Title: 圖的特徵值最大重覆度與最小路徑分割數之探討
Maximal eigenvalue multiplicity and minimal path partition number of a graph
Authors: 蘇育吟
Yu-Ying Su
Chih-Wen Weng
Keywords: 特徵值最大重覆度;最小路徑分割數;Maximal eigenvalue multiplicity;minimal path partition number
Issue Date: 2000
Abstract: G表示一個圖形,我們定義P(G)為最小路徑分割數。而我們定義M(G)所有對應於G圖的對稱方陣之特徵值的最大重覆度。我們研究P(G)和M(G)兩數之間具有的相同性質,並且重證對於任何樹圖T 都滿足P(T)=M (T),我們的方法有別於文獻[1]。最後對其它圖G提出一些關於P(G)及M(G)關係的猜測。
Let G be a graph, P ( G ) denote the minimal number of vertex disjoint pathsthat cover all the vertices of G, and M ( G ) denote the maximal multiplicity occuring for an eigenvalue of a symmetric matrix with presscribed graph G. We study the common properties between the two numbers P ( G ) and M ( G ), and reprove P ( T ) = M ( T ) for any trees T, in a di?erent method from [1]. Some conjectures are given in the end of this thesis.
Appears in Collections:Thesis