  In this paper we disprove three conjectures from [M. Dehmer, F.
Emmert-Streib, Y. Shi, Interrelations of graph distance measures based on
topological indices, PLoS ONE 9 (2014) e94985] on graph distance measures based
on topological indices by providing explicit classes of trees that do not
satisfy proposed inequalities. The constructions are based on the families of
trees that have the same Wiener index, graph energy or Randic index - but
different degree sequences.
