TARU PUBLICATIONS
Journal of Discrete Mathematical Sciences and Cryptography cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

The Wiener index of some algebraic graphs and some applications

, * , , ,

* Corresponding author · click or hover a name for details

pp. 429–437Vol. 28Issue 2March 2025DOI: 10.47974/JDMSC-2059 Crossmark XML
Received:
07 May 2024
Published Online:
21 Mar 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2059
Pages:
429–437

Abstract

In mathematical chemistry, we periodically use the graphs. In particular, the vertex in G is refers to the atom in a molecule, and the edge is refers to the bonds. The main object is to study the characteristics of model’s graph. In our work, we discuss the Wiener index of some algebraic graph (Cayley graph and Dihedral Graph). Moreover, we have given a particular example of Wiener index for the structure of tecovirimat and the structure of cidofovir. Finally, the relationship between the Wiener index BO and boiling point WI is found for the data is approximated by BO = 181(WI)0.1775, where the boiling point of a family of hydrocarbons, by using model’s graph of the molecules.

Keywords

Subject Classifications

05C0905C25

References

[1] H. Al-Janabi and G. Bacsó, “Sanskruti Index of Some Important Bethe Trees,” ICoMS, June 24–26, Paris, France (2021).
[2] H. Al-Janabi and G. Bacsó, “Sanskruti Index of Some Chemical Trees and Unicyclic Graphs,” Journal of Physics: Conference Series, vol. 2287, pp. 012005 (2022).
[3] S. J. Abd and H. B. Shelash, “On Subgroups Product Graph of Finite Groups,” BIO Web of Conferences, vol. 97, pp. 00155 (2024).
[4] A. Alwardi, B. Arsic, I. Gutman, and N. Soner, “The Common Neighborhood Graph and Its Energy,” Iranian Journal of Mathematical Sciences and Informatics, vol. 7, no. 2, pp. 1–8 (2012).
[5] J. A. Bondy and U. S. R. Murty, Graph Theory, Graduate Texts in Mathematics. Springer (2008).
[6] E. Estrada, L. Torres, L. Rodriguez, and I. Gutman, “An Atom-Bond Connectivity Index: Modelling the Enthalpy of Formation of Alkanes,” Indian Journal of Chemistry, vol. 37A, no. 10, pp. 849–855 (1998).
[7] S. S. Muhammad, Z. Soheil, and R. F. Mohammad, “Computing Sanskruti Index of the Polycyclic Aromatic Hydrocarbons,” Geology, Ecology, and Landscapes, vol. 1, no. 1, pp. 37–40 (2017).
[8] H. Wiener, “Structural Determination of Paraffin Boiling Points,” Journal of the American Chemical Society, vol. 69, no. 1, pp. 17–20 (1947).
[9] H. B. Shelash and A. R. Ashrafi, “Table of Marks and Character Table of Certain Finite Groups,” Quasigroups and Related Systems, vol. 28, no. 1, pp. 159–170 (2020).
[10] H. Shelash and A. Shukur, “Pseudospectrum Energy of Graphs,” Iranian Journal of Mathematical Chemistry, vol. 11, no. 2, pp. 89–93 (2020). [Online]. Available: https://doi.org/10.22052/IJMC.2020.221182.1488.
[11] H. B. Shelash and A. R. Ashrafi, “The Number of Subgroups of a Given Type in Certain Finite Groups,” Iranian Journal of Mathematical Sciences and Informatics, vol. 16, no. 2, pp. 73–87 (2021).
[12] W. M. Salah and H. B. Shelash, “Structure Graph of the Finite Group,” Journal of Physics: Conference Series, vol. 1818, no. 1, p. 012126 (2021).
[13] S. Ahmad, H. M. A. Siddiqui, A. Ali, M. R. Farahani, M. Imran, and I. N. Cangul, “On Wiener Index and Wiener Polarity Index of Some Polyomino Chains,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 22, no. 7, pp. 1151–1164 (2019). [Online]. Available: https://doi.org/10.1080/09720529.2019.1688965.
[14] M. Alaeiyan, F. Afzal, M. R. Farahani, and M. A. Rostami, “An Exact Formula for the Wiener Polarity Index of Nanostar Dendrimers,” Journal of Information and Optimization Sciences, vol. 41, no. 4, pp. 933–939 (2020). [Online]. Available: https://doi.org/10.1080/02522667.2020.1748274.
[15] S. Ediz, İ. Çiftçi, M. Cancan, and M. R. Farahani, “On k-Total Distance Degrees and k-Total Wiener Polarity Index,” Journal of Information and Optimization Sciences, vol. 42, no. 7, pp. 1469–1477 (2021). [Online]. Available: https://doi.org/10.1080/02522667.2021.1896652.
[16] W. Gao and M. R. Farahani, “The Hyper-Zagreb Index for an Infinite Family of Nanostar Dendrimers,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 20, no. 2, pp. 515–523 (2017). [Online]. Available: https://doi.org/10.1080/09720529.2016.1220088.
[17] M. Nadeem, S. Ahmad, M. K. Siddiqui, M. A. Ali, M. R. Farahani, and A. J. M. Khalaf, “On Some Applications Related with Algebraic Structures Through Different Well-Known Graphs,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 24, no. 2, pp. 451–471 (2021). [Online]. Available: https://doi.org/10.1080/09720529.2021.1885806.
[18] A. H. Alwan, “Small Intersection Graph of Subsemimodules of a Semimodule,” Communications in Combinatorics, Cryptography & Computer Science, vol. 2022, no. 1, pp. 15–22 (2022).
[19] S. Ediz, M. Cancan, and M. R. Farahani, “Eccentric Connectivity and Connective Eccentricity Indices of Generalized Petersen Graphs,” Communications in Combinatorics, Cryptography & Computer Science, vol. 2021, no. 1, pp. 1–6 (2021).
[20] R. Ponraj, S. Prabhu, and M. Sivakumar, “Pair Mean Cordial Labeling of Total Graph of Some Graphs and Prism Related Graphs,” Communications in Combinatorics, Cryptography & Computer Science, vol. 2024, no. 2, pp. 181–192 (2024).
[21] F. O. Oduol and I. O. Okoth, “Counting Vertices Among All Non-Crossing Trees by Levels and Degrees,” Communications in Combinatorics, Cryptography & Computer Science, vol. 2024, no. 2, pp. 193–212 (2024).

Views: 154Downloads: 7Citations: 0