Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2017, 5(6), 197-201
DOI: 10.12691/tjant-5-6-1
Open AccessArticle

Investigation on Tri-hexagonal Boron Nanotube by Exploiting the Certain Topological Indices and Their M-polynomials

V. Lokesha1, Sushmitha Jain1, and T. Deepika1

1Department of Studies in Mathematics, Vijayanagara Sri Krishnadevaraya University, Ballari, India

Pub. Date: September 21, 2017

Cite this paper:
V. Lokesha, Sushmitha Jain and T. Deepika. Investigation on Tri-hexagonal Boron Nanotube by Exploiting the Certain Topological Indices and Their M-polynomials. Turkish Journal of Analysis and Number Theory. 2017; 5(6):197-201. doi: 10.12691/tjant-5-6-1

Abstract

Due to the presence of multicenter bonds and their novel electronic properties, boron nanotubes are attractive. The tri-hexagonal boron nanotubes are build up from triangles and hexagons. It is useful to the QSPR/QSAR studies. Topological indices are classified in different forms such as, degree based topological indices, distance based topological indices and counting related topological indices etc. Here, we concentrated the reckoning of topological indices such as first zagreb, second zagreb, modified second zagreb index, generalized randic index, symmetric division degree index for the tri-hexagonal boron nanotube. Also, established their M-polynomials and using maple software plotted the 3D structure.

Keywords:
Tri-hexagonal boron nanotube topological indices M-polynomials

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References:

[1]  Amic. D., Beslo. D., Lucic. B., Nikolic. S. and Trinajstic. N, “The vertex connectivity index revisited”, J. Chem. Inf. Comput. Sci. 38, 819-822, 1998.
 
[2]  Bollobas. B. and Erdos, “Graphs of extremal weights, Ars Combin., 50, 225-233, 1998.
 
[3]  K. Clark, A. Hassanien, S. Khan, K. F. Braun, H. Tanaka and S. W. Hla, Nat. Nanotechnol., 5, 261, 2010.
 
[4]  Damir Vukicevi and Marija Gasperov, “Bond additive modeling 1. Adriatic Indices”, Croat. Chem. Acta, 83(3), 243-260, 2010.
 
[5]  Deutsch. E and Klavzar. S, “M-Polynomial, and degree-based topological indices”, Iran. J. Math. Chem., 6, 93-102, 2015.
 
[6]  J. Devillers and A. T. Balaban (Eds.), Topological Indices and Related Descriptors in QSAR and QSPR, Gordon and Breach, Amsterdam, 1999.
 
[7]  G.H. Fath-Tabar “Old and new Zagreb index,” Match-Commun. Math. Compute. Chem., 65, 79-84, 2011.
 
[8]  C. K. Gupta, V. Lokesha and S. B. Shetty, “On the Symmetric division deg index of graph”, South East Asian Journal Of Mathematics, 4(11), 59-80, 2016.
 
[9]  C. K. Gupta, V. Lokesha, S. B. Shetty and P. S. Ranjini, “Graph Operations on Symmetric Division Deg Index of Graphs”, Palestine Journal of Mathematics, 6(1), 280-286, 2017 .
 
[10]  Gutman. I. Some properties of the Wiener polynomials, Graph Theory Notes N. Y., 125, 13-18, 1993.
 
[11]  Gutman. I. and Das. K. Ch., “The first zagreb indices 30 years after”, MATCH Commun. Math.Comput. Chem. 50, 83-92, 2004.
 
[12]  F. Harary, Graph theory, Reading, MA: Addison-Wesley, 1994.
 
[13]  Imran Nadeem, H. Shaker, “On topological indices of tri-hexagonal boron nanotubes”, Journal of Optoelectronics and Advance Materials, 1810(9), 893-898, 2016.
 
[14]  Deutsch. E, Klavzar. S, “M-Polynomial and degree-base topological indices”, Iran. J. Math. Chem., 6, 93-102, 2015.
 
[15]  M. H. Khalifeha, H. Youse -Azari and A. R. Ashra, “The first and second Zagreb indices of some graph operations”, Discrete Applied Mathematics, 157(4), 804-811, 2009.
 
[16]  V. Lokesha, Shwetha. B. S, Ranjini P. S , Cangul Ismail N and Cevik Ahmet S, “New bounds for Randic and GA indices”, Journal of Inequalities and Applications, 180(1), 1-7, 2013.
 
[17]  V. Lokesha, T. Deepika, P. S. Ranjini and I.N. Cangul, “Operation of nanostructures via SDD, ABC4 and GA5 indices”, Applied Mathematics and Nonlinear Sciences, 2(1), 173-180, 2017.
 
[18]  Milicevic, S. Nikolic and N. Trinajstic, “On reformulated zagreb indices”, Mol. Divers., 8, 393-399, 2004.
 
[19]  Randic. M, “On the characterization of molecular branching, J. Am. Chem. Soc., 97, 6609-6615, 1975.
 
[20]  Shwetha. B. Shetty, V. Lokesha, P.S. Ranjini, and K.C. Das, “Computing some topological indices of Smart polymer”, Digest Journal of Nanomaterials and Biostructures, 7(3), 1097-1102, 2012.
 
[21]  Shwetha. B. Shetty, V. Lokesha and P. S. Ranjini, “On The Harmonic Index of Graph Operations”, Transactions on Combinatorics, 4(4), 5-14, 2015.
 
[22]  Shwetha. B. Shetty, V. Lokesha, P.S. Ranjini and Naci cangul, “Computing ABC, GA, Randic and Zagreb Indices”, Enlightens of Pure and Applied Mathematics, 1(1), 17-18, 2015.
 
[23]  Shwetha. B. Shetty, V. Lokesha, A. Bayad and P. S. Ranjini, “A Comparative Study of Topological Indices and Molecular Weight of Some Carbohydrates”, Journal of the Indian Academy of Mathematics, 34(2), 627-636, 2012.
 
[24]  Vukicevic. D and M. Gaperov,” Bond additive modeling 1. Adriatic indices”, Croatica chemica acta, 83(3), 243-260, 2010.
 
[25]  Vukicevic. D, “Bond Additive Modeling 2. Mathematical properties of Max-min rodeg index”, Croatica chemica acta, 83(3), 261-273, 2010.