Centric Topological Indices

A. T. Balaban, S. Bertelsen, and S. C. Basak, New centric topological indices for acyclic molecules (trees) and substituents (rooted trees), and coding of rooted trees, MATCH Commun. Math. Comput. Chem. 30 (1994) 55-72. 

The sums of the local vertex invariants X, and c, over all of the atoms give the corresponding molecular descriptors, called centrocomplexity topological index X and centric topological index C, respectively ... 

Balaban, A.T., Bertelsen, S. and Basak, S.C. (1994b). New Centric Topological Indexes for Acyclic Molecules (Trees) and Substituents (Rooted Trees), and Coding of Rooted Trees. MATCH (Comm.Math.Comp.Chem.), 30, 55-72. 

Diudea, M.V. and PSrv, B. (1988). Molecolar Topology. 3. A New Centric Connectivity Index (CCI). MATCH (Comm.Math.Comp.Chem.), 23, 65-87. 

A normalized centric index C was also introduced in order to reflect the topological shape of alkanes. By definition, C = 0 for n-alkanes (chain-graph) ... 

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 ... 

This index provides a measure of molecular branching the higher the value of B, the more branched the tree. It is called centric index because it reflects the topology of the tree as viewed from the centre. 

The binormalized centric index provides information on the topological shape of trees in a similar way to the - binormalized quadratic index Q. ... 

The binormalized quadratic index was proposed, together with the binormalized centric index C, to provide information on the topological shape of trees, i.e. the trade-off between linear and star graphs. 

Bonchev, D., Balaban, A.T. and Mekenyan, O. (1980a). Generalization of the Graph Center Concept and Derived Topological Centric Indexes. J.ChemJnf.Comput.ScL, 20,10 113. 

D. Bonchev, A. T. Balaban, and O. Mekenyan, Generalization of the graph center concept, and derived topological centric indexes, J. Chem. Inf. Comp. Sci. 20 (1980) 106. 

A chapter reviews the use of topological indices in chemical, physico-chemical, and biological correlations. The philosophy of this approach rests on the translation of molecular structures, especially of the chain branching or of the general topological shape , into a numerical index which can then lead to useful correlations and predictions, Among these topological indices, the centric index was introduced to correlate octane numbers of acyclic hydrocarbons, and the... 

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