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arXiv · 2004.14651

The independence graph of a finite group

Andrea Lucchini
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Abstract

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.

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Andrea Lucchini. 2020-04-30. The independence graph of a finite group. https://arxiv.org/abs/2004.14651

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