Rainbow eulerian multidigraphs and the product of cycles

López Masip, Susana-Clara; Muntaner Batle, F. A.

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2016

Author

López Masip, Susana-Clara

Muntaner Batle, F. A.

Suggested citation

López Masip, Susana-Clara; Muntaner Batle, F. A.; . (2016) . Rainbow eulerian multidigraphs and the product of cycles. Discrete Mathematics and Theoretical Computer Science, 2016, vol. 17, num. 3, p. 91-104. http://hdl.handle.net/10459.1/66438.

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.

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http://hdl.handle.net/10459.1/66438

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Discrete Mathematics and Theoretical Computer Science, 2016, vol. 17, num. 3, p. 91-104

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Except where otherwise noted, this item's license is described as cc-by (c) López Masip, Susana-Clara et al., 2016