On the spectral characterizations of ∞-graphs
On the spectral characterizations of ∞-graphs
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DOI：
10.1016/j.disc.2010.01.021
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发表时间：
2010-07
期刊：
影响因子：
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通讯作者：
Jianfeng Wang;Qiongxiang Huang;Francesco Belardo;E. M. L. Marzi
中科院分区：
文献类型：
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作者：
Jianfeng Wang;Qiongxiang Huang;Francesco Belardo;E. M. L. Marzi
∞ 图是由两个环组成的图，只有一个公共顶点。我们首先寻找共谱图的一些不变量，然后引入一种新方法来确定图的共谱配对的度序列。在本文中，我们证明所有没有三角形的 ∞ 图都由其拉普拉斯谱确定，并且除一个例外外，所有 ∞ 图均由其无符号拉普拉斯谱确定。对于例外情况，我们确定所有与其共谱的图（w.r.t.无符号拉普拉斯谱）。
A ∞-graph is a graph consisting of two cycles with just a vertex in common. We first look for some invariants for cospectral graphs, then we introduce a new method to determine the degree sequence of cospectral mates of a graph. In this paper, we prove that all ∞-graphs without triangles are determined by their Laplacian spectra and that all ∞-graphs, with one exception, are determined by their signless Laplacian spectra. For the exception we determine all graphs that are cospectral (w.r.t. signless Laplacian spectrum) to it.