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GAP Programming
Published in Mihai V. Putz, New Frontiers in Nanochemistry, 2020
Yaser Alizadeh, Ali Iranmanesh
The chemical graph theory is a branch of mathematical chemistry that is mostly concerned with finding topological indices of chemical graphs that correlate well with certain physicochemical properties of the corresponding molecules. The GAP program is used to finding topological indices of molecular graphs. The following GAP program (Iranmanesh et al., 2009) is an example of its nanochemical applications. By this program topological indices as Wiener polynomial, Wiener index and hyper Wiener index of IPR isomers of C80 fullerene. The structure of the IPR Isomer of C80 fullerene is shown in Figure 20.1.
Structure–activity relations for antiepileptic drugs through omega polynomials and topological indices
Published in Molecular Physics, 2022
Medha Itagi Huilgol, V. Sriram, Krishnan Balasubramanian
Wiener index was the first topological index defined by Wiener [12] in QSPR who showed that his index was well aligned with the boiling points of the alkane. Physical and chemical properties of organic substances, which can be expected to depend on the area of the molecular surface and/or on the branching of the molecular carbon-atom skeleton, are usually well correlated with the Wiener index. Its generalisation is named the hyper-Wiener index. There are most important topological indices defined in chemical graph theory based on degrees of vertices. A survey by Gutman [16] lists all these degree-based topological indices. This survey also contained a report on the results of a comparative test of how well some of these distance-based topological indices are correlated with physico-chemical parameters of octane isomers. It is almost like a customary in papers dealing with topological indices is that, for a given family of graphs, determine a closed formula for a given (degree-based) topological index. To overcome this particular approach in the area of degree-based indices, Deutsch et al. [17] introduced the M-polynomial and demonstrate that in numerous cases a degree-based topological index can be expressed as a certain derivative or integral (or both) of the corresponding M-polynomial. This implies that knowing the M-polynomial of a given family of graphs, a closed formula for any such index can be obtained routinely. Hence, the topological indices derived from M-polynomial, all the six ABC indices, Wiener and Hyper-Wiener indices for all chemicals is listed in Table 4.