The Augmented Vertex-Distance Matrix

The augmented vertex-distance matrix (Randid and Pompe, 2001) of a vertex-labeled connected vertex-weighted graph G, denoted by D, is a real symmetric V X V matrix whose elements are defined as 

8 and 5, are variable parameters, which are determined during the regression so that the standard error of estimate for a studied property is as small as possible. The augmented distance matrix has been used for generation of a number of variable distance indices (Randid and Pompe, 2001 Lucic et al., 2003) the variable Wiener index, the variable hyper-Wiener index, the variable Balaban index, and variable complements of these indices based on the augmented distance-complement matrix. 

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