The reciprocal of the complementary vertex-distance matrix, denoted by cvD-1, is simply given by
The reciprocal complementary vertex-distance matrices of T2 and G1 (see structure A in Figure 2) are given below.
cvD-1(T2)= |
0 |
1/5 |
1/4 |
1/3 |
1/2 |
1 |
1/3 |
1/4 |
||
1/5 |
0 |
1/5 |
1/4 |
1/3 |
1/2 |
1/4 |
1/5 |
|||
1/4 |
1/5 |
0 |
1/5 |
1/4 |
1/3 |
1/5 |
1/4 |
|||
1/3 |
1/4 |
1/5 |
0 |
1/5 |
1/4 |
1/4 |
1/3 |
|||
1/2 |
1/3 |
1/4 |
1/5 |
0 |
1/5 |
1/3 |
1/2 |
|||
1 |
1/2 |
1/3 |
1/4 |
1/5 |
0 |
1/2 |
1 |
|||
1/3 |
1/4 |
1/5 |
1/4 |
1/3 |
1/2 |
0 |
1/3 |
|||
1/4 |
1/5 |
1/4 |
1/3 |
1/2 |
1 |
1/3 |
0 |
cvD-1(G1)= |
0 |
1/4 |
1/3 |
1/2 |
1 |
1/2 |
1 |
||
1/4 |
0 |
1/4 |
1/3 |
1/2 |
1/3 |
1/2 |
|||
1/3 |
1/4 |
0 |
1/4 |
1/3 |
1/4 |
1/3 |
|||
1/2 |
1/3 |
1/4 |
0 |
1/4 |
1/3 |
1/2 |
|||
1 |
1/2 |
1/3 |
1/4 |
0 |
1/4 |
1/3 |
|||
1/2 |
1/3 |
1/4 |
1/3 |
1/4 |
0 |
1/4 |
|||
1 |
1/2 |
1/3 |
1/2 |
1/3 |
1/4 |
0 |
Ivanciuc [235] extended the concept of reciprocal of the complementary vertex-distance matrix to the vertex- and edge-weighted graphs and used the derived Wiener-like indices in QSPR modeling.