The Wiener index of hypergraphs

Xiangxiang Liu (), Ligong Wang () and Xihe Li ()
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Xiangxiang Liu: Northwestern Polytechnical University
Ligong Wang: Northwestern Polytechnical University
Xihe Li: Northwestern Polytechnical University

Journal of Combinatorial Optimization, 2020, vol. 39, issue 2, No 4, 364 pages

Abstract: 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.

Keywords: Hypergraph; Hypertree; Wiener index; 05C50; 05C65 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-019-00473-3

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