The independence graph of a finite group
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Delta G
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Abstract Given a finite group G, we denote by $$\Delta (G)$$ 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 $$\Delta (G)$$ Δ ( G ) is connected and classify the groups G for which $$\Delta (G)$$ Δ ( G ) is a planar graph.
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2002 ◽
Vol 133
(1)
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pp. 31-36
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1977 ◽
Vol 24
(1)
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pp. 79-91
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2011 ◽
Vol 2011
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pp. 1-16
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