An algebraic approach to lifts of digraphs
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Cita com:
hdl:2117/126046
Tipus de documentArticle
Data publicació2019-09
Condicions d'accésAccés obert
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Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya
ProjecteCONNECT - Combinatorics of Networks and Computation (EC-H2020-734922)
CONNECT - Combinatorics of Networks and Computation (EC-H2020-734922)
CONNECT - Combinatorics of Networks and Computation (EC-H2020-734922)
Abstract
We study the relationship between two key concepts in the theory of (di)graphs: the quotient digraph, and the lift Ga of a base (voltage) digraph. These techniques contract or expand a given digraph in order to study its characteristics, or obtain more involved structures. This study is carried out by introducing a quotient-like matrix, with complex polynomial entries, which fully represents Ga. In particular, such a matrix gives the quotient matrix of a regular partition of Ga, and when the involved group is Abelian, it completely determines the spectrum of Ga. As some examples of our techniques, we study some basic properties of the Alegre digraph. In addition we completely characterize the spectrum of a new family of digraphs, which contains the generalized Petersen graphs, and that of the Hoffman-Singleton graph
Descripció
© 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
CitacióDalfo, C., Fiol, M., Miller, M., Ryan, J., Siran, J. An algebraic approach to lifts of digraphs. "Discrete applied mathematics", 30 Setembre 2019, vol. 269, p. 68-76.
ISSN0166-218X
Versió de l'editorhttps://www.sciencedirect.com/science/article/pii/S0166218X18305870
Altres identificadorshttps://arxiv.org/pdf/1612.08855.pdf
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