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The Wiener index of hypergraphs

Author

Listed:
  • Xiangxiang Liu

    (Northwestern Polytechnical University
    Northwestern Polytechnical University)

  • Ligong Wang

    (Northwestern Polytechnical University
    Northwestern Polytechnical University)

  • Xihe Li

    (Northwestern Polytechnical University
    Northwestern Polytechnical University)

Abstract

The Wiener index is defined to be the sum of distances between every unordered pair of vertices in a connected hypergraph. In this paper, we first study how the Wiener index of a hypergraph changes under some graft transformations. For $$1\le m\le n-1$$1≤m≤n-1, we obtain the unique hypertree that achieves the minimum (or maximum) Wiener index in the class of hypertrees on n vertices and m edges. Then we characterize the unique hypertrees on n vertices with first three smallest Wiener indices, and the unique hypertree (not 2-uniform) with maximum Wiener index, respectively. In addition, we determine the unique hypergraph that achieves the minimum Wiener index in the class of hypergraphs on n vertices and p pendant edges.

Suggested Citation

  • Xiangxiang Liu & Ligong Wang & Xihe Li, 2020. "The Wiener index of hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 39(2), pages 351-364, February.
    • Handle: RePEc:spr:jcomop:v:39:y:2020:i:2:d:10.1007_s10878-019-00473-3
    DOI: 10.1007/s10878-019-00473-3
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    References listed on IDEAS

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    1. Chunmei Luo & Liancui Zuo & Philip B. Zhang, 2018. "The Wiener index of Sierpiński-like graphs," Journal of Combinatorial Optimization, Springer, vol. 35(3), pages 814-841, April.
    2. Kinkar Ch. Das & M. J. Nadjafi-Arani, 2017. "On maximum Wiener index of trees and graphs with given radius," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 574-587, August.
    3. Goubko, Mikhail, 2018. "Maximizing Wiener index for trees with given vertex weight and degree sequences," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 102-114.
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    Cited by:

    1. Zhongyuan Che, 2022. "k-Wiener index of a k-plex," Journal of Combinatorial Optimization, Springer, vol. 43(1), pages 65-78, January.

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