4.6 The Vertex-Distance-Complement Matrix

The vertex-distance-complement matrix [221-223], denoted by vcD, can be obtained simply from the vertex-distance matrix :

[vcD]ij=
  V - [vD]ii          if i ≠ j
  0                     otherwise                                (52)    

The distance-complement matrix of the vertex-labeled graph G1 (see structure A in Figure 2) is:

vcD(G1)=
0
6
5
4
3
4
3
6
0
6
5
4
5
4
5
6
0
6
5
6
5
4
5
6
0
6
5
4
3
4
5
6
0
6
5
4
5
6
5
6
0
6
3
4
5
4
5
6
0

Several complement distance indices are available [221-224]: the complement Wiener index, the complement hyper-Wiener index, the complement Balaban index.

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