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
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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.