The Balaban Centric Indices

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)  

A further normalization (binormalization) was also made so as to have an upper limit of the. centric index C equal to one for the case of star-graphs (i.e., graphs consisting of one vertex of degree N-l and N-l verties of degree N)  

The centric index C belongs to the quadratic class of indices, together with Mi and N2 indices. If the number of vertices of degree v, is denoted by Vb one obtains for graphs with Vj g 4  

Balaban normalized65 similarly, for alkanes, the Mi index specifying the normalized quadratic index Q  

The pruning procedure, as well as the values of the five topological indices introduced by Balaban are illustrated below for G  

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