First multiplicative Zagreb PM₁(G) = Π d(v)² = (Π d(v))². Todeschini-Consonni (2010). Multiplicative version: replaces Σ with Π. PM₁ is more sensitive to outlier degrees: one vertex with d=1 makes PM₁ small regardless of other degrees.
How to Use
Select graph:
- PM₁: Product of d²
- vs M₁: Compare
- log PM₁: Additive form
Log Connection
log(PM₁) = Σ log(d²) = 2Σlog(d). So log(PM₁)/2 = Σlog(d). The additive version of PM₁ is the sum of log-degrees. This connects multiplicative to additive theories via logarithms.
Sensitivity
M₁: one low-degree vertex adds small term. PM₁: one low-degree vertex MULTIPLIES by small factor → entire product shrinks. PM₁ is 'bottleneck-sensitive': weakest vertex determines scale.
Step-by-Step Instructions
- 1Select graph.
- 2Square each degree.
- 3Multiply all terms.
- 4Compare with M₁.
- 5Compute log PM₁.