Graph theoretical characterization

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. 

Balasubramanian, K., Kaufmann, J.J., Koski, W.S. and Balaban, A.T. (1980). Graph Theoretical Characterization and Computer Generation of Certain Carcinogenic Benzenoid Hydrocarbons and Identification of Bay Regions. J.Comput.Chem., 1,149-157. 

Pogliani, L. (1994b). On a Graph Theoretical Characterization of Cis/Trans Isomers. J.Chem.lnf. Comput.ScL, 34,801-804. 

Graph Theoretical Characterization Computer Generation of Certain Carcinogenic... 

M. Randic, A graph theoretical characterization of proteomics maps, Int. J. Quantum Chem. 90 (2002) 848-858. 

Graph theoretical characterization and computer generation of certain carcinogenic benzenoid hydrocarbons and identification of bay regions were reported by K. Balasubramanian, J. J. Kaufman, and W. S. Kosky in 1980, almost 35 years ago [28]. 

A Brief Review of the QSAR Technique. Most of the 2D QSAR methods employ graph theoretic indices to characterize molecular structures, which have been extensively studied by Radic, Kier, and Hall [see 23]. Although these structural indices represent different aspects of the molecular structures, their physicochemical meaning is unclear. The successful applications of these topological indices combined with MLR analysis have been summarized recently. Similarly, the ADAPT system employs topological indices as well as other structural parameters (e.g., steric and quantum mechanical parameters) coupled with MLR method for QSAR analysis [24]. It has been extensively applied to QSAR/QSPR studies in analytical chemistry, toxicity analysis, and other biological activity prediction. 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-squares (PLS) analysis has been employed [25]. 

A category of reactions with a characteristic irreducible R-matrix is a set of basis reactions. The basis reactions correspond to the traditional classification of organic reactions . A basis reaction is best characterized in graph theoretical terms (ref. 13). The educts and the products of a basis reaction are expressed by a graph (see Fig. 7.2) whose nodes correspond to the reactive centers and whose lines indicate the bond orders of the covalent bonds that are directly affected by the reaction. The... 

Many different approaches to QSAR have been developed since Hansch s seminal work. These include both 2D (two-dimensional) and 3D (three-dimensional) QSAR methods. Most of the 2D QSAR methods employ graph theoretic indices to characterize molecular structures, which have been extensively studied by Radio, Kier and Hall. Similarly, ADAPT system employs topo-... 

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]. 

Basak, S.C., Niemi, G.J. and Veith, G.D. (1990c). Recent Developments in the Characterization of Chemical Structure Using Graph-Theoretic Indices. In Computational Chemical Graph Theory and Combinatorics (Rouvray, D.H., ed.). Nova, New York (NY), pp. 235-277. 

Graph theory offers many useful characterizations of molecules. If the molecular property is bond additive, the modeling by graphs is quite adequate. Graph theory, even when not explicitly mentioned, has been behind many successful mathematical or quantum-chemical models. For example, Hameka studied the magnetic susceptibility of alkanes from a quantum-chemical point of view. " However, the very same quantum-chemical model can be translated without difficulties in the graph theoretical terms when it leads to even simpler expressions for the same magnetic susceptibilities. """"" ... 

Though a powerful classification result for topologically spherical S, this theorem does not seem to extend (simply) to x(-S ) 5 0. Still for thexf-S) = 0 case this theorem reduces the characterization of these equivalence classes to a standard graph-theoretic problem. 

Anisometry. Characterized by properties depending on inertia axes, symmetry axes, and distance distributions. Descriptors include the moments of inertia X,, the molecular eccentricity e, the asphericity fl, and the length of the principal axes of minimal ellipsoidal cavities, as well as distance matrices, contact maps, and some graph-theoretical indices. 

Petri Net is a mathematical formalism it can be considered as a graph theoretical tool to model and analyze discrete event dynamic systems which exhibit parallel evolution and whose behavior is characterized by synchronization and sharing phenomena [19],... 

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