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.
| Published in | American Journal of Mathematical and Computer Modelling (Volume 4, Issue 3) |
| DOI | 10.11648/j.ajmcm.20190403.14 |
| Page(s) | 74-82 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2019. Published by Science Publishing Group |
Wiener Index, K-uniform Hypertree, The Fifth Maximum
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APA Style
Yalan Li, Bo Deng, Chengfu Ye, Feng Fu, Huilong Chen. (2019). The Fifth Maximum Wiener Index of Uniform Hypergraphs. American Journal of Mathematical and Computer Modelling, 4(3), 74-82. https://doi.org/10.11648/j.ajmcm.20190403.14
ACS Style
Yalan Li; Bo Deng; Chengfu Ye; Feng Fu; Huilong Chen. The Fifth Maximum Wiener Index of Uniform Hypergraphs. Am. J. Math. Comput. Model. 2019, 4(3), 74-82. doi: 10.11648/j.ajmcm.20190403.14
AMA Style
Yalan Li, Bo Deng, Chengfu Ye, Feng Fu, Huilong Chen. The Fifth Maximum Wiener Index of Uniform Hypergraphs. Am J Math Comput Model. 2019;4(3):74-82. doi: 10.11648/j.ajmcm.20190403.14
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Download@article{10.11648/j.ajmcm.20190403.14,
author = {Yalan Li and Bo Deng and Chengfu Ye and Feng Fu and Huilong Chen},
title = {The Fifth Maximum Wiener Index of Uniform Hypergraphs},
journal = {American Journal of Mathematical and Computer Modelling},
volume = {4},
number = {3},
pages = {74-82},
doi = {10.11648/j.ajmcm.20190403.14},
url = {https://doi.org/10.11648/j.ajmcm.20190403.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20190403.14},
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.},
year = {2019}
}
TY - JOUR T1 - The Fifth Maximum Wiener Index of Uniform Hypergraphs AU - Yalan Li AU - Bo Deng AU - Chengfu Ye AU - Feng Fu AU - Huilong Chen Y1 - 2019/09/10 PY - 2019 N1 - https://doi.org/10.11648/j.ajmcm.20190403.14 DO - 10.11648/j.ajmcm.20190403.14 T2 - American Journal of Mathematical and Computer Modelling JF - American Journal of Mathematical and Computer Modelling JO - American Journal of Mathematical and Computer Modelling SP - 74 EP - 82 PB - Science Publishing Group SN - 2578-8280 UR - https://doi.org/10.11648/j.ajmcm.20190403.14 AB - 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. VL - 4 IS - 3 ER -
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