Given a finite group G, we denote by Δ (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 Δ (G) is connected and classify the groups G for which Δ (G) is a planar graph.
The independence graph of a finite group
Lucchini A.
2020
Abstract
Given a finite group G, we denote by Δ (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 Δ (G) is connected and classify the groups G for which Δ (G) is a planar graph.
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