| Title:
|
On a problem of E. Prisner concerning the biclique operator (English) |
| Author:
|
Zelinka, Bohdan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
371-373 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The symbol $K(B,C)$ denotes a directed graph with the vertex set $B\cup C$ for two (not necessarily disjoint) vertex sets $B,C$ in which an arc goes from each vertex of $B$ into each vertex of $C$. A subdigraph of a digraph $D$ which has this form is called a bisimplex in $D$. A biclique in $D$ is a bisimplex in $D$ which is not a proper subgraph of any other and in which $B\ne \emptyset $ and $C\ne \emptyset $. The biclique digraph $\vec{C}(D)$ of $D$ is the digraph whose vertex set is the set of all bicliques in $D$ and in which there is an arc from $K(B_1, C_1)$ into $K(B_2,C_2)$ if and only if $C_1 \cap B_2 \ne \emptyset $. The operator which assigns $\vec{C}(D)$ to $D$ is the biclique operator $\vec{C}$. The paper solves a problem of E. Prisner concerning the periodicity of $\vec{C}$. (English) |
| Keyword:
|
digraph |
| Keyword:
|
bisimplex |
| Keyword:
|
biclique |
| Keyword:
|
biclique digraph |
| Keyword:
|
biclique operator |
| Keyword:
|
periodicity of an operator |
| MSC:
|
05C20 |
| idZBL:
|
Zbl 1003.05048 |
| idMR:
|
MR1931321 |
| DOI:
|
10.21136/MB.2002.134064 |
| . |
| Date available:
|
2009-09-24T22:02:23Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134064 |
| . |
| Reference:
|
[1] E. Prisner: Graph Dynamics.Longman House, Burnt Mill, Harlow, 1995. Zbl 0848.05001, MR 1379114 |
| . |
