use them to illustrate the necessary matrix theory background. Next, the eigenvalues of a graph are related to the path structure. Then we examine the construction of eigenvalues via graph labellings. The implications of bounding the eigenvalues (from both above and below) are also explored. Finally, we examine the question of whether a graph is determined by its spectrum. In addition, we note some relationships between a graph and other matrices related to the adjacency matrix.