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On the minimum value of sum-Balaban index

Author

Listed:
  • Knor, Martin
  • Kranjc, Jaka
  • Škrekovski, Riste
  • Tepeh, Aleksandra

Abstract

We consider extremal values of sum-Balaban index among graphs on n vertices. We determine that the upper bound for the minimum value of the sum-Balaban index is at most 4.47934 when n goes to infinity. For small values of n we determine the extremal graphs and we observe that they are similar to dumbbell graphs, in most cases having one extra edge added to the corresponding extreme for the usual Balaban index. We show that in the class of balanced dumbbell graphs, those with clique sizes 2log(1+2)4n+o(n) have asymptotically the smallest value of sum-Balaban index. We pose several conjectures and problems regarding this topic.

Suggested Citation

  • Knor, Martin & Kranjc, Jaka & Škrekovski, Riste & Tepeh, Aleksandra, 2017. "On the minimum value of sum-Balaban index," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 203-210.
    • Handle: RePEc:eee:apmaco:v:303:y:2017:i:c:p:203-210
    DOI: 10.1016/j.amc.2017.01.041
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    References listed on IDEAS

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    1. Knor, M. & Kranjc, J. & Škrekovski, Riste & Tepeh, Aleksandra, 2016. "A search for the minimum value of Balaban index," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 301-310.
    2. Lei, Hui & Yang, Hua, 2015. "Bounds for the Sum-Balaban index and (revised) Szeged index of regular graphs," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1259-1266.
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