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Nanoscience & Nanotechnology-Asia

Editor-in-Chief

ISSN (Print): 2210-6812
ISSN (Online): 2210-6820

Research Article

On the Edge-version of Topological Indices of Titanium Dioxide Nanotube and Nanosheet

Author(s): S. Prabhu*, G. Murugan and M. Arulperumjothi

Volume 11, Issue 2, 2021

Published on: 23 April, 2020

Page: [174 - 188] Pages: 15

DOI: 10.2174/2210681210999200423120222

Price: $65

Abstract

Background: In computational and theoretical chemistry, real numbers programming certain structural skin appearance of natural molecules and derivative from parallel molecular graphs are called the graph invariants or more frequently structural descriptors (topological indices).

Methods: Structural descriptors are numeric quantities, which are resulting from a molecular structure by mathematical calculations.

Results: In Quantitative Structure-Activity Relation (QSAR) and Quantitative Structure-Property Relation (QSPR) study, these parameters are utilized to compute the biological properties of chemical composites.

Conclusion: In this computational research paper, we find a degree based on the edge version of topological indices of Titanium dioxide nanotube and nanosheet.

Keywords: Line graph, topological indices, molecular graph, titania nanotube, titania nanosheet, zagreb index, structureproperty, structure-activity.

Graphical Abstract
[1]
Yang, Y.M.; Qiu, W.Y. MATCH Commun. Math. Comput. Chem., 2007, 58, 635.
[2]
Li, X.; Shi, Y. A survey on the Randic index. MATCH Commun. Math. Comput. Chem., 2008, 59(1), 127-156.
[3]
Shi, Y. Note on two generalizations of the Randic index, Discrete. Appl. Math. Comput., 2015, 265, 1019-1025.
[4]
Estrada, E.; Torres, L.; Rodriguez, L.; Gutman, I. An atom-bond connectivity index: Modelling the enthalpy of formation of Alkanes. Indian J. Chem., 1998, 37A, 849-855.
[5]
Das, K.C.; Mohammed, M.A.; Gutman, I.; Atan, K.A. Comparison between atom-bond connectivity indices of graphs, MATCH. Commun. Math. Comput. Chem., 2016, 76(1), 159-170.
[6]
Lin, W.; Chen, J.; Ma, C.; Zhang, Y.; Chen, J.; Zhang, D.; Jia, F. On trees with minimal ABC index among trees with given number of leaves, MATCH. Commun. Math. Comput. Chem., 2016, 76(1), 131-140.
[7]
Gao, Y.; Shao, Y. The smallest ABC index of trees with n pendent vertices, MATCH. Commun. Math. Comput. Chem., 2016, 76(1), 141-158.
[8]
Bianchi, M.; Cornaro, A.; Palacios, J.L.; Torriero, A. New upper bounds for the ABC index, MATCH. Commun. Math. Comput. Chem., 2016, 76(1), 117-130.
[9]
Farahani, M.R. The edge version of atom bond connectivity index of connected graph. Acta Universitatis Apulensis, 2012, 36, 277-284.
[10]
Wiener, H. Structural determination of paraffin boiling points. J. Am. Chem. Soc., 1947, 69(1), 17-20.
[http://dx.doi.org/10.1021/ja01193a005 PMID: 20291038]
[11]
Gutman, I. Selected properties of the schultz molecular topological index. J. Chem. Inf. Comput. Sci., 1994, 34, 1087-1089.
[http://dx.doi.org/10.1021/ci00021a009]
[12]
Li, Y.Z.; Lee, N.H.; Lee, E.G.; Song, J.S.; Kim, S.J. The characterization and photocatalytic properties of mesoporous rutile TiO2 powder synthesized through cell assembly of nanocrystals. Chem. Phys. Lett., 2004, 389, 124-128.
[http://dx.doi.org/10.1016/j.cplett.2004.03.081]
[13]
Bavykin, D.V.; Friedrich, J.M.; Walash, F.C. Protonated titanates and TiO2 nanostructured materials: Synthesis, properties and applications. Adv. Mater., 2006, 18, 2807-2824.
[http://dx.doi.org/10.1002/adma.200502696]
[14]
Wang, W.; Varghese, O.K.M.; Paulsose, C.A. Grimes. A study on the growth and structure of Titania nonotubes. J. Mater. Res., 2004, 19, 417-422.
[http://dx.doi.org/10.1557/jmr.2004.19.2.417]
[15]
Evarestov, R.A.; Bandura, A.V.; Losev, M.V.; Piskunov, S.; Zhukovskii, Y.F. Titania nanotubes modelled from 3-layered and 6-layered(101) anatase sheets: Line group symmetry and comparative ab initio LCAO calculations. Physica E, 2010, 43, 266-278.
[http://dx.doi.org/10.1016/j.physe.2010.07.068]
[16]
Javaid, M.; Liu, J.B.; Rehman, M.A.; Wang, S. On the certain topological indices of Titania nanotube TiO2[m, n] Z Naturforsch, 2017, 72(7a), 647-654.
[17]
Pattabiraman, K.; Santhakumar, A. On topological indices of sudoku graphs and Titania TiO2 nanotubes. Int. J. Adv. Res. Comput. Sci. Softw. Eng., 2017, 7(12), 96-103.
[http://dx.doi.org/10.23956/ijarcsse.v7i12.514]
[18]
Nilanjan, D. On molecular topological properties of TiO2 nanotubes. J. Nanosci., 2016, 2016, 1028031.
[19]
Liu, J.B.; Gao, W.; Siddiqui, M.K.; Farahani, M.R. Computing three topological indices for Titania nanotubes TiO2[m, n] AKCE Int. J. Graphs Combinatorics., 2016, 13(3), 255-260.
[http://dx.doi.org/10.1016j.akcej.2016.07.001]
[20]
Dobrynin, A.A.; Kochetova, A.A. Degree distance of a graph. A degree analogue of the wiener index. J. Chem. Inf. Comput. Sci., 1994, 34, 1082-1086.
[http://dx.doi.org/10.1021/ci00021a008]
[21]
Estrada, E.; Torres, L.; Rodrguez, L.; Gutman, I. An atom-bond connectivity index: modelling the enthalpy of formation of alkanes. Indian J. Chem. A, 1998, 37, 849-855.
[22]
Dimitrov, D. On structural properties of trees with minimal atom-bond connectivity index. Discrete Appl. Math., 2014, 172, 28-44.
[http://dx.doi.org/10.1016/j.dam.2014.03.009]
[23]
Vukicevic, 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(4), 1369-1376.
[http://dx.doi.org/10.1007/s10910-009-9520-x]
[24]
Randić, M. On characterization of molecular branching. J. Am. Chem. Soc., 1975, 97, 6609-6615.
[http://dx.doi.org/10.1021/ja00856a001]
[25]
Bollobs, B.; Erdo¨s, P. Graphs of extremal weights. Ars Comb., 1998, 50, 225-233.
[26]
Amic, D.; Beslo, D.; Lucic, B.; Nikolic, S.; Trinajstic, N. The vertex-connectivity index revisited. J. Chem. Inf. Comput. Sci., 1998, 38, 819-822.
[http://dx.doi.org/10.1021/ci980039b]
[27]
Ilic, A.; Ilic, M. Generalizations of Wiener polarity index and terminal Wiener index. Graphs Comb., 2013, 29, 1403-1416.
[http://dx.doi.org/10.1007/s00373-012-1215-6]
[28]
Caporossi, G.; Gutman, I.; Hansen, P.; Pavlovic, L. Graphs with maximum connectivity index. Comput. Biol. Chem., 2003, 27, 85-90.
[http://dx.doi.org/10.1016/S0097-8485(02)00016-5] [http://dx.doi.org/10.1016/j.amc.2015.06.019]
[29]
Gutman, I.; Trinajsti’c, N. Graph theory and molecular orbitals. Total -electron energy of alternant hydrocarbons. Chem. Phys. Lett., 1972, 17, 535-538.
[http://dx.doi.org/10.1016/0009-2614(72)85099-1]
[30]
Furtula, B.; Gutman, I.; Ediz, S. On difference of Zagreb indices. Discrete Appl. Math., 2014, 178, 83-88.
[http://dx.doi.org/10.1016/j.dam.2014.06.011]
[31]
Randi’c, M. On characterization of molecular branching. J. Am. Chem. Soc., 1975, 97, 6609-6615.
[http://dx.doi.org/10.1021/ja00856a001]
[32]
Favaran, O.; Maheo, M.J.F. sacle. Some eigenvalue properties of graphs (conjectures of graffiti II). Discrete Math., 1993, 111, 197-220.
[http://dx.doi.org/10.1016/0012-365X(93)90156-N]
[33]
Manso, F.C.G.; Junior, H.S.; Bruns, R.E.; Rubira, A.F.; Miniz, E.C. Development ofa new topological index for the prediction of normal boiling point temperatures of hydrocarbons:the Fi index. J. Mol. Liq., 2012, 165, 125-132.
[http://dx.doi.org/10.1016/j.molliq.2011.10.019]
[34]
Shirdel, G.H.; Rezapour, H.; Sayadi, A.M. The hyper-Zagreb index of graph operations. Iranian J. Math. Chem., 2013, 4(2), 213-220.
[35]
D., Vukicevic Augmented Zagreb index. J. Math. Chem., 2010, 48(2), 370-380.
[http://dx.doi.org/10.1007/s10910-010-9677-3]
[36]
Fajtlowicz, S. On conjectures of Graffiti-II. Congr. Numer., 1987, 60, 187-197.

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