The Generalized Graph Centre Concept

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  

2) the smallest sum of all distances d j in the row or column corresponding to vertex i 3) the lowest number of largest entries in the vertex distance code, VDC  

4) criteria 1)—3) are repeated to the pseudocentre of the graph (obtained by removing the vertices discarded by the first three criteria and their incident edges) until on two successive cycles one and the same subgraph (i.e., the polycentre of the graph) is 

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