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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

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

http://dx.doi.org/10.22199/issn.0717-6279-2019-04-0056 

Articles

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

Roberto C. Díaz1 

Ana I. Julio2 
http://orcid.org/0000-0002-7864-1276

Óscar Rojo3 
http://orcid.org/0000-0003-1530-6697

1Universidad Católica del Norte, Dept. de Matemáticas, Antofagasta, Chile. e. mail: rdiaz01@ucn.cl

2 Universidad Católica del Norte, Dept. de Matemáticas, Antofagasta, Chile. e. mail: ajulio@ucn.cl

3 Universidad Católica del Norte, Dept. de Matemáticas, Antofagasta, Chile. e. mail: orojo@ucn.cl

Abstract

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

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

Acknowledgements.

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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