Topological indices examples

When we are truly clueless, we can nevertheless rely on intuition to propose an ad hoc set of structural and related property parameters for the correlation. We may be lucky and find the hidden variable by chance, and we may be inspired. An example is the topological index, which describes how carbon atoms are connected together, and was proposed in the hope that it would correlate a large range of molecular properties. 

Among the -+ graph-invariants, several substituent descriptors have been defined such as, for example, - Kier steric descriptor, - steric vertex topological index and - fragment molecular connectivity indices. 

Generalized topological indices are calculated by using common formulas of topological indices, where the exponent, if any, is allowed to differ from the standard value (e.g., —1/2 in the Randic connectivity index). Examples of these are the variable Zagreb indices, —> generalized connectivity indices, and —> generalized Wiener indices. 

Besides the most popular —> connectivity indices, Zagreb indices and Schultz molecular topological index, a lot of other topological indices were proposed as a function of vertex degrees of molecule atoms, such as, for example, —> Sh indices, Xu index, and eccentricity-based Madan indices. 

The kappa shape indexes are relatively new descriptors, and few studies have been reported to date. It is expected that the kappa indexes will generally be used along with other topological indexes in QSAR equations rather than by themselves as in most of the examples above. Shape is not the sole determinant... 

The bondonic length of Eq. (1.76) may be further employed into the full partition expression (see below) for modeling the transition between two phases of a nanosystems, for example, an ideal and a modified (with defects) ones, as follows let s consider the topological index computed for ideal net system as well as for the net with (propagating) defects alike, the so called critical temperature 1/ critic phase transition... 

More descriptive topological indexes are sometimes used in place of Schlaefli symbols because of the need to further identify nets with the same Schlaefli symbol (n, p). For example the graphene tessellation with the Wells point symbol 6 has the index (6, 3), which is identical to that of the tessellation of squares, hexagons and octagons with the Well point symbol 4.6.8. Such coincidental patterns are known as topoisomers. 

Full structure search can be developed by using similar approaches to those employed in the case of 2D structure search. Thus, some topological indices can be modified in such a way that they include geometrical information. For example, the global index given by Eq. (4) can be modified to Eq. (11), where are real interatomic distances. 

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