General Randić Rₐ(G) = Σ (dᵢ·dⱼ)ᵃ. Bollobás-Erdős (1998). The mega-unifier: a=-½→Randić, a=1→M₂, a=-1→modified Randić, a=½→reciprocal Randić. Most studied parametric index in chemical graph theory.
How to Use
Select graph and exponent a:
- a=-½: Randić R
- a=1: 2nd Zagreb M₂
- Custom: Any real a
Special Cases
a=-½: R (Randić). a=1: M₂ (2nd Zagreb). a=-1: R⁻¹ (modified Randić). a=½: Σ√(dd). a=2: Σ(dd)². Each a gives different chemical correlation.
Extremal Theory
Bollobás-Erdős conjecture: for a<0, star maximizes Rₐ among trees. For a>0, path maximizes. Deep extremal graph theory connects to Turán-type problems.
Step-by-Step Instructions
- 1Select graph.
- 2Choose exponent a.
- 3For each edge: (dᵢ·dⱼ)ᵃ.
- 4Sum all terms.
- 5Explore a-landscape.