Molecular ID Numbers

The modified connectivity indices have been used for construction of the molecular identification (ID) numbers, a new kind of molecular descriptor, which have been found to have exceptional discrimination power [75]. In Table 6.10, we have illustrated the construction of the molecular ID number for a small molecule containing 

The search for pairs of graphs having the same molecular ID number or molecular prime number ID can be viewed as an illnstration of experimental mathematics or, if you wish, experimental chemical graph theory. The concept of molecular ID numbers has been extended later to cover rings [81] and alternative ID numbers were considered [82]. The examination of the discrimination power of molecular identification numbers has been very recently revisited [83-86], clearly indicating that this topic has not yet been completely explored. New indices have outperformed earlier ones and show limits of classical measnres, such as the Balaban index /. 

FIGURE 6.3 Pair of graphs on 15 vertices having the same molecular ID number. 

9 RECENT MODIFICATION OF THE HIGHER-ORDER CONNECTIVITY INDICES 

and are the degrees of vertices forming a path of length two, and the summation is carried over aU paths of length two in a molecule. Similarly, is defined as 

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A molecular ID number of a graph with A vertices derived from the Randic connectivity ID number with the aim of obtaining much faster calculations, also for large polycyclic graphs [Ivanciuc and Balaban, 1996b]. 

A molecular ID number of a graph with A vertices defined as a function of the sum of weighted walks [Szymanski et al., 1986b]. The weight of an edge is the reciprocal of the square root of the product of the vertex distance degrees a of the vertices incident to the edge. 

The Self-returning ID number (SID) is a molecular ID number [Muller et al., 1993] of a graph defined as the sum of weighted self-returning walks of any length ... 

A molecular ID number where each path ""pij of length m is weighted by the following ... 

As the diagonal entries are just the vertex degrees 6, the first term on the right is the - total adjacency index Ay The topological state index is one of the -> molecular ID numbers. 

Randic, M. (1986b). Molecular ID Numbers By Design. J.Chem.Inf ComputScL, 26,134-136. Randic, M., Oakland, D.O. and Klein, D.J. (1986). Symmetry Properties of Chemical Graphs. IX. 

Szymanski, K., Muller, W.R., Knop, J.V. and Trinajstic, N. (1986a). Molecular ID Numbers. Croat.Chem.Acta, 59,719-723. 

This is a molecular ID number defined in terms of paths " py of length m weighted by the following [Hu and Xu, 1997] ... 

Molecular identification numbers (ID) were introduced in 1984 [10] and have been used as molecular descriptors in QSAR [11] although they were constructed initially as a tool for identification of highly similar molecules. We should add that the problem of identification of highly similar molecules is different and distinct from the problem of graph isomorphism in the sense that for the former occasional occurrence of identical ID numbers for distinct structures is acceptable (as it may point to very similar structures), and in the latter, the occurrence of identical numerical values for different structures points to a failure of the approach. In the following section, we give more information on molecular ID numbers and their properties. 

Hence, one may consider construction of new molecular descriptors of very high discriminatory power specifically designed for screening combinatorial libraries one unsolved problem in this area. Observe that Lahana and coworkers used available molecular descriptors, most of which have limited discrimination powers and have been intended for use in MRA. There have been few molecular descriptors of very high discrimination power available, such as the molecular ID numbers [2,3-5], but they may not be suitable for screening combinatorial libraries because they are computationally intensive. 

Research continues into new and. specialized chemical representations. At the level of indexes, the venerable concept of molecular ID numbers has re.surfaced as a critical component in a 3D chemical diversity partitioning scheme, in addition, hierarchical fragment indexes have been implemented with a tremendous enhancement in search performance. The primary driver for the introduction of new representations is the recent focus on the needs of combinatorial chemistry for library design, specification, storage and retrieval. Noteworthy examples are CHUCKLES and CHORTLES, both extensions of SMILES the former supports the representation of peptide and peptoid sequences on both the monomer and atomic levels, and the latter allows the representation of mixtures as simple strings of characters. 

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