Molecular description of copper(II) oxide

Mohammad Reza Farahani, Wei Gao, Abdul Qudair Baig, Wasaq Khalid


Graph theory has much advancement in the field of mathematical chemistry. Recently, chemical graph theory has become very popular among researchers because of its wide applications in mathematical chemistry. The molecular topological descriptors are the numerical invariants of a molecular graph and are very useful for predicting their bioactivity. A great variety of such indices are studied and used in theoretical chemistry, pharmaceutical researchers, in drugs and in different other fields.

In this article, we study the chemical graph of copper oxide and compute degree based topological indices mainly ABC, GA, ABC4, GA5, general Randić index and Zagreb index for copper(II) oxide, CuO. Furthermore, we give exact formulas of these indices which are helpful in studying the underlying topologies.


Molecular descriptor, Copper Oxide, Atom bond connectivity index, Geometric arithmetic index, General Randic index, Zagreb Index

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D. Amic, D. Beslo, B. Lucić, S. Nikolić, N. Trinajstić, The vertex-connectivity index revisited, J. Chem. Inf. Comput. Sci., 38, 819–822 (1998).

B. Bollobas, P. Erdos, Graphs of extremal weights, Ars Combinatoria, 50, 225–233 (1998).

G. Borkow, Using copper to improve the well-being of the skin, Current Chemical Biology, 8, 89–102 (2014).

G. Borkow, Safety of using copper oxide in medical devices and consumer products, Current Chemical Biology, 6 (1), 86–92 (2012). DOI: 10.2174/2212796811206010086.

G. Caporossi, I. Gutman, P. Hansen, L. Pavlovic, Graphs with maximum connectivity index, Comput. Bio. Chem., 27, 85–90 (2003).

E. Estrada, L. Torres, L. Rodriguez, I. Gutman, An atom-bond connectivity index: Modeling the enthalpy of formation of alkanes, Indian J. Chem., 37A, (1998), 849–855.

W. Gao, W. Wang, M. R. Farahani, Topological indices study of molecular structure in anticancer drugs. Journal of Chemistry 10 (2016). DOI: 10.1155/2016/3216327.

A. Ghorbani, M. A. Hosseinzadeh, Computing ABC4 index of nanostar Dendrimers, Optoelectronics and Ad-vanced Materials–Rapid Communications, 4, (2010), 1419–1422.

A. Graovac, M. Ghorbani, M. A. Hosseinzadeh, Compu-ting fifth geometric-arithmetic index for nanostar Dendrimers, J. Math. Nanosci., 1, 33–42 (2011).

I. Gutman, K. C. Das, The first Zagreb index 30 years after. MATCH Commun. Math. Comput. Chem, 50, (2004), 83–92.

I. Gutman, N. Trinajstić, Graph theory and molecular orbital’s., Total-electron energy of alternant hydrocar-bons. Chemical Physics Letters, 17, (1972), 535–538.

W. Gao, M. R. Farahani, L. Shi, Forgotten topological index of some drug structures, Acta Medica Mediterranea, 32, 579–585 (2016).

W. Gao, M. R. Farahani, Degree-based indices computa-tion for special chemical molecular structures using edge dividing method, Applied Mathematics and Nonlinear Sciences, 1 (1), 94–117 (2015).

W. Gao, W. Wang, M. K. Jamil, M. R. Farahani, Electron energy studying of molecular structures via forgotten topological index computation, Journal of Chemistry, (2016). DOI:10.1155/2016/1053183.

W. Gao, W. F. Wang, M. K. Jamil, R. Farooq, M. R. Farahani, Generalized atom-bond connectivity analysis of several chemical molecular graphs, Bulgarian Chemical Communications, 48 (3), 543–549 2016.

W. Gao, M. K. Siddiqui, M. Imran, M. K. Jamil, M. R. Farahani, Forgotten topological index of chemical struc-ture in drugs, Saudi Pharmaceutical Journal, 24, (2016), 258–264.

D. H. Baker, Cupric oxide should not be used as a copper supplement for either animals or humans, American Society for Nutritional Sciences. J. Nutr., 129, 2278–2279 (1999).

S. Hayat, M. A. Malik, M. Imran, Computing topological indices of honey-comb derived networks, Romanian Journal of Information Science and Technology, 18, 144–165 (2015).

S. Hayat, M. Imran, Computation of certain topological indices of nanotubes covered by C5 and C7, J. Comput. Theor. Nanosci., 12 (4), 533–541 (2015).

S. Hayat, M. Imran, Computation of topological indices of certain networks, Appl. Math. Comput. 240, 213–228 (2014).

Y. Hu, X. Li,Y. Shi, T. Xu, I. Gutman, On molecular graphs with smallest and greatest zeroth-order general Randić index, MATCH Commun. Math. Comput. Chem., 54, 425–434 (2005).

M. Imran, S. Hayat, On computation of topological indi-ces of Aztec diamonds, Sci. Int. (Lahore), 26 (4), 1407–1412 (2014).

I. Iakovidis, I. Delimaris, S. M. Piperakis, Copper and its complexes in medicine: A Biochemical Approach, Mo-lecular Biology International, (2011).


X. Li, I. Gutman, Mathematical aspects of Randić type molecular structure descriptors. Mathematical chemistry monographs No. 1, Kragujevac, 2006.

A. Q. Baig, M. Imran, H. Ali, On topological indices of polyoxide, polysilicate, DOX, and DSL networks, Cana-dian Journal of Chemistry, 93, 730–739 (2015).

M.R. Farahani, Computing fourth atom bond connectivity index of V-phenylenic nanotubes and nanotori. Acta Chimica Slovenica, 60, (2), 429–432 (2013).

B. Rajan, A. William, C. Grigorious, S. Stephen, On certain topological indices of silicate, honeycomb and hexagonal networks, J. Comp. and Math. Sci. 3(5), 530–535 (2012).

M. Randić, On characterization of molecular branching, J. Amer. Chem. Soc., 97 (23), 6609-6615 (1975).

S. Ramakrishnan, J. Senbagamalar, J.B. Babujee, Topo-logical indices of molecular graphs under specific chem-ical reactions, International Journal of Computing Algo-rithm, 2, 224–234 (2013).

P. Szymanski, T. Fraczek, M. Markowicz, Elzbieta Mikiciuk-Olasik, Development of copper based drugs, radiopharmaceuticals and medical materials, Biometals, 25, (2012), 1089–1112.

D. Vukičević, B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem., 46, 1369–1376 (2009).

H. W. Richardson, Copper Compounds, in Ullmann's Encyclopedia of Industrial Chemistry, Wiley-VCH, Weinheim. (2002). DOI:10.1002/14356007.a07 567.

H. Wiener, Structural determination of paraffin boiling points, J. Amer. Chem. Soc., 69, 17–20 (1947).



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