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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.34 no.2 Antofagasta June 2015 

The largest Laplacian and adjacency indices of complete caterpillars of fixed diameter

Nair Abreu *

Universidade Federal do Ro de Janeiro


Eber Lenes

Universidad del Sinu


Oscar Rojo

Universidad Católica del Norte



A complete caterpillar is a caterpillar in which each internal vertex is a quasi-pendent vertex. In this paper, in the class of all complete caterpillars on n vertices and diameter d, the caterpillar attaining the largest Laplacian index is determined. In addition, it is proved that this caterpillar also attains the largest adjacency index.

Keywords : Caterpillar, Laplacian matrix, Laplacian index, adjacency matrix, index, spectral radius.

2010 AMS classification : 05C50.


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Nair Abreu

Production Engineering Program, PEP/COPPE Universidade Federal do Rio de Janeiro Rio de Janeiro,


e-mail: Eber Lenes

Departamento de Investigaciones Universidad del Sinu. Elias Bechara Zainum Cartagena,



O. Rojo

Department of Mathematics Universidad Católica del Norte Antofagasta,


e-mail :

Received : January 2015. Accepted : May 2015

* thanks the support of Grant 305372/2009-2, CNPq, Brazil.

†thanks the support of Project Mecesup UCN 0711 and Project Fondecyt Regular 1130135, Chile.

‡thanks the support of Project Fondecyt Regular 1130135, Chile, and the hospitality of the Center For Mathematical Modeling, Universidad de Chile, Chile, in which this research was finished.

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