Gourava Index Calculator

unified Gourava comparison

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About Gourava Index Calculator

A Gourava index overview calculator comparing GO₁(G) = M₁+M₂ and GO₂(G) = Σ(d+d)·dd. Kulli (2017). Side-by-side analysis with Zagreb decomposition. Shows additive vs multiplicative interaction. GO₂/GO₁ ratio as complexity measure. Client-side.

Gourava Index Calculator Features

  • GO₁ vs GO₂
  • M₁+M₂
  • Ratio
  • Kulli '17
  • Common graphs
Gourava indices: GO₁ = M₁+M₂ (additive unification) and GO₂ = Σ(d+d)·dd (multiplicative interaction). Kulli (2017). This tool compares both side-by-side, showing how additive and multiplicative views interact. GO₂/GO₁ ratio grows with degree.

How to Use

Select graph:

  • GO₁: Sum form
  • GO₂: Product form
  • GO₂/GO₁: Ratio

GO₂/GO₁ Ratio

GO₂/GO₁ measures 'multiplicative amplification'. For regular d-graphs: GO₂/GO₁ = 2d³/[d(d+2)] = 2d²/(d+2). Grows quadratically with degree. High ratio = dense, hub-dominated.

Zagreb Decomposition

GO₁ = M₁ + M₂: clean split into additive and multiplicative Zagreb components. Studying which dominates reveals graph character: M₂>M₁ means hub-hub edges dominate.

Step-by-Step Instructions

  1. 1Select graph.
  2. 2Compute GO₁ = M₁+M₂.
  3. 3Compute GO₂.
  4. 4Compute ratio GO₂/GO₁.
  5. 5Decompose structure.

Gourava Index Calculator — Frequently Asked Questions

Which Gourava is better?+

GO₁ for general QSAR (linear growth). GO₂ for properties needing high discrimination (cubic growth). Use both: the ratio GO₂/GO₁ itself is a useful descriptor!

GO₂/GO₁ for regular graphs?+

2d²/(d+2). For d=2 (cycles): 8/4=2. For d=3 (cubic): 18/5=3.6. For d→∞: ~2d. The ratio grows with regularity degree, measuring 'density intensity'.

Named after what?+

Gourava: a region/community in Karnataka, India. V.R. Kulli named these indices to honor local culture. Following the tradition of Zagreb, Mostar, Sombor — geographical naming in graph theory.

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