星图及星图联图的(a,d)-顶点反魔幻标号  

(a,d)-Vertex Antimagic Total Labelings of Star and Composite Graph of Star

作　　者：火金萍 李敬文[1] 袁清厚 康玉梅 Huo Jing-ping;Li Jing-wen;Yuan Qing-hou;Kang Yu-mei(School of Electronics and Information Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学电子与信息工程学院,甘肃兰州730070

出　　处：《数学的实践与认识》2020年第9期132-140,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11461038)。

摘　　要：设G(p,q)是一个有p个顶点,q条边的图,(a,d)-顶点反魔幻全标号((a,d)-VATL)是一个从V(G)∪E(G)到连续整数(1,2,…,p+q)的双射,顶点及其关联边的标号之和构成首项为a,公差为d的等差数列.本文设计了一种算法,可以判别有限点内所有非同构图是否存在(a,d)-点反魔幻全标号,发现其中的星图及星图联图在一定条件下不存在(a,1)-顶点反魔幻全标号,并对这些图进行了分类和定义,同时总结了非(a,d)-顶点反魔幻规律,并给出定理.Suppose that G(p,q) is a graph with p vertices and q edges,(a,d)-vertexantimagic total labeling((a,d)-VATL)is an bijection λ from V(G) ∪ E(G) to the consecutive integers(1,2,...,p+q),where the sum of the labels of every vertex and its incident edges form an arithmetic progression with the initial term a and difference d.In this project,algorithm is designed to judge the(a,d)-vertex-antimagic total labelings of nonisomorphic graphs within finite vertices,it is found that some of them don’t have(a,1)-vertex-antimagic total labelings to certain conditions,and these graphs are classified and defined,at the same time,the rules of non-(a,d)-vertex antimagic are summarized,and the theorems are given.

关 键 词：图标号 (a d)-顶点反魔幻标号 算法 星图联图 

分 类 号：O157.5[理学—数学]