Elliptic Sombor Index Calculator

weighted Euclidean degree norm

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About Elliptic Sombor Index Calculator

An elliptic Sombor index calculator computing ESO(G) = Σ (dᵢ+dⱼ)·√(dᵢ²+dⱼ²). Introduced alongside Sombor (2021). Multiplies Sombor term by degree sum. Named for elliptic integral resemblance. More weight to high-degree edges. Client-side.

Elliptic Sombor Index Calculator Features

  • ESO(G)
  • (d+d)·√(d²+d²)
  • Weighted
  • Gutman '21
  • Common graphs
Elliptic Sombor ESO(G) = Σ (dᵢ+dⱼ)·√(dᵢ²+dⱼ²). Amplifies Sombor by degree sum factor. High-degree edges contribute cubically. ESO = SO × (degree sum) per edge. More discriminating than basic Sombor for dense graphs.

How to Use

Select graph:

  • ESO: Elliptic Sombor
  • vs SO: Compare
  • Weighted: Amplified

ESO vs SO

SO: √(d²+d²) per edge. ESO: (d+d)·√(d²+d²) per edge. ESO weights by degree sum: edges between high-degree vertices get massive amplification. ESO/SO = average (d+d) weighted by Sombor contribution.

Bounds

ESO ≥ 2√2·m (minimum: all degree-1). ESO(K_n) = n(n-1)²(n-1)√2. For d-regular: ESO = 2d·SO = 2√2·m·d².

Step-by-Step Instructions

  1. 1Select graph.
  2. 2For each edge: (dᵢ+dⱼ)·√(dᵢ²+dⱼ²).
  3. 3Sum all terms.
  4. 4Compare with SO.
  5. 5Assess amplification.

Elliptic Sombor Index Calculator — Frequently Asked Questions

Why 'elliptic'?+

The formula (a+b)√(a²+b²) resembles certain terms in elliptic integral expansions. It's also related to the arc length of an ellipse with semi-axes a,b. Mathematical analogy, not direct application.

ESO vs HM (hyper-Zagreb)?+

HM = Σ(d+d)² = Σ(d²+2dd+d²). ESO = Σ(d+d)√(d²+d²). Different: HM squares, ESO uses Euclidean norm. Both amplify high-degree edges, but differently.

Is ESO practically better than SO?+

For some QSAR applications: yes. ESO better separates dense molecular substructures. For sparse (tree-like) molecules: SO is sufficient. Use ESO when extra discrimination is needed.

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