For a d-generated finite group G we consider the graph Δd(G) (swap graph) in which the vertices are the ordered generating d-tuples and in which two vertices (x1, ⋯ , xd) and (y1, ⋯ , yd) are adjacent if and only if they differ only by one entry. It was conjectured by Tennant and Turner that Δd(G) is a connected graph. We prove that this conjecture is true if G is a finite soluble group.

The swap graph of the finite soluble groups

DI SUMMA, MARCO;LUCCHINI, ANDREA
2016

Abstract

For a d-generated finite group G we consider the graph Δd(G) (swap graph) in which the vertices are the ordered generating d-tuples and in which two vertices (x1, ⋯ , xd) and (y1, ⋯ , yd) are adjacent if and only if they differ only by one entry. It was conjectured by Tennant and Turner that Δd(G) is a connected graph. We prove that this conjecture is true if G is a finite soluble group.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3213078
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