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On automorphisms of digraphs without symmetric cycles. (English) Zbl 0881.05051
Summary: A digraph is a symmetric cycle if it is symmetric and its underlying graph is a cycle. It is proved that if \(D\) is an asymmetric digraph not containing a symmetric cycle, then \(D\) remains asymmetric after removing some vertex. It is also showed that each digraph \(D\) without a symmetric cycle, whose underlying graph is connected, contains a vertex which is a common fixed point of all automorphisms of \(D\).

MSC:
05C20 Directed graphs (digraphs), tournaments
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