Eccentric connectivity polynomial and Total eccentricity polynomial of \(NA^n_m\) Nanotube

Authors

  • Rajarethinam Dhavaseelan Department of Mathematics, Sona College of Technology, Salem, Tamilnadu
  • Abdul Qudair Baig Department of Mathematics, COMSATS Institute of Information Technology, Attock Campus
  • Wasim Sajjad Department of Mathematics, COMSATS Institute of Information Technology, Attock Campus
  • Mohammad Reza Farahani Department of Applied Mathematics, Iran University of Science and Technology, Narmak, Tehran

DOI:

https://doi.org/10.26713/jims.v9i1.521

Keywords:

Eccentric connectivity polynomial, Total eccentricity polynomial, Nanotube

Abstract

Let \(G\) be a molecular graph with vertex set \(V(G)\) and edge set \(E(G)\). In chemical graph theory, for a molecular graph we have many invariant polynomials and topological indices. The length of a shortest path between two vertices of \(G\) is called distance. In a connected graph \(G\), the eccentricity \(\epsilon(v)\) of vertex \(v\) is the distance between \(v\) and a vertex farthest from \(v\) in \(G\). In this paper, we consider \(NA^n_m\) nanotube and compute eccentric connectivity polynomial and total eccentricity polynomial. Furthermore, we also compute some eccentricity based Zagreb indices of \(NA^n_m\).

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References

M. Alaeiyan, R. Mojarad and J. Asadpour, A new method for computing eccentric connectivity polynomial of an infinite family of linear Polycene parallelogram benzenod, Optoelectronics and Advanced Materials-Rapid Communications 5 (7) (2011), 761 – 763.

J. Asadpour and L. Safikhani, A study of CNC7[n] carbon nanocone by M-eccentric connectivity polynomial, Australian Journal of Basic and Applied Sciences 7 (7) (2013), 883 – 887.

A.R. Ashrafi, M. Ghorbani and M.A. Hossein-Zadeh, The eccentric connectivity polynomial of some graph operations, Serdica J. Computing 5 (2011), 101 – 116.

A.R. Ashrafi, M. Ghorbani and M. Jalali, Eccentric connectivity polynomial of an infinite family of Fullerenes, Optoelectron. Adv. Mater. - Rapid Comm. 3 (2009), 823 – 826.

A.R. Ashrafi and M. Saheli, The eccentric connectivity index of a new class of nanostar dendrimers, Optoelectron. Adv. Mater. - Rapid Comm. 4 (6) (2010), 898 – 899.

M. Bac, J. Horvathova, M. Mokrisova, A. Semanicova and A. Suhanyiova, On topological indices of carbonnanotube network, Can. J. Chem. 93 (10) (2015), 1157 – 1160.

A.R. Bindusree, V. Lokesha and P.S. Ranjini, Eccentric connectivity index and polynomial of some graphs, British J. Math. Comp. Sc. 6 (6) (2015), 457 – 463, doi:10.9734/BJMCS/2015/15137.

N. De, On eccentric connectivity index and polynomial of Thorn graph, Applied Mathematics 3 (2012), 931 – 934, doi:10.4236/am.2012.38139.

N. De, S.M. Nayeem and A. Pal, Bounds for the Modified Eccentric connectivity index, Advanced Modeling and Optimization 16 (1) (2014), 133 – 142.

M. V. Diudea, I. Gutman and J. Lorentz, Molecular Topology, Nova, Huntington (2001).

T. Doslic, M. Saheli and D. Vukicevic, Eccentric connectivity index: external graphs and values, Iranian Journal of Mathematical Chemistry 1 (2) (2010), 45 – 56.

M.R. Farahani, Connective eccentric index of an infinite family of linear polycene parallelogram benzenoid, International Letters of Chemistry, Physics and Astronomy 18 (2014), 57 – 62, doi:10.18052/www.scipress.com/ILCPA.37.57.

M.R. Farahani and M.R. Rajesh Kanna, On multiple Zagreb indices of armchair polyhex nanotubes, Physical Science International Journal 9 (1) (2016), 1 – 5.

M.R. Farahani, Computing the Hyper-Zagreb index of hexagonal nanotubes, Journal of Chemistry and Materials Research 2 (1) (2015), 16 – 18.

M.R. Farahani, On the SD-polynomial and SD-index of an infinite class of "Armchair Polyhex Nanotubes”, International Letters of Chemistry, Physics and Astronomy 12 (2014), 63 – 68, doi:10.18052/www.scipress.com/ILCPA.31.63.

H. Yang, W. Sajjad, A.Q. Baig and M.R. Farahani, The Edge Version of RANDIC, Zagreb, Atom Bond Connectivity and Geometric-Arithmetic Indices of NAPQ Nanotube„ International Journal of Advanced Biotechnology and Research (IJBR) 8 (2) (2017), 1582 – 1589

M.R. Farahani, The generalized Zagreb index of the armchair polyhex nanotube TUAC6[p, q], Global Journal of Chemistry 1 (1) (2015), 33 – 36

M.R. Farahani, The second-connectivity and second-sum-connectivity indices of Armchair Polyhex Nanotubes TUAC6[m,n], International Letters of Chemistry, Physics and Astronomy 11 (1) (2014), 74 – 80, doi:10.18052/www.scipress.com/ILCPA.44.73.

M.R. Farahani, (phi(G, x)) polynomials of armchair polyhex nanotubes TUAC6[p, q], International Letters of Chemistry, Physics and Astronomy 17 (2) (2014), 201 – 206, doi:10.18052/www.scipress.com/ILCPA.36.201.

M.R. Farahani, Computing GA5 index of armchair polyhex nanotube, Le Matematiche 69 (2) (November-December 2014), 69 – 76.

M.R. Farahani, Computing the omega and theta polynomials and their indices of an armchair polyhex nanotubes, Journal of Applied Physical Science International 4 (3) (2015), 160 – 164.

M.R. Farahani, Fifth geometric-arithmetic index of polyhex zigzag TUZC6[p, q] nanotube and nanotori, Journal of Advances in Physics 3 (1) (2013), 191 – 196.

M.R. Farahani, Fourth Atom-Bond Connectivity (ABC4) index of nanostructures, Sci-Afric Journal of Scientific Issues, Research and Essays 2 (12) (December, 2014), 567 – 570.

M.R. Farahani, On the fourth atom-bond connectivity index of armchair polyhex nanotubes, Proceedings of the Romanian Academy Series B Chemistry 15 (1) (2013), 3 – 6.

M.R. Farahani, Some connectivity indices and Zagreb index of polyhex nanotubes, Acta Chim. Slov. 59 (2012), 779 – 783.

R. Farooq and M. Ali Malik, Some eccentricity based topological indices of nanostar dendrimers, Optoelectron. Adv. Mater.-Rapid Comm. 9 (5-6) (2015), 842 – 849.

W. Gao, M. Reza Farahani and M. Kamran Jamil, The eccentricity version of atom-bond connectivity index of linear polycene parallelogram benzenoid ABC5(P(n,n)), Acta Chim. Slov. 63 (2016), in press.

Y. Gao, M.R. Farahani and W. Gao, A neighborhood union condition for fractional (k,n0,m)-critical deleted graphs, Transactions on Combinatorics 6 (1) (2017), 13 – 19.

W. Gao and M.R. Farahani, Computing the reverse eccentric connectivity index for certain family of nanocone and fullerene structures, Journal of Nanotechnology, 2016, Article ID 3129561, 6 pages, doi:10.1155/2016/3129561.

W. Gao and M.R. Farahani, Degree-based indices computation for special chemical molecular structures using edge dividing method, Applied Mathematics and Nonlinear Sciences 1 (1) (2015), 94 – 117, doi:10.21042/AMNS.2016.1.00009.

W. Gao, L. Shi and M.R. Farahani, Szeged Related Indices of TUAC6[p, q], Journal of Discrete Mathematical Sciences and Cryptography 20 (2) (2017), 553 – 563, doi:10.1080/09720529.2016.1228312.

M. Ghorbani and M.A. Hosseinzadeh, A new version of Zagreb indices, Filomat 26 (1) (2012), 93 – 100.

S. Gupta, M. Singh and A.K. Madan, Application of graph theory: relationship of eccentric connectivity index and Wiener's index with anti-inflammatory activity, J. Math. Anal. Appl. 266 (2002), 259 – 268.

I. Gutman and N. Trinajstic, Graph theory and molecular orbitals, total (pi)-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), 535 – 538, doi:10.1016/0009-2614(72)85099-1.

I. Gutman and O.E. Polansky, Mathematical Concepts in Organic Chemistry, Springer-Verlag, New York (1986).

S. Hayat and M. Imran, Computation of certain topological indices of nanotubes covered by C5 and C7, J. Comput. Theor. Nanosci. 12 (2015), 533 – 541, doi:10.1166/jctn.2015.3761.

Y. Huo, J.B. Liu, A.Q. Baig, W. Sajjad, M. Rezaei, Z. Foruzanfar and M.R. Farahani, Connective eccentric index of NA nanotube, J. Comput. Theor. Nanosci. 14 (4) (2017), 1832 – 1836, doi:10.1166/jctn.2017.651.

A. Kulandai Therese, Eccentric connectivity index, first and second Zagreb indices of Corona Graph, International Journal of Mathematical, Computational, Physical, Electrical, and Computer Engineering 9 (1) (2015), 71 – 75.

P.S. Ranjini and V. Lokesha, Eccentric connectivity index, hyper and reverse-wiener indices of the subdivision graph, Gen. Math. Notes. 2 (2) (2011), 34 – 46.

M. Rezaei, A.Q. Baig, W. Sajjad and M.R. Farahani, Fourth geometric arithmetic index of (NA^n_m) nanotube, International Journal of Pure and Applied Mathematics 111 (3) (2016), 467 – 477.

M. Saheli and A.R. Ashrafi, The eccentric connectivity index of armchair polyhex nanotubes, Macedonian Journal of Chemistry and Chemical Engineering 29 (1) (2010), 71 – 75.

V. Sharma, R. Goswami and A.K. Madan, Eccentric connectivity index: a novel highly discriminating topological descriptor for structure-property and structure-activity studies, J. Chem. Inf. Comput. Sci. 37 (2) (1997), 273 – 282, doi:10.1021/ci960049h.

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

H. Wu, M.R. Farahani, Bo Zhao and W. Gao, The second ABC index and second GA index of TUAC6[p, q], Journal of Computational and Theoretical Nanoscience, in press (2017).

B. Zhou and Z. Du, On eccentric connectivity index, MATCH Commun. Math. Comput. Chem. 63 (2010), 181 – 198.

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Published

2017-12-02
CITATION

How to Cite

Dhavaseelan, R., Baig, A. Q., Sajjad, W., & Farahani, M. R. (2017). Eccentric connectivity polynomial and Total eccentricity polynomial of \(NA^n_m\) Nanotube. Journal of Informatics and Mathematical Sciences, 9(1), 201–215. https://doi.org/10.26713/jims.v9i1.521

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Research Articles