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arXiv · 1310.8078

On the eigenvalues of certain Cayley graphs and arrangement graphs

Bai Fan Chen·Ebrahim Ghorbani·Kok Bin Wong
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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.

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Bai Fan Chen, Ebrahim Ghorbani, Kok Bin Wong. 2013-12-16. On the eigenvalues of certain Cayley graphs and arrangement graphs. https://arxiv.org/abs/1310.8078

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