On a signless Laplacian spectral characterization of T-shape trees
On a signless Laplacian spectral characterization of T-shape trees
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DOI：
10.1016/j.laa.2009.05.035
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发表时间：
2009-10
影响因子：
1.1
通讯作者：
G. Omidi
中科院分区：
文献类型：
--
作者：
G. Omidi
设M是图G的伴随矩阵（邻接矩阵、拉普拉斯矩阵和无号拉普拉斯矩阵）.如果两个图具有相同的M谱，则称它们关于M是共谱的。一个图称为由M谱决定的，如果不存在其它非同构图与M具有相同的谱。结果表明，T形树是由其拉普拉斯谱决定的。并对其中由邻接谱决定的部分进行了表征。在本文中，我们确定的图是一个给定的T-形树的无符号拉普拉斯矩阵的共谱。随后，T-形树，这是由它们的无符号拉普拉斯谱确定。
Let M be an associated matrix of a graph G (the adjacency, Laplacian and signless Laplacian matrix). Two graphs are said to be cospectral with respect to M if they have the same M spectrum. A graph is said to be determined by M spectrum if there is no other non-isomorphic graph with the same spectrum with respect to M. It is shown that T-shape trees are determined by their Laplacian spectra. Moreover among them those are determined by their adjacency spectra are characterized. In this paper, we identify graphs which are cospectral to a given T-shape tree with respect to the signless Laplacian matrix. Subsequently, T-shape trees which are determined by their signless Laplacian spectra are identified.