Redefined Zagreb ReZM(G) = Σ dᵢdⱼ/(dᵢ+dⱼ) over edges. Note: dd/(d+d) = ½·H(d,d) where H is harmonic mean! Ranjini-Lokesha-Usha (2013). For regular d-graphs: ReZM = m·d/2. Combines multiplicative and additive degree info.
How to Use
Select graph:
- ReZM: Redefined Zagreb
- dd/(d+d): Per edge
- H-mean: View
Harmonic Mean View
dd/(d+d) = ½·2dd/(d+d) = ½·H(d,d). So ReZM = ½ΣH(dᵢ,dⱼ). Half the sum of harmonic means! This connects to the classical harmonic index H = Σ2/(d+d).
Bounds
m·δ²/(2Δ) ≤ ReZM ≤ m·Δ/2 where δ=min, Δ=max degree. For regular: equality in both bounds. ReZM = m·d/2.
Step-by-Step Instructions
- 1Select graph.
- 2For each edge: dᵢ·dⱼ/(dᵢ+dⱼ).
- 3Sum all terms.
- 4Compare with H.
- 5Check regular: m·d/2.