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The Wiener Index and the Hosoya Polynomial of the Jahangir Graphs

Received: 21 April 2016     Accepted: 3 May 2016     Published: 13 July 2016
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Abstract

Let G be a simple connected graph having vertex set V and edge set E. The vertex-set and edge-set of G denoted by V(G) and E(G), respectively. The length of the smallest path between vertices u,v V(G) is called the distance, d(u,v), between the vertices u,v. Mathematical chemistry is the area of research engaged in new application of mathematics in chemistry. In mathematics chemistry, we have many topological indices for any molecular graph, that they are invariant on the graph automorphism. In this research paper, we computing the Wiener index and the Hosoya polynomial of the Jahangir graphs J 5,m for all integer number m ≥3. The Wiener index is the sum of distances between all pairs of vertices of G as W(G)= And the Hosoya polynomial of G is H(G,x)= , where d(u,v) denotes the distance between vertices u and v.

Published in Applied and Computational Mathematics (Volume 5, Issue 3)
DOI 10.11648/j.acm.20160503.17
Page(s) 138-141
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

Regular Graphs, Connected Graphs, Jahangir Graphs, Topological Indices, Hosoya Polynomial, Wiener Index, Distances

References
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Cite This Article
  • APA Style

    Shaohui Wang, Mohammad Reza Farahani, M. R. Rajesh Kanna, Muhammad Kamran Jamil, R. Pradeep Kumar. (2016). The Wiener Index and the Hosoya Polynomial of the Jahangir Graphs. Applied and Computational Mathematics, 5(3), 138-141. https://doi.org/10.11648/j.acm.20160503.17

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    ACS Style

    Shaohui Wang; Mohammad Reza Farahani; M. R. Rajesh Kanna; Muhammad Kamran Jamil; R. Pradeep Kumar. The Wiener Index and the Hosoya Polynomial of the Jahangir Graphs. Appl. Comput. Math. 2016, 5(3), 138-141. doi: 10.11648/j.acm.20160503.17

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    AMA Style

    Shaohui Wang, Mohammad Reza Farahani, M. R. Rajesh Kanna, Muhammad Kamran Jamil, R. Pradeep Kumar. The Wiener Index and the Hosoya Polynomial of the Jahangir Graphs. Appl Comput Math. 2016;5(3):138-141. doi: 10.11648/j.acm.20160503.17

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  • @article{10.11648/j.acm.20160503.17,
      author = {Shaohui Wang and Mohammad Reza Farahani and M. R. Rajesh Kanna and Muhammad Kamran Jamil and R. Pradeep Kumar},
      title = {The Wiener Index and the Hosoya Polynomial of the Jahangir Graphs},
      journal = {Applied and Computational Mathematics},
      volume = {5},
      number = {3},
      pages = {138-141},
      doi = {10.11648/j.acm.20160503.17},
      url = {https://doi.org/10.11648/j.acm.20160503.17},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160503.17},
      abstract = {Let G be a simple connected graph having vertex set V and edge set E. The vertex-set and edge-set of G denoted by V(G) and E(G), respectively. The length of the smallest path between vertices u,v V(G) is called the distance, d(u,v), between the vertices u,v. Mathematical chemistry is the area of research engaged in new application of mathematics in chemistry. In mathematics chemistry, we have many topological indices for any molecular graph, that they are invariant on the graph automorphism. In this research paper, we computing the Wiener index and the Hosoya polynomial of the Jahangir graphs J 5,m  for all integer number m ≥3. The Wiener index is the sum of distances between all pairs of vertices of G as W(G)=  And the Hosoya polynomial of G is H(G,x)= , where d(u,v) denotes the distance between vertices u and v.},
     year = {2016}
    }
    

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    AU  - Shaohui Wang
    AU  - Mohammad Reza Farahani
    AU  - M. R. Rajesh Kanna
    AU  - Muhammad Kamran Jamil
    AU  - R. Pradeep Kumar
    Y1  - 2016/07/13
    PY  - 2016
    N1  - https://doi.org/10.11648/j.acm.20160503.17
    DO  - 10.11648/j.acm.20160503.17
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    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
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    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20160503.17
    AB  - Let G be a simple connected graph having vertex set V and edge set E. The vertex-set and edge-set of G denoted by V(G) and E(G), respectively. The length of the smallest path between vertices u,v V(G) is called the distance, d(u,v), between the vertices u,v. Mathematical chemistry is the area of research engaged in new application of mathematics in chemistry. In mathematics chemistry, we have many topological indices for any molecular graph, that they are invariant on the graph automorphism. In this research paper, we computing the Wiener index and the Hosoya polynomial of the Jahangir graphs J 5,m  for all integer number m ≥3. The Wiener index is the sum of distances between all pairs of vertices of G as W(G)=  And the Hosoya polynomial of G is H(G,x)= , where d(u,v) denotes the distance between vertices u and v.
    VL  - 5
    IS  - 3
    ER  - 

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Author Information
  • Department of Mathematics, University of Mississippi, University, MS, USA

  • Department of Applied Mathematics, Iran University of Science and Technology (IUST) Narmak, Tehran, Iran

  • Department of Mathematics, Maharani's Science College for Women, Mysore, India

  • Department of Mathematics, Riphah Institute of Computing and Applied Sciences (RICAS), Riphah International University, Lahore, Pakistan

  • Department of Mathematics, the National Institute of Engineering, Mysuru, India

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