Title:

On a problem of E. Prisner concerning the biclique operator (English) 
Author:

Zelinka, Bohdan 
Language:

English 
Journal:

Mathematica Bohemica 
ISSN:

08627959 (print) 
ISSN:

24647136 (online) 
Volume:

127 
Issue:

3 
Year:

2002 
Pages:

371373 
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:

20090924T22:02:23Z 
Last updated:

20200729 
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 
. 