圖G 的秩是一個鄰接矩陣G 的秩。2009 年，黃良豪博士、張鎮華教授、葉鴻國教授等人已經完整的描繪出當連通圖之秩為4 時此圖的所有特徵。在本篇碩士論文中我們考慮以下兩個問題：(1)考慮連通圖G具有rank(G) = 5且從圖G中拿掉任何點v 皆會有rank(G-v)=3 時，圖G 的特徵。(2) 考慮連通圖G 具有rank(G) = 5且從圖G中拿掉任何點v皆會有rank(G-v)=4 時，圖G的特徵。在這篇論文我們已經完全解決這兩個問題。 The rank of a graph G is the rank of the adjacency matrix of G. In 2009, Chang, Huang and Yeh completely characterized the structure of a connected graph of rank 4. In this paper we consider the following two questions: (1) What is the structure of a connected graph G with the property that rank(G) = 5 and rank(G-v) = 3 for all v belong to V(G)? (2) What is the structure of a connected graph G with the property that rank(G) = 5 and rank(G-v) = 4 for all v belong to V(G)? In this paper we completely resolve these two questions.
