On the eigenvalues of distance powers of circuits
arXiv:1112.3202 · doi:10.1016/j.laa.2010.01.012
Abstract
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.
14 pages