三角形棒棒糖圖的無號拉普拉斯矩陣之特徵值探討

Abstract

假設G 是一個由點1,2,…,n 所構成的簡單圖，其中每個點相對應的價數 分別為d1,d2,…,dn..設A(G) 是G 的 (0,1)-鄰接矩陣，D(G) 是一個對角 矩陣，其對角線上分別是d1,d2,…,dn..矩陣L(G)=D(G)-A(G) 稱為G 的 拉普拉斯矩陣，矩陣 |L|(G)=D(G)+A(G) 稱為G 的無號拉普拉斯矩陣.. A(G)，L(G)，|L|(G) 的特徵值給了我們很多訊息去了解G 的構造..在這個論 文中，我們研究一種圖形叫做三角形棒棒糖圖，其由一個三個點的完全圖與 一個路徑圖共用一點而接起來..我們探討三角形棒棒糖圖的無號拉普拉斯矩 陣的特徵值..特徵多項式及它們的相關比較問題..

Let G be a simple graph with vertices 1,...,n of degrees d1,...,dn respectively. Let A(G) be the (0,1)-adjacency matrix of G, and let D(G) be the diagonal matrix diag(d1,...,dn). The matrix L(G)=D(G)−A(G) is the Laplacian matrix of G, while |L|(G)=D(G)+A(G) is called the signless laplacian matrix of G. The eigenvalues of A(G), L(G), and |L|(G) give many hints to the structure of G. In this thesis we study a class of graphs, called lollipop graph with a triangle, which are obtained from paths by adding a new vertex to a path and adding two edges from the new vertex to one end of the path and to the neighbor of this end, forming a triangle K3. We study the signless Laplacian eigenvalues and characteristic polynomial of lollipop graphs with K3.