On Certain Integral Schreier Graphs of the Symmetric Group

We compute the spectrum of the Schreier graph of the symmetric group Sn corresponding to the Young subgroup S2 × Sn−2 and the generating set consisting of initial reversals. In particular, we show that this spectrum is integral and for n ≥ 8 consists precisely of the integers {0, 1, . . . , n}. This implies that these graphs form a family of expanders (with unbounded degree).

• Type: Journal
• Year: 2007
• Where: COMBINATORICS
• Authors: Paul E. Gunnells, Richard A. Scott, Byron L. Walden
• Keywords: COMBINATORICS 2007, Schreier Graph, Symmetric Group Sn, Young Subgroup