Molecular identification number

Burden, F. R. Molecular identification number for substructure searches. 

In most the cases, molecular identification numbers are obtained as the half-sum of atomic identification numbers over all graph vertices. Otherwise, by summing atomic ID numbers only over the atoms belonging to molecular fragments such as functional groups, fragment ID numbers (or subgraph ID numbers) are obtained. 

A list of molecular identification numbers is given below. Other important ones are the Hosoya ID number, the -> hyper-Wiener index, the - restricted walk ID number, and the total topological state, defined elsewhere. 

It is the molecular identification number proposed first [Randic, 1984b Szymanski et al, 1985 Randic and Trinajstic, 1993a] and is defined as a weighted molecular path count ... 

A molecular identification number [Balaban, 1987a] defined as ... 

Burden, F.R. (1989). Molecular Identification Number for Substructure Searches. J.Chem.lnf... 

Randic, M. (1984b). On Molecular Identification Numbers. J.Chem.Inf.Comput.Sci, 24,164-175. Randic, M. (1986a). Compact Molecular Codes. J.Chem.Inf.Comput.ScL, 26,136-148. 

Burden, P. R. Molecular identification numbers for substructure searches. J. Chem. Inform. Comput. Sci. 1989,29, 225—228. 

This is a molecular identification number defined as [Balaban, 1987]... 

Randic, M. (1984b) On molecular identification numbers./. Chem. Inf. Comput. Sci., 24,164—175. 

Hydrogen bonding potential of molecule Molecular identification numbers Volume of molecule 3D Wiener number including hydrogens 3D Wiener number without hydrogens... 

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. 

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 /. 

M. Dehmer and M. Grabner, The discrimination power of molecular Identification Numbers revisited, MATCH Commun. Math. Comput. Chem. 69 (2013) 785-794. 

Pearlman RS (1995) Diverse solutions user s manual. University of Texas, Austin Burden F (1989) Molecular identification number for substructure searches. J Chem Inf Comput Sci 29 225-227... 

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