Geodesic
Coverings of graphs and maps, orthogonality, and eigenvectors
Journal of Algebraic Combinatorics, Tome 14 (2001) no. 1, pp. 57-72.

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Summary: Lifts of graph and map automorphisms can be described in terms of voltage assignments that are, in a sense, compatible with the automorphisms. We show that compatibility of ordinary voltage assignments in Abelian groups is related to orthogonality in certain $Z$ mathcalZ -modules. For cyclic groups, compatibility turns out to be equivalent with the existence of eigenvectors of certain matrices that are naturally associated with graph automorphisms. This allows for a great simplification in characterizing compatible voltage assignments and has applications in constructions of highly symmetric graphs and maps.
Keywords: graph, map, covering, voltage assignment, orthogonality, eigenvectors, automorphism 
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     title = {Coverings of graphs and maps, orthogonality, and eigenvectors},
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Širáň, Jozef. Coverings of graphs and maps, orthogonality, and eigenvectors. Journal of Algebraic Combinatorics, Tome 14 (2001) no. 1, pp. 57-72. http://geodesic.mathdoc.fr/item/JAC_2001__14_1_a1/