M-Polynomial and topological indices of benzene ring embedded in p-type surface network

• Cancan, Murat ^[1] ; Ediz, Suleyman ^[1] ; Baig, Abdul ^[2] ; Khalid, Waqas ^[3]
  1. [1] Yüzüncü Yıl University

     Yüzüncü Yıl University

     Turquía

     
  2. [2] COMSATS Institute of Information Technology

     COMSATS Institute of Information Technology

     Pakistán

     
  3. [3] Punjab College of Commerce and Science.

  Mostrar afiliaciones +
• 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. 749-768
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2020-04-0047
• Enlaces
  • Texto completo
• Resumen

  • The representation of chemical compounds and chemical networks with the M-polynomials is a new idea and it gives nice and good results of the topological indices. These results are used to correlate the chemical compounds and chemical networks with their chemical properties and bioactivities.

    Particular attention is paid to the derivation of the M polynomia- for the benzene ring embedded in the P-type surface network in 2D. Furthermore, the topological indices based on the degrees are also derived by using the general form of M-polynomial of benzene ring embedded in the P-type surface network BR(m, n). In the end, the graphical representation and comparison of the M-polynomial and the topological indices of benzene ring embedded in P-type surface network in 2D are described.

• Referencias bibliográficas
  • D. Ami?, D. Bešlo, B. Lu?i?, S. Nikoli?, and N. Trinajsti?, “The Vertex-Connectivity Index Revisited”, Journal of chemical information and...
  • K. Yu. Amsharov and M. Jansen, A C78 fullerene precursor: toward the direct synthesis of higher fullerenes, The journal of organic chemistry,...
  • B. Bollobás, P. Erdös, “Graphs of extremal weights”, Ars combinatoria, vol. 50, pp. 225-233, 1998.
  • A. Q. Baig, M. Imran, and H. Ali, “On topological indices of poly oxide, poly silicate, DOX, and DSL networks”, Canadian journal of chemistry,...
  • A. Q. Baig, M. Imran, W. Khalid, and M. Naeem, “Molecular description of carbon graphite and crystal cubic carbon structures”, Canadian journal...
  • G. Caporossi, I. Gutman, P. Hansen, and L. Pavlovi?, “Graphs with maximum connectivity index”, Computational biology and chemistry, vol. 27,...
  • K. C. Das, I. Gutman, “Some properties of the second Zagreb Index”, MATCH communications in mathematical and in computer chemistry, vol. 52,...
  • H. Deng, J. Yang, and F. Xia, “A general modeling of some vertex-degree based topological indices in benzenoid systems and phenylenes”, Computers...
  • E. Deutsch and S. Klavzar, “M-Polynomial, and degree-based topological indices”, Iranian journal of mathematical chemistry, vol. 6, no. 2,...
  • M. V. Diudea, Ed., Nanostructures: novel architecture. New York, NY: Nova Science Publ., 2005.
  • M. V. Diudea and C. L. Nagy, Periodic nanostructures. Dordrecht: Springer, 2007, doi: 10.1007/978-1-4020-6020-5
  • A. A. Dobrynin, R. Entringer, and I. Gutman, “Wiener index of trees: theory and applications”, Acta applicandae mathematicae, vol. 66, no....
  • M. Eliasi and B. Taeri, “Hosoya polynomial of zigzag polyhex nanotorus”, Journal of the Serbian Chemical Society, vol. 73, no. 3, pp. 311–319,...
  • E. Estrada, L. Torres, L. Rodríguez, and I. Gutman, “An atom-bond connectivity index: Modelling the enthalpy of formation of alkanes”, Indian...
  • M. R. Farahani, “Computing fourth atom bond connectivity index of V-phenylenic nanotubes and nanotori”, Acta chimica slovenica, vol. 60, no....
  • M. R. Farahani, “Hosoya polynomial, Wiener and Hyper Wiener indices of some regular graphs”, Informatics engineering, an international journal,...
  • M. R. Farahani, W. Gao, A. Q. Baig, and W. Khalid, “Molecular description of copper(II) oxide”, Macedonian journal of chemistry and chemical...
  • B. Furtula, A. Graovac, and D. Vuki?evi?, “Augmented Zagreb index”, Journal of mathematical chemistry, vol. 48, no. 2, pp. 370–380, Aug. 2010,...
  • W. Gao and M. R. Farahani, “Degree-based indices computation for special chemical molecular structures using edge dividing method”, Applied...
  • W. Gao, M. R. Farahani, and L. Shi, “Forgotten topological index of some drug structures”, Acta medica mediterranea, vol. 32, pp. 579-585,...
  • W. Gao, M. K. Siddiqui, M. Imran, M. K. Jamil, and M. R. Farahani, “Forgotten topological index of chemical structure in drugs”, Saudi pharmaceutical...
  • C. K. Gupta, V. Lokesha, B. S. Shetty, 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 index 30 years after”, MATCH communications in mathematical and in computer chemistry, vol. 50,...
  • I. Gutma and O. E. Polansky, Mathematical concepts in organic chemistry. Berlin: Springer, 1986, doi: 10.1007/978-3-642-70982-1
  • I. Gutman and N. Trinajsti?, “Graph theory and molecular orbitals. Total ?-electron energy of alternant hydrocarbons”, Chemical physics letters,...
  • H. Hosoya, “On some counting polynomials in chemistry”, Discrete applied mathematics, vol. 19, no. 1-3, pp. 239–257, Mar. 1988, doi: 10.1016/0166-218X(88)90017-0
  • S. Hayat, M. A. Malik, and M. Imran, “Computing topological indices of honeycomb derived networks”, Romanian journal of Information science...
  • Y. Hu, X. Li,Y. Shi, T. Xu, and I. Gutman, “On molecular graphs with smallest and greatest zeroth-order general Randi? index”, MATCH communications...
  • Y. Huang, B. Liu, and L. Gan, “Augmented Zagreb index of connected graphs”, MATCH communications in mathematical and in computer chemistry,...
  • Y. C. Kwun, M. Munir, W. Nazeer, S. Rafique, and S. M. Kang, “M-Polynomials and topological indices of V-Phenylenic Nanotubes and Nanotori”,...
  • X. Li and I. Gutman, Mathematical aspects of Randic-type molecular structure descriptors, vol. 1. Kragujevac: University of Kragujevac, 2006.
  • V. Lokesha and T. Deepika, “Symmetric division deg index of tricyclic and tetracyclic graphs”, International journal of scientific & engineering...
  • M. Munir, W. Nazeer, S. Rafique, and S. Kang, “M-Polynomial and related topological indices of nanostar dendrimers”, Symmetry, vol. 8, no....
  • M. O’Keeffe, G. B. Adams, and O. F. Sankey, “Predicted new low energy forms of carbon”, Physical review letters, vol. 68, no. 15, pp. 2325–2328,...
  • K. Pattabiraman, “Inverse sum indeg index of graphs”, AKCE international journal of graphs and combinatorics, vol. 15, no. 2, pp. 155–167,...
  • M. Randi?, “On history of the Randi? index and emerging hostility toward chemical graph theory”, MATCH communications in mathematical and...
  • M. Randi?, “On characterization of molecular branching”, Journal of the American Chemical Society, vol. 97, no. 23, pp. 6609-6615, Nov.1975,...
  • G. Rücker and C. Rücker, “On topological indices, boiling points, and cycloalkanes”, Journal of chemical information and computer sciences,...
  • Y. Shi, “Note on two generalizations of the Randi? index”, Applied mathematics and computation, vol. 265, pp. 1019–1025, Aug. 2015, doi: 10.1016/j.amc.2015.06.019
  • N. Trinajsti?, S. Nikoli?, A. Mili?evi?, and I. Gutman, “O Zagrebaèkim indeksima”, Kemija u industriji, vol. 59, no. 12, pp. 577-589, 2010....
  • D. Vuki?evi? and A. Graovac, “Valence connectivities versus Randi?, Zagreb, and modified Zagreb index: a linear algorithm to check discriminative...
  • D. Vuki?evi? and B. Furtula, “Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges”,...
  • H. Wiener, “Structural Determination of Paraffin Boiling Points”, Journal of the American Chemical Society, vol. 69, no. 1, pp. 17–20, Jan....
  • L. Zhong, “The harmonic index for graphs”, Applied mathematics letters, vol. 25, no. 3, pp. 561–566, Mar. 2012, doi: 10.1016/j.aml.2011.09.059