The Open UniversitySkip to content
 

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/10.1023/A:1011218020755
Google Scholar: Look up in Google Scholar

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 Širáň
Date Deposited: 14 Jun 2007
Last Modified: 02 Dec 2010 20:00
URI: http://oro.open.ac.uk/id/eprint/8100
Share this page:

Altmetrics

Scopus Citations

Actions (login may be required)

View Item
Report issue / request change

Policies | Disclaimer

© The Open University   + 44 (0)870 333 4340   general-enquiries@open.ac.uk