Rainbow eulerian multidigraphs and the product of cycles
| Autor: | S. C. López, Francesc-Antoni Muntaner-Batle |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya [Barcelona] (UPC), University of Newcastle [Australia] (UoN) |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
$\otimes_h$-product Mathematics::Combinatorics General Computer Science direct product Rainbow Eulerian path Digraph [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] (super) edge-magic Theoretical Computer Science Combinatorics [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM] symbols.namesake Computer Science::Discrete Mathematics eulerian multidigraph rainbow eulerian multidigraph symbols Discrete Mathematics and Combinatorics Direct product Mathematics |
| Zdroj: | Discrete Mathematics and Theoretical Computer Science Discrete Mathematics and Theoretical Computer Science, DMTCS, 2016, Vol. 17 no. 3 (3), pp.90-104 |
| ISSN: | 1462-7264 1365-8050 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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