Geodesic
On a Graph Associated to Groups
Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 3 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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Let $G$ be a group such that the subgroup $T^2(G)=\{x\in G\mid (gx)^2=(xg)^2, \ \mbox{for all }\ g\in G\}$ is a proper subgroup. We define a graph $\Gamma$ with the vertex set $G\setminus T^2(G)$ in which two vertices $x,y$ are joined by an edge if $(xy)^2\neq (yx)^2$. In this note we study this graph and find a characterization of some dihedral groups in terms of this graph.
Classification : 20D60, 05C25. 
@article{BMMS_2011_34_3_a12,
     author = {Mohammad Mashkouri and Bijan Taeri},
     title = {On a {Graph} {Associated} to {Groups}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2011},
     volume = {34},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2011_34_3_a12/}
}
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AU  - Mohammad Mashkouri
AU  - Bijan Taeri
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ID  - BMMS_2011_34_3_a12
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%A Mohammad Mashkouri
%A Bijan Taeri
%T On a Graph Associated to Groups
%J Bulletin of the Malaysian Mathematical Society
%D 2011
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%F BMMS_2011_34_3_a12
Mohammad Mashkouri; Bijan Taeri. On a Graph Associated to Groups. Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 3. http://geodesic.mathdoc.fr/item/BMMS_2011_34_3_a12/