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The Steiner Wiener index of trees with a given segment sequence

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  • Zhang, Jie
  • Wang, Hua
  • Zhang, Xiao-Dong

Abstract

The Steiner distance of vertices in a set S is the minimum size of a connected subgraph that contain these vertices. The sum of the Steiner distances over all sets S of cardinality k is called the Steiner k-Wiener index and studied as the natural generalization of the famous Wiener index in chemical graph theory. In this paper we study the extremal structures, among trees with a given segment sequence, that maximize or minimize the Steiner k-Wiener index. The same extremal problems are also considered for trees with a given number of segments.

Suggested Citation

  • Zhang, Jie & Wang, Hua & Zhang, Xiao-Dong, 2019. "The Steiner Wiener index of trees with a given segment sequence," Applied Mathematics and Computation, Elsevier, vol. 344, pages 20-29.
    • Handle: RePEc:eee:apmaco:v:344-345:y:2019:i::p:20-29
    DOI: 10.1016/j.amc.2018.10.007
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    References listed on IDEAS

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    1. Gutman, Ivan, 2016. "On Steiner degree distance of trees," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 163-167.
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    Cited by:

    1. Li, Shuchao & Liu, Xin & Sun, Wanting & Yan, Lixia, 2023. "Extremal trees of a given degree sequence or segment sequence with respect to average Steiner 3-eccentricity," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    2. Al-Yakoob, Salem & Stevanović, Dragan, 2020. "On transmission irregular starlike trees," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    3. Wanping Zhang & Jixiang Meng & Baoyindureng Wu, 2022. "The upper bounds on the Steiner k-Wiener index in terms of minimum and maximum degrees," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1199-1220, September.

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