On the eigenvalues of certain Cayley graphs and arrangement graphs
Combinatorics
2013-12-17 v2
Abstract
In this paper, we show that the eigenvalues of certain classes of Cayley graphs are integers. The (n,k,r)-arrangement graph A(n,k,r) is a graph with all the k-permutations of an n-element set as vertices where two k-permutations are adjacent if they differ in exactly r positions. We establish a relation between the eigenvalues of the arrangement graphs and the eigenvalues of certain Cayley graphs. As a result, the conjecture on integrality of eigenvalues of A(n,k,1) follows.
Keywords
Cite
@article{arxiv.1310.8078,
title = {On the eigenvalues of certain Cayley graphs and arrangement graphs},
author = {Bai Fan Chen and Ebrahim Ghorbani and Kok Bin Wong},
journal= {arXiv preprint arXiv:1310.8078},
year = {2013}
}
Comments
12 pages, final version