Direct product decompositions of digraphs.

*(English)*Zbl 0673.05042For 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

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