## López, Susana and Muntaner-Batle, Francesc-Antoni - Rainbow eulerian multidigraphs and the product of cycles

dmtcs:2153 - Discrete Mathematics & Theoretical Computer Science, April 21, 2016, Vol. 17 no. 3
Rainbow eulerian multidigraphs and the product of cycles

Authors: López, Susana and Muntaner-Batle, Francesc-Antoni

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.

Volume: Vol. 17 no. 3
Section: Graph Theory
Published on: April 21, 2016
Submitted on: November 10, 2014
Keywords: $\otimes_h$-product, direct product,rainbow eulerian multidigraph, eulerian multidigraph, (super) edge-magic,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]