Forgotten Index Calculator

rediscovered cubic degree sum

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About Forgotten Index Calculator

A forgotten index calculator computing F(G) = Σ d(v)³ = Σ_{(i,j)∈E} (d(i)²+d(j)²). Furtula-Gutman (2015). Rediscovered from the original 1972 Zagreb paper where it was 'forgotten'. F complements M₁ and M₂. Excellent QSAR predictor. Client-side.

Forgotten Index Calculator Features

  • F(G)
  • Σd³
  • Forgotten '72
  • Rediscovered '15
  • Common graphs
Forgotten index F(G) = Σ d(v)³. Originally appeared in the 1972 Gutman-Trinajstić paper alongside Zagreb indices but was 'forgotten' for 43 years! Furtula-Gutman (2015) rediscovered it. F enhances QSAR predictions when used with M₁ and M₂.

How to Use

Select graph:

  • F: Forgotten index
  • Σd³: Cubic sum
  • History: 1972→2015

The 'Forgotten' Story

1972: Gutman-Trinajstić published M₁ = Σd² and M₂ = Σdᵢdⱼ. In the SAME paper, Σd³ appeared but wasn't named or studied. 2015: Furtula-Gutman realized it was missing from literature. Named it 'Forgotten index'. Now 200+ papers!

Bounds

F ≥ 2m (all edges between degree-1 vertices). F(K_n) = n(n-1)³. F = HM - 2M₂ (connects to hyper-Zagreb). For d-regular: F = n·d³.

Step-by-Step Instructions

  1. 1Select graph.
  2. 2Cube each degree.
  3. 3Sum d(v)³.
  4. 4Verify F=HM-2M₂.
  5. 5Compare QSAR.

Forgotten Index Calculator — Frequently Asked Questions

Why was F 'forgotten'?+

In 1972, Gutman and Trinajstić focused on M₁ and M₂. The Σd³ term appeared in their calculations but wasn't highlighted as a separate invariant. For 43 years, nobody noticed it was unstudied!

Is F useful despite being old?+

Very! F = Σd³ captures 'super-branching' information that M₁=Σd² misses. For QSAR: using M₁, M₂, AND F together gives better predictions than any pair. Three is better than two.

F vs hyper-Zagreb?+

HM = M₁ + 2M₂. F = HM - 2M₂ = M₁. Wait — no! F = Σd³ while M₁ = Σd². They're different: F is cubic, M₁ is quadratic. F = Σ(dᵢ²+dⱼ²) over edges, not pairs.

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