- Title
- On quotient digraphs and voltage digraphs
- Creator
- Dalfó, C.; Fiol, M. A.; Miller, M.; Ryan, J.
- Relation
- Australasian Journal of Combinatorics Vol. 69, Issue 3, p. 368-374
- Relation
- https://ajc.maths.uq.edu.au/?page=get_volumes&volume=69
- Publisher
- Centre for Discrete Mathematics and Computing, University of Queensland
- Resource Type
- journal article
- Date
- 2017
- Description
- We study the relationship between two key concepts in the theory of digraphs, those of quotient digraphs and voltage digraphs. These techniques contract or expand a given digraph in order to study its characteristics, or to obtain more involved structures. As an application, we relate the spectrum of a digraph ⌈, called a voltage digraph or base, with the spectrum of its lifted digraph ⌈α . We prove that all the eigenvalues of ⌈ (including multiplicities) are, in addition, eigenvalues of ⌈α. This study is carried out by introducing several reduced matrix representations of ⌈α. As an example of our techniques, we study some basic properties of the Alegre digraph and its base.
- Subject
- voltage digraphs; diagraphs theory; Alegre digraphs
- Identifier
- http://hdl.handle.net/1959.13/1349259
- Identifier
- uon:30377
- Identifier
- ISSN:1034-4942
- Rights
- © Copyright 2017 Combinatorial Mathematics Society of Australasia (Inc.) Any individual is entitled to download a copy of any paper from this site for purposes of individual study or research.
- Language
- eng
- Full Text
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