Graphs encoding the generating properties of a finite group

Cristina Acciarri and Andrea Lucchini

Mathematische Nachrichten, 2020, vol. 293, issue 9, 1644-1674

Abstract: Assume that G is a finite group. For every a,b∈N, we define a graph Γa,b(G) whose vertices correspond to the elements of Ga∪Gb and in which two tuples (x1,⋯,xa) and (y1,⋯,yb) are adjacent if and only if ⟨x1,⋯,xa,y1,⋯,yb⟩=G. We study several properties of these graphs (isolated vertices, loops, connectivity, diameter of the connected components) and we investigate the relations between their properties and the group structure, with the aim of understanding which information about G is encoded by these graphs.

Date: 2020
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