Reduced Sombor SOred(G) = Σ √((dᵢ-1)²+(dⱼ-1)²). Uses d-1 (reduced degree) instead of d. Pendant vertices have reduced degree 0, contributing nothing. SOred captures connectivity beyond the trivial pendant bonds.
How to Use
Select graph:
- SOred: Reduced Sombor
- d-1: Reduced deg.
- vs SO: Compare
Reduced Degree
d(v)-1: pendant vertex → 0 (no excess). Hub with d=5 → 4 excess connections. Reduced degree measures connectivity 'beyond the minimum'. Removes trivial single-bond contribution.
Bounds
SOred = 0 for stars (all leaves have reduced degree 0). SOred(K_n) = n(n-1)/2 · (n-2)√2. Trees: SOred depends only on internal vertices.
Step-by-Step Instructions
- 1Select graph.
- 2Compute d-1 for all vertices.
- 3For each edge: √((d₁-1)²+(d₂-1)²).
- 4Sum all norms.
- 5Compare with SO.