Narumi-Katayama NK(G) = Π d(v): product of all vertex degrees. Narumi-Katayama (1984). Multiplicative analogue of first Zagreb (M₁ = Σ d²). log(NK) = Σ log d. NK captures multiplicative branching complexity.
How to Use
Select graph:
- NK: Degree product
- Π d: Per vertex
- log: Additive form
Properties
NK(K_n) = (n-1)ⁿ. NK(star) = (n-1)·1^(n-1) = n-1. NK(cycle) = 2ⁿ. NK = 0 iff any isolated vertex. Among trees: star minimizes, path maximizes NK.
Multiplicative Indices
NK started the 'multiplicative indices' family: Π₁ = Π d², Π₂ = Π(dᵢdⱼ). Products are more sensitive to extreme values. One zero degree kills the entire product!
Step-by-Step Instructions
- 1Select graph.
- 2Multiply all d(v).
- 3Take log.
- 4Compare bounds.
- 5Apply to molecules.