Topological properties of four types of porphyrin dendrimers




Dendrimers, Zagreb indices, Randić index, Sum-connectivity index


A chemical compound can be represented as a chemical graph. A topological index of a (chemical) graph is a numeric value of a graph which characterize its topology and is usually graph invariant. The Zagreb indices, Randić index and sum-connectivity indices are useful in the study of anti-inflammatory activities, boiling point, molecular complexity heterosystems of certain chemical instances, and in elsewhere. In this paper, we calculate the mentioned topological indices of some infinite classes of prophyrin dendrimers.

Author Biographies

Abdul Jalil M. Khalaf, University of Kufa.

Dept. of Mathematics.

Aisha Javed, Government College University.

Abdus Salam School of Mathematical Sciences.

Muhammad Kamran Jamil, Riphah International University.

RICAS, Dept. of Mathematics.

Mehdi Alaeiyan, Iran University of Science and Technology.

Dept.of Mathematics.

Mohammad Reza Farahani, Iran University of Science and Technology.

Dept.of Mathematics.


S. S. Alamoti, M. Alaeiyan, and A. R. Gilani, “Studying thermodynamic properties of linear acenes molecules (C4n+2H2n+4) using hyper-Zagreb index”, Journal of discrete mathematical science and cryptography, vol. 22, no. 7, pp. 1261-1268, Dec. 2019, doi:10.1080/09720529.2019.1694258

A. Q. Baig, M. Naeem, W. Gao, and J.-B. Liu, “General fifth M-Zagreb indices and fifth M-Zagreb polynomials of carbon graphite”, Eurasian chemical communications, vol. 2, no. 3, pp. 634–640, Feb. 2020, doi:10.33945/SAMI/ECC.2020.5.10

M. Alaeiyan, C. Natarajan, G. Sathiamoorthy, and M. R. Farahani, “The eccentric connectivity index of polycyclic aromatic hydrocarbons (PAHs)”, Eurasian chemical communications, vol. 2, no. 6, pp. 646–651, Mar. 2020, doi: 10.33945/SAMI/ECC.2020.6.1

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 science and cryptograghy, vol. 22, no. 7, pp. 1151-1164, 2019, doi: 10.1080/09720529.2019.1688965

A. T. Balaban, “Topological indices based on topological distances in molecular graphs”, Pure and applied chemistry, vol. 55, no. 2, pp. 199–206, Jan. 1983, doi: 10.1351/pac198855020199

M. Cancan, S. Ediz and M. R. Farahani, “On ve-degree atom-bond connectivity, sum-connectivity, geometric-arithmetic and harmonic indices of copper oxide”, Eurasian chemical communication, vol. 2, no. 5, pp. 641-645, May 2020, doi: 10.33945/SAMI/ECC.2020.5.11

J. Devillers and A. T. Balaban, Eds., Topological indices and related descriptors in QSAR and QSPR. Singapure: Gordon and Breach Science Publishers, 1999, doi: 10.1021/ci010441h

I. Gutman and N. Trinajstić, “Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons”, Chemical physics letters, vol. 17, no.4, pp. 535-538, Dec. 1972, doi: 10.1016/0009-2614(72)85099-1

I. Gutman, B. Ruščić, N. Trinajstić, and C. F. Wilcox, “Graph theory and molecular orbitals. XII. Acyclic polyenes”, The journal chemical physics, vol. 62, no. 2, pp. 3399-3405, 1975, doi: 10.1063/1.430994

S. M. Hosamani, S. G. Gadinaik, M. H. Kambar, and N. Padmannavar, “QSPR analysis of certain distance and degree-distance based topological indices”, in press.

H. Hosoya, “Topological index: a newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons”, Bulletin of the Chemical Society of Japan, vol. 44, no. 9, pp. 2332-2339, 1971, doi: 10.1246/bcsj.44.2332

M. Imran, A. A. E. Abunamous, D. Adi, S. H. Rafique, A.Q. Baig, and M. R. Farahani, “Eccentricity based topological indices of honeycomb networks”, Journal of discrete mathematical science and crypography, vol. 22, no. 7, pp. 1199-1213, 2019, doi: 10.1080/09720529.2019.1691326

M. Imran, S. A. H. Bokhary, S.Manzoor, and M. K. Siddiqui, “On molecular topological descriptors of certain families of nanostar dendrimers”, Eurasian chemical communication, vol. 2, no. 6, pp. 680-687, Jun. 2020, doi: 10.33945/SAMI/ECC.2020.6.5

R. H. Jin, T. Aida, and S. Inoue, “Caged porphyrin: the first dendritic molecule having a core photochemical functionality”, Journal chemical society, chemical communication, no. 16, 1993, doi: 10.1039/C39930001260

N. Kezele, L. Klasinc, J. V. Knop, S. Ivaniš, and S. Nikolić, “Computing the variable vertex connectivity index”, Croatica chemica acta, vol. 75, no. 2, pp. 651-661, 2002. [On line]. Available:

B. Lučić and N. Trinajstić, “New developments in QSPR/QSAR modeling based on topological indices”, SAR and QSAR in environmental research, vol. 7, no. 1-4, pp. 45-62, 1997, doi: 10.1080/10629369708039124

M. Kimura, Y. Nakano, N. Adachi, Y. Tatewaki, H. Shirai, and N. Kobayashi, “Intramolecular axial ligation of zinc porphyrin cores with triazole links within dendrimers”, Chemistry a europen journal, vol. 15, no. 11, pp. 2617-2624, Mar. 2009, doi: 10.1002/chem.200801557

J. B. Liu, C. Wang, S. Wang, and B. Wei, “Zagreb Indices and Multiplicative Zagreb Indices of Eulerian Graphs”, Bulletin Malaysian Mathematical Science Society, vol. 42, pp. 67-78, 2019, doi: 10.1007/s40840-017-0463-2

J. B. Liu, J. Zhao, H. He, and Z. Shao, “Valency-based topological descriptors and structural property of the generalized Sierpi?ski networks”, Journal of statistical physics, vol. 177, pp. 1131-1147, Dec. 2019, doi: 10.1007/s10955-019-02412-2

W. Maes and W. Dehaen, “Synthetic aspects of porphyrin dendrimers”, European journal of organic chemistry, pp. 4719-4752, Oct. 2009, doi: 10.1002/ejoc.200900512

G. R. Newkome, C. N. Moorefield, and F. Vögtle, Dendrimers and dendrons: concepts, syntheses, applications. Weinheim: Wiley-VCH, 2001, doi: 10.1002/3527600612

S. Nikolić, N. Trinajstić, and I. Baučić “Comparison between the vertex and edge connectivity indices for benzenoid hydrocarbons”, Journal chemical information and computer sciences, vol. 38, no.1, pp. 42-46, Jan. 1998, doi: 10.1021/ci970031m

M. Randić, “On characterization of molecular attributes”, Acta chimica slovenica, vol. 45, no. 3, pp. 239-252, 1998. [On line]. Available:

M. Randić, “Quantitative Structure property relationship: boiling points of planar benzenoids”, New journal of chemistry, vol. 20, pp. 1001-1009, 1996.

M. Randić and S. C. Basak, “Multiple regression analysis with optimal molecular descriptors”, SAR and QSAR in environmental research, vol. 11, no. 1, pp. 1-23, 2000, doi: 10.1080/10629360008033226

N. Trinajstić, S. Nikolić, D. Babic, and Z. Mihalić, “The vertex and edge connectivity indices of platonic and archimedean molecules”, Bulletin of the chemists and technologists of Macedonia, vol. 16, no. 1, pp. 43-51, 1997. [On line]. Available:

B. Zhou and N. Trinajstić, “On a novel connectivity index”, Journal mathematical chemistry, vol. 46, pp. 1252-1270, 2009, doi: 10.1007/s10910-008-9515-z



How to Cite

A. J. M. Khalaf, A. Javed, M. K. Jamil, M. Alaeiyan, and M. Reza Farahani, “Topological properties of four types of porphyrin dendrimers”, Proyecciones (Antofagasta, On line), vol. 39, no. 4, pp. 979-993, Jul. 2020.