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Coverings of Graphs and Maps, Orthogonality, and Eigenvectors

Siran, Jozef (2001). Coverings of Graphs and Maps, Orthogonality, and Eigenvectors. Journal of Algebraic Combinatorics: An International Journal, 14(1) pp. 57–72.

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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 {\cal Z}-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.

Item Type: Journal Article
ISSN: 1572-9192
Keywords: automorphism; covering; eigenvectors; graph; map; orthogonality; voltage assignment
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
Item ID: 8100
Depositing User: Jozef Širáň
Date Deposited: 14 Jun 2007
Last Modified: 14 Jan 2016 16:32
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