Thesis (Ph. D., Mathematics)--University of Idaho, May 2009. / Major professor: Hong Wang. Includes bibliographical references (leaves 77-86). Also available online (PDF file) by subscription or by purchasing the individual file.

Thesis (Ph. D.)--West Virginia University, 2009. / Title from document title page. Document formatted into pages; contains vi, 45 p. : ill. Includes abstract. Includes bibliographical references (p. 42-45).

Thesis (M.A.)--University of Louisville, 2004. / Department of Mathematics. Vita. "August 2004." Includes bibliographical references (leaves 87-91).

Thesis--University of Wisconsin--Madison. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 187-190).

Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2004. / Includes bibliographical references (p. 58-59).

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.

D.Phil.

M.Sc. (Mathematics) / Please refer to full text to view abstract.

Philosophiae Doctor - PhD / In this thesis only Binary codes are studied. Firstly, the codes overs the field GF(2) by the adjacency matrix of the complement T(n), ofthe triangular graph, are examined. It is shown that the code obtained is the full space F2 s(n/2) when n= 0 (mod 4) and the dual code of the space generated by the j-vector when n= 2(mod 4). The codes from the other two cases are less trivial: when n=1 (mod 4) the code is [(n 2), (n 2 ) - n + 1, 3] code, and when n = 3 (mod 4) it is an [(n 2), (n 2) - n, 4 ] code. / South Africa

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