  The Brauldi-Hoffman conjecture, proved by Rowlinson in 1988, characterized
the graph with maximal spectral radius among all simple graphs with prescribed
number of edges. In 2008, Bhattacharya, Friedland, and Peled proposed an
analog, which will be called the BFP conjecture in the following, of the
Brauldi-Hoffman conjecture for the bipartite graphs with fixed numbers of edges
in the graph and vertices in the bipartition. The BFP conjecture was proved to
be correct if the number of edges is large enough by several authors. However,
in this paper we provide some counterexamples of the BFP conjecture.
