Third Redefined Zagreb Calculator

product of degree sum and product

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About Third Redefined Zagreb Calculator

A third redefined Zagreb calculator computing ReZM₃(G) = Σ (dᵢ+dⱼ)·dᵢ·dⱼ over edges. Ranjini-Lokesha-Usha (2013). Product of degree sum and degree product. Same as GO₂ (second Gourava). Cubic growth in degree. Client-side.

Third Redefined Zagreb Calculator Features

  • ReZM₃(G)
  • (d+d)·dd
  • Cubic
  • Ranjini '13
  • Common graphs
Third redefined Zagreb ReZM₃(G) = Σ (dᵢ+dⱼ)·dᵢ·dⱼ. Ranjini-Lokesha-Usha (2013). Note: ReZM₃ = GO₂ (second Gourava of Kulli 2017). Same formula, different lineage. Cubic in degree — most sensitive of the redefined family.

How to Use

Select graph:

  • ReZM₃: 3rd redefined
  • (d+d)dd: Per edge
  • vs ReZM₂: Compare

Cubic Growth

For d-regular: ReZM₃ = m·2d·d² = 2md³. Cubic! Compare ReZM₁ (linear), ReZM₂ (sub-linear). ReZM₃ amplifies degree effects most strongly among the three.

GO₂ Connection

ReZM₃ = GO₂ exactly. Same formula: Σ(d+d)·dd. Named independently by Ranjini (2013) and Kulli (2017). Shows how graph theory reinvents concepts under different names.

Step-by-Step Instructions

  1. 1Select graph.
  2. 2For each edge: (dᵢ+dⱼ)·dᵢ·dⱼ.
  3. 3Sum all terms.
  4. 4Compare with ReZM₂.
  5. 5Verify = GO₂.

Third Redefined Zagreb Calculator — Frequently Asked Questions

Three redefined Zagrebs?+

ReZM₁ = Σ(d+d)/dd (mild). ReZM₂ = Σdd/(d+d) (moderate). ReZM₃ = Σ(d+d)·dd (strong). Three operations on same ingredients: sum×product, product/sum, sum/product.

ReZM₃ = GO₂?+

Yes! Same formula, independently proposed 4 years apart. Ranjini (2013) called it 'third redefined Zagreb'. Kulli (2017) called it 'second Gourava'. Convergent discovery in mathematics.

Which redefined is best?+

ReZM₁ for mild discrimination. ReZM₂ for balanced view (harmonic mean). ReZM₃ for strong hub detection (cubic). Together they provide a complete picture. Each has different QSAR strengths.

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