Bounds for the Randic connectivity index

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:

• 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.