# Article

 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 .

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