Randić index R(G) = Σ 1/√(d(i)·d(j)) over edges. The most widely used topological index in chemical graph theory! Randić (1975). Over 1000 papers. Correlates with boiling point, enthalpy, toxicity, water solubility.
How to Use
Select graph:
- R: Randić index
- 1/√(dd): Per edge
- QSAR: Correlation
Chemical Applications
R predicts: boiling point (r²≈0.97 for alkanes!), chromatographic retention, surface area, partition coefficient. The single most successful topological index for QSAR (Quantitative Structure-Activity Relationship).
Bounds
R ≤ n/2 (equality: regular graphs). R ≥ √(n-1)/2 (star achieves minimum among trees). For trees: R(star) < R(path) < R(balanced tree). Path maximizes R among trees!
Step-by-Step Instructions
- 1Select graph.
- 2For each edge: 1/√(dᵢdⱼ).
- 3Sum all terms.
- 4Compare bounds.
- 5Apply to QSAR.