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研究生： 林政寬
Cheng-Kuan Lin
論文名稱： n 階置換Cayley 圖之研究
指導教授： 黃華民
Hua-Min Huang
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
畢業學年度： 90
語文別： 中文
論文頁數： 87
中文關鍵詞： Cayley
相關次數： 點閱：7  下載：0 
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    • 一個有漢米頓圈的圖，代表圖中任意兩點都有一對內點互斥且通過所有頂點的路徑。
    根據Menger′s 定理，在n連通圖中，任意的兩點p, q之間存在著n條內點互斥的路徑。若此n條內點互斥的路徑包含著圖中所有的頂點，則稱p, q是n覆蓋連通。
    本論文將以n規則Cayley圖為例來討論覆蓋連通性及其相關特性。

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    表次 ..................... 2 圖次 ................... 3 摘要 .............................. 4 前言 ........................... 5 第一章 基本定義 ..... 6 1.1 基本定義 1.2 Cayley圖 1.3 立方圖 1.4 Transposition Tree圖 1.5 Pancake圖 第二章 有遞迴結構Cayley圖上的漢米頓相關性質 .................. 16 2.1 漢米頓連接 2.2漢米頓圈 第三章 k-覆蓋連通性質 .............. 24 3.1 Pancake圖的k-覆蓋連通性質 3.2 立方圖的k-偶覆蓋連通性質 3.3 星圖的k-偶覆蓋連通性質 3.4 泡沫圖的k-偶覆蓋連通性質 附錄........................ 60 參考文獻................ 69

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