The reciprocal Szeged matrices, denoted by SZ-1, are matrices whose off-diagonal elements are the reciprocal of the corresponding elements of the Szeged matrices:
[SZ-1]ij = [SZ]ij-1 (99)
All elements equal to zero in the Szeged matrices are left unchanged in the reciprocal Szeged matrices. Below we give the reciprocal Szeged matrices of the edge-Szeged matrix, the path-Szeged matrix and the Szeged difference matrix of G1 (see structure A in Figure 2).
eSZ-1(G1)= |
0 |
1/6 |
0 |
0 |
0 |
0 |
0 |
||
1/6 |
0 |
1/10 |
0 |
0 |
0 |
0 |
|||
0 |
1/10 |
0 |
1/10 |
0 |
1/12 |
0 |
|||
0 |
0 |
1/10 |
0 |
1/12 |
0 |
0 |
|||
0 |
0 |
0 |
1/12 |
0 |
10 |
0 |
|||
0 |
0 |
1/12 |
0 |
1/10 |
0 |
1/6 |
|||
0 |
0 |
0 |
0 |
0 |
1/6 |
0 |
pSZ-1(G1)= |
0 |
1/6 |
1/5 |
1/10 |
1/8 |
1/10 |
1/6 |
||
1/6 |
0 |
1/10 |
1/4 |
1/12 |
1/6 |
1/12 |
|||
1/5 |
1/10 |
0 |
1/10 |
1/3 |
1/12 |
1/4 |
|||
1/10 |
1/4 |
1/10 |
0 |
1/12 |
1/2 |
1/10 |
|||
1/8 |
1/12 |
1/3 |
1/12 |
0 |
1/10 |
1/2 |
|||
1/10 |
1/6 |
1/12 |
1/2 |
1/10 |
0 |
1/6 |
|||
1/6 |
1/12 |
1/4 |
1/10 |
1/2 |
1/6 |
0 |
dSZ-1(G1)= |
0 |
0 |
1/5 |
1/10 |
1/8 |
1/10 |
1/6 |
||
0 |
0 |
0 |
1/4 |
1/12 |
1/6 |
1/12 |
|||
1/5 |
0 |
0 |
0 |
1/3 |
0 |
1/4 |
|||
1/10 |
1/4 |
0 |
0 |
0 |
1/2 |
1/10 |
|||
1/8 |
1/12 |
1/3 |
0 |
0 |
0 |
1/2 |
|||
1/10 |
1/6 |
0 |
1/2 |
0 |
0 |
0 |
|||
1/6 |
1/12 |
1/4 |
1/10 |
1/2 |
0 |
0 |
These matrices have not been used so far to generate molecular descriptors.