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On the relationship between variable Wiener index and variable Szeged index

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  • Cambie, Stijn
  • Haslegrave, John

Abstract

We resolve two conjectures of Hriňáková et al. (2019)[10] concerning the relationship between the variable Wiener index and variable Szeged index for a connected, non-complete graph, one of which would imply the other. The strong conjecture is that for any such graph there is a critical exponent in (0,1], below which the variable Wiener index is larger and above which the variable Szeged index is larger. The weak conjecture is that the variable Szeged index is always larger for any exponent exceeding 1. They proved the weak conjecture for bipartite graphs, and the strong conjecture for trees.

Suggested Citation

  • Cambie, Stijn & Haslegrave, John, 2022. "On the relationship between variable Wiener index and variable Szeged index," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    • Handle: RePEc:eee:apmaco:v:431:y:2022:i:c:s0096300322003940
    DOI: 10.1016/j.amc.2022.127320
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    1. Hriňáková, Katarína & Knor, Martin & Škrekovski, Riste, 2019. "An inequality between variable wiener index and variable szeged index," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
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