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Journal of Combinatorial Optimization

, Volume 39, Issue 2, pp 351–364 | Cite as

The Wiener index of hypergraphs

  • Xiangxiang Liu
  • Ligong WangEmail author
  • Xihe Li
Article
  • 38 Downloads

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 \(1\le m\le n-1\), 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.

Keywords

Hypergraph Hypertree Wiener index 

Mathematics Subject Classification

05C50 05C65 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied Mathematics, School of ScienceNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China
  2. 2.Xi’an-Budapest Joint Research Center for CombinatoricsNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China

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