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Bounds for the Randic connectivity index

Gutman1, Araujo, Morales

  • 1Faculty of Science, University of Kragujevac, Yogoslavia.

Journal of Chemical Information and Computer Sciences
|June 13, 2000
PubMed
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New bounds for the Randic connectivity index (chi) in saturated hydrocarbons have been established. These improved mathematical limits, L(n,m) and U(n,m), are tighter and more applicable to real chemical structures.

Area of Science:

  • Chemical graph theory
  • Molecular descriptors
  • Structure-property relationships

Background:

  • The Randic connectivity index (chi) is a crucial molecular descriptor in cheminformatics.
  • Existing bounds for chi in saturated hydrocarbons lack precision for many chemical applications.

Purpose of the Study:

  • To derive novel, tighter mathematical bounds for the Randic connectivity index (chi) in saturated hydrocarbons.
  • To establish the applicability and superiority of these new bounds compared to prior estimations.

Main Methods:

  • Mathematical analysis of molecular graphs representing saturated hydrocarbons.
  • Derivation of lower (L) and upper (U) bound functions based on the number of carbon atoms (n) and carbon-carbon bonds (m).

Main Results:

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  • Two functions, L = L(n,m) and U = U(n,m), were determined, defining the range L <= chi < U.
  • The derived bounds are demonstrably better than previously reported bounds.
  • The study shows that for most chemically relevant n and m, hydrocarbons exist where chi equals L or U, validating the bounds.

Conclusions:

  • The new bounds provide a more accurate and refined estimation for the Randic connectivity index in saturated hydrocarbons.
  • These improved bounds have potential applications in predicting molecular properties and in the development of QSPR models.