Reciprocal distance matrix

Ivanciuc, O., Balaban, T.S., and Balaban, A.T., Design of topological indices. Part 4. Reciprocal distance matrix, related local vertex invariants and topological indices, J. Math. Chem., 12 309-318, 1993. 

The reciprocal distance matrix (or Harary matrix) is a square symmetric Ax A matrix derived from the distance matrix whose entries are defined as ... 

The reciprocal distance sum RDSi of the i th vertex is a local invariant defined as the sum of the reciprocal distance matrix elements in the i th row ... 

A modified reciprocal distance matrix was proposed in order to obtain constant interval reciprocal indices the idea was that reciprocal distances should be uniformly spaced as topological distances [Schultz and Schultz, 1998 Schultz and Schultz, 2000]. The matrix elements are ... 

The diagonal entries are zero by definition. This matrix is the reciprocal distance matrix of the line graph of the molecular graph Q [Ivanciuc et al., 1997a]. 

Using the reciprocal distance matrix instead of the simple distance matrix in the Hadamard matrix product, new expanded reciprocal distance matrices HM are obtained as ... 

The Harary index H (also called Harary number) is a molecular topological index [Ivanciuc et al, 1993b Plavsic et al, 1993b] derived from the -> reciprocal distance matrix D- by the Wiener operator YF ... 

Another set of topological indices based on a modified reciprocal distance matrix are the constant interval reciprocal indices. 

Harary matrix reciprocal distance matrix - distance matrix... 

Table C2 Some Hosoya-type indices for the data set of 18 octane isomers (Appendix C - Set 1) calculated on the unweighted molecular graph and the following graph-theoretical matrices A, adjacency matrix D, distance matrix L, Lapiacian matrix D , reciprocal distance matrix % matrix C reciprocal geometry matrix.

For vertex- and edge-weighted molecular graphs, the reciprocal distance matrix was defined as [Ivanciuc, 2000ij ... 

Reciprocal distance matrix D and related molecular descriptors of 2-methylpentane. RDS, is the reciprocal distance sum of the /th vertex. 

The Harary index H [Plavsic, Nikolic et al., 1993b], also called RDSUMindex [Ivanciuc, Balaban et al., 1993b], is a molecular topological index derived from the reciprocal distance matrix by the Wiener operator Wi ... 

Reciprocal distance matrix D and Harary index H for 2-methylpentane. 

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. 

These molecular descriptors were derived from several graph-theoretical matrices such as reciprocal distance matrix [Ivanciuc and Balaban, 1999c], reverse Wiener matrix [Ivanciuc,... 

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