The reverse Wiener matrix, denoted by RW, is a symmetric V × V matrix, defined by means of the vertex-distance matrix vD [221]:
[RW]ij=  |
D - [vD]ij if i ≠ j |
| 0 otherwise (95) |
where D is the diameter of a graph. The diameter of a graph G is the longest geodesic distance between any two vertices i and j in G, i.e., the largest [vD]ij value in the vertex-distance matrix [12].
As an example of the the reverse-Wiener matrix, the RW matrix for T2 is given below.
RW(T2)= |
 |
0 |
4 |
3 |
2 |
1 |
0 |
2 |
3 |
 |
4 |
0 |
4 |
3 |
2 |
1 |
3 |
4 |
|||
3 |
4 |
0 |
4 |
3 |
2 |
4 |
3 |
|||
2 |
3 |
4 |
0 |
4 |
3 |
3 |
2 |
|||
1 |
2 |
3 |
4 |
0 |
4 |
2 |
1 |
|||
0 |
1 |
2 |
3 |
4 |
0 |
1 |
0 |
|||
2 |
3 |
4 |
3 |
2 |
1 |
0 |
2 |
|||
3 |
4 |
3 |
2 |
1 |
0 |
2 |
0 |
Molecular descriptors such as the reverse-Wiener index and the reverse-distance sum can be obtained from the reverse-Wiener matrix.
