Balaban’s J index

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 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 ... 

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. 

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

Balaban, A.T., Mills, D. and Basak, S.C. (2002) Alkane ordering as a criterion for similarity between topological indices index J as sharpened Wiener... 

Balaban, T.-S., Balaban, A.T. and Bonchev, D. (2001) A topological approach to predicting properties of infinite polymers. Part VI. Rational formulas for the normalized Wiener index and a comparison with index J.J. Mol. Struct. (Theochem), 535,81-92. 

Nikolic, S Trinajstic, N. and Mihalic, Z. (1999b) The Detour matrix and the Detour index, in Topological Indices and Related Descriptors in QSAR and QSPR (eds J. Devillers and A.T. Balaban), Gordon and Breach Science Publishers, Amsterdam,... 

Figure 11.65. Cl index of neat PVC and PVC plasticized with diisoundecyl phthalate vs. time of exposure to 290 nm in the presence of air. [Data from Balaban-ovich A 1 Denizligil S Schnabel W, J. Vinyl Additive Technol., 3, No.l, March 1997, p.42-52.]...

R283 R. S. Balaban and A. P. Koretsky, Standard Magnetic Resonance - Based Measurements of the Pi ATP Rate Do Not Index the Rate of Oxidative Phosphorylation in Cardiac and Skeletal Muscles. Comments , Am. J. Physiol., 2011, 301, C12. 

S. Nikolic, N. Trinajstid, and Z. Mihahd, The detour matrix and the detour index, in Topological indices and related descriptors in QSAR and QSPR, ed. J. Devillers and A.T. Balaban, Gordon Breach, Amsterdam, 1999, pp. 279-306. 

D. Babic, D.J. Klein, 1. Lukovits, S. Nikolic, and N. Trinajstic, Resistance-distance matrix A computional algorithm and its application, Int. J. Quantum Chem. 90 (2002) 166-176. A.T. Balaban, Highly discriminating distance-based topological index, Chem. Phys. Lett. 89 (1989) 399-404. 

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