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.

DOI (Digital Object Identifier) Link:	http://dx.doi.org/doi:10.1023/A:1011218020755
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Abstract

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
Item ID:	8100
Depositing User:	Jozef Siran
Date Deposited:	14 Jun 2007
Last Modified:	02 Dec 2010 20:00
URI:	http://oro.open.ac.uk/id/eprint/8100

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