The Edge Version of Degree Based Topological Indices of HAC5C6C7[p, q] Nanotube

Mohammad Reza Farahani; Yingying Gao; Wasim Sajjad; Abdul Qudair Baig

Mohammad Reza Farahani Department of Applied Mathematics, Iran University of Science and Technology (IUST), Narmak,Tehran 16844, Iran
Yingying Gao College of Pharmacy and Biological Engineering, Chengdu University, Chengdu, 610106, China
Wasim Sajjad Department of Mathematics University of Sargodha, Mandi Bahauddin Campus, Mandi Bahauddin, Pakistan
Abdul Qudair Baig Department of Mathematics, University of Sargodha, Mandi Bahauddin Campus, Mandi Bahauddin, Pakistan

Keywords: Augmented-Zagreb Index, Hyper-Zagreb Index, Harmonic Index, Sum-Connectivity Index, Nanotubes.

Abstract

Let G be a simple molecular graph with vertex set V (G) and edge set E(G) respectively. The degree deg(v) of the vertex v 2 V (G) is the number of vertices adjacent with vertex v. A graph can be recognized by a numeric number, a polynomial, a sequence of numbers or a matrix. A topological index is a numeric quantity associated with a graph which characterize the topology of graph and is invariant under graph automorphism. Topological indices play important role in mathematical chemistry especially in the quantitative structureproperty
relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies. In this paper we compute the edge version of some important degree based topological indices like Augmented Zagreb Index, Hyper-Zagreb Index, Harmonic Index and Sum-Connectivity Index of HAC5C6C7[p, q] Nanotube.

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References

A. Ali, Z. Raza, A. Bhatti, On the Augmented Zagreb index, Kuwait. J. Sci. 43(2)pp.48-63,2016.

M. Baca, J. Horvathova, M. Mokrisova, A. Semanicova, Fenovcikova, A. Suhanyiova, On topological indices of carbon nanotube network, Can. j. Chem. 2015, 93(10): 1157-1160.

B. Basavanagoud, S. Patil, A Note on Hyper-Zagreb index of Graph operations, Iranian Journal of mathematical chemistry, Vol.7, No.1, March 2016, pp.89-92.

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

Z. Du, B. Zhou and N. Trinajstic, A note on generalized sum-connectivity index, Appl. Math. Lett. 24(2010), 402-405.

Z. Du, B. Zhou, On Sum-connectivity index of bycyclic graphs, Bull. Malays. Math. Sci. Soc. 35(1), 2012, 101-117.

M. Essalih, M. Marraki, G. Hagri, Calculation of Some Topological Indices of Graphs, Journal of Theoretical and Applied Information Technology, Vol.30, No.2, August 2011.

M. R. Farahani, The edge version of atom bond connectivity index of connected graph, Acta Universitatis Apulensis, No.36/2013, pp.277-284.

M. R. Farahani, On the Randic and Sum-connectivity index of nanotubes, Seria Matematica-Informatica, LI, 2, (2013), 39-46.

M. R. Farahani, The second connectivity and second-sum-connectivity indices of Armchair Polyhex Nanotubes TUAC6[m; n]. Intt. Letters of Chemistry, Physics and Astronomy. 11(1), (2014), 74-80.

M. R. Farahani, The Hyper-Zagreb index of TUSC4C8(S) Nanotubes, International journal of engineering and technology research, Vol.3, No.1 February 2015, pp.1-6.

M. R. Farahani, Computing the Hyper-Zagreb index of Hexagonal Nanotubes, Journal of chemistry and materials research, Vol.2(1), 2015, 16-18.

M. R. Farahani, M. R. Kanna, Generalized Zagreb index of V-Phenylenic nanotubes and nanotori, Journal of chemical and pharamaceutical research, 2015, 7(11): 241-245.

S. Fajtlowicz, Congr. Number.60 (1987)187.

B. Furtula, A. Graovac, D. Vukicevic, J. Math. Chem. 48(2010) 370.

I. Gutman, O. E. Polansky, Mathematical concepts in organic chemistry, Springer-Verlag, New York, 1986.

I. Gutman, Degree based topological indices, Croatica. Chemica. Acta, 86(4)(2013) 351-361.

I. Gutmasn, Edge-decomposition of topological indices, Iranian journal of mathematical chemistry, Vol.6, No.2, October 2015, pp. 103-108.

S. Hayat, M. Imran, Computation of certain topological indices of nanotubes, J. Comput. Theor. Nanosci. 12(2015), 70-76.

S. Hayat, M. Imran, Computation of certain topological indices of nanotubes covered by C5 and C7, J. Comput. Theor. Nanosci. Accepted, in press.

S. Hayat, M. Imran, Computation of topological indices of certain networks, Appl. Math. Comput. 240(2014), 213-228.

G.H Shirdel, H. Rezapour and A.M. Sayadi, The Hyper-Zagreb index of graph operations, Iranian J. Math. Chem. 4(2)(2013) 213-220.

A. Iranmanesh, Y. Pakravish, Szeged index of HAC5C6C7[k; p] nanotube, Journal of Applied sciences 7(23): 3606-3617, 2007, ISSN: 1812-5654.

A. Ilic, Note on the Harmonic index of a graph, 1204.3313v1.

M. Randic, On Characterization of molecular branching, J. Amer. Chem. Soc., 97(1975), 6609-6615.

M. Randic, Chemical Graph Theory-Facts and fiction, Indian Journal of chemistry, Vol.42A, June 2003, pp.1207-1218.

N. K. Raut, Degree based topological indices of Isomers of organic compounds, International Journal of Scientific and Research Publications, Vol.4, Issue 8, August 2014.

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

R. Xing, B. Zhou and N. Trinajstic, Sum-connectivity index of molecular trees, J. Math. Chem. 47(2001) 583-591.

L. Zhong, Appl. Math. Lett. 25(2012) 561.

L. Zhong, Ars Combin. 104(2012) 261.

B. Zhou and N. Trinajstic, On general Sum-connectivity index, J. Math. Chem. 47(2010), 210-218.

B. Zhou, I. Gutman, Further properties of Zagreb indices, MATCH Commun. Math. Comput. Chem. 54(2005)233-239.

B. Zhou, N. Trinajstic, J. Math. Chem. 46(2009) 1252.

B. Zhou, N. Trinajstic, Minimum general sum-connectivity index of unicyclic graphs, J. Math. Chem. 48. (2010) 697-703.