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Paper   IPM / M / 8002
School of Mathematics
  Title:   About noncommuting graphs
  Author(s):  A. R . Moghaddamfar
  Status:   Published
  Journal: Siberian Math. J.
  Vol.:  47
  Year:  2006
  Pages:   911-914
  Supported by:  IPM
The noncommuting graph ∇(G) of a nonabelian finite group G is defined as follows: The vertices of ∇(G) are represented by the non-central elements of G, and two distinct vertices x and y are joined by an edge if xyyx. In [2], it was conjectured that: Let G and H be two nonabelian finite groups such that ∇(G) ≅ ∇(H), then |G|=|H|. In this article we give, some counterexamples to this conjecture.

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