二分圖其特徵值的上界

Abstract

令G為一個圖且A(G)為G的相鄰矩陣。G的特徵多項式記作PG(x)，其定義為( xI - A(G) )該矩陣的特徵值，其中I是單位矩陣。而圖的相鄰矩陣所對應的特徵值視為該圖的特徵值。在本篇論文中，我們將討論二分圖其最大的特徵值。主要而言，對於某幾個類別的二分圖的最大特徵值給一個上界。

Let G be a graph and A(G) be the adjacency matrix of G. The characcteristic polynomial of G, denoted by PG(x), is det ( xI - A(G ) ) where I is the identity matrix. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. In this thesis, we study the largest eigenvalue of bipartite graphs. Mainly, an upper bound for the largest eigenvalues of certain families of bipartite graphs is obtained.