Reciprocal Szeged Matrices

The reciprocal Szeged matrices, denoted by SZ-, are matrices whose off-diagonal elements are the reciprocal of the corresponding elements of the Szeged matrices, discussed above  

These matrices have not been used so far to generate molecular descriptors. 

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These are molecular indices derived from —> reciprocal Szeged matrices. The Harary-type index is obtained from the reciprocal edge-Szeged matrix SZ as ]Diudea, 1997c]... 

All elements equal to zero are left unchanged in the reciprocal Szeged matrices. 

The Harary index and hyper-Harary index are obtained from, respectively, the P -order sparse -> reciprocal Szeged matrix SZ ... 

The most popular reciprocal matrices are obtained for 2, = 1, such as the Harary matrix, reciprocal geometry matrix, reciprocal detour matrix, reciprocal Szeged matrix, reciprocal Cluj matrix. The reciprocal square distance matrix is derived from the distance matrix by setting X = 2. 

The most popular expanded matrices are —> expanded distance matrices, D M, derived as the Hadamard product between the —> distance matrix D and some different graph-theoretical matrix M, such as the —> Wiener matrix, —> Cluj matrices, Szeged matrix, and walk matrices. Moreover, —> expanded reciprocal distance matrices, D M, were defined by analogy with the expanded distance matrices by using the —> reciprocal distance matrix instead of the... 

Selecting different combinations of Mi and M2 matrices leads to the derivation of several Schultz-type indices. The original Schultz molecular topological index MTI is obtained for Ml = A and M2 = D, where D is the topological —> distance matrix. Typical Schultz indices are derived from (D, A, D), A, D ), (W, A, D), (W A, D ), (W, A, W), (UCJ, A, UCJ), (USZ, A, USZ), where is the reciprocal distance matrix, W is one among —> walk matrices, is the reciprocal walk matrix, UCJ and USZ the unsymmetrical Cluj and Szeged matrices, respectively. 

However, the reciprocal edge-Cluj matrix is equal to the reciprocal edge-Szeged matrix ... 

Characteristic polynomials and Hosoya-type indices were also derived from distance-valency matrices, —> distance-path matrix, reciprocal distance-path matrix, distance-delta matrix, —> Szeged matrices [Ivanciuc and Ivanciuc, 1999], —> layer matrices, and edge adjacency matrix. 

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