Proyecciones Journal of Mathematics Vol. 31, N^o 1, pp. 39-49, March 2012. Universidad Católica del Norte Antofagasta - Chile

An upper bound on the largest signless Laplacian of an odd unicyclic graph

Macarena Collao

Universidad Católica del Norte, Chile

Pamela Pizarro

Universidad Católica del Norte, Chile

OSCAR ROJO

Universidad Católica del Norte, Chile

 

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ABSTRACT

We derive an upper bound on the largest signless Laplacian eigenvalue of an odd unicyclic graph. The bound is given in terms of the largest vertex degree and the largest height of the trees obtained removing the edges of the unique cycle in the graph.

AMS classification : 05C50, 15A48.

Keywords : Laplacian matrix; signless Laplacian matrix; adjacency matrix; spectral radius; generalized Bethe tree.

 

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Macarena Collao

Departamento de Matemáticas Universidad Católica del Norte

Casilla 1280

Antofagasta

Chile

e-mail : maca_collaom@hotmail.com

Pamela Pizarro

Departamento de Matemáticas Universidad Católica del Norte

Casilla 1280

Antofagasta

Chile

e-mail : parkinzon_triste@hotmail.com

and

Oscar Rojo

Departamento de Matemáticas Universidad Católica del Norte

Casilla 1280

Antofagasta

Chile

e-mail : orojo@ucn.cl

Received : November 2011. Accepted : January 2012

*Work supported by Project Fondecyt 1100072, Chile.