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Geometric-Arithmetic Index
Published in Mihai V. Putz, New Frontiers in Nanochemistry, 2020
A chemical reaction can be represented as the transformation of the chemical (molecular) graph representing the reaction’s substrate into another chemical graph representing the product. The type of chemical reaction where two substrates combine to form a single product (combination reaction) motivated Ramakrishnan et al. (2013) to study the effect of topological indices, particularly GA, when a bridge is introduced between the respective vertices (of degree i, i = 1,2,3) of two copies of the same graph. The authors claimed that the graph obtained in this manner may or may not represent a stable chemical compound in reality, but it is the interest of the chemist to check the stability of the so obtained structure of the resulting graph. Ramakrishnan et al. (2013) also presented an algorithm to compute the distance matrix of the resultant graph obtained after each iteration and thereby tabulated various topological indices including GA.
Studying some networks using topological descriptors and multi-criterion decision making
Published in Molecular Physics, 2023
Guoping Zhang, Arfa Mushtaq, Adnan Aslam, Saima Parveen, Salma Kanwal
In 1947, the chemist ‘Harold Wiener’ [1] firstly used the term of topological index. In graph theoretical language, the wiener index is equal to the sum of lengths of minimum paths between all the pair of vertices in a graph [2]. Let G be a simple connected graph with the vertex set and edge set denoted by and respectively. In a molecular graph, the atoms represent the vertices and the bond between the atoms is represented by the edges. If e is an edge/bond of G, that connects the two vertices/atoms and , then we write and say that the two vertices ‘ and are adjacent’. For a vertex , the number of edges incident to the vertex is called the degree of vertex and is denoted as [3].
Analysis of porphyrin, PETIM and zinc porphyrin dendrimers by atom-bond sum-connectivity index for drug delivery
Published in Molecular Physics, 2023
Rong-Rong Huang, Sahar Aftab, Sadia Noureen, Adnan Aslam
There have been numerous research papers on dendrimers found in [27–31]. In this study, we compute the atom-bond sum-connectivity index (ABS) for three dendrimers . This contains information regarding the implementations of PETIM and porphyrin in [32,33]. We contemplate their structure in terms of chemical graphs. In a molecular graph, atoms are depicted as vertices, while the edges display the bonds linking those atoms. A molecular graph's vertex and edge sets are denoted by the symbols and , respectively. The degree of a vertex is denoted by . We use the notation to denote that the vertices x, y are adjacent. For basic definitions related to graph theory, the readers can see [7].
Mathematical analysis of one-dimensional lead sulphide crystal structure using molecular graph theory
Published in Molecular Physics, 2022
Yogesh Singh, Sunny Kumar Sharma, Purnima Hazra
Mathematical chemistry is a field of study that focuses on new mathematical applications in chemistry. It is primarily concerned with the mathematical modelling of chemical phenomena which include molecular graphs and their topological indices. This is concerned with topologies, such as the mathematical study of isomerism and the establishment of topological indices or descriptors that are used in quantitative structure–property relationships. Secondly, there are chemical aspects of group theory, which are useful in quantum chemistry and stereochemistry. Apart, topological indices are invariants that are used to study the properties of chemical compounds, which results in understanding the structural formula of chemical compounds. In a molecular graph, the atoms of a chemical compound are represented by the vertices of a graph, while the chemical bonds are represented by the edges [6].