On quotient digraphs and voltage digraphs
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Inclou dades d'ús des de 2022
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hdl:2117/108606
Tipus de documentArticle
Data publicació2017-10
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Abstract
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 Γ, called a voltage digraph or base, with the spectrum of its lifted digraph Γα. We prove that all the eigenvalues of Γ (including multiplicities) are, in addition, eigenvalues of Γα. This study is carried out by introducing several reduced matrix representations of Γα. As an example of our techniques, we study some basic properties of the Alegre digraph and its base.
CitacióDalfo, C., Fiol, M., Miller, M., Ryan, J. On quotient digraphs and voltage digraphs. "The australasian journal of combinatorics", Octubre 2017, vol. 69, núm. 3, p. 368-374.
ISSN1034-4942
Versió de l'editorhttps://ajc.maths.uq.edu.au/?page=get_volumes&volume=69
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AJC-22juny2017-Dalfo.pdf | Article principal | 286,2Kb | Visualitza/Obre |