On a problem of E. Prisner concerning the biclique operator

Zelinka, Bohdan. "On a problem of E. Prisner concerning the biclique operator." Mathematica Bohemica 127.3 (2002): 371-373. <http://eudml.org/doc/249036>.

@article{Zelinka2002,
abstract = {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 $\vec\{C\}$.},
author = {Zelinka, Bohdan},
journal = {Mathematica Bohemica},
keywords = {digraph; bisimplex; biclique; biclique digraph; biclique operator; periodicity of an operator; digraph; bisimplex; biclique digraph; biclique operator; periodicity of an operator},
language = {eng},
number = {3},
pages = {371-373},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a problem of E. Prisner concerning the biclique operator},
url = {http://eudml.org/doc/249036},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Zelinka, Bohdan
TI - On a problem of E. Prisner concerning the biclique operator
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 3
SP - 371
EP - 373
AB - 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 $\vec{C}$.
LA - eng
KW - digraph; bisimplex; biclique; biclique digraph; biclique operator; periodicity of an operator; digraph; bisimplex; biclique digraph; biclique operator; periodicity of an operator
UR - http://eudml.org/doc/249036
ER -