Graph theoretic methods

Koch, I., Kaden, R, Selbig, J. Analysis of protein sheet topologies by graph theoretical methods. Prot Struc. Func. Genet. 12 314-323, 1992. 

Anwander R (1996) Routes to Monomeric Lanthanide Alkoxides. 179 149-246 Anwander R, Herrmann WA (1996) Features of Organolanthanide Complexes. 179 1-32 Artymiuk PJ, Poirette AR, Rice DW, Willett P (1995) The Use of Graph Theoretical Methods for the Comparison of the Structures of Biological Macromolecules. 174 73-104 Astruc D (1991) The Use of p-Organoiron Sandwiches in Aromatic Chemistry. 160 47-96 Baerends EJ, see van Leeuwen R (1996) 180 107-168 Balbds LC, see Alonso JA (1996) 182 119-171... 

Our work has already identified a number of eigenvalue correlations [20], The presence and minimum degeneracy of eigenvalues of e = 0 and + l.Op can be rapidly determined by graph theoretical methods. The following two rules are germane. 

The Use of Graph Theoretical Methods for the Comparison of the Structures of Biological Macromolecules... 

For several years we have been involved in a wide-ranging project to develop methods for the representation and searching of the three-dimensional (3-D) protein structures in the Brookhaven Protein Data Bank [28, 29], Our work derives from the graph-theoretic methods that are used for the storage and retrieval of information pertaining to both two-dimensional (2-D) and 3-D small molecules [1, 58]. 

The publication of Mitchell et al. (1990) [52] led to interest in other groups in the use of graph theoretical methods for protein structure comparison. Notable... 

The graph-theoretical methods are extensively used in the theory of conjugated systems. It is only natural since in this area of chemistry the HMO method was used most frequently. In the next chapters we shall dwell on some interesting results derived in the topological theory of conjugated and aromatic systems. 

In this chapter we shall discuss some significant results obtained in the theory of conjugated organic molecules by the graph-theoretical methods. 

Counting indistinguishable reactions. The number of indistinguishable reactions is determined by means of the enumeration polynomial whose coefficients are calculated by the graph-theoretical methods and the methods of permutation group theory. We cannot describe here the procedure of finding the coefficients of the enumeration polynomial, and so we shall consider only several concepts that are necessary for translation of mathematical results into the language of chemistry. 

In this section we shall describe two approaches to the shape characterization of the large-scale features of chain molecules one based on a graph-theoretical method, the other on a family of knot theoretical polynomials [112,197,198]. 

Romanowska, K. (1992). The Application of the Graph Theoretical Method in the QSAR Scheme Possibilities and Limits. Int.J.Quant.Chem., 43,175-195. 

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