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The independence graph of a finite group
Monatshefte für Mathematik ( IF 0.9 ) Pub Date : 2020-07-22 , DOI: 10.1007/s00605-020-01445-0
Andrea Lucchini

Given a finite group $G,$ we denote by $\Delta(G)$ the graph whose vertices are the elements $G$ and where two vertices $x$ and $y$ are adjacent if there exists a minimal generating set of $G$ containing $x$ and $y.$ We prove that $\Delta(G)$ is connected and classify the groups $G$ for which $\Delta(G)$ is a planar graph.

中文翻译:

有限群的独立图

给定一个有限群 $G,$ 我们用 $\Delta(G)$ 表示顶点是元素 $G$ 并且两个顶点 $x$ 和 $y$ 相邻的图,如果存在 $ 的最小生成集G$ 包含$x$ 和$y.$ 我们证明$\Delta(G)$ 是连通的并对$\Delta(G)$ 是平面图的群$G$ 进行分类。
更新日期:2020-07-22
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