| Symmetric graphs have been more and more important in algebraic graph theory.While Cayley graphs are a large family of symmetric graphs which can be constructed from groups.In the past several years,researchers have investigated Cayley graphs from many aspects.We will focus on the eigenvalues of Cayley graphs in this thesis.The eigenvalues of a graph refer to the eigenvalues of its adjacent matrix.If the multiplicity of an eigenvalue is 1,we call this eigenvalue a single eigenvalue.Singe eigenvalues reflect some properties of graphs,so they are attracting the attentions of more and more researchers.In this thesis,we give necessary conditions a value should satisfy to be the simple eigenvalue of a Cayley graph corresponding to a cyclic group,a dihedral group,a direct product group or a generalized dihedral group. |
