Minimum Wiener Index Value and Polar Graph of Book Graphs

Fuyi Wei; Yongyu Yang; Meijun Liang; Qu Wei

doi:doi:10.11648/j.sd.20160404.12

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Minimum Wiener Index Value and Polar Graph of Book Graphs

Fuyi Wei, Yongyu Yang, Meijun Liang, Qu Wei

Published in Science Discovery (Volume 4, Issue 4)

Received: 19 July 2016 Accepted: Published: 20 July 2016

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Abstract

Topological molecular index, which is widely applied in QSPR/QSAR studies of chemical theory, is one of the most active research fields in modern chemical graph theory. Wiener index is the sum of the distance between any two points in the graph. In this paper, we use the method of graph theory, we define three transformations, and prove the six lemma, get minimum value of the wiener index of book graphs, and determines the book graph with smallest wiener index.

Published in	Science Discovery (Volume 4, Issue 4)
DOI	10.11648/j.sd.20160404.12
Page(s)	213-219
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.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Book Graph, Wiener Index, Minimum Values, Polar Diagram

References

[1]	Chen Ya-hong. The Wiener Index of Unicyclic Graphs with Perfect Matching [J]. Journal of Shanghai Jiaotong University, 2010.
[2]	Hosoya H. Topologicalindex. A newly proposed quantity characterizing the topological nature of struc-tural isomers of saturated hydrocarbons [J]. Bull Chem Soc Japan, 1971, 44(9): 2332-2339.
[3]	Plesnik J. On the sum of all distances in a graph or digraph [J]. J Graph Theory,1984,8(1): 1-12.
[4]	Wiener H. Structral determination of paraffin boiling points [J]. J Am Chem Soc, 1947, 69(1): 17-20.
[5]	GutmanI, KlavzarS, MoharB.Fifty years of the Wiener index [J]. MATCH Commun Math Comput hem, 1997, 35(1): 1-159.
[6]	Gutman I ,Klavzar S, Mohar B. Fiftieth anniversary of the Wiener index [J]. Discrete Appl Math, 1997, 80 (1): 1-113.
[7]	Jiao Shijie, Zhou Bo, On the spectral radius of books [D]. South China Normal University. 2015.
[8]	R. Todeschini, V. Consonni, Handbook of Molecular Descriptors, Wiley-VCH, Weinheim, 2000.
[9]	Xiaotie Deng Jie Zhang,Equiseparability on terminal Wiener index, Applied Mathematics Letters 25(2012): 580--585.
[10]	Liu Wu-xin,Wei Fu-yi#,On the incidence Estrada index of graphs,Util. Math. 2015,98: 43-52.
[11]	The Variable Wiener Index of Trees with Given Maximum Degree，Communications and Information Technology，16-17, 2014， P36-37.

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APA Style

Fuyi Wei, Yongyu Yang, Meijun Liang, Qu Wei. (2016). Minimum Wiener Index Value and Polar Graph of Book Graphs. Science Discovery, 4(4), 213-219. https://doi.org/10.11648/j.sd.20160404.12

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ACS Style

Fuyi Wei; Yongyu Yang; Meijun Liang; Qu Wei. Minimum Wiener Index Value and Polar Graph of Book Graphs. Sci. Discov. 2016, 4(4), 213-219. doi: 10.11648/j.sd.20160404.12

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AMA Style

Fuyi Wei, Yongyu Yang, Meijun Liang, Qu Wei. Minimum Wiener Index Value and Polar Graph of Book Graphs. Sci Discov. 2016;4(4):213-219. doi: 10.11648/j.sd.20160404.12

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@article{10.11648/j.sd.20160404.12,
  author = {Fuyi Wei and Yongyu Yang and Meijun Liang and Qu Wei},
  title = {Minimum Wiener Index Value and Polar Graph of Book Graphs},
  journal = {Science Discovery},
  volume = {4},
  number = {4},
  pages = {213-219},
  doi = {10.11648/j.sd.20160404.12},
  url = {https://doi.org/10.11648/j.sd.20160404.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sd.20160404.12},
  abstract = {Topological molecular index, which is widely applied in QSPR/QSAR studies of chemical theory, is one of the most active research fields in modern chemical graph theory. Wiener index is the sum of the distance between any two points in the graph. In this paper, we use the method of graph theory, we define three transformations, and prove the six lemma, get minimum value of the wiener index of book graphs, and determines the book graph with smallest wiener index.},
 year = {2016}
}

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TY  - JOUR
T1  - Minimum Wiener Index Value and Polar Graph of Book Graphs
AU  - Fuyi Wei
AU  - Yongyu Yang
AU  - Meijun Liang
AU  - Qu Wei
Y1  - 2016/07/20
PY  - 2016
N1  - https://doi.org/10.11648/j.sd.20160404.12
DO  - 10.11648/j.sd.20160404.12
T2  - Science Discovery
JF  - Science Discovery
JO  - Science Discovery
SP  - 213
EP  - 219
PB  - Science Publishing Group
SN  - 2331-0650
UR  - https://doi.org/10.11648/j.sd.20160404.12
AB  - Topological molecular index, which is widely applied in QSPR/QSAR studies of chemical theory, is one of the most active research fields in modern chemical graph theory. Wiener index is the sum of the distance between any two points in the graph. In this paper, we use the method of graph theory, we define three transformations, and prove the six lemma, get minimum value of the wiener index of book graphs, and determines the book graph with smallest wiener index.
VL  - 4
IS  - 4
ER  -

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Author Information

Fuyi Wei

Institute of Mathematics and Information Software College, South China Agricultural University, Guangzhou, China
Yongyu Yang

Institute of Mathematics and Information Software College, South China Agricultural University, Guangzhou, China
Meijun Liang

Institute of Mathematics and Information Software College, South China Agricultural University, Guangzhou, China
Qu Wei

School of Accountancy, Central University of Finance and Economics, Beijing, China

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APA Style

Fuyi Wei, Yongyu Yang, Meijun Liang, Qu Wei. (2016). Minimum Wiener Index Value and Polar Graph of Book Graphs. Science Discovery, 4(4), 213-219. https://doi.org/10.11648/j.sd.20160404.12

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ACS Style

Fuyi Wei; Yongyu Yang; Meijun Liang; Qu Wei. Minimum Wiener Index Value and Polar Graph of Book Graphs. Sci. Discov. 2016, 4(4), 213-219. doi: 10.11648/j.sd.20160404.12

Copy | Download

AMA Style

Fuyi Wei, Yongyu Yang, Meijun Liang, Qu Wei. Minimum Wiener Index Value and Polar Graph of Book Graphs. Sci Discov. 2016;4(4):213-219. doi: 10.11648/j.sd.20160404.12

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@article{10.11648/j.sd.20160404.12,
  author = {Fuyi Wei and Yongyu Yang and Meijun Liang and Qu Wei},
  title = {Minimum Wiener Index Value and Polar Graph of Book Graphs},
  journal = {Science Discovery},
  volume = {4},
  number = {4},
  pages = {213-219},
  doi = {10.11648/j.sd.20160404.12},
  url = {https://doi.org/10.11648/j.sd.20160404.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sd.20160404.12},
  abstract = {Topological molecular index, which is widely applied in QSPR/QSAR studies of chemical theory, is one of the most active research fields in modern chemical graph theory. Wiener index is the sum of the distance between any two points in the graph. In this paper, we use the method of graph theory, we define three transformations, and prove the six lemma, get minimum value of the wiener index of book graphs, and determines the book graph with smallest wiener index.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Minimum Wiener Index Value and Polar Graph of Book Graphs
AU  - Fuyi Wei
AU  - Yongyu Yang
AU  - Meijun Liang
AU  - Qu Wei
Y1  - 2016/07/20
PY  - 2016
N1  - https://doi.org/10.11648/j.sd.20160404.12
DO  - 10.11648/j.sd.20160404.12
T2  - Science Discovery
JF  - Science Discovery
JO  - Science Discovery
SP  - 213
EP  - 219
PB  - Science Publishing Group
SN  - 2331-0650
UR  - https://doi.org/10.11648/j.sd.20160404.12
AB  - Topological molecular index, which is widely applied in QSPR/QSAR studies of chemical theory, is one of the most active research fields in modern chemical graph theory. Wiener index is the sum of the distance between any two points in the graph. In this paper, we use the method of graph theory, we define three transformations, and prove the six lemma, get minimum value of the wiener index of book graphs, and determines the book graph with smallest wiener index.
VL  - 4
IS  - 4
ER  -

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