Sombor index SO(G) = Σ √(dᵢ²+dⱼ²) over edges. Gutman (2021). The newest blockbuster in chemical graph theory! Geometric: each edge contributes the Euclidean norm of its endpoint degrees. Named after Sombor, Serbia. Already 500+ papers in 3 years.
How to Use
Select graph:
- SO: Sombor index
- √(d²+d²): Per edge
- Norm: Euclidean
Geometric View
Each edge (i,j) maps to point (dᵢ,dⱼ) in 2D. SO sums distances from origin. Larger degrees → farther from origin → larger contribution. Beautiful geometric interpretation of graph topology.
Bounds
SO(K_n) = n(n-1)²√2/2. SO ≥ √2·m (all edges between degree-1). For regular d-graphs: SO = m·d·√2. SO relates to M₁ and M₂ via Cauchy-Schwarz.
Step-by-Step Instructions
- 1Select graph.
- 2For each edge: √(dᵢ²+dⱼ²).
- 3Sum all norms.
- 4Compare graphs.
- 5Geometric view.