Nirmala index N(G) = Σ √(dᵢ+dⱼ) over edges. Kulli (2021). Sub-linear in degree sums: √ dampens extreme degrees. N lies between sum-connectivity χ (which uses 1/√) and first Zagreb M₁ (which uses no root). A 'Goldilocks' index.
How to Use
Select graph:
- N: Nirmala index
- √(d+d): Per edge
- vs χ: Compare
Index Landscape
χ = Σ1/√(d+d): decreasing in d. N = Σ√(d+d): increasing in d, sub-linear. M₁ = Σ(d+d): linear. F = Σ(d²+d²): quadratic. N fills the sub-linear niche between χ and M₁.
Bounds
N ≥ m·√(2δ) where δ = min degree. N ≤ m·√(2Δ). For regular d-graphs: N = m·√(2d). N(K_n) = n(n-1)/2·√(2(n-1)).
Step-by-Step Instructions
- 1Select graph.
- 2For each edge: √(dᵢ+dⱼ).
- 3Sum all terms.
- 4Compare with χ, M₁.
- 5Assess sub-linearity.