Design of topological indices. Part 4. Reciprocal distance matrix, related local vertex invariants and topological indices

A new molecular graph matrix, the reciprocal distance (RD) matrix, is defined. Its nondiagonal elements are equal to the reciprocals of the topological distances between the corresponding vertices, while the diagonal elements are all equal to zero. Based on the RD matrix, a real-number local vertex invariant, RDS was proposed, and three topological indices, namely RDSUM, RDSQ, and RDCHI, were defined. Their degeneracy was investigated and proved to be lower than that of the topological index W based on the distance matrix. The correlational ability of the new molecular descriptors was tested against van der Waals molecular surfaces and boiling points of alkanes, showing a satisfactory monoparametric dependence.

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