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Sibirskii Matematicheskii Zhurnal, 2006, Volume 47, Number 5, Pages 1112–1116
(Mi smj917)
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This article is cited in 28 scientific papers (total in 28 papers)
About noncommuting graphs
A. R. Moghaddamfar K. N. Toosi University of Technology
Abstract:
The noncommuting $\nabla(G)$ of a nonabelian finite group $G$ is defined as follows: The vertices of $\nabla(G)$ are represented by the noncentral elements of $G$, and two distinct vertices $x$ and $y$ are joined by an edge if $xy\ne yx$. In [1], the following was conjectured: Let $G$ and $H$ be two nonabelian finite groups such that $\nabla(G)\cong\nabla(H)$ then $|G|=|H|$. Here we give some counterexamples to this conjecture.
Keywords:
noncommuting graph, truncated skew-polynomial ring, group, Jacobson radical, regular graph.
Received: 02.08.2005
Citation:
A. R. Moghaddamfar, “About noncommuting graphs”, Sibirsk. Mat. Zh., 47:5 (2006), 1112–1116; Siberian Math. J., 47:5 (2006), 911–914
Linking options:
https://www.mathnet.ru/eng/smj917 https://www.mathnet.ru/eng/smj/v47/i5/p1112
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Abstract page: | 381 | Full-text PDF : | 119 | References: | 61 |
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