Author

Peng Huang

Year of Award

2016

Degree Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Mathematics.

Principal Supervisor

Shiu, Wai-chee

Keywords

Graph theory.

Language

English

Abstract

The adjacency matrix of a graph is a (0, 1)-matrix indexed by the vertex set of the graph. And the signless Laplacian matrix of a graph is the sum of its adjacency matrix and its diagonal matrix of vertex degrees. The eigenvalues and the signless Laplacian eigenvalues of a graph are the eigenvalues of the adjacency matrix and the signless Laplacian matrix, respectively. These two matrices of a graph have been studied for several decades since they have been applied to many research field, such as computer science, communication network, information science and so on. In this thesis, we study k-connected graphs and focus on their spectral radius and signless Laplacian spectral radius. Firstly, we determine the graphs with maximum spectral radius among all k-connected graphs of fixed order with given diameter. As we know, when a graph is regular, its spectral radius and signless Laplacian spectral radius can easily be found. We obtain an upper bound on the signless Laplacian spectral radius of k-connected irregular graphs. Finally, we give some other results mainly related to the signless Laplacian matrix.

Comments

Principal supervisor: Dr. Shiu Wai Chee.;Thesis submitted to the Department of Mathematics. Thesis (Ph.D.)--Hong Kong Baptist University, 2016.

Bibliography

Includes bibliographical references (pages 63-70).

Available for download on Saturday, July 07, 2018



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