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Minimum Wiener Index Value and Polar Graph of Book Graphs

Received: 19 July 2016     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), 2016. 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
  • Institute of Mathematics and Information Software College, South China Agricultural University, Guangzhou, China

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

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

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

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