Hosoya index

The Hosoya index was applied 2,60 63) to correlations with boiling points, entropies, calculated bond orders, as well as for coding of chemical structures. 

In addition to these, only a limited number of other topological indices of benzenoid molecules have been studied. With a few not too important exceptions, generally valid mathematical results were obtained only for one of them — namely for the Wiener index. Therefore the remaining part of this section is devoted to the Wiener index of benzenoid systems. (Further graph invariants worth mentioning in connection with benzenoids, especially unbranched catacondensed systems, are the Hosoya index [119-121], the Merrifield — Simmons index [122, 123], the modified Hosoya index [38] and the polynomials associated with them.)... 

Other structural invariants have also been considered as parameters influencing the E-value of benzenoid molecules (e.g. the length of linear polyacene fragments [82], the modified Hosoya index [65, 83-85], the number of bay regions [86, 87] etc.). In what follows we focus our attention only to approximate formulas of (n,m)- and of (n,m,K)-type. 

Gutman, I. (1988). On the Hosoya Index of Very Large Molecules. MATCH (Comm.Math.-Comp.Chem.), 23,95-104. 

A modified Hosoya index (or Z index) was defined by a generalization of the Z-counting polynomial by treating the powers of x as independent variables [Randic and Zupan, 2001] ... 

The Wiener-Hosoya index, denoted as W-H, was defined as [Randic, 2004b] ... 

Gutman, I. (1988a) Hosoya index of a class of benzenoid hydrocarbons. /. Serb. Chem. Soc., 53, 129-132. 

Gutman, I. (1988b) On the Hosoya index of very large molecules. MATCH Commun. Math. Comput. Chem., 23, 95-104. 

Gutman, 1., Kolakovic, N., Graovac, A. and Babic, D. (1989b) A method for calculation of the Hosoya index of polymers, in MATH/CHEM/COMP 1988 (ed. A. Graovac), Elsevier, Amsterdam,... 

Gutman, I., Vidovic, D. and Furtula, B. (2002a) Coulson function and Hosoya index. Chem. Phys. Lett., 355, 378-382. 

Randic, M. (2004b) Wiener-Hosoya index - a novel graph theoretical molecular descriptor. J. Chem. Inf. Comput. Sci., 44, yil-im. 

Other well-established indices include the Zagreb index (the sum of the squared vertex valencies, where valency means number of connections to heavy atoms, regardless of bond order) and the Hosoya index [51]. New indices are published regularly to add to the many hundreds that already exist. Many are highly correlated with others procedures to reduce redundancy are discussed in Sec. 3. 

Local vertex invariant based on the adjacency matrix, atomic numbers, and vertex degrees Mean distance topological index for any graph Mean distance topological index for acyclic graphs Hosoya index... 

Garg and Achenie also demonstrated a reasonable approach to the solution of the I-QSAR problem in 2001. " ° Taking a target scaffold of an antifolate molecule for dihydrofolate reductase inhibition, these authors generated a QSAR for both activity and selectivity. They solved the I-QSAR problem to maximize selectivity through changing substitutents on the scaffold, subject to a constraint of a threshold activity. Finally, a work by Skvortsova, et al. " from 2003 demonstrated that the I-QSAR problem could be solved for the Hosoya index plus constraints on the number of carbon atoms for a system of 78 hydrocarbons. 

Des., 2, 70 (2003). Molecular Design of Chemical Compounds with Prescribed Properties from QSAR Models Containing the Hosoya Index. 

The first numerical matrix, using the Hosoya index, is called the edge-Hosoya matrix and is denoted by Z. This matrix was already discussed in the Section 5.12, where it was called simply the Hosoya matrix. If we sum the elements in one triangle of the Z matrix as originally suggested by Hosoya (1971) when he defined the Wiener index from the distance matrix, the double invariant so obtained is called the edge-Hosoya-Wiener index. 

The characteristic polynomial is related to another important polynomial of interest in physics and chemistry, the matching polynomial, the coefficients of which count independent sets of edges in a graph [1]. When added, these counts give the Hosoya index Z [2], one of the early molecular descriptors for structure-property regressions. 

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