4. 14 The Reciprocal of the Complementary Vertex-Distance Matrix

The reciprocal of the complementary vertex-distance matrix, denoted by cvD-1, is simply given by

cvD-1 = 1/ cvD                       (64)    

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.

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