najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2020-11-5-501-509najo-390Research ArticleMATHEMATICSМАТЕМАТИКАComputational analysis of some degree based topological indices of cubic structured tungsten trioxide [l,m,n] nanomultilayerDuraisamiM. S.

Melaiyur – 609107, Tamilnadu

tharmamithran@gmail.comParasuramanK.

Melaiyur – 609107, Tamilnadu

PG & Research Department of Physics, Poompuhar College (Autonomous)India202029072025115501–509Copyright © Duraisami M.S., Parasuraman K., 20252025Duraisami M.S., Parasuraman K.Duraisami M.S., Parasuraman K.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/390

Topological indices are numerical invariants of molecular graphs and are beneficial for predicting the physicochemical properties of chemical compounds. In this view, a topological index can be considered as a score function which maps each molecular structure to a real number. In the past two decades, tungsten trioxide (WO3) nanostructures have been extensively studied for their diverse technological applications. They have received greater attention by researchers, owing to their novel functionalities and unique physicochemical properties. We, for the first time, compute the Sum Connectivity index, Variable Sum index, ABC index, Harmonic index, Ordinary Geometric Arithmetic index, SK indices, Forgotten index, Symmetric Division index, Augmented Zagreb index, Inverse sum index, IRM index, Modified second Zagreb index, Inverse Randic index,´ Albertson and Bell topological indices of cubic structured WO3 [l, m, n] nanomultilayer. We also present a graphical analysis of all indices with respect to the dimension of this nanomultilayer.

topological indexchemical graphcubic WO3nanomultilayerReferencesWest D.B. Introduction to Graph Theory, 2nd Edition, Prentice Hall, 2000.West D.B. Introduction to Graph Theory, 2nd Edition, Prentice Hall, 2000.Wiener H.J. Structural determination of paraffin boiling points. Journal of the American Chemical Society, 1947, 69 (1), P. 17–20.Wiener H.J. Structural determination of paraffin boiling points. Journal of the American Chemical Society, 1947, 69 (1), P. 17–20.Gutman I., Trinajstic N. Graph theory, and molecular orbitals total f-electron energy of alternant hydrocarbons. Chem. Phys. Lett., 1972, 17, P. 535–538.Gutman I., Trinajstic N. Graph theory, and molecular orbitals total f-electron energy of alternant hydrocarbons. Chem. Phys. Lett., 1972, 17, P. 535–538.Rucker G., Rucker C. On topological indices, boiling points, and cycloalkanes. J. Chem. Inf. Comput. Sci., 1999, 39, P. 788.Rucker G., Rucker C. On topological indices, boiling points, and cycloalkanes. J. Chem. Inf. Comput. Sci., 1999, 39, P. 788.Gutman I. Molecular graphswith minimal andmaximal Randic indices. Croatica Chem. Acta., 2002, 75, P. 357–369.Gutman I. Molecular graphswith minimal andmaximal Randic indices. Croatica Chem. Acta., 2002, 75, P. 357–369.Gutman I. Degree-based topological indices. Croat. Chem. Acta., 2013, 86, P. 351–361.Gutman I. Degree-based topological indices. Croat. Chem. Acta., 2013, 86, P. 351–361.Dearden J.C. The Use of Topological Indices in QSAR and QSPR Modeling. In: Advances in QSAR Modeling. Challenges and Advances in Computational Chemistry and Physics, Roy K. (ed.), 2017, 24, P. 57–88.Dearden J.C. The Use of Topological Indices in QSAR and QSPR Modeling. In: Advances in QSAR Modeling. Challenges and Advances in Computational Chemistry and Physics, Roy K. (ed.), 2017, 24, P. 57–88.Samir A. Senior, Magdy D. Madbouly., Abdel-Moneim Elmassry. QSTR of the toxicity of some organophosphorus compounds by using the quantum chemical and topological descriptors. Chemosphere, 2011, 85 (1), P. 7–12.Samir A. Senior, Magdy D. Madbouly., Abdel-Moneim Elmassry. QSTR of the toxicity of some organophosphorus compounds by using the quantum chemical and topological descriptors. Chemosphere, 2011, 85 (1), P. 7–12.Fei Deng, Xiujun Zhang, et al. Topological Indices of the Pent-Heptagonal Nanosheets VC5C7 and HC5C7. Advances in Materials Science and Engineering, 2019, 9594549.Fei Deng, Xiujun Zhang, et al. Topological Indices of the Pent-Heptagonal Nanosheets VC5C7 and HC5C7. Advances in Materials Science and Engineering, 2019, 9594549.Munir M., Nazeer W., Rafique S., Kang S.M. MPolynomial and Degree-Based Topological Indices of Polyhex Nanotubes. Symmetry, 2016, 8 (12), P. 149.Munir M., Nazeer W., Rafique S., Kang S.M. MPolynomial and Degree-Based Topological Indices of Polyhex Nanotubes. Symmetry, 2016, 8 (12), P. 149.Munir M., Nazeer W., Rafique S., Kang S.M. Mpolynomial and degree- based topological indices of Nano star dendrimers. Symmetry, 2016, 8 (9), P. 97.Munir M., Nazeer W., Rafique S., Kang S.M. Mpolynomial and degree- based topological indices of Nano star dendrimers. Symmetry, 2016, 8 (9), P. 97.Diudea M.V., Gutman I., Lorentz J. Molecular topology, Nova Science Publishers, Huntington, NY, 2001.Diudea M.V., Gutman I., Lorentz J. Molecular topology, Nova Science Publishers, Huntington, NY, 2001.Trinajstic N. Chemical Graph theory, CRC Press, Boca Raton, 1992.Trinajstic N. Chemical Graph theory, CRC Press, Boca Raton, 1992.Zhou B., Trinajstic N. On a novel connectivity index.´ J. Math. Chem., 2009, 46, P. 1252–1270.Zhou B., Trinajstic N. On a novel connectivity index.´ J. Math. Chem., 2009, 46, P. 1252–1270.Zhou B., Luo W. A note on general Randic index. Match Commun. Math. Comput. Chem., 2009, 62, P. 155–162.Zhou B., Luo W. A note on general Randic index. Match Commun. Math. Comput. Chem., 2009, 62, P. 155–162.Vukiceviˇ c D. Bond Additive Modeling 4. QSPR and QSAR studies of the variable Adriatic indices.´ Croat. Chem. Acta., 2011, 84 (1), P. 87–91.Vukiceviˇ c D. Bond Additive Modeling 4. QSPR and QSAR studies of the variable Adriatic indices.´ Croat. Chem. Acta., 2011, 84 (1), P. 87–91.Vukiceviˇ c D. Bond additive modeling 5. mathematical properties of the variable sum exdeg index.´ Croat. Chem. Acta., 2011, 84 (1), P. 93–101.Vukiceviˇ c D. Bond additive modeling 5. mathematical properties of the variable sum exdeg index.´ Croat. Chem. Acta., 2011, 84 (1), P. 93–101.Estrada E., Torres L., Rodriguez L., Gutman I. An atom-bond connectivity index: modelling the enthalpy of formation of alkanes. Indian Journal of Chemistry, 1998, 37A, P. 849–855.Estrada E., Torres L., Rodriguez L., Gutman I. An atom-bond connectivity index: modelling the enthalpy of formation of alkanes. Indian Journal of Chemistry, 1998, 37A, P. 849–855.Favaron O., Maheo M., Sacl´ e J.-F. Some eigenvalue properties in graphs (conjectures of graffiti-II).´ Discrete Mathematics, 1993, 111 (1–3), P. 197–220.Favaron O., Maheo M., Sacl´ e J.-F. Some eigenvalue properties in graphs (conjectures of graffiti-II).´ Discrete Mathematics, 1993, 111 (1–3), P. 197–220.Fajtlowicz S. On conjectures of graffiti-ii. Congr. Numer., 1987, 60, P. 187–197.Fajtlowicz S. On conjectures of graffiti-ii. Congr. Numer., 1987, 60, P. 187–197.Vukiceviˇ c D., Furtula B. Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges.´ J. Math. Chem., 2009, 46, P. 1369–1376.Vukiceviˇ c D., Furtula B. Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges.´ J. Math. Chem., 2009, 46, P. 1369–1376.Shigehalli V.S., Kanabur R. Computation of new degree-based topological indices of graphene. Journal of Nanomaterials, 2016, 4341919.Shigehalli V.S., Kanabur R. Computation of new degree-based topological indices of graphene. Journal of Nanomaterials, 2016, 4341919.Furtula B., Gutman I. A forgotten topological index. J. Math. Chem., 2015, 53, P. 184–1190.Furtula B., Gutman I. A forgotten topological index. J. Math. Chem., 2015, 53, P. 184–1190.Vukiceviˇ c D., Ga´ sperov M. Bond additive modeling 1. Adriatic indices.ˇ Croatica Chemica Acta, 2010, 83 (3), P. 243–260.Vukiceviˇ c D., Ga´ sperov M. Bond additive modeling 1. Adriatic indices.ˇ Croatica Chemica Acta, 2010, 83 (3), P. 243–260.Furtula B., Graovac A., Vukicceviˇ c D. Augmented zagreb index.´ Journal of Mathematical Chemistry, 2010, 48 (2), P. 370–380.Furtula B., Graovac A., Vukicceviˇ c D. Augmented zagreb index.´ Journal of Mathematical Chemistry, 2010, 48 (2), P. 370–380.Sedlar J., Stevanovic D., Vasilyev A. On the inverse sum indeg index.´ Discrete Applied Mathematics, 2015, 184, P. 202–212.Sedlar J., Stevanovic D., Vasilyev A. On the inverse sum indeg index.´ Discrete Applied Mathematics, 2015, 184, P. 202–212.Hamzeh A., Reti T. An Analogue of Zagreb Index Inequality Obtained from Graph Irregularity Measures.´ Match Commun. Math. Comput. Chem., 2014, 72, P. 669–683.Hamzeh A., Reti T. An Analogue of Zagreb Index Inequality Obtained from Graph Irregularity Measures.´ Match Commun. Math. Comput. Chem., 2014, 72, P. 669–683.Miliceviˇ c A., Nikoli´ c S., Trinajsti´ c N. On reformulated zagreb indices.´ Molecular Diversity, 2004, 8, P. 393–399.Miliceviˇ c A., Nikoli´ c S., Trinajsti´ c N. On reformulated zagreb indices.´ Molecular Diversity, 2004, 8, P. 393–399.Amic D., Be´ slo D., et al. The vertex-connectivity index revisited.ˇ Journal of Chemical Information and Computer Sciences, 1998, 38 (5), P. 819–822.Amic D., Be´ slo D., et al. The vertex-connectivity index revisited.ˇ Journal of Chemical Information and Computer Sciences, 1998, 38 (5), P. 819–822.Albertson M. The irregularity of a graph. Ars. Combin., 1997, 46, P. 219–225.Albertson M. The irregularity of a graph. Ars. Combin., 1997, 46, P. 219–225.Bell F. A note on the irregularity of graphs. Linear Algebra Appl., 1992, 161, P. 45–54.Bell F. A note on the irregularity of graphs. Linear Algebra Appl., 1992, 161, P. 45–54.Randic M. Characterization of molecular branching.´ Journal of the American Chemical Society, 1975, 97 (23), P. 6609–6615.Randic M. Characterization of molecular branching.´ Journal of the American Chemical Society, 1975, 97 (23), P. 6609–6615.Haidong Zheng, Jian Zhen Ou, et al. Nanostructured Tungsten Oxide-Properties, Synthesis, and Applications. Adv. Funct. Mater., 2011, 21, P. 2175–2196.Haidong Zheng, Jian Zhen Ou, et al. Nanostructured Tungsten Oxide-Properties, Synthesis, and Applications. Adv. Funct. Mater., 2011, 21, P. 2175–2196.Liu X., Wang F., Wang Q. Nanostructure-based WO3 Photoanodes for Photoelectrochemical Water Splitting. Phys. Chem. Chem. Phys., 2012, 14, P. 7894–7911.Liu X., Wang F., Wang Q. Nanostructure-based WO3 Photoanodes for Photoelectrochemical Water Splitting. Phys. Chem. Chem. Phys., 2012, 14, P. 7894–7911.Chang-Mou Wu., Saba Naseem, et al. Recent Advances in Tungsten-Oxide-Based Materials and Their Applications. Front. Mater., 2019, 6 (49), P. 1–17.Chang-Mou Wu., Saba Naseem, et al. Recent Advances in Tungsten-Oxide-Based Materials and Their Applications. Front. Mater., 2019, 6 (49), P. 1–17.Jijie Zhang, Peng Zhang, Tuo Wang, Jinlong Gong. Monoclinic WO3 nanomultilayers with preferentially exposed (002) facets for photoelectrochemical water splitting. Nano Energy, 2015, 11, P. 189–195.Jijie Zhang, Peng Zhang, Tuo Wang, Jinlong Gong. Monoclinic WO3 nanomultilayers with preferentially exposed (002) facets for photoelectrochemical water splitting. Nano Energy, 2015, 11, P. 189–195.

The authors declare that there are no conflicts of interest present.