Some Topological Indices of Carbon Nanocones [CNC_k(n)] and Nanotori [C₄C₆C₈(P, Q)]

Keerthi G. Mirajkar¹ , Bhagyashri R. Doddamani²

1. Dept. of Mathematics, Karnatak University’s Karnatak Arts College, Dharwad, India.
2. Dept. of Mathematics, Karnatak University’s Karnatak Arts College, Dharwad, India.

Correspondence should be addressed to: keerthi.mirajkar@gmail.com.

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.2 , pp.35-39, Apr-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i2.3539

Online published on Apr 30, 2018

Copyright © Keerthi G. Mirajkar, Bhagyashri R. Doddamani . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Chemical graph theory is a branch of graph theory which focuses on the topological indices of chemical molecular graphs, which correlate well with chemical properties of the chemical molecules. Topological indices play important role in mathematical chemistry especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies. In this article, we compute the sum connectivity index, product connectivity index, geometric-arithmetic index and inverse sum indeg index for Carbon Nanocones [CNC_k(n)] and Nanotori [C₄C₆C₈(P, Q)].

Key-Words / Index Term :
Sum connectivity index, Product connectivity index, Geometric-arithmetic index, Inverse sum indeg index, Carbon Nanocones [CNCk(n)] and Nanotori [C4C6C8(p,q)].

References :
[1] F. Harary, “Graph Theory”, Addison - Wesely, Reading, 1969.
[2] R. Todeschini, V. Consonni, “Handbook of Molecular Descriptors”, Weinheim, Wiley-VCH, 2000.
[3] H. Wiener, “Structural determination of paraffin boiling points”, Journal of the American Chemical Society, Vol.69, pp. 17-20, 1947.
[4] B. Zhou and N. Trinajstić, “On a Novel Connectivity Index”, Journal of Mathematical Chemistry, Vol.46, pp. 1252-1270, 2009.
[5] M. Randić, “On Characterization of Molecular Branching”, Journal of the American Chemical Society, Vol.97, Issue.2, pp.6609-6615, 1975.
[6] D. Vukičević, B. Furtula, “Topological Index Based on the Ratios of Geometrical and Arithmetical Means of End-Vertex Degrees of Edges”, Journal of Mathematical Chemistry, Vol.46, pp.1369-1376, 2009.
[7] D. Vukičević and M. Gaśperov, “Bond Additive Modeling 1. Adriatic Indices”, Croatica Chemica Acta, Vol.83, pp. 243-260, 2010.
[8] J. Gillot, W. Bollmann and B. Lux, “Cristaux De Graphite En Forme De Cigare Et A Structure Conique”, Carbon, Vol.6, Issue.3, pp.381-384, 1968.
[9] S. Iijima, “Helical Microtubules of Graphitic Carbon”, Nature, Vol.354, pp.56-58, 1991.
[10] M. Yudasaka, S. Iijima and V. H. Crespi, “Single-wall Carbon Nanohorns and Nanocones”, Topics in Applied Physics, Vol.111, pp.605-629, 2008.
[11] M. V. Diudea, “Graphenes From 4-Valent Tori”, Bulletin of the Chemical Society of Japan, Vol.75, pp.487-492, 2002.
[12] M. V. Diudea, A. Graovac, “Generation and Graph-Theoretical Properties of C4-Tori”, MATCH Communication in Mathematical and in Computer Chemistry, Vol.44, pp.93-102, 2001.
[13] M. V. Diudea, P. E. John, “Covering Polyhedral Tori”, MATCH Communication in Mathematical and in Computer Chemistry, Vol.44, pp.103-116, 2001.
[14] M. V. Diudea, M. Stefu, “Wiener Index of C4C8 Nanotube”, MATCH Communication in Mathematical and in Computer Chemistry, Vol.50, pp.133-144, 2004.
[15] M. Ge and K. Sattler, “Observation of Fullerence Cones”, Chemical Physics Letters, Vol.220, Issue.35, pp.192-196, 1994.
[16] M. R. Farahani, “Computing Randi´c, Geometric-Arithmetic and Atom-Bond Connectivity indices of Circumcoronene Series of Benzenoid”, International Journal of Chemical Modelling, Vol.5, Issue.4, pp.485-493, 2013.
[17] M. Ghorbani, M. Jalali, “The vertex PI, Szeged and Omega Polynomials of Carbon Nanocones CNC4[n]”, MATCH Communication in Mathematical and in Computer Chemistry, Vol.62, Issue.2, pp.353-362, 2009.
[18] M. H. Khalifeh, H. Y. Azari and A. R. ashrafi, “A Method for Computing the Wiener Index of One-Penta gonal Carbon Nanocones”, Current Nanoscience, Vol.6, Issue.2, pp.155-157, 2010.
[19] A. Nejati and M. Alaeiyan, The Edge-Version of MEC Index of One-Pentagonal Carbon Nanocones”, Bulgerian Chemical Communications, Vol.46, Issue.3, pp.462-464, 2014.
[20] W. Gao, M. R. Farahani, M. K. Siddiqui and M. K. Jamil, “On the First and Second Zagreb and First and Second Hyper-Zagreb Indices of Carbon Nanocones CNCk[n]”, Journal of Computation and Theoretical Nanosciences, Vol.13, pp.7475-7482, 2016.