Chemical graph theory is an important branch of mathematical chemistry which has wide range applications. In chemical graph theory a molecular graph can be recognized by a numerical quantity which is called a Topological index. Topological indices have some major classes but among these classes degree based topological indices have prominent role in chemical graph theory. 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 NA q p Nanotube.
KeywordsAugmented Zagreb IndexHyper-Zagreb IndexHarmonic IndexSum-Connectivity IndexNA<sub>q</sub><sup style="margin-left:-6px">p</sup>Nanotube
Raut, N.K. (2014) Degree Based Topological Indices of Isomers of Organic Compounds. International Journal of Scientific and Research Publications, 4, 1-4.
Wiener, H. (1947) Structural Determination of Paraffin Boiling Points. Journal of the American Chemical Society, 69, 17-20. https://doi.org/10.1021/ja01193a005
Randic, M. (1975) On Characterization of Molecular Branching. Journal of the American Chemical Society, 97, 6609-6615. https://doi.org/10.1021/ja00856a001
Ali, A., Raza, Z. and Bhatti, A. (2016) On the Augmented Zagreb Index. Kuwait Journal of Science, 43, 48-63.
Furtula, B., Graovac, A. and Vukicevic, D. (2010) Augmented Zagreb Index. Journal of Mathematical Chemistry, 48, 370-380. https://doi.org/10.1007/s10910-010-9677-3
Gutman, I. (2013) Degree Based Topological Indices. Croatica Chemica Acta, 86, 351-361. https://doi.org/10.5562/cca2294
Shirdel, G.H., Rezapour, H. and Sayadi, A.M. (2013) The Hyper-Zagreb Index of Graph Operations. Iranian Journal of Mathematical Chemistry, 4, 213-220.
Zhong, L. (2012) The Harmonic Index for Graphs. Applied Mathematics Letters, 25, 561-566. https://doi.org/10.1016/j.aml.2011.09.059
Zhong, L. (2012) The Harmonic Index on Unicyclic Graphs. Ars Combinatoria, 104, 261-269. http://dblp.org/rec/journals/arscom/Zhong12
Zhou, B. and Trinajstic, N. (2009) On a Novel Connectivity Index. Journal of Mathematical Chemistry, 46, 1252-1270. https://doi.org/10.1007/s10910-008-9515-z
Balaban, A.T. (1985) Applications of Graph Theory in Chemistry. Journal of Chemical Information and Modeling, 25, 334-343. https://doi.org/10.1021/ci00047a033
Basavanagoud, B. and Patil, S. (2016) A Note on Hyper-Zagreb index of Graph Operations. Iranian Journal of Mathematical Chemistry, 7, 89-92.
Diudea, M.V., Gutman, I. and Lorentz, J. (2001) Molecular Topology. Nova, Huntington.
Du, Z., Zhou, B. and Trinajstic, N. (2010) A Note on Generalized Sum-Connectivity Index. Applied Mathematics Letters, 24, 402-405. https://doi.org/10.1016/j.aml.2010.10.038
Du, Z. and Zhou, B. (2012) On Sum-Connectivity Index of Bycyclic Graphs. Bulletin of the Malaysian Mathematical Sciences Society, 35, 101-117.
Ebrahimi, M. and Alaeiyan, M. (2016) Topological Indices and Interpolation of Sequences. Indian Journal of Science and Technology, 9, 1-4.
Essalih, M., Marraki, M. and Hagri, G. (2011) Calculation of Some Topological Indices of Graphs. Journal of Theoretical and Applied Information Technology, 30, 122-127.
Farahani, M.R. (2013) The Edge Version of Atom Bond Connectivity Index of Connected Graph. Acta Universitatis Apulensis, 36, 277-284.
Farahani, M.R. (2013) On the Randic and Sum-Connectivity Index of Nanotubes. Annals of West University of Timisoara-Mathematics and Computer Science, 51, 29-37. https://doi.org/10.2478/awutm-2013-0014
Farahani, M.R. (2014) The Second Connectivity and Second-Sum-Connectivity Indices of Armchair Polyhex Nanotubes TUAC6[m, n]. International Letters of Chemistry, Physics and Astronomy, 11, 74-80. https://doi.org/10.18052/www.scipress.com/ILCPA.30.74
Farahani, M.R. (2015) The Hyper-Zagreb Index of TUSC4C8(S) Nanotubes. International Journal of Engineering and Technology Research, 3, 1-6.
Farahani, M.R. (2015) Computing the Hyper-Zagreb Index of Hexagonal Nanotubes. Journal of Chemistry and Materials Research, 2, 16-18.
Farahani, M.R. and Kanna, M.R. (2015) Generalized Zagreb Index of V-Phenylenic Nanotubes and Nanotori. Journal of Chemical and Pharmaceutical Research, 7, 241-245.
Fajtlowicz, S. (1987) On Conjectures of Graffiti-II. Congr. Numer., 60, 187-197.
Gutman, I.O. and Polansky, E. (1986) Mathematical Concepts in Organic Chemistry. Springer-Verlag, New York. https://doi.org/10.1007/978-3-642-70982-1
Gutman, I. (2015) Edge-Decomposition of Topological Indices. Iranian Journal of Mathematical Chemistry, 6, 103-108.
Hayat, S. and Imran, M. (2014) Computation of Certain Topological Indices of Nanotubes. Journal of Computational and Theoretical Nanoscience, 12, 1-7. https://doi.org/10.1166/jctn.2015.3699
Hayat, S. and Imran, M. (2015) Computation of Certain Topological Indices of Nanotubes Covered by C5 and C7. Journal of Computational and Theoretical Nanoscience, 12, 533-541. https://doi.org/10.1166/jctn.2015.3761
Hayat, S. and Imran, M. (2014) Computation of Topological Indices of Certain Networks. Applied Mathematics and Computation, 240, 213-228. https://doi.org/10.1016/j.amc.2014.04.091
Iranmanesh, A. and Pakravish, Y. (2007) Szeged Index of HAC5C6C7 [k, p] Nanotube. Journal of Applied Sciences, 7, 3606-3617.
Ilic, A. Note on the Harmonic Index of a Graph, 1204.3313v1.
Randic, M. (2003) Chemical Graph Theory-Facts and Fiction. Indian Journal of Chemistry A, 42, 1207-1218.
Raut, N.K. and Ipper, S.N. (2015) Computing Some Topological Indices of Nanotubes. International Journal of Scientific and Research Publications, 5, 1-2. http://www.ijsrp.org/research-paper-0815/ijsrp-p4454.pdf
Shehnaz, A. and Imran, M. (2016) On Molecular Topological Properties of Benzenoid Structures. Canadian Journal of Chemistry, 94, 687-698. https://doi.org/10.1139/cjc-2016-0032
Xing, R., Zhou, B. and Trinajstic, N. (2001) Sum-Connectivity Index of Molecular Trees. Journal of Mathematical Chemistry, 47, 583-591. https://doi.org/10.1007/s10910-010-9693-3
Zhong, L. and Xu, K. (2014) Inequalities between Vertex Degree Based Topological Indices. MATCH Communications in Mathematical and in Computer Chemistry, 71, 627-642.
Zhou, B. and Trinajstic, N. (2010) On General Sum-Connectivity Index. Journal of Mathematical Chemistry, 47, 210-218. https://doi.org/10.1007/s10910-009-9542-4
Zhou, B. and Gutman, I. (2005) Further Properties of Zagreb Indices. MATCH Communications in Mathematical and in Computer Chemistry, 54, 233-239.
Zhou, B. and Trinajstic, N. (2010) Minimum General Sum-Connectivity Index of Unicyclic Graphs. Journal of Mathematical Chemistry, 48, 697-703. https://doi.org/10.1007/s10910-010-9702-6
Baca, M., Horváthová, J., Mokrisová, M. and Suhányiova, A. (2015) On Topological Indices of Fullerenes. Applied Mathematics and Computation, 251, 154-161. https://doi.org/10.1016/j.amc.2014.11.069