First Redefined Zagreb Calculator

sum/product of degrees per edge

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About First Redefined Zagreb Calculator

A first redefined Zagreb calculator computing ReZM₁(G) = Σ (dᵢ+dⱼ)/(dᵢ·dⱼ) over edges. Ranjini-Lokesha-Usha (2013). = Σ(1/dᵢ + 1/dⱼ) = inverse degree index recast. Emphasizes low-degree endpoints. Client-side.

First Redefined Zagreb Calculator Features

  • ReZM₁(G)
  • (d+d)/dd
  • 1/d+1/d
  • Ranjini '13
  • Common graphs
First redefined Zagreb ReZM₁(G) = Σ (dᵢ+dⱼ)/(dᵢ·dⱼ) = Σ (1/dᵢ + 1/dⱼ) over edges. Ranjini-Lokesha-Usha (2013). Each edge contributes sum of reciprocal degrees. ReZM₁ = ID (inverse degree) rewritten as edge sum. Emphasizes peripheral edges.

How to Use

Select graph:

  • ReZM₁: 1st redefined
  • 1/d+1/d: Per edge
  • vs ReZM₂: Compare

Simplification

(d+d)/dd = 1/d + 1/d. So ReZM₁ = Σ_edges (1/dᵢ + 1/dⱼ) = Σ_v d(v)·(1/d(v)) = Σ_v 1 = ... wait, more carefully: = Σ_v Σ_edges(v) 1/d(v) relating back to inverse degree.

Bounds

For d-regular: ReZM₁ = m·2/d. So ReZM₁ = 2m/d = n for regular (since 2m = nd). Compare: ID = n/d. Different normalization.

Step-by-Step Instructions

  1. 1Select graph.
  2. 2For each edge: (dᵢ+dⱼ)/(dᵢ·dⱼ).
  3. 3Sum all terms.
  4. 4Compare with ReZM₂, ReZM₃.
  5. 5Check family relations.

First Redefined Zagreb Calculator — Frequently Asked Questions

ReZM₁ = sum of reciprocals?+

Yes! (d+d)/dd = 1/d + 1/d. So each edge contributes the sum of reciprocal endpoint degrees. This is the mildest of the three redefined Zagrebs.

Three redefined compared?+

ReZM₁ = Σ(d+d)/dd ≈ Σ2/d (mild, low-degree focused). ReZM₂ = Σdd/(d+d) ≈ Σd/2 (balanced). ReZM₃ = Σ(d+d)·dd ≈ Σ2d³ (strong, high-degree focused).

ReZM₁ for pendant edges?+

Pendant edge e=(u,v) with d(u)=1: contributes 1/1+1/d(v) = 1+1/d(v). Maximum per-edge contribution! Pendant edges dominate ReZM₁. Opposite of ReZM₃ behavior.

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