Rainbow eulerian multidigraphs and the product of cycles
| dc.contributor.author | López Masip, Susana-Clara | |
| dc.contributor.author | Muntaner Batle, Francesc Antoni | |
| dc.date.accessioned | 2019-06-11T07:54:15Z | |
| dc.date.available | 2019-06-11T07:54:15Z | |
| dc.date.issued | 2016 | |
| dc.date.updated | 2019-06-11T07:54:18Z | |
| dc.description.abstract | An arc colored eulerian multidigraph with $l$ colors is rainbow eulerian if there is an eulerian circuit in which a sequence of $l$ colors repeats. The digraph product that refers the title was introduced by Figueroa-Centeno et al. as follows: let $D$ be a digraph and let $\Gamma$ be a family of digraphs such that $V(F)=V$ for every $F\in \Gamma$. Consider any function $h:E(D)\longrightarrow\Gamma $. Then the product $D\otimes_{h} \Gamma$ is the digraph with vertex set $V(D)\times V$ and $((a,x),(b,y))\in E(D\otimes_{h}\Gamma)$ if and only if $ (a,b)\in E(D)$ and $ (x,y)\in E(h (a,b))$. In this paper we use rainbow eulerian multidigraphs and permutations as a way to characterize the $\otimes_h$-product of oriented cycles. We study the behavior of the $\otimes_h$-product when applied to digraphs with unicyclic components. The results obtained allow us to get edge-magic labelings of graphs formed by the union of unicyclic components and with different magic sums. | |
| dc.description.sponsorship | Supported by the Spanish Research Council under project MTM2011-28800-C02-01 and by the Catalan Research Council under grant 2009SGR1387. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.idgrec | 028496 | |
| dc.identifier.issn | 1462-7264 | |
| dc.identifier.uri | http://hdl.handle.net/10459.1/66438 | |
| dc.language.iso | eng | |
| dc.publisher | DMTCS | |
| dc.relation | info:eu-repo/grantAgreement/MICINN//MTM2011-28800-C02-01/ES/OPTIMIZACION Y PROBLEMAS EXTREMALES EN TEORIA DE GRAFOS Y COMBINATORIA. APLICACIONES A LAS REDES DE COMUNICACION/ | |
| dc.relation.isformatof | Reproducció del document publicat a https://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/2731.1.html | |
| dc.relation.ispartof | Discrete Mathematics and Theoretical Computer Science, 2016, vol. 17, num. 3, p. 91-104 | |
| dc.rights | cc-by (c) López Masip, Susana-Clara et al., 2016 | |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | Rainbow eulerian multidigraph | |
| dc.subject | Eulerian multidigraph | |
| dc.subject | Direct product | |
| dc.subject | ⊗h-product | |
| dc.subject | (super) edge-magic | |
| dc.subject.classification | Teoria de grafs | |
| dc.subject.classification | Matemàtica discreta | |
| dc.subject.other | Graph theory | |
| dc.subject.other | Discrete mathematics | |
| dc.title | Rainbow eulerian multidigraphs and the product of cycles | |
| dc.type | info:eu-repo/semantics/article | |
| dc.type.version | info:eu-repo/semantics/publishedVersion |