Abstract
Graph theory, which has become a powerful area of mathematics, owns much advancement in the field of mathematical chemistry. Recently, chemical graph theory has turned into a very popular area among researchers because of its wide-ranging applications in the field of mathematical chemistry. The manipulation and inspection of chemical structural information is made feasible using molecular descriptors. The molecular topological descriptors are the numerical invariants of a molecular graph and are valuable for predicting their bioactivity. An abundant variety of such indices are taken into consideration and used in pharmaceutical researchers, in theoretical chemistry, in drugs and in several other fields. A topological index actually relates a chemical structure by means of a numeric number. In this recent research work, we have considered the chemical graph of magnesium iodide. We computed degree based topological indices. Mainly, we addressed atom-bond connectivity index (ABC), geometric arithmetic index (GA), fourth atom-bond connectivity index (ABC4), The fifth geometric-arithmetic index (GA5), general Randic' index Ra(G) and First Zagreb index M1(G), Second Zagreb index M2(G) for magnesium iodide, MgI2. Furthermore, the results are analysed and we have provided general formulas for all these above mentioned families of graphs that are in fact very helpful in studying the underlying topologies.
Highlights
The branch of chemistry which deals with the chemical structures with the help of mathematical tools is called the mathematical chemistry
Let G be the graph of magnesium iodide with m = 2n + 1 where n ... 1 its first Zagreb index is equal to M (G) = 284n + 172
Let G be the graph of magnesium iodide with m = 2n + 1 where n ≥ 1 its second Zagreb index is equal to M (G) = 543n + 199
Summary
The branch of chemistry which deals with the chemical structures with the help of mathematical tools is called the mathematical chemistry. A molecular graph is a representation of the structural formula of a chemical compound in terms of graph theory, whose vertices correspond to the atoms of the compound and edges corresponds to chemical bonds. The path number was renamed as Wiener index, defined as half of the sum of distances between all ordered pairs of vertices in a graph. With summation going over all pairs of adjacent vertices of the molecular graph G, Randic himself named it “branching index”. The term d d in the definition of the Randic index, is the product of the degrees of the end-vertices of the edge e. In order to take this information into account, Ernesto Estrada conceived a new topological index, He named it “atom-bond connectivity index” which is conveniently abbreviated by ABC. In [10] re-introduced this quantity, and called it “harmonic index”
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