Biclique graphs and biclique matrices

A biclique of a graph G is a maximal induced complete bipartite 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 Contract grant sponsor: Prosul-Cnpq; Contract grant number: 490333/04-4 (to M. G.); Contract grant sponsor: UBACyT Grants; Contract grant numbers: X184; X212 (to M. G.); Contract grant sponsor: PICT ANPCyT Grant; Contract grant number: 11-09112 (to M. G.); Contract grant sponsor: PID Conicet Grant (to M. G.); Contract grant sponsors: Conselho Nacional de Desenvolvimento Científico e Tecnológico (to J. L. S.); CNPq (to J. L. S.); Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro, FAPERJ (to J. L. S.). Journal of Graph Theory 2009 Wiley Periodicals, Inc.