Second Gourava GO₂(G) = Σ (dᵢ+dⱼ)·dᵢ·dⱼ over edges. Kulli (2017). Multiplies degree sum by degree product: captures the interaction effect. For edge (i,j): contribution = dᵢdⱼ(dᵢ+dⱼ). Relates to forgotten index F.
How to Use
Select graph:
- GO₂: Second Gourava
- (d+d)·dd: Per edge
- vs GO₁: Compare
Algebraic View
GO₂ = Σ dᵢdⱼ(dᵢ+dⱼ) = Σ(dᵢ²dⱼ + dᵢdⱼ²) = Σ dᵢdⱼ(dᵢ+dⱼ). This connects to the forgotten index F: GO₂ relates to degree-cube sums.
Bounds
GO₂(K_n) = n(n-1)/2·(n-1)²·2(n-1) = n(n-1)²(n-1)². For regular: GO₂ = m·2d·d² = 2m·d³. GO₂ grows as degree cubed!
Step-by-Step Instructions
- 1Select graph.
- 2For each edge: (dᵢ+dⱼ)·dᵢ·dⱼ.
- 3Sum all terms.
- 4Compare with GO₁.
- 5Analyze degree³ scaling.