Signless Laplacians of finite graphs
Signless Laplacians of finite graphs
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DOI：
10.1016/j.laa.2007.01.009
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发表时间：
2007-05-01
影响因子：
1.1
通讯作者：
Simic, Slobodan K.
中科院分区：
文献类型：
--
作者：
Cvetkovic, Dragos;Rowlinson, Peter;Simic, Slobodan K.
我们调查了图的无符号拉普拉斯谱的性质，并讨论了基于该矩阵发展图的谱理论的可能性。对于正则图，邻接矩阵和拉普拉斯矩阵的整个现有谱理论直接转移到无符号拉普拉斯，因此我们考虑任意图，特别强调非正则情况。我们调查的结果（旧的和新的）有两种类型：（a）通过将与邻接矩阵的相应结果相同的推理应用于无符号拉普拉斯而获得的结果，（b）通过线图间接获得的结果。除其他外，我们提出了几个图不变量的特征值界、特征多项式系数的解释、无符号拉普拉斯幂的定理以及对星补的一些评论。 (C) 2007 Elsevier Inc. 保留所有权利。
We survey properties of spectra of signless Laplacians of graphs and discuss possibilities for developing a spectral theory of graphs based on this matrix. For regular graphs the whole existing theory of spectra of the adjacency matrix and of the Laplacian matrix transfers directly to the signless Laplacian, and so we consider arbitrary graphs with special emphasis on the non-regular case. The results which we survey (old and new) are of two types: (a) results obtained by applying to the signless Laplacian the same reasoning as for corresponding results concerning the adjacency matrix, (b) results obtained indirectly via line graphs. Among other things, we present eigenvalue bounds for several graph invariants, an interpretation of the coefficients of the characteristic polynomial, a theorem on powers of the signless Laplacian and some remarks on star complements. (C) 2007 Elsevier Inc. All rights reserved.