Chemical graph

The DENDRAL project initiated in 1964 at Stanford was the prototypical application of artificial intelligence techniques - or what was understood at that time under this name - to chemical problems. Chemical structure generators were developed and information from mass spectra was used to prune the chemical graphs in order to derive the chemical structure associated with a certain mass spectrum. 

Clearly, the next step is the handling of a molecule as a real object with a spatial extension in 3D space. Quite often this is also a mandatory step, because in most cases the 3D structure of a molecule is closely related to a large variety of physical, chemical, and biological properties. In addition, the fundamental importance of an unambiguous definition of stereochemistry becomes obvious, if the 3D structure of a molecule needs to be derived from its chemical graph. The moleofles of stereoisomeric compounds differ in their spatial features and often exhibit quite different properties. Therefore, stereochemical information should always be taken into ac-count if chiral atom centers are present in a chemical structure. 

WC. Herndon, Canonical labelling and linear notation for chemical graphs, in Chemical AppUcations of Topology and Graph Theory, R.B. King (Ed.), Elsevier, Amsterdam, 1983, pp. 231-242. 

Figure 6-1. Different forms of representation of a chemical graph a) labeled (numbered) graph b) adjacency matrix c) connectivity table, type I d) connectivity table, type II f) line notations g) structural index.

El-Basil, S. Caterpillar (Gutman) Trees in Chemical Graph Theory. 153, 273-290 (1990)... 

Dias, J.R. Molecular Orbital Calculations Using Chemical Graph Theory Spring-Verlag Berlin, 1993. 

Lajiness MS. Molecular similarity-based methods for selecting compounds for screening. In Rouvray DH, editor, Computational chemical graph theory. New York Nova Science Publishers, 1990 299-316. 

Kier LB (1990) In Rouvray DH (ed) Computational chemical graph theory. Nova Press, NY, chap 6,p 152... 

Wilkens SJ, Janes J, Su AL. (2005) HierS Hierarchical scaffold clustering using topological chemical graphs. J. Med. Chem. 48 3182-3193. 

N. Trinajstic, Chemical Graph Theory. CRC Press, Boca Raton, FL, 1983. 

A brief introduction to the types of molecular representations typically encountered in MSA is presented at the beginning of Subheading 2. followed in Subheading 2.1. by a discussion of similarity measures based on chemical-graph representations. Although graph-based representations are the most familiar to chemists, their use has been somewhat limited in similarity studies due to the difficulty of evaluating the appropriate similarity measures. This section is followed by a discussion of similarity measures based on finite vector representations, the most ubiquitous types of representations. In these cases, the vector components can be of four types ... 

Chemical graphs are ubiquitous in chemistry. A chemical graph, G, can be defined as an ordered triple of sets... 

A key concept in the assessment of molecular similarity based on chemical graphs is that of a maximum common substructure, MCS(G,GJ), of two chem-... 

Fig. 1. An example of two hydrogen-suppressed graphs G1 G2 and a common substructure CSIG,, G2) and the maximum common substructure MCS(G1 G2) are shown above. The Tanimoto similarity index and the distance between the two chemical graphs are computed below.

The edge cardinality of the intersection and union of two chemical graphs is... 

The inner-product terms (, is the labeled graph corresponding to Zth basis fragment, vA is the labeled graph corresponding to molecule A, and STan(G ,GA) is the chemical graph-theoretical Tanimoto similarity coefficient. 

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