兩圖相連之優美標號

機構典藏 > College of Sciences > Graduate Institute & Department of Mathematics > Thesis > Item 987654321/105286

Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/105286

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:	[Graduate Institute & Department of Mathematics] Thesis

Files in This Item:

File	Description	Size	Format
index.html		0Kb	HTML	128	View/Open

Loading...