Study of topology of block shift networks via topological indices

• Cancan, Murat ^[1] ; Ahmad, Iftikhar ^[2] ; Ahmad, Sarfarz ^[2]
  1. [1] Yüzüncü Yıl University

     Yüzüncü Yıl University

     Turquía

     
  2. [2] COMSATS Institute of Information Technology

     COMSATS Institute of Information Technology

     Pakistán

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. Extra 4, 2020 (Ejemplar dedicado a: Special Issue: Mathematical Computation in Combinatorics and Graph Theory; i), págs. 887-902
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2020-04-0055
• Enlaces
  • Texto completo
• Resumen

  • Topological indices(TIs) are important numerical number associate with the molecular graph of a chemical structure/compound because due to these parameters, one can guess almost all properties of concerned structure/compound with our performing experiments. In recent years, huge amount work has been done for calculating degreedependent indices for different structures/compouds. In order to compute TIs, one need to do many calculations. Our aim of this paper is to present a simple method to compute degree-dependent TIs. We computed M-polynomials for Block Shift Networks and with the help of this simple algebraic polynomials, we recovered nine important TIs for Block Shift Networks. Our work is important for chemists, physicians and pharmaceutical industry.

• Referencias bibliográficas
  • M. S. Anjum and M. U. Safdar, “K Banhatti and K hyper-Banhatti indices of nanotubes”, Engineering and applied science letters, vol. 2, no....
  • A. T. Balaban, “Highly discriminating distance-based topological index”, Chemical physics letters, vol. 89, no. 5, pp. 399–404, Jul. 1982,...
  • G. Caporossi, I. Gutman, P. Hansen, and L. Pavlovi?, “Graphs with maximum connectivity index”, Computational biology and chemistry, vol. 27,...
  • N. De, “Hyper Zagreb index of bridge and Chain graphs”, Open journal of mathematical sciences, pp. 1–17, 2018, doi: 10.30538/oms2018.0013
  • E. Deutsch and Klavžar, “S. M-Polynomial, and degree-based topological indices”, Iranian journal of mathematical chemistry, vol. 6, no. 2,...
  • O. Favaron, M. Mahéo, and J.-F. Saclé, “Some eigenvalue properties in graphs (conjectures of Graffiti — II)”, Discrete mathematics, vol. 111,...
  • B. Furtula, A. Graovac, and D. Vuki?evi?, “Augmented Zagreb index”, Journal of mathematical chemistry, vol. 48, no. 2, pp. 370–380, Apr. 2010,...
  • W. Gao, W. Wang, D. Dimitrov, and Y. Wang, “Nano properties analysis via fourth multiplicative ABC indicator calculating”, Arabian journal...
  • W. Gao, W. Wang, and M. R. Farahani, “Topological indices study of molecular structure in anticancer drugs”, Journal of chemistry, vol. 2016,...
  • M. Ghorbani and N. Azimi, “Notes on mulyiple Zagreb indices”, Iranian journal of mathematical chemistry, vol. 3, no. 2, pp. 137-143, 2012,...
  • C. K. Gupta, V. Lokesha, S. B. Shwetha, and P. S. Ranjini, “On the symmetric division deg index of graph”, Southeast asian bulletin of mathematics,...
  • I. Gutman and K. C. Das, “The first Zagreb indices 30 years after”, MATCH communications in mathematical and in computer chemistry, vol. 50,...
  • G. Liu, Z. Jia, and W. Gao, “Ontology similarity computing based on stochastic primal dual coordinate technique,” Open Journal of Mathematical...
  • J.-B. Liu and X.-F. Pan, “Minimizing Kirchhoff index among graphs with a given vertex bipartiteness”, Applied mathematics and computation,...
  • J.-B. Liu, X.-F. Pan, F.-T. Hu, and F.-F. Hu, “Asymptotic Laplacian-energy-like invariant of lattices”, Applied mathematics and computation,...
  • J.-B. Liu, C. Wang, S. Wang, and B. Wei, “Zagreb indices and multiplicative Zagreb indices of Eulerian graphs”, Bulletin of the Malaysian...
  • J.-B. Liu, J. Zhao, and Z. Zhu, “On the number of spanning trees and normalized Laplacian of linear octagonal?quadrilateral networks”, International...
  • A. Mili?evi?, S. Nikoli?, and N. Trinajsti?, “On reformulated Zagreb indices,” Molecular diversity, vol. 8, no. 4, pp. 393–399, Dec. 2004,...
  • M. Munir, W. Nazeer, S. Rafique, and S. Kang, “M-Polynomial and related topological indices of nanostar dendrimers”, Symmetry, vol. 8, no....
  • M. Munir, W. Nazeer, S. Rafique, and S. Kang, “M-Polynomial and degree-based topological indices of polyhex nanotubes”, Symmetry, vol. 8,...
  • M. Munir, W. Nazeer, S. Rafique, A. R. Nizami, and S. M. Kang, “Some computational aspects of triangular boron nanotube”, Symmetry, vol. 9,...
  • M. Munir, W. Nazeer, Z. Shahzadi, and S. Kang, “Some invariants of circulant graphs”, Symmetry, vol. 8, no. 11, pp. Art ID. 134, Nov. 2016,...
  • S. Noreen and A. Mahmood, “Zagreb polynomials and redefined Zagreb indices for the line graph of carbon nanocones”, Open journal of mathematical...
  • M. Randi?, “Characterization of molecular branching”, Journal of the American Chemical Society, vol. 97, no. 23, pp. 6609–6615, Nov. 1975,...
  • H. M. U. Rehman, R. Sardar, and A. Raza, “Computing topological indices of Hex Board and its line graph”, Open journal of mathematical sciences,...
  • M. Riaz, W. Gao, and A. Q. Baig, “M-Polynomials and degree-based topological indices of some families of convex polytopes”, Open journal of...
  • M. S. Sardar, S. Zafar, and M. R. Farahani, “The generalized Zagreb index of Capra-designed planar benzenoid series Cak(C6),” Open journal...
  • H. Siddiqui and M. R. Farahani, “Forgotten polynomial and forgotten index of certain interconnection networks”, Open journal of mathematical...
  • H. Wiener, “Structural determination of paraffin boiling points”, Journal of the American Chemical Society, vol. 69, no. 1, pp. 17–20, Jan....
  • L. Yan, M. R. Farahani, and W. Gao, “Distance-based Indices computation of symmetry molecular structures”, Open journal of mathematical sciences,...