Four Vertex-Degree-Based Topological Indices of VC\(_5\)C\(_7[p;q]\) Nanotubes

Authors

  • Muhammad K. Jamil Department of Mathematics, Riphah Institute of Computing and Applied Sciences (RICAS), Riphah International University, 14 Civic Center, Lahore
  • Aisha Javed Abdus Salam School of Mathematical Sciences, GC University, Lahore
  • Waqas Nazeer Division of Science and Technology, University of Education, Lahore 54000
  • Mohammad R. Farahani Department of Applied Mathematics, Iran University of Science and Technology, Narmak, Tehran
  • Yingying Gao School of Biological Science, Guangzhou University, Guangzhou 510006

DOI:

https://doi.org/10.26713/cma.v8i1.543

Keywords:

Reciprocal Randić index, Reduced reciprocal Randić index, Reduced second Zagreb index, Forgotten index, VC5C7[p, q] nanotube

Abstract

Recently, I. Gutman et al. presented four vertex-degree based graph invariants, that earlier have been considered in the chemical and/or mathematical literature, but, that evaded the attention of most mathematical chemists. These are the reciprocal Randić index (RR), the reduced reciprocal Randić index (RRR), the reduced second Zagreb index (RM\(_2\)) and the forgotten index (F). In this article, we compute these indices of VC\(_5\)C\(_7[p;q]\) Nanotubes.

Downloads

Download data is not yet available.

References

A.R. Ashrafi, B. Bazigaran and M. Sadati, Some experimental conjectures on energy and Estrada index of VC5C7 [4p,8] nanotubes, Optoelectronics and Advanced Materials-Rapid Communications 3 (10) (2009), 1080 – 1082.

A.R. Ashrafi, H. Saati and M. Ghorbani, On distance-based topological indices of HC5C7[4p,8] nanotubes, Digest Journal of Nanomaterials and Biostructures 3 (2008), 227 – 236.

A. Bahrami and J. Yazdani, Padmakar-Ivan index of H-phenylinic nanotubes and nanotore, Digest Journal of Nanomaterials and Biostructures 3 (2008), 265 – 267.

K.C. Das, I. Gutman and B. Furtula, Survey on geometric-arithmetic in-dices of graphs, MATCH Commun. Math. Comput. Chem. 65 (2011) 595 – 644.

K.C. Das and I. Gutman, Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem. 52 (2004), 103 – 112.

T. Doslic, B. Furtula, A. Graovac, I. Gutman, S. Moradi and Z. Yarah-Madi, On vertex-degree-based molecular structure descriptors, MATCH Commun. Math. Comput Chem. 66 (2011), 613 – 626.

M.R. Farahani, Atom bond connectivity and geometric-arithmetic indices Of HAC5C7[p,q] nanotube, International Journal of Chemical Modeling 5 (1) (2013), 127 – 132.

M.R. Farahani, Computing the geometric-arithmetic and atom bond connectivity indices for some nanotubes, Polymers Research Journal 7 (3) (2013), 1 – 6.

M.R. Farahani, Connectivity indices of pent-heptagonal nanotubes VAC5C7[p, q], Advances in Materials and Corrosion 2 (2013), 33 – 35.

M.R. Farahani, First and second Zagreb polynomials of VC5C7[p,q] and HC5C7[p,q] nanotubes, International Letters of Chemistry, Physics and Astronomy 12 (2) (2014), 56 – 62, doi:10.18052/www.scipress.com/ILCPA.31.56.

M.R. Farahani, On the geometric-arithmetic and atom bond connectivity index of HAC5C6C7[p,q] nanotube, Chemical Physics Research Journal 6 (1) (2013), 21 – 26.

M.R. Farahani, On the Randic and sum-connectivity index of nanotubes, Annals of West University of Timisoara-Mathematics and Computer Science 51 (2) (2013), 39 – 46, doi:10.2478/awutm-2013-0013.

M.R. Farahani, On the Randic and sum-connectivity index of some graphs, Algebras, Goups and Geometries 29 (4) (2012), 415 – 422.

M.R. Farahani, The atom bond connectivity ABC and geometric-arithmetic GA indices of pentheptagonal nanotube, PJAM-Pacific Journal of Applied Mathematics 7 (1) (2015), in press.

M.R. Farahani, The first and second Zagreb indices, first and second Zagreb polynomials of HAC5C6C7[p,q] And HAC5C7[p,q] nanotubes, Int. J. Nanosci. Nanotechnol. 8 (3) (September 2012), 175 – 180

M.R. Farahani, Zagreb indices and Zagreb polynomials of pent-heptagon nanotube VAC5C7(S), Chemical Physics Research Journal 6 (1) (2013), 35 – 40.

W. Gao, M.K. Siddiqui, M. Imran, M.K. Jamil and M.R. Farahani, Forgotten topological index of chemical structure in drugs, Saudi Pharmaceutical Journal 24 (3) (2016), 258 – 264, doi:10.1016/j.jsps.2016.04.012.

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

W. Gao, M.R. Farahani, S.H.Wang and M.N. Husin, On the edge-version atom-bond connectivity and geometric arithmetic indices of certain graph operations, Applied Mathematics and Computation 308 (2017), 11 – 17, doi:10.1016/j.amc.2017.02.046

W. Gao, W.F. Wang and M.R. Farahani, Topological indices study of molecular structure in anticancer drugs, Journal of Chemistry ID 3216327, 2016, doi:10.1155/2016/3216327.

W. Gao and W.F. Wang, The eccentric connectivity polynomial of two classes of nanotubes, Chaos, Solitons and Fractals 89 (2016), 290 – 294.

W. Gao and W.F. Wang, The fifth geometric arithmetic index of bridge graph and carbon nanocones, Journal of Difference Equations and Applications 2016, doi:10.1080/10236198.2016.1197214.

M. Ghojavand and, A.R. Ashrafi, Computing the bipartite edge frustration of some nanotubes, Digest J. Nanomaterials and Biostructures 3 (2008), 209 – 214.

I. Gutman and B. Furtula (Eds.), Novel Molecular Structure Descriptors Theory and Applications I, Univ. Kragujevac, Kragujevac (2010).

I. Gutman and B. Furtula (Eds.), Recent Results in the Theory of Randic Index, Univ. Kragujevac, Kragujevac, 2008.

I. Gutman, B. Furtula and C. Elphick, Three new/old vertex-degree based topological indices, MATCH Commun. Math. Comput. Chem. 72 (2014), 617 – 632.

I. Gutman, D. Dimitrov and H. Abdo, On extremal trees with respect to the F-index, arXive:1509303574v1.

I. Gutman and K.C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem 50 (2004), 83 – 92.

I. Gutman and N. Trinajstic, Graph theory and molecular orbitals. Total-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1971), 535 – 538, doi:10.1016/0009-2614(72)85099-1.

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.

A. Iranmanesh, Y. Alizadeh and B. Taherkhani, Computing the Szeged and PI indices of VC5C7[p,q] and HC5C7[p,q] nanotubes, Int. J. Mol. Sci. 9 (2) (2008), 131 – 144.

M.K. Jamil, I. Tomescu and N. Akhter, Extremal degree-product indices of graphs with fixed number of pendant vertices and cyclomatic number, International Letters of Chemistry, Physics and Astronomy 59 (2015), 53 – 61, doi:10.18052/www.scipress.com/ILCPA.59.53.

R. Lang, T. Li, D. Mo and Y. Shi, A novel method for analyzing inverse problem of topological indices of graphs using competitive agglomeration, Appl. Math. Comput. 291 (2016), 115 – 121, doi:10.1016/j.amc.2016.06.048.

Y. Li, L. Yan, M.K. Jamil, M.R. Farahani, W. Gao and J.B. Liu, Four new/old vertex-degree-based topological indices of HAC5C7[p,q] and HAC5C6C7[p,q] nanotubes, J. Comput. Theor. Nanosci. 14 (1) (2017), 796 – 799, doi:10.1166/jctn.2017.6275.

S. Nikolic, G. Kovacevic, A. Milicevic and N. Trinajstic, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003), 113 – 124.

M. Randic, On history of the Randic index and emerging hostility toward chemical graph theory, MATCH Commun. Math. Comput. Chem. 59 (2008), 5124.

M. Randic, The connectivity index 25 years after, Journal of Molecular Graphics and Modelling 20 (2001), 19 – 35, doi:10.1016/S1093-3263(01)00098-5.

Y. Shi, Note on two generalizations of the Randi´c index, Appl. Math. Comput. 265 (2015), 1019 – 1025, doi:10.1016/j.amc.2015.06.019.

S. Wang and B. Wei, Multiplicative Zagreb indices of cacti, Discrete Math. Algorithm. Appl. 8, 1650040 (2016) [15 pages], doi:10.1142/S1793830916500403.

S. Wang and B. Wei, Multiplicative Zagreb indices of k-trees, Discrete Appl. Math. 180 (2015), 168 – 175.

Downloads

Published

30-06-2017
CITATION

How to Cite

Jamil, M. K., Javed, A., Nazeer, W., Farahani, M. R., & Gao, Y. (2017). Four Vertex-Degree-Based Topological Indices of VC\(_5\)C\(_7[p;q]\) Nanotubes. Communications in Mathematics and Applications, 8(1), 99–105. https://doi.org/10.26713/cma.v8i1.543

Issue

Section

Research Article