General inverse degree IDₐ(G) = Σ d(v)^(-a). Vertex-based parametric family. a=1: ID (inverse degree). a=2: mM₁ (modified Zagreb). a=-1: Σd=2m. a=0: n. Unifies vertex-based degree indices under one parameter.
How to Use
Select graph and exponent:
- a=1: ID
- a=2: mM₁
- Custom: Any a
Special Cases
a=0: n (vertex count). a=-1: Σd = 2m. a=-2: M₁. a=1: ID = Σ1/d. a=2: mM₁ = Σ1/d². Negative a→classical, positive a→inverse. Smooth transition.
Behavior in a
Increasing a: low-degree vertices dominate more. Decreasing a: high-degree dominate. a=0: all equal. The parameter a controls the 'lens' from hub-centric (a<0) to leaf-centric (a>0).
Step-by-Step Instructions
- 1Select graph.
- 2Choose exponent a.
- 3For each vertex: d(v)^(-a).
- 4Sum all terms.
- 5Explore different a values.