Biclique graphs and biclique matrices
A biclique of a graph G is a maximal induced complete bipar tite subgraph of G. Given a graph G, the biclique matrix of G is a {0,1, -1} matrix having one row for each biclique and one column for each vertex of G, and such that a pair of 1, -1 entries in a same row corresponds exactly to adjacent ve...
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2010
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Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03649024_v63_n1_p1_Groshaus http://hdl.handle.net/20.500.12110/paper_03649024_v63_n1_p1_Groshaus |
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paper:paper_03649024_v63_n1_p1_Groshaus2023-06-08T15:35:37Z Biclique graphs and biclique matrices Biclique graphs Bicliques Bipartite matrices Clique graphs Cliques Adjacent vertices Biclique Bipartite graphs Clique graphs Graph G Intersection graph matrix Subgraphs A biclique of a graph G is a maximal induced complete bipar tite subgraph of G. Given a graph G, the biclique matrix of G is a {0,1, -1} matrix having one row for each biclique and one column for each vertex of G, and such that a pair of 1, -1 entries in a same row corresponds exactly to adjacent vertices in the corresponding biclique. We describe a characterization of biclique matrices, in similar terms as those employed in Gilmore's characterization of clique matrices. On the other hand, the biclique graph of a graph is the intersection graph of the bicliques of G. Using the concept of biclique matrices, we describe a Krausz-type char acterization of biclique graphs. Finally, we show that every induced P3 of a biclique graph must be included in a diamond or in a 3-fan and we also characterize biclique graphs of bipartite graphs. © 2009 Wiley Periodicals, inc. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03649024_v63_n1_p1_Groshaus http://hdl.handle.net/20.500.12110/paper_03649024_v63_n1_p1_Groshaus |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-134 |
collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
topic |
Biclique graphs Bicliques Bipartite matrices Clique graphs Cliques Adjacent vertices Biclique Bipartite graphs Clique graphs Graph G Intersection graph matrix Subgraphs |
spellingShingle |
Biclique graphs Bicliques Bipartite matrices Clique graphs Cliques Adjacent vertices Biclique Bipartite graphs Clique graphs Graph G Intersection graph matrix Subgraphs Biclique graphs and biclique matrices |
topic_facet |
Biclique graphs Bicliques Bipartite matrices Clique graphs Cliques Adjacent vertices Biclique Bipartite graphs Clique graphs Graph G Intersection graph matrix Subgraphs |
description |
A biclique of a graph G is a maximal induced complete bipar tite subgraph of G. Given a graph G, the biclique matrix of G is a {0,1, -1} matrix having one row for each biclique and one column for each vertex of G, and such that a pair of 1, -1 entries in a same row corresponds exactly to adjacent vertices in the corresponding biclique. We describe a characterization of biclique matrices, in similar terms as those employed in Gilmore's characterization of clique matrices. On the other hand, the biclique graph of a graph is the intersection graph of the bicliques of G. Using the concept of biclique matrices, we describe a Krausz-type char acterization of biclique graphs. Finally, we show that every induced P3 of a biclique graph must be included in a diamond or in a 3-fan and we also characterize biclique graphs of bipartite graphs. © 2009 Wiley Periodicals, inc. |
title |
Biclique graphs and biclique matrices |
title_short |
Biclique graphs and biclique matrices |
title_full |
Biclique graphs and biclique matrices |
title_fullStr |
Biclique graphs and biclique matrices |
title_full_unstemmed |
Biclique graphs and biclique matrices |
title_sort |
biclique graphs and biclique matrices |
publishDate |
2010 |
url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03649024_v63_n1_p1_Groshaus http://hdl.handle.net/20.500.12110/paper_03649024_v63_n1_p1_Groshaus |
_version_ |
1768542888569864192 |