On a relation between Szeged and Wiener indices of bipartite graphs

Hansen et. al., using the AutoGraphiX software package, conjectured that the Szeged index Sz(G) and the Wiener index W(G) of a connected bipartite graph G with n ≥ 4 vertices and m ≥ n edges, obeys the relation Sz(G) W(G) ≥ 4n 8. Moreover, this bound would be the best possible. This paper offers a proof to this conjecture.