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Counterexamples to conjectures on graph distance measures based on topological indexes

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  • Ilić, Aleksandar
  • Ilić, Milovan

Abstract

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.

Suggested Citation

  • Ilić, Aleksandar & Ilić, Milovan, 2017. "Counterexamples to conjectures on graph distance measures based on topological indexes," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 148-152.
    • Handle: RePEc:eee:apmaco:v:296:y:2017:i:c:p:148-152
    DOI: 10.1016/j.amc.2016.10.024
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    References listed on IDEAS

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    1. Dehmer, Matthias & Emmert-Streib, Frank & Shi, Yongtang, 2015. "Graph distance measures based on topological indices revisited," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 623-633.
    2. Ilić, Aleksandar & Dehmer, Matthias, 2015. "On the distance based graph entropies," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 647-650.
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