关于非交换群的非交换图的度量维数

Metric Dimension of Noncommutative Graphs in Noncommutative Groups

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.