Towards a spectral theory of graphs based on the signless Laplacian, II
Towards a spectral theory of graphs based on the signless Laplacian, II
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DOI：
10.1016/j.laa.2009.05.020
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发表时间：
2010-04
影响因子：
1.1
通讯作者：
D. Cvetkovic;S. Simic
中科院分区：
文献类型：
--
作者：
D. Cvetkovic;S. Simic
谱图论是一种通过矩阵 M 的特征值来研究图的理论，该矩阵 M 是以规定的方式为任何图定义的。该理论称为 M 理论。我们概述了基于无符号拉普拉斯 Q 的图谱理论，并将其与其他谱理论进行比较，特别是基于邻接矩阵 A 和拉普拉斯 L 的谱理论。如第一部分所示，Q 理论可以部分地使用与其他理论的各种联系来构建：与正则图的 A 理论和 L 理论等价，与二分图的 L 理论的共同特征，与 A 理论的一般类比以及与通过线图和细分图的 A 理论。在这一部分中，我们介绍了丰富谱理论和限制谱理论的概念，并给出了积分图、生成树枚举、特征值表征、共谱图和图角度的结果。
A spectral graph theory is a theory in which graphs are studied by means of eigenvalues of a matrix M which is in a prescribed way defined for any graph. This theory is called M-theory. We outline a spectral theory of graphs based on the signless Laplacians Q and compare it with other spectral theories, in particular to those based on the adjacency matrix A and the Laplacian L. As demonstrated in the first part, the Q-theory can be constructed in part using various connections to other theories: equivalency with A-theory and L-theory for regular graphs, common features with L-theory for bipartite graphs, general analogies with A-theory and analogies with A-theory via line graphs and subdivision graphs. In this part, we introduce notions of enriched and restricted spectral theories and present results on integral graphs, enumeration of spanning trees, characterizations by eigenvalues, cospectral graphs and graph angles.