Abstract
Hypergraph theory has been found many applications in chemistry. As an important descriptor of molecular structures, the Wiener index of a graph also has many applications. The Wiener index of a connected hypergraph is defined as the summation of distances between all pairs of vertices. If each edge contains exactly k vertices, then a hypergraph G is called k-uniform. A hypertree is a connected hypergraph with no cycles. For k-uniform hypertree, H. Guo, B. Zhou et al. have determined the first, second and third maximum and minimum Wiener indices of uniform hypertrees. And give the unique structure of the k-uniform hypertree corresponding to the Wiener index, Moreover, in this paper, We first find out the relationship between the first few Wiener indices, then according to the structure of the graph, determine the unique k-uniform hypertree with the fifth maximum Wiener index. Through the determination of the fifth Wienr index k-uniform hypertree, the structure of the NTH Wiener index k-uniform hypertree can be found.
Highlights
Let V (G) and E(G) be the vertex a hypergraph G is called k -uniform
The reseach in the study [3] indicated that the hypergraph model shows a higher accuracy of molecular structure
Gu,v ( p, q) be the k -uniform hypergraph obtained from G by attaching a pendant path of length p at u and a pendant path of length q at v [4]
Summary
Let V (G) and E(G) be the vertex a hypergraph G is called k -uniform. A hypertree is a connected hypergraph with no cycles. A k -uniform hypertree with m edges always has 1+ (k −1)m vertices. A cycle in G is a sequence of vertices and edges (v0 , e1, v1,..., v p−1, e p , v p ) with p ≥ 2 , all vi s distinct except v0 = v p and all ei s distinct such that vi−1, vi ∈ ei for i = 1, 2,... The reseach in the study [3] indicated that the hypergraph model shows a higher accuracy of molecular structure. The Wiener index W (G) of G is defined as the summation of distances among all unordered pairs of. In this paper, We determine the unique kuniform hypertree with the fifth maximum Wiener index
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