Counterexamples to conjectures on graph distance measures based on topological indexes

摘要

In this paper we disprove three conjectures from Dehmer et al. (2014) 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 Randić index – but different degree sequences.