秩為5的圖形; On the Graphs of Rank Five

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/43903

Title:	秩為5的圖形;On the Graphs of Rank Five
Authors:	蕭景文;Jing-Wen Shiao
Contributors:	數學研究所
Keywords:	秩;五;鄰接矩陣;multiplication of vertices;graph;rank;five
Date:	2010-06-28
Issue Date:	2010-12-08 14:26:05 (UTC+8)
Publisher:	國立中央大學
Abstract:	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.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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