Bounds for neighborhood Zagreb index and its explicit expressions under some graph operations

• Mondal, Sourav ^[1] ; Ali , Muhammad Arfan ; De , Nilanjan ; Pal, Anita ^[1]
  1. [1] National Institute Of Technology

     National Institute Of Technology

     Japón

     
• 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. 799-819
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2020-04-0050
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• Resumen

  • Topological indices are useful in QSAR/QSPR studies for modeling biological and physiochemical properties of molecules. The neighborhood Zagreb index (MN) is a novel topological index having good correlations with some physiochemical properties. For a simple connected graph G, the neighborhood Zagreb index is the totality of square of ?G(v) over the vertex set, where ?G(v) is the total count of degrees of all neighbors of v in G. In this report, some bounds are established for the neighborhood Zagreb index. Some explicit expressions of the index for some graph operations are also computed, which are used to obtain the index for some chemically significant molecular graphs.

• Referencias bibliográficas
  • A. R. Ashrafi, T. Došli?, and A. Hamzeh, “The Zagreb coindices of graph operations”, Discrete applied mathematics, vol. 158, no. 15, pp. 1571–1578,...
  • M. Azari, “Sharp lower bounds on the Narumi-Katayama index of graph operations”, Applied mathematics and computation, vol. 239, pp. 409-421,...
  • R. Bhatia and C. Davis, “A Better Bound on the Variance”, The american mathematical monthly, vol. 107, no. 4, pp. 353–357, Apr. 2000, doi:...
  • Z. Che and Z. Chen, “Lower and upper bounds of the forgotten topological index”, MATCH communications in mathematical and in computer chemistry,...
  • K. C. Das, “On geometrical-arithmetic index of graphs”, MATCH communications in mathematical and in computer chemistry, vol. 64, no. 3, pp....
  • K. C. Das, A. Yurttas, M. Togan, A. Cevik, and I. Cangul, “The multiplicative Zagreb indices of graph operations”, Journal of inequalities...
  • N. De, “Some bounds of reformulated Zagreb indices”, Applied mathematical sciences, vol. 6, no. 101, pp. 5005-5012, 2012. [On line]. Available:...
  • N. De, S. M. A. Nayeem, and A. Pal, “F-Index of some graph operations”, Discrete mathematics, algorithms and applications, vol. 8, no. 2,...
  • J. B. Diaz and F. T. Metcalf, “Stronger forms of a class of inequalities of G. Pólya-G. Szegö, and L. V. Kantorovich”, Bulletin of the American...
  • T. Dosli?, “Splices, links and their degree-weighted Wiener polynomials”, Graph Theory Notes New York, vol. 48, pp. 47-55, 2005.
  • M. Ghorbani and M. A. Hosseinzadeh, “The third version Of Zagreb index”, Discrete mathematics, algorithms and applications, vol. 05, no. 04,...
  • I. Gutman 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,...
  • G. H. Hardy, J. E. Littlewood, and P. George, Inequalities, 2nd ed. Cambridge: Cambridge University Press, 1988.
  • M. H. Khalifeh, H. Yousefi-Azari, and A. R. Ashrafi, “The first and second Zagreb indices of some graph operations”, Discrete applied mathematics,...
  • S. Mondal, N. De, and A. Pal, “On neighborhood Zagreb index of product graphs”, May 2018, arXiv:1805.05273
  • K. Pattabiraman and P. Kandan, “Weighted PI index of corona product of graphs”, Discrete mathematics, algorithms and applications, vol. 06,...
  • G. Pólya and G. Szegö, Problems and theorems in analysis. Berlin: Springer, 1972.
  • N. Trinajsti?, Chemical graph theory. Boca Raton, FL: CRC, 1983.
  • H. Wiener, “Structural determination of the paraffin boiling points”, Journal of the American Chemical Society, vol. 69, no. 1, pp. 17-20,...