Some Properties of Order-Divisor Graphs of Finite Groups

Shafiq ur Rehman, Raheela Tahir, Farhat Noor
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Abstract

This article investigates the properties of order-divisor graphs associated with finite groups. An order-divisor graph of a finite group is an undirected graph in which the set of vertices includes all elements of the group, and two distinct vertices with different orders are adjacent if the order of one vertex divides the order of the other. We prove some beautiful results in order-divisor graphs of finite groups. The primary focus is on examining the girth, degree of vertices, and size of the order-divisor graph. In particular, we provide a comprehensive description of these parameters for the order-divisor graphs of finite cyclic groups and dihedral groups.
有限群的阶分图的一些性质
本文研究了与有限群相关的阶因子图的性质。有限群的阶因子图是一个无向图,其中顶点集包括群的所有元素,如果一个顶点的阶除以另一个顶点的阶,则具有不同阶的两个不同顶点相邻。我们在有限群的阶除图中证明了一些漂亮的结果。我们的主要重点是研究阶分图的长、顶点度和大小。特别是,我们为有限循环群和二面群的阶分维图提供了这些参数的全面描述。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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