First Zagreb coindex M̄₁(G) = Σ (dᵢ+dⱼ) over non-adjacent pairs {i,j}. Došlić (2008). The 'missing edge' perspective. M̄₁ = 2m(n-1) - M₁. M̄₁(G) = M₁(Ḡ) where Ḡ is complement. Reveals what topology is NOT there.
How to Use
Select graph:
- M̄₁: 1st coindex
- Non-edges: Pairs
- M̄₁+M₁: Verify
Complement View
M̄₁(G) = M₁(Ḡ): Zagreb coindex of G = Zagreb index of complement. For K_n: M̄₁=0 (no non-edges). For empty graph: M̄₁ = M₁ of K_n.
Key Identity
M̄₁ + M₁ = 2m(n-1). Total = index + coindex. Beautiful partition: every pair contributes to either M₁ (edges) or M̄₁ (non-edges), summing to 2m(n-1).
Step-by-Step Instructions
- 1Select graph.
- 2Find non-adjacent pairs.
- 3Sum (dᵢ+dⱼ) for each.
- 4Or: 2m(n-1) - M₁.
- 5Compare M₁ and M̄₁.