The Quotient Matrices

Quotient matrices have been introduced by Randic (1994b) and applied to structure-property modeling by Plavsid and his coworkers (Plavsic et al., 1998) and Nikolid and her coworkers (Nikolid et al., 2001a). The quotient matrices, denoted by M /M, are obtained by dividing the off-diagonal elements of matrices and M  

The molecular index based on the vertex-distance/detour matrix is called the Wiener-sum index (Randid, 1994b)  

The molecular index based on the resistance-distance/vertex-distance matrix is called the Kirchhoff-sum index (Babic et al 2002). Matrices D/Q and QAD have been used to study the graph cyclicity (Klein and Ivanciuc, 2002)  

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The reciprocal of a quotient matrix is still a quotient matrix, obtained by reversing the role of M2 and Ml matrices. In the lower part of Table M2, reciprocal matrices (11-20) of the quotient matrices defined above (1-10) are reported. 

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