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arXiv · 1308.3427

Some sharp bounds on the distance signless Laplacian spectral radius of graphs

Wenxi Hong·Lihua You
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Abstract

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.

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Wenxi Hong, Lihua You. 2013-08-15. Some sharp bounds on the distance signless Laplacian spectral radius of graphs. https://arxiv.org/abs/1308.3427

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