关于非交换群的非交换图的度量维数  

Metric Dimension of Noncommutative Graphs in Noncommutative Groups

作　　者：钟欣怡 马儇龙 钟国 ZHONG Xinyi;MA Xuanlong;ZHONG Guo(School of Information Science and Technology,Guangdong University of Foreign Studies,Guangzhou 510006,China;School of Science,Xi an Shiyou University,Xi an 710065,China)

机构地区：[1]广东外语外贸大学信息科学与技术学院,广东广州510006 [2]西安石油大学理学院,陕西西安710065

出　　处：《杭州师范大学学报（自然科学版）》2023年第6期637-640,共4页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11801441)。

摘　　要：给定一个非交换群,该群的非交换图以该群所有非中心元素构成的集合为顶点集,两个不同的顶点x和y相邻的充分必要条件是xy≠yx.文章研究非交换群的非交换图的度量维数问题,确定了二面体群的非交换图的度量维数,且对任意非交换群的非交换图的度量维数给出了紧的上下界.Given a noncommutative group,the noncommutative graph of this group takes a set of all noncentral elements as the vertex set.The necessary and sufficient condition for two different vertices x and y to be adjacent is xy≠yx.In this paper,the metric dimension of noncommutative graphs in noncommutative groups were studied.Specifically,the metric dimension of noncommutative graphs of dihedral groups were determined,and a compact upper and lower bound for the metric dimension of noncommutative graphs in any noncommutative group were provided.

关 键 词：二面体群 非交换图 度量维数 

分 类 号：O157.5[理学—数学]