%0 Journal Article
%T On the eigenvalues of distance powers of circuits
%A Jščrgen W. Sander
%A Torsten Sander
%J Mathematics
%D 2011
%I arXiv
%R 10.1016/j.laa.2010.01.012
%X Taking the d-th distance power of a graph, one adds edges between all pairs of vertices of that graph whose distance is at most d. It is shown that only the numbers -3, -2, -1, 0, 1, 2d can be integer eigenvalues of a circuit distance power. Moreover, their respective multiplicities are determined and explicit constructions for corresponding eigenspace bases containing only vectors with entries -1, 0, 1 are given.
%U http://arxiv.org/abs/1112.3202v1