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Title: Eigenvalues of the derangement graph
Authors: Ku, C.Y. 
Wales, D.B.
Keywords: Cayley graph
Symmetric group
Issue Date: Apr-2010
Citation: Ku, C.Y., Wales, D.B. (2010-04). Eigenvalues of the derangement graph. Journal of Combinatorial Theory. Series A 117 (3) : 289-312. ScholarBank@NUS Repository.
Abstract: We consider the Cayley graph on the symmetric group Sn 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. © 2009 Elsevier Inc. All rights reserved.
Source Title: Journal of Combinatorial Theory. Series A
ISSN: 00973165
DOI: 10.1016/j.jcta.2009.10.002
Appears in Collections:Staff Publications

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