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Partition graphs for finite symmetric groups

✍ Scribed by Conder, Marston; Morton, Margaret; Praeger, Cheryl E.

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
130 KB
Volume
25
Category
Article
ISSN
0364-9024

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✦ Synopsis

This paper outlines an investigation of a class of arc-transitive graphs admitting a f inite 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 Γ— 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.

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