Balaban J index

Z eb index, Wiener index. Balaban J index, connectivity indices chi (x), kappa (k) shape indices, molecular walk counts, BCUT descriptors, 2D autocorrelation vector... 

Wiener-type index from Z weighted distance matrix (Barysz matrix) Wiener-type index from mass weighted distance matrix Wiener-type index from van der Waals weighted distance matrix Wiener-type index from electronegativity weighted distance matrix Wiener-type index from polarizability weighted distance matrix Balaban J index... 

Estrada, E. and Gutierrez, Y. (2001) The Balaban J index in the multidimensional space of generalized topological indices. Generalizations and QSPR improvements. MATCH Commun. Math. Comput. Chem., 44, 155—167. 

The number of vertices and edges in a molecular graph are examples of simple topological indices. More complex structural descriptors were presented in Section 7 on molecular matrices and Section 8 on molecular graph polynomials. We mention here some of the most used topological indices the Wiener W index the Randid connectivity index x extended by Kier and Hall the Hosoya Z index and the Balaban J index. > ... 

Jenkins steric parameter -> steric descriptors Jt index -> Balaban distance connectivity indices J/J index -> bond order indices (O graphical bond order)... 

Moreover, the complement Balaban index J [Nikolic, Plavsic et al, 2001] or reversed Balaban index 1/J [Randic and Pompe, 2001b] was derived as a Balaban-like index as... 

Moreover, the spectral indices MinSp RW) and MaxSp RW), the Hosoya-type index Ho (RW), the hyper-Wiener-type index HyWi(RW), the Balaban-like index J(RW), and Balahan-like information indices (J(RW), V(RW), X(RW), and Y(RW) were tested in property modeling of some alkanes [Ivanciuc, Ivanciuc et al., 2002b],... 

Half-sum of the cube of the adjacency matrix Polarity number number of third neighbors Gordon-Scantlebury index number of second neighbors Number of paths of length /i = 0-10 Balaban s J index based on distance Balaban s J index based on multigraph bond orders Balaban s J index based on relative electronegativities Balaban s 7 index based on relative covalent radii Balaban s information-based indexes on distance sums... 

Balaban " defined a series of indexes based on distance sums within the distance matrix for a molecular graph which he designated as J indexes. Unlike W, these indexes are independent of molecular size and have low degeneracy. 

Balaban s J index—for each of the adjacent pairs of vertices i, j one computes the product of distance sums SiSj and then obtains the average distance sum connectivity denoted by J ... 

The third model (QSAR 25) developed using the hvdrogen bond descriptor FCPSA (a charge-weighted analog of FPSA [91]), first moment of inertia (J ) and the Balaban topological index (/, a measure of molecular... 

One such new theory has been the common vertex matrix [2], which has led to a novel approach to graph eccentricities and network eccentricities, based on the count of pairs of vertices at equal distance from each vertex in a graph [3]. A preliminary study has shown that the connectivity-type index based on the vertex centrality values displays considerable discriminatory power in differentiating between similar structures, including very similar structures among isomers. The discriminatory power of a centrality-based connectivity index exceeds visibly the discriminatory power of Balaban s J index [4-6], which is a distance matrix analog of the connectivity index. 

FIGURE 8.1 The six pairs of dodecane graphs that have identical Balaban s index J. 

When the row sums as entries in construction of the connectivity-type indices are applied to the adjacency matrix of molecular graphs, one obtains the connectivity index % of Randid [10,11]. When they are applied to the graph distance matrix, one obtains Balaban s index J [12]. Both indices, x and J, have been very nseful in QSAR, which is an incentive to explore properties of additional structural indices of this type. At our disposal are several novel sparse matrices that have been recently introduced in chemical graph theory, which, in the view that their row sums cover a wider range of values, can be expected to produce novel highly discriminatory topological indices. 

R. Natarajan, S. C. Basak, A. T. Balaban, J. A. Klun, and W. F. Schmidt. Chirality index, molecular overlay and biological activity of diastereoisomeric mosquito repellents. Pest Management Science, 61, 1193-1201, 2005. 

Balaban Index The Balaban index, J, has been introduced as the average-distance sum defined as the sum of the squares of the reciprocal nonzero distances in D (6,7] ... 

Ivanciuc T, Klein DJ, Seitz WA, Balaban AT, Wiener index extension by counting even/odd graph distances, J. Chem. Inf. Comput. Sci., 41(3), 2001. 

In order to account for both bond multiplicity and heteroatoms, Balaban modified distance connectivity indices and J were proposed [Balaban, 1986a Balaban et al., 1990a]. These are defined in the same way as the Balaban distance connectivity index but derived from the multigraph distance matrix D instead of the original distance matrix D ... 

Another generalization of the Balaban index J, so as to account for heteroatoms in the molecule, is the - Barysz index calculated on the - Barysz distance matrix. 

In analogy with the Kier-Hall - connectivity indices x and the Balaban distance connectivity index J, JJ indices [Randic et al, 1994a] are derived from the Wiener matrix based on the Wiener matrix degrees q, ... 

Balaban, A.T. and Quintar, L.B. (1983). The Smallest Graphs, Trees and 4-lVees with Degenerate Topological Index J. MATCH (Comm.Math.Comp.Chem.), 14, 213-233. 

Balaban, A.T. (1986a). Chemical Graphs. Part 48. Topological Index J for Heteroatom-Containing Molecules Taking into Account Periodicities of Element Properties. MATCH (Comm. Math.Comp.Chem.), 21,115-122. 

Balaban, A.T. and Ivanciuc, O. (1989). FORTRAN-77 Computer Program for Calculating Topological Index J for Molecules Containing Heteroatoms. In MATH / CHEM / COMP 1988 (Graovac, A., ed.), Elsevier, Amsterdam (The Netherlands), pp. 193-211. 

Balaban, A.T., Catana, C., Dawson, M. and Niculescu-Duvaz, I. (1990a). Applications of Weighted Topological Index J for QSAR of Carcinogenesis Inhibitors (Retinoic Acid Derivatives). Rev.Roum.Chim.,35, 997-1003. 

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