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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:
Reference: [1] E. Prisner: Graph Dynamics.Longman House, Burnt Mill, Harlow, 1995. Zbl 0848.05001, MR 1379114


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