### On connectedness of graphs on Weyl groups of type ${A}_{n}$ ($n\ge 4$)

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

Back to Simple Search
# Advanced Search

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.

The girth of graphs on Weyl groups, with no restriction on the associated root system, is determined. It is shown that the girth, when it is defined, is 3 except for at most four graphs for which it does not exceed 4.

**Page 1**