The independence graph of a finite group
Copyright policy )The independence graph of a finite group
AbstractGiven 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.
Connectivity; Generating graph; Generating sets; Planarity; Soluble groups, Group Theory (math.GR), planarity, Graphs and abstract algebra (groups, rings, fields, etc.), soluble groups, connectivity, FOS: Mathematics, generating sets, generating graph, Mathematics - Group Theory, Arithmetic and combinatorial problems involving abstract finite groups
Connectivity; Generating graph; Generating sets; Planarity; Soluble groups, Group Theory (math.GR), planarity, Graphs and abstract algebra (groups, rings, fields, etc.), soluble groups, connectivity, FOS: Mathematics, generating sets, generating graph, Mathematics - Group Theory, Arithmetic and combinatorial problems involving abstract finite groups
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