Arithmetical, topological, and geometrical descriptors

As D neglects hydrogen atoms, it is helpful to introduce the following notation for the non-H atoms in a given labeled molecular graph M = (e, y) M , 

Moreover, we recall that we consider the multigraph y, the bond graph y , a simple graph obtained by reducing the multiplicities to 1, as well as the graph y of the H-suppressed molecule, and also its bond graph y . All in all, the evaluation of descriptor values makes use of the following data  

1 Example (Arithmetical descriptors) We recall a few basic arithmetical descriptors - Let M = (e, y) M be a molecular graph. The purely arithmetic indices A and A are the counts of all or of the non-H atoms, obtained from the function A with its values 

There is, of course, also the count of atoms of element X, using NxiM) = (n 

Here is the meeui atomic mass of element X (see Definition 8.22). Table 7.1 shows mean atomic masses (in daltons, 1 Da is defined as 1/12 of the mass of a C atom) of the X e u. 

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The standard reference for molecular descriptors is the encyclopedic book [304]. Descriptors can be split into three main groups arithmetical, topological and geometrical descriptors. 

This appendix contains lists of molecular descriptors available in MOLGEN-QSPR, arithmetical, topological, and geometrical descriptors. Some were introduced in this book, the specifications of others can be found in [34,262). 

MOLGEN MOLGEN Freely available web-service that calculates 708 arithmetical, topological and geometrical descriptors http // molgen.de/... 

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