Piotr W\'ojcik
On automorphisms of digraphs without symmetric cycles

Comment.Math.Univ.Carolinae 37,3 (1996) 457-467.

Abstract: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 $D$.

Keywords: asymmetric diagraphs
AMS Subject Classification: 05C20

PDF