Zagreb indices: M₁(G) = Σ d(v)² (first) and M₂(G) = Σ d(i)·d(j) over edges (second). Gutman-Trinajstić (1972). Among the oldest topological indices in chemical graph theory. M₁ correlates with total π-electron energy and branching.
How to Use
Select graph:
- M₁: First Zagreb
- M₂: Second Zagreb
- Compare: M₁ vs M₂
Chemical Meaning
M₁: total branching contribution. High-degree vertices contribute d² each. M₂: edge-branch coupling. Edges between high-degree vertices contribute most. Both predict thermodynamic properties.
Bounds
M₁ ≥ 4m²/n (Cauchy-Schwarz). M₁(K_n) = n(n-1)². M₂ ≥ M₁²/(2m) (Nordhaus-Gaddum type). Many sharp bounds for trees, unicyclic, bicyclic graphs.
Step-by-Step Instructions
- 1Select graph.
- 2Sum d(v)² for M₁.
- 3Sum d(i)·d(j) for M₂.
- 4Compare indices.
- 5Apply to molecules.