Algorithm, Morgan

R. K. Belew and L. B. Booker, Eds., Proceedings of the Fourth International Conference on Genetic Algorithms, Morgan Kaufman, San Mateo, CA, 1991. 

Gallier, J. Curves and Surfaces in Geometric Modeling Theory and Algorithms, Morgan Kaufmann, London, 1999. 

Various methods have been developed for a unique and unambiguous numbering of the atoms of a molecule and thus for deriving a canonical code for this molecule [76]. Besides eigenvalues of adjacency matrices [77], it is mainly the Morgan Algorithm that is used [79]. 

The Morgan Algorithm classifies all the congeneric atoms of a compound and selects invariant-labeled atoms (see Section 2.5.3.1). The classification uses the concept of considering the number of neighbors of an atom (connectivity), and does so in an iterative manner (extended connectivity, EC). On the basis of certain rules. 

Figure 2-42. The Morgan Algorithm generates an unambiguous and unique numbering of phenylalanine (see Tutorial, Section 2,S,J,1).

Two aspects of tlie Morgan Algorithm play a dominant role for structure coding ... 

However, it should not be concealed that in some cases the Morgan Algorithm has problems. In some structures the numbering show oscillatoiy behavior (for an example, sec Figure 2-44). Moreover, although equivalent atoms obtain the same extended connectivity value, it cannot always be concluded that atoms with the same extended connectivity value are equivalent. 

Many variations of the Morgan Algorithm were introduced, because of problems finding the terminating condition of stage 1 (oscillating number of equivalent classes [80]) or special atoms with isospcctral points [81],... 

First, both the skeleton and the ligands at a stereocenter have to be numbered independently of each other. The sites of the skeleton can be numbered arbitrarily but then this numbering has to remain fixed all the time in any further operations. The atoms directly bonded to the stereocenter have to be numbered according to rules such as the CIP rules or the Morgan Algorithm (Figure 2-79). 

The constitution can be represented in an unambiguous and unique manner by canonicalization (Morgan Algorithm). 

T. Leighton, Introduction to Parallel Algorithms and Architectures Arrays, Trees, Hypercuhes, Morgan-Kaufmann, San Mateo, Calif., 1991. 

The Morgan algorithm 5> is a device used by the Chemical Abstracts Service for assigning indices to the nodes of constitutional formulas whose H-atoms have been omitted, i. e. their reduced graphs. If the indices of all atoms are needed, e.g. for the representation of stereochemistry, an additional procedure is needed for establishing those for the H-atoms. Constitutional symmetry is not indicated directly by Morgan indices. 

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