若干太阳图的顶点魔幻全标号优化算法

On Vertex-Magic Total Labelings Optimization Algorithm of Some Sun-graphs

图的顶点魔幻全标号指:对于图G(p,q),任意顶点v及其关联边的标号值之和等于常数k,其中标号值集合与集合{1,2,…,p+q}一一映射.该文实现了一种针对随机图的顶点魔幻全标号优化算法,能够求解得到有限点内简单连通图的标号,通过结果分析,发现了两类太阳图S_(n)和GS_(n)、广义太阳图S_(n,m)以及图P(n,1)的标号特性,总结出若干定理并给出证明.

For graph G(p,q),vertex-magic total labeling means that the sum of the labeling values of any vertex v and its incident edges is equal to the constant k,where the mapping of labeling values are:{1,2,…,p+q}.In this paper,a vertex magic-total labeling optimization algorithm is designed and used to obtain the labeling of simple connected graph within finite vertices.By analyzing and summarizing the labeling results of sun-graphs S_(n),GS_(n) and general sun graph S_(n,m) and graphs P(n,1),the labeling rules for these graphs are found,some theorems are summed up and proved as well.