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

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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    T1  - Some Invariants of Cartesian Product of a Path and a Complete Bipartite Graph
    AU  - Ramy Shaheen
    AU  - Suhail Mahfud
    AU  - Qays Alhawat
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    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
  • Department of Mathematics, Faculty of Science Tishreen University, Lattakia, Syria

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

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

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