非边幻和图的若干定理及证明

Some Theorems and Proofs of Non-Edge-Magic Total Labeling Graphs

若G(p,q)的点边标号一一映射到{1,2,…,p+q},使得任意边与其关联顶点的标号值之和为一个常数,这种标号被称之为边幻和全标号。本文设计了一种算法得到了9个点以内所有简单无向连通图中的非边幻和图,发现其中一些图具有某种相同的特征,因此定义了新的图运算符Kn▷Cm和KnΔSm来刻画这两类联图,通过引入西顿序列,证明了在特定条件下,两类联图为非边幻和图。

If the labeling values of edges and vertices for a graph G(p,q)are mapped one by one to{1,2,…,p+q},the sum of the labeling values for the edge and its incident vertices equals to a constant,and this labeling is called edge-magic total labeling.In this paper,an algorithm is designed to find all non-edge-magic total labeling graphs of all simple undirected connected graphs within 9 vertices.And we also find that some of the graphs have the same characteristics,thus define the new graph's operational characters Kn▷Cm and KnΔSm to depict them.Finally,by introducing the Sidon sequence,it is proved that two types of composite graphs are non-edge-magic total labeling graphs under certain conditions.