On the eigenvalues of distance powers of circuits

Details On the eigenvalues of distance powers of circuits On the eigenvalues of distance powers of circuits

2011-12-14

arxiv.org/abs/1112.3202v1

Linear Algebra Appl., Vol. 432 (2010), pp. 3132-3140

Mathematics

Combinatorics

14 pages

Scientific paper

10.1016/j.laa.2010.01.012

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.

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