Ischia Group Theory 2008 2009
DOI: 10.1142/9789814277808_0014
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Some results and questions related to the generating graph of a finite group

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Cited by 22 publications
(22 citation statements)
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“…For a finite group G let Γ(G) denote the graph defined on the non-identity elements of G in such a way that two distinct vertices are connected by an edge if and only if they generate G. The graph Γ(G) is called the generating graph of G. The generating graph was investigated in [15], [16], and [17]. For example, in [16], it is shown that for a nilpotent by nilpotent finite group G the clique number of Γ(G) is equal to the chromatic number of Γ(G).…”
Section: Introductionmentioning
confidence: 99%
“…For a finite group G let Γ(G) denote the graph defined on the non-identity elements of G in such a way that two distinct vertices are connected by an edge if and only if they generate G. The graph Γ(G) is called the generating graph of G. The generating graph was investigated in [15], [16], and [17]. For example, in [16], it is shown that for a nilpotent by nilpotent finite group G the clique number of Γ(G) is equal to the chromatic number of Γ(G).…”
Section: Introductionmentioning
confidence: 99%
“…This graph was defined in a paper of Lucchini and Maróti [19]. It is very similar to the unit graph.…”
Section: Graphs Similar To Known Graphsmentioning
confidence: 99%
“…Such groups G have long been studied by means of the generating graph, whose vertices are the elements of G, the edges being the 2-element generating sets. The generating graph was defined by Liebeck and Shalev in [16], and has been further investigated by many authors: see for example [3,5,6,12,18,19,20,23] for some of the range of questions that have been considered. Many deep structural results about finite groups can be expressed in terms of the generating graph.…”
Section: Introductionmentioning
confidence: 99%