| Title:
|
On automorphisms of digraphs without symmetric cycles (English) |
| Author:
|
Wójcik, Piotr |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
457-467 |
| . |
| Category:
|
math |
| . |
| 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 $D$. (English) |
| Keyword:
|
asymmetric diagraphs |
| MSC:
|
05C20 |
| MSC:
|
05C25 |
| idZBL:
|
Zbl 0881.05051 |
| idMR:
|
MR1426910 |
| . |
| Date available:
|
2009-01-08T18:25:15Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118852 |
| . |
| Reference:
|
[1] Nešetřil J.: A congruence theorem for asymmetric trees.Pacific J. Math. 37 (1971), 771-778. MR 0307955 |
| Reference:
|
[2] Nešetřil J., Sabidussi G.: Minimal asymmetric graphs of induced length 4.Graphs and Combinatorics 8.4 (1992), 343-359. MR 1204119 |
| Reference:
|
[3] Sabidussi G.: Clumps, minimal asymmetric graphs, and involutions.J. Combin. Th. Ser. B 53.1 (1991), 40-79. Zbl 0686.05028, MR 1122296 |
| . |
