Bipartite graphs obtained from adjacency matrices of orientations of graphs (Q1117951)

Let G be a graph with the vertex set \(\{u_ 1,...,u_ n\}\) and let \(\vec G\) be an orientation of G. B(\(\vec G)\) is a bipartite graph with bipartition \(\{v_ 1,...,v_ n\}\), \(\{w_ 1,...,w_ n\}\) where \(v_ i\) is adjacent to \(w_ j\) if \(u_ i\) and \(u_ j\) are adjacent in \(\vec G\). Bounds for the number of components of B(\(\vec G)\) are studied.