Some sharp bounds on the distance signless Laplacian spectral radius of graphs
Some sharp bounds on the distance signless Laplacian spectral radius of graphs
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发表时间：
2013-08
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通讯作者：
W. Hong;L. You
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作者：
W. Hong;L. You
M. Aouchiche 和 P. Hansen 提出了连通图的距离拉普拉斯算子和距离无符号拉普拉斯算子 [图的距离矩阵的两个拉普拉斯算子，LAA 439 (2013) 21{33]。在本文中，我们获得了关于非负矩阵谱半径的锐上界的三个定理，然后将这些定理分别应用于无符号拉普拉斯矩阵和距离无符号拉普拉斯矩阵，以获得谱半径上的一些锐界。我们还提出了关于无符号拉普拉斯谱半径的锐界的已知结果存在缺陷。
M. Aouchiche and P. Hansen proposed the distance Laplacian and the distance signless Laplacian of a connected graph [Two Laplacians for the distance matrix of a graph, LAA 439 (2013) 21{33]. In this paper, we obtain three theorems on the sharp upper bounds of the spectral radius of a nonnegative matrix, then apply these theorems to signless Laplacian matrices and the distance signless Laplacian matrices to obtain some sharp bounds on the spectral radius, respectively. We also proposed a known result about the sharp bound of the signless Laplacian spectral radius has a defect.