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: https://doi.org/10.1023/A:1011218020755

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 -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.

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About

• Item ORO ID
• 8100
• Item Type
• Journal Item
• ISSN
• 1572-9192
• Keywords
• automorphism; covering; eigenvectors; graph; map; orthogonality; voltage assignment
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Depositing User
• Jozef Širáň