圖論上代數方法的探討

Abstract

代數方法在圖論上被廣泛的使用。如圖上的自同態群的研究，利用特徵值及線性代數的方法來探討圖的性質、以及與圖有關的多項式。這篇論文的目的主要是收集了已知的圖論上使用的代數方法。

Algebraic methods provide many new and powerful ways in the study of graph theory. These include the study of the group of homomorphisms on graphs, the construction of graphs from a group, using the eigenvalue or other linear algebraic techniques in the study of graph theory and the study of polynomials associated with a graph. The purpose of this thesis is to collect the known results in graph theory with algebraic techniques involved.