Eigenvalues of the derangement graph

Authors:
Cheng Yeaw Ku;David B. Wales
Affiliations:
Department of Mathematics, National University of Singapore, Singapore 117543;Department of Mathematics, Caltech, Pasadena, CA 91125, USA
Venue:
Journal of Combinatorial Theory Series A
Year:
2010

Citing 4
Cited 2

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Abstract

We consider the Cayley graph on the symmetric group S"n generated by derangements. It is well known that the eigenvalues of this graph are indexed by partitions of n. We investigate how these eigenvalues are determined by the shape of their corresponding partitions. In particular, we show that the sign of an eigenvalue is the parity of the number of cells below the first row of the corresponding Ferrers diagram. We also provide some lower and upper bounds for the absolute values of these eigenvalues.