Indices Randic

Other quite frequently used indices are the Randic index and the information-topological indices such as the Bonchev index (see Chapter VIll, Section 1 in the Handbook), Up to now several hundred indices have been devised. 

The information analogue of the Randic index, %R, was defined 83) by partitioning the graph edges into classes, depending on the equality of their partial connectivity... 

There are numerous reports on good performances of the molecular connectivity index, Randic index [55], and its modifications [44] in predicting retention of congeneric analytes, including isomers. The correlations are good when retention is on non-polar stationary phases, but not good when on polar phases. Whereas on the non-polar phases the nonspecific dispersive interactions determine differences in retention among the analytes, the more specific polar interactions become discriminative in the case of polar phases (and polar solutes) [7]. 

Kier and Hall defined [Kier and Hall, 1986 Kier and Hall, 1977b] a general scheme based on the Randic index to calculate also zero-order and higher-order descriptors, thus obtaining connectivity indices of m th order, usually known as Kier-Hall connectivity indices. They are calculated by the following ... 

Connectivity Index (Randic index) is a molecular descriptor based on the sum of degrees over all adjacent atoms in a molecular graph. 

NikoUc-Trinajstic-Randic index Wiener index... 

The Nikolic-Trinajstic-Randic index, denoted by " W and called by the authors of this book modified Wiener index, is defined according to the original Wiener definition but using the reciprocal of the number of vertices on each side of the bond [Nikolic, Trinajstic et al, 2001b Randic and Zupan, 2001] ... 

Araujo, O. and Rada, J. (2000) Randic index and lexicographic order./. Math. Chem., 27, 201-212. 

Favaron, O., Maheo, M. and Sacle, J.-F. (2003) The Randic index and other Graffiti parameters of graphs. MATCH Commun. Math. Comput. Chem., 47, 7-23. 

Hu, Y, Li, X., Shi, Y, Xu, T. and Gutman, I. (2005) On molecular graphs with smallest and greatest zeroth-order general Randic index. MATCH Commun, Math, Comput. Chem., 54, 425-434. 

Rada, J., Araujo, O. and Gutman, 1. (2001) Randic index of benzenoid systems and phenylenes. Croat. Chem. Acta, 74, 225-235. 

Molecular graph-based descriptors can also be calculated using the cxcalc command. Here, let us compute Randic index [40] and Wiener index [41] which are important molecular connectivity descriptors. Randic index, also called bond index, is the snm of bond contribntions in a molecnle and Wiener path is a topo-logic index describing the shortest path between all pairs of vertices. The syntax of the commands is cxcalc randicindex test ameslOO.smi and cxcalc wienerindex test ameslOO.smi (Fig. 2.6). 

Xueliang L, Yongtang S, Wang L (2012) On a relation between randic index and algebraic connectivity. Match 68(3) 843-839... 

In spite of existence of a large number of descriptors [9], the main idea of their calculation can be illustrated with Wiener number (W) and connectivity indices of zero-order ( ) and hrst-order the latter is also known as Randic index [8, 12-15]. 

I. Gutman and B. Furtula, eds.. Recent results in the theory of Randic index, University of Kragujevac, Kragujevac, Serbia, 2008. 

The Randic index (x) is the sum of the p, terms. Let 8 be the degree of a vertex of the graph and then define 5, and Sj as the degrees of two vertices that are connected. The link (edge) between these vertices is characterized by p (the inverse of the geometrical mean of the degrees). The sum of all p values is the index Randic X... 

Gravitation index (all atoms) 1001.7 Gravitation index (bonded atoms) 712.7 Electronic index (all atoms) 6.83 Electronic index (bonded atoms) 4.49 Wiener index 26.0 Randic index 2.87 Balaban index 2.10... 

Gravitation index (all atoms) 10420.2 Gravitation index (bonded atoms) 4265.5 Electronic index (all atoms) 29.55 Electronic index (bonded atoms) 12.69 Wiener index 4044.0 Randic index 20.35 Balaban index 0.83... 

Gravitation index (all atoms) 10297.0 Gravitation index (bonded atoms) 4216.75 Electronic index (all atoms) 43.63 Electronic index (bonded atoms) 21.84 Wiener index 4336.0 Randic index 18.59 Balaban index 0.94... 

Electronic index (bonded atoms) 19.46 Wiener index 2086.0 Randic index 13.94 Balaban index 0.94... 

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