Distances between bicliques and structural properties of bicliques in graphs

08/31/2017

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by   Marina Groshaus, et al.

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A biclique is a maximal bipartite complete induced subgraph of G. The biclique graph of a graph G, denoted by KB(G), is the intersection graph of the family of all bicliques of G. In this work we give a natural definition of the distance between bicliques in a graph. We give a useful formula that relates the distance between bicliques in a graph G and the distance between their respectives vertices in KB(G). As application of the concept of the distance between bicliques, we show some results about the structure of bicliques in a graph and properties of the biclique graph. We obtain some corollaries from this result and finally we present some interesting related open problems.