Abstract
The noncommuting graph ∇(G) of a nonabelian finite group G is defined as follows: The vertices of ∇(G) are represented by the noncentral elements of G, and two distinct vertices x and y are joined by an edge if xy ≠ yx. In [1], the following was conjectured: Let G and H be two nonabelian finite groups such that ∇(G) ≅ ∇(H); then ¦G¦ = ¦H¦. Here we give some counterexamples to this conjecture.
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Moghaddamfar A. R., Shi W. J., Zhou W., and Zokayi A. R., “On the noncommuting graph associated with a finite group,” Siberian Math. J., 46, No. 2, 325–332 (2005).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 5, pp. 1112–1116, September–October, 2006.
Original Russian Text Copyright © 2006 Moghaddamfar A. R.
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Reza Moghaddamfar, A. About noncommuting graphs. Sib Math J 47, 911–914 (2006). https://doi.org/10.1007/s11202-006-0101-y
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DOI: https://doi.org/10.1007/s11202-006-0101-y