論文摘要

在離散數學的領域中有一熱門的分支一圖學論就是將問題以圖形的觀念來研究，其中優美圖問題是由來已久，尤其是在太空訊息的接收，雷達站之設立位置等科學性的研究中廣泛的被討論，我們企圖將優美圖的必要條件cordial 圖作適當的推展以這算子為架構將圖形類別視為運算元則

{ (運算元) ，運算子} ===新圖形

結合將可得到新的圓形使得新圖形是cordial 圖這樣一來就可製造出更多更複雄史實用的cordial 圖，有cordial 圖才有可能是優美圖.

研究之初我們收集有關優美圖的論文想知道一些優美圖標法與尚未解決的圖形，和由優美圖衍生出的特殊圖形，我們整理得到壹拾貳大類這些類別的圖形在簡單的情形時已有了不錯的結論，但是稍為複雜或條件放鬆則結果說不得而知，由於優美國的重要及熱門迫使我們不得不有這種動機嘗試將已無圓形配和圓形運算子而得到複雜的圖形式得到新類別的圓形並企圖使新圖形式複雜圖形是cordial 圖在論文中，我們找到一些還算子例如link ，

corona, join , bridge and newcorona 並且導出一些結果.

Abstract

Suppose G is a graph with vertex set V(G) and edge set E(G). Consider a labeling f: V(G) → { 0, 1} where f induces an edge-labeling i*: E(G) -+ {0,1} defined by f*(uv) = I f(u) - f(v) I for each edge uv E E( G). Let V f(i) be the set of vertices v of G with f( v)=i, and Ef(i) be the set of edges uv with f*(uv)=i. The cardinalities of Yf(i) and Ef(i) are denoted by vf(i) and ef(i), respectively. A labeling f of a graph is cordial if Ivf (0)-vf (1) ? I and lef(0)- ef(1)?1. A graph G is cordial if it has a: cordial labeling. In this paper, we will study some operators such as link (0), corona( *), join(+), bridge (?), and newcorona( ?), and derive some results on cordial graphs.

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