Centric indices

The centric indices correlated the best out of the known topological indices with the octane number of alkanes 66). 

The classical definition for the graph centre is not helpful for cyclic graphs where often a large number of vertices (most of them topologically non-equivalent) appear as central. Recently, Bonchev, Balaban and Mekenyan 67) proposed a generalized concept for the graph centre, and several centric indices were derived on this basis. The new definition consists of four hierarchically ordered criteria based on the distance matrix 1) the smallest maximum distance in the row or column of the vertex ... 

The topological centric indices 65,67) can be expressed both in quadratic and logarithmic (information) form. In general, each partition of the quantity X into a set of constituents X can be converted into quadratic, Q, or information index, I, as ... 

Bonchev centric information indices centric indices... 

The main centric indices are listed below they have been divided into two main groups, one containing the indices proposed by Balaban and the other the indices proposed by Bonchev. 

Bonchev centric information indices are centric indices derived from the vertex - distance matrix D and the -> edge distance matrix "D, based on the concept of - graph centre and calculated as mean information content [Bonchev et al, 1980a Bonchev, 1983 Bonchev, 1989],... 

Several shape descriptors are defined within more general approaches to - molecular descriptors. This is the case of - Kier shape descriptors, -> shape profiles, -> shadow indices, -> WHIM shape descriptors, - Sterimol shape parameters L/Bj and B1/B5, molecular - periphery codes, and -> centric indices. Other approaches to the study of molecular surface and shape are Mezey 3D shape analysis and Hopfinger - molecular shape analysis. -> Triangular descriptors have also been used to characterize molecular shape to search for similarities among molecules. 

Some - shape descriptors and -> centric indices contain information about symmetry, while -> WHIM symmetry, - Bertz complexity index, - indices of neighbourhood symmetry, and - symmetry number obtained by the automorphism group of a graph are explicitly related to the symmetry. 

Verloop parameters Sterimol parameters Verloop Sterimol parameters Sterimol parameters vertex adjacency matrix adjacency matrix vertex centric indices - centric indices vertex chromatic decomposition chromatic decomposition... 

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