The Fifth Maximum Wiener Index of Uniform Hypergraphs
American Journal of Mathematical and Computer Modelling
Volume 4, Issue 3, September 2019, Pages: 74-82
Received: Aug. 1, 2019; Accepted: Aug. 23, 2019; Published: Sep. 10, 2019
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Authors
Yalan Li, School of Computer, Qinghai Normal University, Xining, China
Bo Deng, School of Mathematics and Statistics, Qinghai Normal University, Xining, China; College of Science, Guangdong University of Petrochemical Technology, Maoming, China
Chengfu Ye, School of Mathematics and Statistics, Qinghai Normal University, Xining, China
Feng Fu, School of Mathematics and Statistics, Qinghai Normal University, Xining, China
Huilong Chen, School of Mathematics and Statistics, Qinghai Normal University, Xining, China
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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.
Keywords
Wiener Index, K-uniform Hypertree, The Fifth Maximum
To cite this article
Yalan Li, Bo Deng, Chengfu Ye, Feng Fu, Huilong Chen, The Fifth Maximum Wiener Index of Uniform Hypergraphs, American Journal of Mathematical and Computer Modelling. Vol. 4, No. 3, 2019, pp. 74-82. doi: 10.11648/j.ajmcm.20190403.14
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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