English  |  正體中文  |  简体中文  |  Items with full text/Total items : 51483/86598 (59%)
Visitors : 8246231      Online Users : 86
RC Version 7.0 © Powered By DSPACE, MIT. Enhanced by NTU Library & TKU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
  • Adv. Search
    HomeLoginUploadHelpAboutAdminister Goto mobile version
    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/32937


    Title: 可追蹤圖的探討
    Other Titles: The study of traceable graphs
    Authors: 林欣誼;Lin, Hsin-i
    Contributors: 淡江大學數學學系碩士班
    高金美;Kau, Chin-mei
    Keywords: 可追蹤圖;全部可追蹤圖;traceable graphs;totally traceable graphs
    Date: 2005
    Issue Date: 2010-01-11 03:00:25 (UTC+8)
    Abstract: 在本論文中,我們討論全部可追蹤圖的性質,並獲得利用米希爾斯基建構法建構出的圖M(G)中,只要圖G是一個迴圈或是漢米爾頓圖,則圖M(G)就會是一個是全部可追蹤的圖。
    接著,我們定義了π(G)為圖G中,可追蹤的邊數佔所有邊數的比例,即當G有b個邊,其中a個邊為可追蹤邊的個數,則π(G)=a/b。並獲得下面的結果:
    (1) 任給兩個正整數a, b,只要 a≦b≦[(a2 +4)/4],則存在一個邊數為b的圖G中含有a個可追蹤的邊,即π(G)=a/b。
    (2) 任給正整數n,則對於所有介於n – 1和1+(n – 1)2/4 之間的整數b,存在一個點數為n,邊數為b的圖G,使得π(G)=(n – 1)/b。
    (3) 任給大於等於5的正整數n,則對於所有介於 和(n2–5n+14)/2之間的整數b,存在一個點數為n,邊數為b的圖G,使得π(G)=(b – 1)/b。
    In this thesis, we discuss the properties of a totally traceable graph, and using Mycielski’s construction to construct a sequence of totally traceable graphs M(G) as G is a Hamiltonian graph.

    Next, we define π(G) to be the ratio of traceable edges and total edges of G. That is if G has b edges which contains a traceable edges, then π(G) = a/b. We obtains the following results:
    (1) Given any two positive integers a, b and a≦b≦[(a2 +4)/4], then there is a graph G with b edges such that π(G) = a/b.
    (2) Given any positive integer n, then there is a graph G with n vertices and b edges such that π(G) = (n – 1)/b, for each b, n–1≦b≦1+(n – 1)2/4.
    (3) Given any positive integer n, then there is a graph G with n vertices and b edges such that π(G) = (b – 1)/b, for each b, ≦b≦(n2–5n+14)/2.
    Appears in Collections:[數學學系暨研究所] 學位論文

    Files in This Item:

    File SizeFormat
    0KbUnknown128View/Open

    All items in 機構典藏 are protected by copyright, with all rights reserved.


    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library & TKU Library IR teams. Copyright ©   - Feedback