Second Zagreb coindex M̄₂(G) = Σ dᵢ·dⱼ over non-adjacent pairs. Došlić (2008). M̄₂ measures the 'potential connectivity' — what would M₂ gain if non-edges became edges? M̄₂ = 2m² - ½M₁ - M₂.
How to Use
Select graph:
- M̄₂: 2nd coindex
- dd product: Non-edges
- M̄₂+M₂: Verify
Key Identity
M̄₂ + M₂ = ½(Σdᵢ)² - ½M₁ = 2m² - ½M₁. The sum M̄₂+M₂ accounts for ALL pairs (edges + non-edges). A clean algebraic identity.
Applications
M̄₂ predicts molecular 'flexibility': high M̄₂ means many high-degree vertices are NOT connected, suggesting potential for conformational changes.
Step-by-Step Instructions
- 1Select graph.
- 2Find non-adjacent pairs.
- 3Multiply dᵢ·dⱼ.
- 4Sum products.
- 5Or: 2m²-½M₁-M₂.