On automorphisms of digraphs without symmetric cycles

Wójcik, Piotr. "On automorphisms of digraphs without symmetric cycles." Commentationes Mathematicae Universitatis Carolinae 37.3 (1996): 457-467. <http://eudml.org/doc/247890>.

@article{Wójcik1996,
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 $D$.},
author = {Wójcik, Piotr},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {asymmetric diagraphs; asymmetric digraphs},
language = {eng},
number = {3},
pages = {457-467},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On automorphisms of digraphs without symmetric cycles},
url = {http://eudml.org/doc/247890},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Wójcik, Piotr
TI - On automorphisms of digraphs without symmetric cycles
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 3
SP - 457
EP - 467
AB - 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 $D$.
LA - eng
KW - asymmetric diagraphs; asymmetric digraphs
UR - http://eudml.org/doc/247890
ER -