Volume 11 • Issue 2 • PP: 15-21 • 2024
A Study on the Wiener Polynomials for the Paraffin Polynomial-Rings
Open Access & Copyright
© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
View PDF 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
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
Choose your preferred format
Publisher's Note
The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.