Chemical graph theory
The chemical graph theory deals with the formalization and application of graph theoretical principles in the field of chemistry , especially chemoinformatics . The subject of chemical graph theory is the processing of molecular structures .
Important applications are the identification of substructures , for example for group contribution methods , topological indices , the speculation of molecular structures and the calculation of characteristic polynomials .
Typical molecular representations as a graph
Molecular structures are mostly stored in matrix form; these are typical forms of representation
- Adjacency matrix , which has as many columns and rows as there are atoms, and which records the existence of the connection between the atoms
- Distance matrix , which has as many columns and rows as atoms and shows the distances between two atoms. The distance can be the number of bonds on the shortest path or the spatial distance.
- Incidence matrix that has as many columns as atoms and rows as bonds, listing the atoms that each bond connects.
- Binding matrix, which is a variant of the adjacency matrix, but which also records the binding order.
An alternative representation is the link list, which is mostly used by graphics programs and offers space for more information. The bond list usually contains a list of atoms including, for example, the coordinates, atom types, charges, etc. and then a list of the bonds with the details of the connected atoms including the bond order and other geometric information.
literature
- Ivan Gutman, " Mathematical concepts in organic chemistry ", Berlin, Springer 1986
- IS Dimitriev, “ Molecules without chemical bonds? Topology, graph theory and structure of the molecules. “, Leipzig, VEB German publishing house for basic industry, 1982
- Karl Kaindl, " Graph Theoretical Modeling and Analysis of Protein Structures ", Diss., University of Munich, 1998