Título:	Graphs encoding the generating properties of a finite group
Autor(es):	Acciarri, Cristina Lucchini, Andrea
Assunto:	Grupos finitos Gráficos
Data de publicação:	2020
Referência:	ACCIARRI, Cristina; LUCCHINI, Andrea. Graphs encoding the generating properties of a finite group. Mathematische Nachrichten, 2020.
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 G a ∪ G b and in which two tuples (x1, . . . , xa) and (y1, . . . , yb) are adjacent if and only if hx1, . . . , xa, y1, . . . , ybi = 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.
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