Some Invariants of Cartesian Product of a Path and a Complete Bipartite Graph

Ramy Shaheen; Suhail Mahfud; Qays Alhawat

doi:doi:10.11648/j.dmath.20190402.11

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Some Invariants of Cartesian Product of a Path and a Complete Bipartite Graph

Ramy Shaheen, Suhail Mahfud, Qays Alhawat

Published in International Journal of Discrete Mathematics (Volume 4, Issue 2)

Received: 11 November 2019 Accepted: 16 December 2019 Published: 6 January 2020

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Abstract

A topological index of graph G is a numerical parameter related to G, which characterizes its topology and is preserved under isomorphism of graphs. Properties of the chemical compounds and topological indices are correlated. In this paper we will compute M-polynomial, first and second Zagreb polynomials and forgotten polynomial for the Cartesian Product of a path and a complete bipartite graph for all values of n and m. From the M-polynomial, we will compute many degree-based topological indices such that general Randić index, inverse Randić index, first and second Zagreb index, modified Zagreb index, Symmetric division index, Inverse sum index augmented Zagreb index and harmonic index for the Cartesian Product of a path and a complete bipartite graph. Also, we will compute the hyper- Zagreb index, the first and second multiple Zagreb index and forgotten index for the Cartesian Product of a path and a complete bipartite graph.

Published in	International Journal of Discrete Mathematics (Volume 4, Issue 2)
DOI	10.11648/j.dmath.20190402.11
Page(s)	61-70
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), 2020. Published by Science Publishing Group

Keywords

M-polynomial, Topological Index, Path, Complete Graph, Cartesian Product

References

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APA Style

Ramy Shaheen, Suhail Mahfud, Qays Alhawat. (2020). Some Invariants of Cartesian Product of a Path and a Complete Bipartite Graph. International Journal of Discrete Mathematics, 4(2), 61-70. https://doi.org/10.11648/j.dmath.20190402.11

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ACS Style

Ramy Shaheen; Suhail Mahfud; Qays Alhawat. Some Invariants of Cartesian Product of a Path and a Complete Bipartite Graph. Int. J. Discrete Math. 2020, 4(2), 61-70. doi: 10.11648/j.dmath.20190402.11

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AMA Style

Ramy Shaheen, Suhail Mahfud, Qays Alhawat. Some Invariants of Cartesian Product of a Path and a Complete Bipartite Graph. Int J Discrete Math. 2020;4(2):61-70. doi: 10.11648/j.dmath.20190402.11

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@article{10.11648/j.dmath.20190402.11,
  author = {Ramy Shaheen and Suhail Mahfud and Qays Alhawat},
  title = {Some Invariants of Cartesian Product of a Path and a Complete Bipartite Graph},
  journal = {International Journal of Discrete Mathematics},
  volume = {4},
  number = {2},
  pages = {61-70},
  doi = {10.11648/j.dmath.20190402.11},
  url = {https://doi.org/10.11648/j.dmath.20190402.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20190402.11},
  abstract = {A topological index of graph G is a numerical parameter related to G, which characterizes its topology and is preserved under isomorphism of graphs. Properties of the chemical compounds and topological indices are correlated. In this paper we will compute M-polynomial, first and second Zagreb polynomials and forgotten polynomial for the Cartesian Product of a path and a complete bipartite graph for all values of n and m. From the M-polynomial, we will compute many degree-based topological indices such that general Randić index, inverse Randić index, first and second Zagreb index, modified Zagreb index, Symmetric division index, Inverse sum index augmented Zagreb index and harmonic index for the Cartesian Product of a path and a complete bipartite graph. Also, we will compute the hyper- Zagreb index, the first and second multiple Zagreb index and forgotten index for the Cartesian Product of a path and a complete bipartite graph.},
 year = {2020}
}

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TY  - JOUR
T1  - Some Invariants of Cartesian Product of a Path and a Complete Bipartite Graph
AU  - Ramy Shaheen
AU  - Suhail Mahfud
AU  - Qays Alhawat
Y1  - 2020/01/06
PY  - 2020
N1  - https://doi.org/10.11648/j.dmath.20190402.11
DO  - 10.11648/j.dmath.20190402.11
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 61
EP  - 70
PB  - Science Publishing Group
SN  - 2578-9252
UR  - https://doi.org/10.11648/j.dmath.20190402.11
AB  - A topological index of graph G is a numerical parameter related to G, which characterizes its topology and is preserved under isomorphism of graphs. Properties of the chemical compounds and topological indices are correlated. In this paper we will compute M-polynomial, first and second Zagreb polynomials and forgotten polynomial for the Cartesian Product of a path and a complete bipartite graph for all values of n and m. From the M-polynomial, we will compute many degree-based topological indices such that general Randić index, inverse Randić index, first and second Zagreb index, modified Zagreb index, Symmetric division index, Inverse sum index augmented Zagreb index and harmonic index for the Cartesian Product of a path and a complete bipartite graph. Also, we will compute the hyper- Zagreb index, the first and second multiple Zagreb index and forgotten index for the Cartesian Product of a path and a complete bipartite graph.
VL  - 4
IS  - 2
ER  -

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Author Information

Ramy Shaheen

Department of Mathematics, Faculty of Science Tishreen University, Lattakia, Syria
Suhail Mahfud

Department of Mathematics, Faculty of Science Tishreen University, Lattakia, Syria
Qays Alhawat

Department of Mathematics, Faculty of Science Tishreen University, Lattakia, Syria

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Plain Text BibTeX RIS

APA Style

Ramy Shaheen, Suhail Mahfud, Qays Alhawat. (2020). Some Invariants of Cartesian Product of a Path and a Complete Bipartite Graph. International Journal of Discrete Mathematics, 4(2), 61-70. https://doi.org/10.11648/j.dmath.20190402.11

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ACS Style

Ramy Shaheen; Suhail Mahfud; Qays Alhawat. Some Invariants of Cartesian Product of a Path and a Complete Bipartite Graph. Int. J. Discrete Math. 2020, 4(2), 61-70. doi: 10.11648/j.dmath.20190402.11

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AMA Style

Ramy Shaheen, Suhail Mahfud, Qays Alhawat. Some Invariants of Cartesian Product of a Path and a Complete Bipartite Graph. Int J Discrete Math. 2020;4(2):61-70. doi: 10.11648/j.dmath.20190402.11

Copy | Download

@article{10.11648/j.dmath.20190402.11,
  author = {Ramy Shaheen and Suhail Mahfud and Qays Alhawat},
  title = {Some Invariants of Cartesian Product of a Path and a Complete Bipartite Graph},
  journal = {International Journal of Discrete Mathematics},
  volume = {4},
  number = {2},
  pages = {61-70},
  doi = {10.11648/j.dmath.20190402.11},
  url = {https://doi.org/10.11648/j.dmath.20190402.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20190402.11},
  abstract = {A topological index of graph G is a numerical parameter related to G, which characterizes its topology and is preserved under isomorphism of graphs. Properties of the chemical compounds and topological indices are correlated. In this paper we will compute M-polynomial, first and second Zagreb polynomials and forgotten polynomial for the Cartesian Product of a path and a complete bipartite graph for all values of n and m. From the M-polynomial, we will compute many degree-based topological indices such that general Randić index, inverse Randić index, first and second Zagreb index, modified Zagreb index, Symmetric division index, Inverse sum index augmented Zagreb index and harmonic index for the Cartesian Product of a path and a complete bipartite graph. Also, we will compute the hyper- Zagreb index, the first and second multiple Zagreb index and forgotten index for the Cartesian Product of a path and a complete bipartite graph.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Some Invariants of Cartesian Product of a Path and a Complete Bipartite Graph
AU  - Ramy Shaheen
AU  - Suhail Mahfud
AU  - Qays Alhawat
Y1  - 2020/01/06
PY  - 2020
N1  - https://doi.org/10.11648/j.dmath.20190402.11
DO  - 10.11648/j.dmath.20190402.11
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 61
EP  - 70
PB  - Science Publishing Group
SN  - 2578-9252
UR  - https://doi.org/10.11648/j.dmath.20190402.11
AB  - A topological index of graph G is a numerical parameter related to G, which characterizes its topology and is preserved under isomorphism of graphs. Properties of the chemical compounds and topological indices are correlated. In this paper we will compute M-polynomial, first and second Zagreb polynomials and forgotten polynomial for the Cartesian Product of a path and a complete bipartite graph for all values of n and m. From the M-polynomial, we will compute many degree-based topological indices such that general Randić index, inverse Randić index, first and second Zagreb index, modified Zagreb index, Symmetric division index, Inverse sum index augmented Zagreb index and harmonic index for the Cartesian Product of a path and a complete bipartite graph. Also, we will compute the hyper- Zagreb index, the first and second multiple Zagreb index and forgotten index for the Cartesian Product of a path and a complete bipartite graph.
VL  - 4
IS  - 2
ER  -

Copy | Download