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

Investigating the topological properties of porphyrin-based dendrimers using discrete Adriatic indices

, *

* Corresponding author · click or hover a name for details

pp. 2711–2730Vol. 29Issue 7July 2026DOI: 10.47974/JDMSC-2397 Crossmark XML
Received:
04 Dec 2024
Published Online:
29 Dec 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2397
Pages:
2711–2730

Abstract

Topological indices serve as molecular structure descriptors that characterize the topology of a molecule while remaining invariant under graph isomorphism. Discrete Adriatic indices, explored by Vukičević and Gašperov in 2010, are a significant category of topological indices that have demonstrated strong predictive capabilities in assessments implemented by the International Academy of Mathematical Chemistry. Some of the most effective discrete Adriatic indices include the max-min sdeg index, misbalance indeg index, symmetric division deg index, and variable sum exdeg index, all of which have been proposed as potentially useful measures with better quality compared to some existing measures. This paper aims to explore these descriptors for several infinite families of porphyrin-based dendrimers using the edge partition technique.

Keywords

Subject Classifications

05C9292E1005C0705C09

References

[1] N. Trinajstić, Chemical Graph Theory. 2nd ed. Boca Raton, FL, USA: CRC Press (1992), doi: 10.1201/9781315139111.
[2] R. Todeschini and V. Consonni, Handbook of Molecular Descriptors. Weinheim, Germany: Wiley-VCH (Sep. 2000), doi: 10.1002/9783527613106.
[3] M. V. Diudea, QSPR/QSAR Studies by Molecular Descriptors. Huntingdon, NY, USA: Nova Science (2001). 
[4] D. Vukičević and M. Gašperov, “Bond additive modeling 1. Adriatic indices,” Croat. Chem. Acta, vol. 83, no. 3, pp. 243–260 (Oct. 2010).
[5] G.-C. Lau, W. C. Shiu, H.-K. Ng, Z.-B. Gao, and K. Schaffer, “On k-super graceful graphs with extremal maximum vertex degree,” J. Discrete Math. Sci. Cryptogr., vol. 27, no. 6, pp. 1765–1783 (Oct. 2024), doi: 10.47974/JDMSC-1722.
[6] B. Furtula, K. C. Das, and I. Gutman, “Comparative analysis of symmetric division deg index as potentially useful molecular descriptor,” Int. J. Quantum Chem., vol. 118, Art. no. e25659 (Jul. 2018), doi: 10.1002/qua.25659.
[7] A. Ali, I. Gutman, I. Redžepović, A. M. Albalahia, Z. Raza, and A. E. Hamza, “Symmetric division deg index: Extremal results and bounds,” MATCH Commun. Math. Comput. Chem., vol. 90, pp. 263–299 (Oct. 2023), doi: 10.46793/match.90-2.263A.
[8] D. Vukičević, “Bond additive modeling 5. Mathematical properties of the variable sum exdeg index,” Croat. Chem. Acta, vol. 84, no. 1, pp. 93–101 (Jan. 2011), doi: 10.5562/cca1667.
[9] A. Ali, E. Milovanović, M. Matejić, and I. Milovanović, “On the variable sum exdeg index/coindex of graphs,” MATCH Commun. Math. Comput. Chem., vol. 87, no. 1, pp. 133–146 (Apr. 2022), doi: 10.46793/match.87-1.133A.
[10] M. Javaid, A. Ali, I. Milovanović, and E. Milovanović, “On the extremal cactus graphs for variable sum exdeg index with a fixed number of cycles,” AKCE Int. J. Graphs Comb., vol. 17, no. 3, pp. 920–923 (Sep. 2020), doi: 10.1016/j.akcej.2019.08.007.
[11] M. Rizwan, A. A. Bhatti, M. Javaid, and Y. Shang, “Conjugated tricyclic graphs with maximum variable sum exdeg index,” Heliyon, vol. 9, no. 5, Art. no. e15706 (May 2023), doi: 10.1016/j.heliyon.2023.e15706.
[12] G. R. Newcome, C. N. Moorefield, and F. Vögtle, Dendritic Macromolecules: Concepts, Syntheses, Perspectives, Weinheim, Germany: VCH (1996), doi: 10.1002/9783527614875.fmatter.
[13] A. Bharali, A. Pegu, J. Buragohain, and B. Deka, “Generalized ISI index of certain families of nanostar dendrimers,” J Interdiscip. Math., vol. 24, no. 7, pp. 2021–2034 (Sep. 2021), doi: 10.1080/09720502.2021.1995181.
[14] J. B. Liu, D. A. Xavier, E. S. Varghese, A. Baby, and D. Mathew, “Computing molecular descriptors of polyphenylene dendrimer,” Polycycl. Aromat. Compd., vol. 44, no. 4, pp. 2775–2790 (May 2024), doi: 10.1080/10406638.2023.2222457.
[15] N. H. A. M. Saidi, M. N. Husin, and N. B. Ismail, “On the Zagreb indices of the line graphs of polyphenylene dendrimers,” J. Discret. Math. Sci. Cryptogr., vol. 23, no. 6, pp. 1239–1252 (Dec. 2020), doi: 10.1080/09720529.2020.1822041.
[16] T. R. Krishnasamy and M. Angamuthu, “Neighborhood-based descriptors for porphyrin dendrimers,” Biointerface Res. Appl. Chem., vol. 12, no. 5, pp. 6297–6307 (Sep. 2020), doi: 10.33263/BRIAC125.62976307. 
[17] S. Mondal, N. De, and A. Pal, “Neighborhood degree sum-based molecular descriptors of fractal and Cayley tree dendrimers,” Eur. Phys. J. Plus, vol. 136, Art. no. 303 (Apr. 2021), doi: 10.1140/epjp/s13360-021-01292-4.
[18] A. Amin, A. U. R. Virk, M. Rehman, and N. A. Shah, “Analysis of dendrimer generation by Sombor indices,” J. Chem., vol. 2021, Art. no. 930645 (2021), doi: 10.1155/2021/9930645. 
[19] C. G. Huo, F. Azhar, A. U. R. Virk, and T. Ismaeel, “Investigation of dendrimer structures by means of K-Banhatti invariants,” J Math., vol. 2022, Art. no. 4451899 (2022), doi: 10.1155/2022/4451899.
[20] S. Zaman, A. Ullah, and A. Shafaqat, “Structural modeling and topological characterization of three kinds of dendrimer networks,” Eur. Phys. J. E. Soft Matter, vol. 46, no. 5, Art. no. 36 (May 2023), doi: 10.1140/epje/s10189-023-00297-4. 
[21] M. Azari and A. Iranmanesh, “Dendrimer graphs as thorn graphs and their topological edge properties,” Natl. Acad. Sci. Lett., vol. 39, no. 6, pp. 455–460 (Nov.–Dec. 2016), doi: 10.1007/s40009-016-0514-5.
[22] M. Azari, A. Iranmanesh, and M. V. Diudea, “Vertex-eccentricity descriptors in dendrimers,” Studia Univ Babes Bolyai Chem., vol. 62, no. 1, pp. 129–142 (Jan. 2017), doi: 10.24193/subbchem.2017.1.11.
[23] F. Falahati-Nezhad and M. Azari, “Some bond-additive topological indices of four types of dendrimers,” Eur. Phys. J. Plus, vol. 138, no. 10, Art. no. 892 (Oct. 2023), doi: 10.1140/epjp/s13360-023-04513-0.
[24] J. Ramezani Tousi and M. Ghods, “Some polynomials and degree-based topological indices of molecular graph and line graph of Titanium dioxide nanotubes,” J. Inform. Optim. Sci., vol. 45, no. 1, pp. 95–106 (Jan. 2024), doi: 10.47974/JIOS-1284.
[25] W. Maes and W. Dehaen, “Synthetic aspects of porphyrin dendrimers,” Eur. J. Org. Chem., vol. 2009, no. 28, pp. 4719–4752 (Jul. 2009),  doi: 10.1002/ejoc.200900512.
[26] Y. Kim, M. F. Mayer, and S. C. Zimmerman, “A new route to organic nanotubes from porphyrin dendrimers,” Angew Chem. Int. Ed. Engl., vol. 42, no. 10, pp. 1121–1126 (Mar. 2023), doi: 10.1002/anie.200390295.
[27] S. Thyagarajan, T. Leiding, S. P. Arskold, A. V. Cheprakov, and S. A. Vinogradov, “Highly non-planar dendritic porphyrin for pH sensing: observation of porphyrin monocation,” Inorg Chem., vol. 49, no. 21, pp. 9909–9920 (Nov. 2010) doi: 10.1021/ic100968p.
[28] L. L. Li and E. W. G. Diau, “Porphyrin-sensitized solar cells,” Chem. Soc. Rev., vol. 42, no. 1, pp. 291–304 (Jan. 2013), doi: 10.1039/c2cs35257e.

Views: 84Downloads: 38Citations: 0