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    Title: 兩圖相連之優美標號
    Other Titles: Graceful labelings for the join of two graphs
    Authors: 林淑靜;Lin, Shu-Ching
    Contributors: 淡江大學中等學校教師在職進修數學教學碩士學位班
    高金美
    Keywords: 路徑;迴圈;相連;優美標號;優美圖;path;cycle;join;graceful labeling;graceful graph
    Date: 2015
    Issue Date: 2016-01-22 14:52:20 (UTC+8)
    Abstract: 令G為含有m個邊的簡單圖,若存在一個函數f,其中f : V(G)→{0,1,2,…,m}且f為一對一函數。若由f 所衍生出的函數 g,g : E(G)→{1,2,…,m},∀e={u,v}∈E(G),g(e)=|f(u)-f(v)| 且g 為一對一且映成函數,則稱此圖G為優美圖。
    在本論文中,我們證明了:
    (1)利用PnvKm是優美圖,獲得設m、n為正整數,若G為n個點,n-1個邊的優美圖,則GvKm為優美圖。
    (2)若t為正整數,則當m=3,4,5時,CmvKt為優美圖。
    Let G be a simple graph with m edges. If there is a function f : V(G)→{0,1,2,…,m} and fis one-to-one. From the function f we can get a function
    g : E(G)→{1,2,…,m}, defined by g(e)=|f(u)-f(v)|, for e={u,v}∈E(G), and g is bijective, then we call f is a graceful labeling and G is a grace graph.
    In this thesis, we obtain the following results.
    (1)Let m and n be positive integers. If G is a graph with n vertices and n–1 edges and G is graceful, then GvKm is a graceful graph.
    (2)Let t be appositive integer. If m=3,4,or 5,then CmvKtis a graceful graph.
    Appears in Collections:[數學學系暨研究所] 學位論文

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