Graph-theoretic

Another approach applies graph theory. The analogy between a structure diagram and a topological graph is the basis for the development of graph theoretical algorithms to process chemical structure information [33-35]. 

P Koehl, M Delame. A self consistent mean field approach to simultaneous gap closure and side-chain positioning m protein homology modelling. Nature Struct Biol 2 163-170, 1995. R Samudrala, J Moult. A graph-theoretic algorithm for comparative modeling of protein structure. J Mol Biol 279 287-302, 1998. 

Most of the 2D QSAR methods are based on graph theoretic indices, which have been extensively studied by Randic [29] and Kier and Hall [30,31]. Although these structural indices represent different aspects of molecular structures, their physicochemical meaning is unclear. Successful applications of these topological indices combined with multiple linear regression (MLR) analysis are summarized in Ref. 31. On the other hand, parameters derived from various experiments through chemometric methods have also been used in the study of peptide QSAR, where partial least square (PLS) [32] analysis has been employed [33]. 

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

Chinoin-1045 (108) was including a series of structurally divers compounds designing sedative/hypnotic derivatives from novel substruc-tural graph-theoretical approach (98MI11). 

The power group enumeration theorem has been put to a great number of uses, especially in graph theoretical and chemical enumeration. One simple example will illustrate the value of the theorem. 

BalKSO Balasubramanian, K. Graph theoretical characterization of NMR groups, non-rigid nuclear spin species and the construction of symmetry adapted NMR spin functions. J. Chem. Phys. 73 (1980) 3321-3337. 

BalK84 Balasubramanian, K. Comments on graph theoretical analysis of NQR spectra of crystals. Theor. Chem. Acta 64 (1984) 415-419. 

Thomas L. Saaty, On the Problems of Jockeying, Collusion, Scheduling, Optimization, and Graph Theoretic Queues, Office of Naval Research Notes, June, 1961. 

S.C. Basak, V.R. Magnuson, G.J. Niems and R.R. Regal, Determining structural similarity of chemicals using graph-theoretic indices. Discr. Appl. Math., 19 (1988) 17-44. 

A thiepin is formally isoelectronic with the 8ic-electron 1,3,5,7-cyclooctatetraene and 1,3,5-cycloheptatrienide ion and, if planar, may actually be antiaromatic. Recently, the question of the antiaromaticity of thiepin has been the subject of interest for both synthetic and theoretical chemists. The apparent instability of the thiepin ring system is in good agreement with theoretical calculations. Dewar and Trinajstic 68) have reported that the thiepin is considered to be weakly antiaromatic (RE = — 1.45 kcal mol-1) based on PPP SCF MO calculations. On the other hand, Hess Jr. and Schaad 69) have found it to be substantially antiaromatic (RE = —0.232 J) by using the Huckel MO method. This result was also supported by a graph-theoretical treatment by Aihara 70). 

The vertices v and vk are said to be incident with the edge Vj, vkj or adjacent to each other. It should be noted that the pictorial rendition of the set of vertices and edges of an actual network is not always unique. However, if there is a one-to-one correspondence between the vertices and between the edges of two graphs, their graph-theoretic properties will be identical and the two graphs are then said to be isomorphic to each other. 

It is possible to treat dendrograms according to graph-theoretical principles (Frank and Todeschini [1994]). However, in general, the results of clustering are evaluated qualitatively and taken as a basis of extensive studies on data structure. 

A similar approach was undertaken by Mah et al. (1976) in their attempt to organize the analysis of process data and to systematize the estimation and measurement correction problem. In this work, a simple graph-theoretic procedure for single component flow networks was developed. They then extended their treatment to multicomponent flow networks (Kretsovalis and Mah, 1987), and to generalized process networks, including bilinear energy balances and chemical reactions (Kretsovalis and Mah, 1988a,b). 

Randic, M. Graph theoretical descriptors of two-dimensional chirality with possible extension to three-dimensional chirality. J. Chem. Inf. Comput. Sci. 2001, 41, 639-649. 

Other procedures for generating chains from polycyclic fused ring systems and for disconnecting fused rings which use simple graph theoretical approaches have been described.35 They make use of the dual of the molecular graph, i.e. the figure... 

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