Gutman index Gut(G) = Σ d(i)·d(j)·dist(i,j). Each pair's distance is weighted by the product of their degrees. High-degree hubs that are far apart contribute most. For trees: Gut = 4W - (n-1)M₁ + M₂.
How to Use
Select graph:
- Gut: Gutman index
- d·d·dist: Per pair
- Trees: 4W formula
Tree Formula
For trees: Gut(T) = 4·W(T) - (n-1)·M₁(T) + M₂(T). Beautiful connection between distance (W), first Zagreb (M₁), and second Zagreb (M₂). Shows Gutman contains all three!
Applications
Gut combines structural and distance information. Better than pure distance indices for some molecular properties. Used when both vertex importance (degree) and topological distance matter.
Step-by-Step Instructions
- 1Select graph.
- 2For each pair: d(i)·d(j)·dist(i,j).
- 3Sum all terms.
- 4Check tree formula.
- 5Compare indices.