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Some results on characterization of finite group by non commuting graph | ||
| Transactions on Combinatorics | ||
| مقاله 4، دوره 1، شماره 2، شهریور 2012، صفحه 41-48 اصل مقاله (407.73 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2012.1180 | ||
| نویسندگان | ||
| Mohammad Reza Darafsheh1؛ Pedram Yousefzadeh* 2 | ||
| 1University of Tehran | ||
| 2K. N. Toosi University of Technology | ||
| چکیده | ||
| The non commuting graph $\nabla(G)$ of a non-abelian finite group $G$ is defined as follows: its vertex set is $G- Z (G)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. In this paper we prove some new results about this graph. In particular we will give a new proof of Theorem 3.24 of [A. Abdollahi, S. Akbari, H. R, Maimani, Non-commuting graph of a group, J. Algebra, 298 (2006) 468-492.]. We also prove that if $G_1, G_2, \ldots, G_n$ are finite groups such that $Z(G_i)=1$ for $i=1, 2,\ldots, n$ and they are characterizable by non commuting graph, then $G_1 \times G_2 \times \cdots \times G_n$ is characterizable by non-commuting graph. | ||
| کلیدواژهها | ||
| non commuting graph؛ Nilpotent groups؛ Finite groups | ||
| مراجع | ||
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A. Abdollahi, S. Akbari, H. R. Maimani (2006) Non-commuting graph of a group J. Algebra 298, 468-492
M. R. Darafsheh (2009) Groups with the same non-commuting graph Discrete Appl.
Math. 157 (4), 833-837
Ron Solomon and Andrew Woldar (2012) All Simple groups are characterized by their
non-commuting graphs preprint
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