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Layer structure of De Bruijn and Kautz digraphs: an application to deflection routing
dc.contributor.author | Fàbrega Canudas, José |
dc.contributor.author | Martí Farré, Jaume |
dc.contributor.author | Muñoz López, Francisco Javier |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2017-03-29T12:12:53Z |
dc.date.available | 2018-10-31T01:30:28Z |
dc.date.issued | 2016-10-17 |
dc.identifier.citation | Fàbrega, J., Martí-Farré, J., Muñoz, X. Layer structure of De Bruijn and Kautz digraphs: an application to deflection routing. "Electronic notes in discrete mathematics", 17 Octubre 2016, vol. 54, p. 157-162. |
dc.identifier.issn | 1571-0653 |
dc.identifier.uri | http://hdl.handle.net/2117/103040 |
dc.description.abstract | In the main part of this paper we present polynomial expressions for the cardinalities of some sets of interest of the nice distance-layer structure of the well-known De Bruijn and Kautz digraphs. More precisely, given a vertex $v$, let $S_{i}^\star(v)$ be the set of vertices at distance $i$ from $v$. We show that $|S_{i}^\star(v)|=d^i-a_{i-1}d^{i-1}-\cdots -a_{1} d-a_{0}$, where $d$ is the degree of the digraph and the coefficients $a_{k}\in\{0,1\}$ are explicitly calculated. Analogously, let $w$ be a vertex adjacent from $v$ such that $S_{i}^\star(v)\cap S_j^{\ast}(w)\neq \emptyset$ for some $j$. We prove that $\big |S_{i}^\star(v) \cap S_j^{\ast}(w) \big |=d^i-b_{i-1}d^{i-1}-\ldots -b_{1} d-b_{0},$ where the coefficients $b_{t}\in\{0,1\}$ are determined from the coefficients $a_k$ of the polynomial expression of $|S_{i}^\star(v)|$. An application to deflection routing in De Bruijn and Kautz networks serves as motivation for our study. It is worth-mentioning that our analysis can be extended to other families of digraphs on alphabet or to general iterated line digraphs. |
dc.format.extent | 6 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de cossos i polinomis |
dc.subject.lcsh | Polynomials |
dc.subject.lcsh | Matrices |
dc.subject.other | De Bruijn and Kautz digraphs |
dc.subject.other | General iterated line digraphs |
dc.subject.other | Deflection routing |
dc.title | Layer structure of De Bruijn and Kautz digraphs: an application to deflection routing |
dc.type | Article |
dc.subject.lemac | Polinomis |
dc.subject.lemac | Matrius (Matemàtica) |
dc.contributor.group | Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
dc.identifier.doi | 10.1016/j.endm.2016.09.028 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::11 Number theory::11C Polynomials and matrices |
dc.subject.ams | Classificació AMS::12 Field theory and polynomials::12Y05 Computational aspects of field theory and polynomials |
dc.relation.publisherversion | http://www.sciencedirect.com/science/article/pii/S1571065316301226 |
dc.rights.access | Open Access |
local.identifier.drac | 19721647 |
dc.description.version | Postprint (author's final draft) |
dc.relation.projectid | info:eu-repo/grantAgreement/MINECO//MTM2014-60127-P/ES/TECNICAS DE OPTIMIZACION EN TEORIA DE GRAFOS, GRUPOS Y COMBINATORIA. APLICACIONES A REDES, ALGORITMOS Y PROTOCOLOS DE COMUNICACION./ |
local.citation.author | Fàbrega, J.; Martí-Farré, J.; Muñoz, X. |
local.citation.publicationName | Electronic notes in discrete mathematics |
local.citation.volume | 54 |
local.citation.startingPage | 157 |
local.citation.endingPage | 162 |
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