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Title:
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Rainbow eulerian multidigraphs and the product of cycles
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Author:
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López Masip, Susana-Clara; Muntaner Batle, F. A.
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Notes:
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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.
Supported by the Spanish Research Council under project MTM2011-28800-C02-01 and by the Catalan Research Council under grant 2009SGR1387. |
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Subject(s):
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-Rainbow eulerian multidigraph
-Eulerian multidigraph
-Direct product
-⊗h-product
-(super) edge-magic
-Teoria de grafs
-Matemàtica discreta
-Graph theory
-Discrete mathematics |
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Rights:
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cc-by (c) López Masip, Susana-Clara et al., 2016
https://creativecommons.org/licenses/by/4.0/
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Document type:
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Article
Article - Published version |
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Published by:
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DMTCS
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