First Gourava GO₁(G) = Σ [(dᵢ+dⱼ) + dᵢ·dⱼ] over edges. Kulli (2017). Beautiful: GO₁ = M₁ + M₂, unifying the two most important Zagreb indices into one. Named after a region in India. Additive + multiplicative in one formula.
How to Use
Select graph:
- GO₁: First Gourava
- M₁+M₂: Verify
- Split: Components
M₁ + M₂ Unification
GO₁ = M₁ + M₂. Instead of studying two indices separately, GO₁ captures both in one number. The additive part (d+d) measures local size, the multiplicative part (d·d) measures local connectivity.
Bounds
GO₁(K_n) = n(n-1)/2·[(2(n-1) + (n-1)²)] = n(n-1)/2·(n-1)(n+1)/... For regular: GO₁ = m·(2d + d²) = m·d·(d+2).
Step-by-Step Instructions
- 1Select graph.
- 2For each edge: (dᵢ+dⱼ) + dᵢ·dⱼ.
- 3Sum all terms.
- 4Verify GO₁ = M₁+M₂.
- 5Decompose contributions.