群的素图参数

IF 0.7 Q2 MATHEMATICS

International Journal of Group Theory Pub Date : 2021-09-01 DOI:10.22108/IJGT.2020.112121.1489

Jessica Hamm, A. Way

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引用次数: 3

摘要

‎有许多不同的图可以关联到一个组‎. ‎一些例子是著名的Cayley图‎, ‎（环的）零除数图‎, ‎功率图‎, ‎以及最近引入的群的互质图‎. ‎群$G的互素图$‎, ‎表示为$Gamma_G$‎, ‎是顶点是$g$与$h$相邻的群元素的图，当且仅当$（o（g），o（h））=1$‎. ‎本文计算了二面体群互质图的独立数‎. ‎此外‎, ‎我们刻画互素图是完美的群‎.

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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Parameters of the coprime graph of a group

‎There are many different graphs one can associate to a group‎. ‎Some examples are the well-known Cayley graph‎, ‎the zero divisor graph (of a ring)‎, ‎the power graph‎, ‎and the recently introduced coprime graph of a group‎. ‎The coprime graph of a group $G$‎, ‎denoted $Gamma_G$‎, ‎is the graph whose vertices are the group elements with $g$ adjacent to $h$ if and only if $(o(g),o(h))=1$‎. ‎In this paper we calculate the independence number of the coprime graph of the dihedral groups‎. ‎Additionally‎, ‎we characterize the groups whose coprime graph is perfect‎.

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来源期刊

International Journal of Group Theory MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

30 weeks

期刊介绍： International Journal of Group Theory (IJGT) is an international mathematical journal founded in 2011. IJGT carries original research articles in the field of group theory, a branch of algebra. IJGT aims to reflect the latest developments in group theory and promote international academic exchanges.