Augmented Zagreb Index Calculator

best heat-of-formation predictor

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About Augmented Zagreb Index Calculator

An augmented Zagreb index calculator computing AZI(G) = Σ_{(i,j)∈E} (d(i)·d(j)/(d(i)+d(j)-2))³. Furtula et al. (2010). Cubic augmentation of Zagreb. AZI outperforms ALL other degree-based indices for predicting heat of formation! Client-side.

Augmented Zagreb Index Calculator Features

  • AZI(G)
  • (dd/(d+d-2))³
  • Best QSAR
  • Furtula '10
  • Common graphs
Augmented Zagreb AZI(G) = Σ (dᵢdⱼ/(dᵢ+dⱼ-2))³. Furtula et al. (2010). The cube makes AZI extremely sensitive to degree disparity. Empirically: AZI is the BEST degree-based predictor of heat of formation, outperforming all 20+ competing indices!

How to Use

Select graph:

  • AZI: Aug. Zagreb
  • Cubic: (dd/(d+d-2))³
  • #1: Best predictor

Why AZI Wins

Tested against Randić, Zagreb M₁/M₂, ABC, harmonic, and 15+ others. AZI achieves highest r² for heat of formation across diverse molecular sets. The cubic power amplifies structural differences that matter chemically.

Bounds

AZI(K_n) = n(n-1)/2 · ((n-1)/2)³·(n-1)³. For trees: AZI minimized by star, maximized by path. 8 ≤ AZI(tree on n≥3) ≤ f(n).

Step-by-Step Instructions

  1. 1Select graph.
  2. 2For each edge: (dᵢdⱼ/(dᵢ+dⱼ-2))³.
  3. 3Sum all terms.
  4. 4Compare vs others.
  5. 5Predict ΔHf.

Augmented Zagreb Index Calculator — Frequently Asked Questions

Why is AZI the 'best' index?+

Empirical testing on octanes, benzenoid hydrocarbons, and diverse organics: AZI consistently achieves highest correlation (r²>0.99) with heat of formation. No other degree-based index comes close.

Why the cube?+

The cube amplifies differences: edges between similar-degree vertices get much larger weight than asymmetric ones. This captures the stabilization from symmetric bonding environments, which directly relates to enthalpic stability.

Relation to original Zagreb?+

Zagreb M₂: Σ dᵢdⱼ. AZI: Σ (dᵢdⱼ/(dᵢ+dⱼ-2))³. The normalization dᵢ+dⱼ-2 removes the trivial size dependence, and the cube sharpens discrimination. AZI is a 'refined, amplified' Zagreb.

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