標題: | 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 |
作者: | 蘇育吟 Yu-Ying Su 翁志文 Chih-Wen Weng 應用數學系所 |
關鍵字: | 特徵值最大重覆度;最小路徑分割數;Maximal eigenvalue multiplicity;minimal path partition number |
公開日期: | 2000 |
摘要: | 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. |
URI: | http://140.113.39.130/cdrfb3/record/nctu/#NT890507021 http://hdl.handle.net/11536/67702 |
顯示於類別: | 畢業論文 |