The Barysz Vertex-Distance Matrix

There have also been other equally pragmatic attempts to parameterize the heteroatoms and heterobonds in the distance matrix of weighted graphs (Ivanciuc et al 1999)  

The relative electronegativity X-weighting scheme (Balaban, 1986 Balaban and Ivanciuc, 1989) Sanderson electronegativities (Sanderson, 1983). 

The atomic mass A-weighting scheme (Ivanciuc, 2000a). 

The AH-scheme (Ivanciuc, 2000a) A weighting scheme based on the atomic mass A that produces parameters different from those of the Z-scheme by considering the mass of heavy (nonhydrogen) atom together with that of hydrogen atoms connected to it. 

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The complement of the Barysz vertex-distance matrix, denoted by is defined by means of the matrix ... 

THE RECIPROCAL OF THE COMPLEMENT OF THE BARYSZ VERTEX-DISTANCE MATRIX... 

The reciprocal of the complement of the Barysz vertex-distance matrix, denoted by 1/ = D, of a vertex- and edge-weighted molecular graph G with V vertices, is the square VxV symmetric matrix and is defined as... 

The sum of the entries in the upper matrix-triangle (or the lower matrix-triangle) gives the Wiener index of G4. The molecular descriptors based on the reciprocal Barysz vertex-distance matrix have been used in QSAR modeling by Ivanciuc (2000b). 

Various distance indices can be computed using the Barysz (weighted) vertex-distance matrix. 

Derived from vertex- and edge-weighted molecular graphs, the Barysz distance matrix is a... 

Derived from the Barysz distance matrix, a general weighting scheme was proposed by Ivanciuc [Ivanciuc, Ivanciuc et al, 1999a Ivanciuc, 2000a, 2000i] in terms of the conventional bond order n and any atomic property Pj. The vertex weight Wi associated with the vertex V was defined as... 

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