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On the Steiner hyper-Wiener index of a graph

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  • Tratnik, Niko

Abstract

In this paper, we study the Steiner hyper-Wiener index of a graph, which is obtained from the standard hyper-Wiener index by replacing the classical graph distance with the Steiner distance. It is shown how this index is related to the Steiner Hosoya polynomial, which generalizes similar result for the standard hyper-Wiener index. Next, we show how the Steiner 3-hyper-Wiener index of a modular graph can be expressed by using the classical graph distances. As the main result, a method for computing this index for median graphs is developed. Our method makes computation of the Steiner 3-hyper-Wiener index much more efficient. Finally, the method is used to obtain the closed formulas for the Steiner 3-Wiener index and the Steiner 3-hyper-Wiener index of grid graphs.

Suggested Citation

  • Tratnik, Niko, 2018. "On the Steiner hyper-Wiener index of a graph," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 360-371.
    • Handle: RePEc:eee:apmaco:v:337:y:2018:i:c:p:360-371
    DOI: 10.1016/j.amc.2018.05.035
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    References listed on IDEAS

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    1. Cai, Qingqiong & Cao, Fuyuan & Li, Tao & Wang, Hua, 2018. "On distances in vertex-weighted trees," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 435-442.
    2. Črepnjak, Matevž & Tratnik, Niko, 2017. "The Szeged index and the Wiener index of partial cubes with applications to chemical graphs," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 324-333.
    3. Lan, Yongxin & Li, Tao & Ma, Yuede & Shi, Yongtang & Wang, Hua, 2018. "Vertex-based and edge-based centroids of graphs," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 445-456.
    4. Lei, Hui & Li, Tao & Ma, Yuede & Wang, Hua, 2018. "Analyzing lattice networks through substructures," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 297-314.
    5. Gutman, Ivan, 2016. "On Steiner degree distance of trees," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 163-167.
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