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

作　　者：席晓慧 王遂缠 高鹏 XI Xiaohui;WANG Suichan;GAO Peng(Gansu Meteorological Information and Technical Equipment Support Center, Lanzhou 730020, China)

机构地区：[1]甘肃省气象信息与技术装备保障中心,兰州730020

出　　处：《西南师范大学学报（自然科学版）》2022年第7期27-34,共8页Journal of Southwest China Normal University(Natural Science Edition)

摘　　要：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.

关 键 词：顶点魔幻全标号 优化算法 太阳图 标号特性 

分 类 号：O157.5[理学—数学]