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Direct product decompositions of digraphs. (English) Zbl 0673.05042
For an arbitrary digraph $$\bar G=(V,E)$$ the covering graph $$C(\bar G)=(V,E)$$ of $$\bar G$$ is the graph, whose edges are those pairs (a,b)$$\in E$$ for which (a,b)$$\in E$$ or (b,a)$$\in E$$. It is said that the direct product $$\prod_{i\in I}G_ i$$ of graphs $$G_ i$$ (i$$\in I)$$ is the decomposition of the graph G if G is isomorphic to $$\prod_{i\in I}G_ i$$. It is said that the decomposition $$\prod_{i\in I}G_ i$$ of the graph $$C(\bar G)$$ induces a decomposition of the digraph $$\bar G$$ if there exist such digraphs $$G_ i$$ (i$$\in I)$$ that $$C(\bar G_ i)=G_ i$$ for each $$i\in I$$ and $$\bar G=\prod_{i\in I}\bar G_ i$$. In the paper the question when the decomposition of $$C(\bar G)$$ induces a decomposition of $$\bar G$$ is investigated.
Reviewer: V.Fleischer

##### MSC:
 05C20 Directed graphs (digraphs), tournaments 05C99 Graph theory
##### Keywords:
direct product of graphs; decomposition of graphs; digraph
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##### References:
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