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On the noncommuting graph associated with a finite group

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Abstract

Let G be a finite group. We define the noncommuting graph ∇(G) as follows: the vertex set of ∇(G) is G\Z(G) with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity. We study some properties of ∇(G) and prove that, for many groups G, if H is a group with ∇(G) isomorphic to ∇(H) then |G| = |H|.

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Authors and Affiliations

  1. K. N. Toosi University of Technology, Tehran, Iran

    A. R. Moghaddamfar & A. R. Zokayi

  2. Southwest Normal University, Chongqing, People’s Republic of China

    W. J. Shi & W. Zhou

  3. Soochow University, Suzhou, People’s Republic of China

    W. J. Shi & W. Zhou

Authors
  1. A. R. Moghaddamfar
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  2. W. J. Shi
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  3. W. Zhou
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  4. A. R. Zokayi
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Additional information

Original Russian Text Copyright © 2005 Moghaddamfar A. R., Shi W. J., Zhou W., and Zokayi A. R.

A. R. Moghaddamfar was supported by the Research Institute for Fundamental Sciences, Tabriz, Iran. W. J. Shi was supported by the National Natural Science Foundation of China (Grant 10171074).

Translated from Sibirski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath}\) Matematicheski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath}\) Zhurnal, Vol. 46, No. 2, pp. 416–425, March–April, 2005.

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Moghaddamfar, A.R., Shi, W.J., Zhou, W. et al. On the noncommuting graph associated with a finite group. Sib Math J 46, 325–332 (2005). https://doi.org/10.1007/s11202-005-0034-x

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  • DOI: https://doi.org/10.1007/s11202-005-0034-x

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