Eigenvalues of the derangement graph
نویسندگان
چکیده
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. keywords: derangement, Cayley graph, eigenvalue, symmetric group AMS 2000 Mathematics Subject Classification: 05Axx, 05Cxx
منابع مشابه
ON THE SPECTRUM OF DERANGEMENT GRAPHS OF ORDER A PRODUCT OF THREE PRIMES
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 117 شماره
صفحات -
تاریخ انتشار 2010