Graph-theoretical descriptors

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. 

Local (Atomic) and Global (Molecular) Graph-Theoretical Descriptors ... 

Qraph-Theoretical Indices - Boiling Point Relationships Randic et al. [25] have compared several graph-theoretical descriptors and their use in correlation with boiling points of alkanes [25]. Schultz and Schultz [26] reported the following correlation for alkanes (C2-C15) ... 

However, before progressing further, it is important to note that the prefixes cis vs. trans are metric vs. graph theoretic descriptors... 

Identification of Groupings of Graph Theoretical Descriptors Using a Hybrid Cluster Analysis Approach. 

In addition to the physicochemical domain, the topological features of selected HIV-1 RT inhibitors, 2-(2,6-dihalophenyl)-3-(substituted pyridin-2-yl)-thiazolidin-4-ones (Fig. 26, Table 16), have been analyzed [182] with the empirical, constitutional, and graph theoretical descriptors from the DRAGON software package [47]. This study has resulted in the identification of several influential descriptors to model the inhibitory activity and the equations shown below represent some models stemming from these descriptors. 

Balaban, A.T. (1995b). Local (Atomic) and Global (Molecular) Graph-Theoretical Descriptors. SAR QSAR Environ.Res., 3,81-95. 

Estrada, E. and Gonzalez, H. (2003) What are the limits of applicability for graph theoretic descriptors in QSPR/QSAR Modeling dipole moments of aromatic compormds with TOPS-MODE descriptors. /. Chem. Inf. Comput. Sci., 43, 75-84. 

Estrada, E. and Molina, E. (2001c) QSPR/QSAR by graph theoretical descriptors. Beyond the frontiers, in QSPR/QSAR Studies by Molecular Descriptors (ed. M.V. Diudea), Nova Science, Huntington, NY, pp. 83-107. 

Estrada, E. and Patlewicz, G. (2004) On the usefulness of graph-theoretic descriptors in predicting theoretical parameters. Phototoxicity of polycyclic aromatic hydrocarbons (PAHs). Croat. Chem. Acta, 77, 203-211. 

Taraviras SL, Ivanciuc O, Cabrol-Bass D. Identification of groupings of graph theoretical descriptors using a hybrid cluster analysis approach. J Chem Inf Comput Sci 2000 40 1128-1146. 

Flexibility indices have been developed in terms of distance matrices and related graph-theoretical descriptors. These methods are based on the number of rotatable bonds in a molecule. The actual conformers that are accessible in a given condition are not considered. Nevertheless, these indices can be useful in database searching. A number of techniques have been discussed and compared.2i4... 

The greedy descriptor of Tables 7.7 and 7.8 is quite good but also quite convoluted. The best normal non-convoluted descriptor is the graph-theoretical descriptor of Tables 7.9 and 7.10. The description here needs M as a helpful index, which is a choice physically groimded as this property is really M-dependent. In this descriptor only and ar configuration-dependent. With growing number of indices worsens. The zero-level description has very poor (f (Tables 7.11 and 7.12). 

L. Pogliani, From molecular connectivity to semiempirical terms Recent trends in graph-theoretical descriptors, Chem. Rev. 100 (2000) 3827-3858. 

Thus Randic and Trinajstid [84] found good correlation of chemical shift sums in octanes with the difference of path numbers (p2 - P3), and Miyashita and coworkers [85] found a graph theoretical descriptor, a combination of path numbers (Po + Pi + P2 Ps) to be an excellent descriptor for correlation of chemical shift sums in alkanes. Rucker and Rucker [86] followed by using as descriptors the count of walks of length two (Wj) and of walks of length three (W3) in a molecule, which can be easily obtained from the second and the third power of the adjacency matrix. 

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