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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.4 Antofagasta dic. 2019 


New bounds on the distance Laplacian and distance signless Laplacian spectral radii

Roberto C. Díaz1 

Ana I. Julio2

Óscar Rojo3

1Universidad Católica del Norte, Dept. de Matemáticas, Antofagasta, Chile. e. mail:

2 Universidad Católica del Norte, Dept. de Matemáticas, Antofagasta, Chile. e. mail:

3 Universidad Católica del Norte, Dept. de Matemáticas, Antofagasta, Chile. e. mail:


Let G be a simple undirected connected graph. In this paper, new upper bounds on the distance Laplacian spectral radius of G are obtained. Moreover, new lower and upper bounds for the distance signless Laplacian spectral radius of G are derived. Some of the above mentioned bounds are sharp and the graphs attaining the corresponding bound are characterized. Several illustrative examples are included.

Keywords: Distance matrix; Vertex transmission; Wiener index; Distance Laplacian matrix; Distance signless Laplacian matrix; Spectral radius

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The authors are very grateful to an anonymous referee for all his/her comments and corrections. The research of R. Díaz was supported by Conicyt-Fondecyt de Postdoctorado 2017 No 3170065, Chile. The research of A. Julio was supported by Conicyt-PAI 79160002, 2016, Chile. The research of O. Rojo was supported by Project Fondecyt Regular 1170313, Chile.


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Received: June 2019; Accepted: July 2019

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