On quotient digraphs and voltage digraphs
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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 Γ α . As an example of our techniques, we study some basic properties of the Alegre digraph and its base.
Is part ofAustralasian Journal of Combinatorics, 2017, vol. 69, núm. 3, p. 368-374
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Dalfó, Cristina; Fiol, Miguel Angel; Miller, Mirka; Ryan, Joe (Combinatorial Mathematics Society of Australasia (CMSA), 2017)In this note we present a general approach to construct large digraphs from small ones. These are called expanded digraphs, and, as particular cases, we show the close relationship between lifted digraphs of voltage digraphs ...
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