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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3371888
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