| 摘要: | 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. |
