Chemical Significance of Some Neighborhood Degree-Based Molecular Descriptors

Molecular graphs encrypt the structure of a chemical compound and their topological indices provide an insight into its physical and chemical properties and activities. In this article, the chemical applicability of some neighborhood-degree based topological indices like the neighborhood modified first Zagreb index ( \(~^{m}{N M_{1}}(\Gamma )\) ), neighborhood inverse degree index ( \(NID(\Gamma )\) ), neighborhoood zeroth order index ( \(N Z(\Gamma )\) ) and the fifth geometric-arithmetic index ( \(GA_5\) ) has been explored. Furthermore, four cases have been considered in terms of number of rows of hexagon (r) and number of hexagons in each row (s) in the honeycomb-lattice of graphene and explicit expressions for aforesaid indices as well as the neighborhood versions of the sum-connectivity index and the Randic index like the general fifth \(M_1\) -Zagreb index ( \(M_{1}^{a}G_5(\Gamma )\) ) and general fifth \(M_2\) -Zagreb index ( \(M_{2}^{a}G_5(\Gamma )\) ) have been determined. Also, a graphical comparison of the four indices \(~^{m}{N M_{1}}(\Gamma )\) , \(NID(\Gamma )\) , \(N Z(\Gamma )\) and \(GA_5(\Gamma )\) is made for graphene.