Reduced reciprocal Randić RRR(G) = Σ √((dᵢ-1)(dⱼ-1)). Product of reduced degrees under square root. RRR = 0 if any edge has a pendant vertex. Only backbone (internal) edges contribute. Li-Gutman (2006).
How to Use
Select graph:
- RRR: Reduced Randić
- d-1: Reduced
- =0?: Has pendants
Backbone Focus
Any edge with a degree-1 endpoint: (d-1) = 0 → product = 0 → contribution = 0. Only edges between internal vertices (d≥2) contribute. RRR is a pure backbone measure.
Properties
RRR = 0 for trees (every tree has pendant edges touching leaves). RRR > 0 only for graphs where minimum degree δ ≥ 2. For d-regular: RRR = m·(d-1).
Step-by-Step Instructions
- 1Select graph.
- 2Compute d-1 for all v.
- 3For each edge: √((d₁-1)(d₂-1)).
- 4Sum contributions.
- 5Assess backbone.