Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4599734 | Linear Algebra and its Applications | 2014 | 8 Pages |
Abstract
In this paper, we show that the eigenvalues of certain classes of Cayley graphs are integers. The (n,k,r)(n,k,r)-arrangement graph A(n,k,r)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)A(n,k,1) follows.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Bai Fan Chen, Ebrahim Ghorbani, Kok Bin Wong,