Geodesic
On connectedness of graphs on direct product of Weyl groups
Archivum mathematicum, Tome 31 (1995) no. 4, pp. 299-304 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper, we have studied the connectedness of the graphs on the direct product of the Weyl groups. We have shown that the number of the connected components of the graph on the direct product of the Weyl groups is equal to the product of the numbers of the connected components of the graphs on the factors of the direct product. In particular, we show that the graph on the direct product of the Weyl groups is connected iff the graph on each factor of the direct product is connected.
In this paper, we have studied the connectedness of the graphs on the direct product of the Weyl groups. We have shown that the number of the connected components of the graph on the direct product of the Weyl groups is equal to the product of the numbers of the connected components of the graphs on the factors of the direct product. In particular, we show that the graph on the direct product of the Weyl groups is connected iff the graph on each factor of the direct product is connected.
Classification : 05C25, 05E10, 20E22, 20F55
Keywords: root systems; Weyl Groups; connectivity in a graph 
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     title = {On connectedness of graphs on direct product of {Weyl} groups},
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Youssef, Samy A.; Hulsurkar, S. G. On connectedness of graphs on direct product of Weyl groups. Archivum mathematicum, Tome 31 (1995) no. 4, pp. 299-304. http://geodesic.mathdoc.fr/item/ARM_1995_31_4_a6/

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[6] Youssef, Samy A., Hulsurkar S.G.: On Connectedness of graphs on Weyl Groups of type $ A_n (n \ge 4) $. Arch. Math. (Brno) 31(1995), 163-170. | MR