Partition graphs for finite symmetric groups

This paper outlines an investigation of a class of are-transitive graphs admitting a finite symmetric group S-n acting primitively on vertices, with vertex-stabilizer isomorphic to the wreath product S-m wr S-r (preserving a partition of {1, 2,...,n} into r parts of equal size m). Several properties of these graphs are considered, including their correspondence with r x r matrices with constant row- and column-sums equal to m, their girth, and the local action of the vertex-stabilizer. Also, it is shown that the only instance where S-n acts transitively on 2-arcs occurs in the case m = r = 2, (C) 1997 John Wiley & Sons, Inc.