Second multiplicative Zagreb PM₂(G) = Π dᵢ·dⱼ over edges. Todeschini-Consonni (2010). Edge-based multiplicative: each edge contributes its degree product to the overall product. One pendant edge (dd=d·1=d) can dramatically affect PM₂.
How to Use
Select graph:
- PM₂: Product of dd
- vs M₂: Compare
- log PM₂: = Σlog(dd)
Additive Form
log(PM₂) = Σ log(dᵢ·dⱼ) = Σ [log(dᵢ)+log(dⱼ)]. The additive version is the sum of log-products over edges. Connects to M₂ through logarithmic transformation.
Bounds
For d-regular: PM₂ = (d²)^m = d^{2m}. For star: PM₂ = ((n-1)·1)^{n-1} = (n-1)^{n-1}. Path: PM₂ = 2·4^{n-3}·2 = 4^{n-2}.
Step-by-Step Instructions
- 1Select graph.
- 2For each edge: dᵢ·dⱼ.
- 3Multiply all terms.
- 4Compare with M₂.
- 5Compute log PM₂.