Galoitica: Journal of Mathematical Structures and Applications

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https://doi.org/10.54216/GJSMA

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Volume 11 , Issue 2 , PP: 15-21, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

A Study on the Wiener Polynomials for the Paraffin Polynomial-Rings

Sandra Terazic 1 *

  • 1 Department of Mathematics, University of Rijeka, City of Rijeka, Croatia - (Sandy1997te@Uniri.hr)
  • Doi: https://doi.org/10.54216/GJMSA.0110202

    Received: December 04, 2023 Revised: March 29, 2024 Accepted: July 25, 2024
    Abstract

    In this paper, we find the Wiener polynomial of multi-circles of Paraffin structural. We prove that this obtained formula is better than the formulas, which are previously presented. Also, we evaluate the coefficients for any limited power of  without depending on the number of circles, and we find the Wiener index and average distance for this structural. On the other hand, we build a MATLAB program to evaluate the Wiener polynomial coefficient, Wiener index, and average distance.

    Keywords :

    Weiner index , Wiener polynomial , Polynomial ring , Paraffin structural

    References

    [1]       J.I. Doyle and J.E. Graver (1977) “Mean distance in a graph“, Discrete Math., Vol. 17, PP.147-154.

    [2]       A.A. Dobrynin (1993) “On decomposition of the Wiener index for Graphs of Catacondensed Hexagonal Systems”, Graph Theory Notes of New York; XXV. PP.19-21.

    [3]       Gutman (1993) “Some properties of the Wiener polynomial”, Graph Theory Notes of New York; XXV. PP.13-18.

    [4]       H. Hosoya (1988) “On some counting polynomials in chemistry”, Discrete Applied Math. 19, PP.239-257.

    [5]       Walid A.M. Saeed (1999) Wiener Polynomials of Graphs, Ph.D. Thesis, Mousl University.

    [6]       H. Wiener (1947) “Structural determination of paraffin boiling points”, J. Amer. Chem. Soc., 69, PP.17-20.

    [7]       Ahmadi, M. R, Nezhad, R. J. (2011). Energy and Wiener index of zero-divisor graphs. Iran. J. Math. Chem. 2(1): 45–51.

    [8]       Afkhami, M., Barati, Z, Khashyarmanesh, K. (2014). When the unit, unitary and total graphs are ring graphs and outer planar. Rocky Mountain J. Math. 44(3): 705–716.

    [9]       Koam, A. N. A., Ahmad, A, Haider, A. (2019). On eccentric topological indices based on edges of zero-divisor graphs. Symmetry 11(7): 907.

    Cite This Article As :
    Terazic, Sandra. A Study on the Wiener Polynomials for the Paraffin Polynomial-Rings. Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , 2024, pp. 15-21. DOI: https://doi.org/10.54216/GJMSA.0110202
    Terazic, S. (2024). A Study on the Wiener Polynomials for the Paraffin Polynomial-Rings. Galoitica: Journal of Mathematical Structures and Applications, (), 15-21. DOI: https://doi.org/10.54216/GJMSA.0110202
    Terazic, Sandra. A Study on the Wiener Polynomials for the Paraffin Polynomial-Rings. Galoitica: Journal of Mathematical Structures and Applications , no. (2024): 15-21. DOI: https://doi.org/10.54216/GJMSA.0110202
    Terazic, S. (2024) . A Study on the Wiener Polynomials for the Paraffin Polynomial-Rings. Galoitica: Journal of Mathematical Structures and Applications , () , 15-21 . DOI: https://doi.org/10.54216/GJMSA.0110202
    Terazic S. [2024]. A Study on the Wiener Polynomials for the Paraffin Polynomial-Rings. Galoitica: Journal of Mathematical Structures and Applications. (): 15-21. DOI: https://doi.org/10.54216/GJMSA.0110202
    Terazic, S. "A Study on the Wiener Polynomials for the Paraffin Polynomial-Rings," Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , pp. 15-21, 2024. DOI: https://doi.org/10.54216/GJMSA.0110202