The Non-centralizer Graph of a Finite Group
نویسنده
چکیده
In this paper, we define the non-centralizer graph associated to a finite group G, as the graph whose vertices are the elements of G, and whose edges are obtained by joining two distinct vertices if their centralizers are not equal. We denote this graph by ΥG. The non-centralizer graph is used to study the properties of the non-commuting graph of an AC-group. We prove that the non-centralizer graphs associated to two isoclinic groups for which the order of their centers are equal are isomorphic. Moreover, we observe that the converse holds for two isomorphic 4-partite graphs. We finally prove that if ΥG ∼= ΥS , then G ∼= S, where S is a simple group which is not Bn(q) or Cn(q).
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