On quotient digraphs and voltage digraphs
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 o...
| Autores: | , , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2017 |
| País: | España |
| Recursos: | Universitat de Lleida (UdL) |
| Repositorio: | Repositori Obert UdL |
| OAI Identifier: | oai:repositori.udl.cat:10459.1/72563 |
| Acesso em linha: | http://hdl.handle.net/10459.1/72563 |
| Access Level: | acceso abierto |
| Palavra-chave: | Theory of digraphs Voltage digraphs Quotient digraphs |
| Resumo: | 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. |
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