The Wiener Index and the Hosoya Polynomial of the Jahangir Graphs

Shaohui Wang; Mohammad Reza Farahani; M. R. Rajesh Kanna; Muhammad Kamran Jamil; R. Pradeep Kumar

doi:doi:10.11648/j.acm.20160503.17

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The Wiener Index and the Hosoya Polynomial of the Jahangir Graphs

Shaohui Wang, Mohammad Reza Farahani, M. R. Rajesh Kanna, Muhammad Kamran Jamil, R. Pradeep Kumar

Published in Applied and Computational Mathematics (Volume 5, Issue 3)

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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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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TY  - JOUR
T1  - The Wiener Index and the Hosoya Polynomial of the Jahangir Graphs
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
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 138
EP  - 141
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

Shaohui Wang

Department of Mathematics, University of Mississippi, University, MS, USA
Mohammad Reza Farahani

Department of Applied Mathematics, Iran University of Science and Technology (IUST) Narmak, Tehran, Iran
M. R. Rajesh Kanna

Department of Mathematics, Maharani's Science College for Women, Mysore, India
Muhammad Kamran Jamil

Department of Mathematics, Riphah Institute of Computing and Applied Sciences (RICAS), Riphah International University, Lahore, Pakistan
R. Pradeep Kumar

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

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Plain Text BibTeX RIS

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - The Wiener Index and the Hosoya Polynomial of the Jahangir Graphs
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
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 138
EP  - 141
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  -

Copy | Download