Super connectivity κ₁(G): minimum vertices to remove so that G-S is disconnected AND has no isolated vertices. Stricter than ordinary κ. Models scenarios where total isolation of a node is unrealistic (each node retains at least one neighbor).
How to Use
Select graph:
- κ₁: Super conn.
- vs κ: Compare
- Isolates: None!
Why Super?
Standard κ allows any disconnection. But in real networks, completely isolating a node (all neighbors removed) is an extreme, unlikely scenario. Super connectivity requires non-trivial components on both sides.
Key Results
κ₁ ≥ κ always. For Kneser graphs, Cayley graphs: κ₁ often equals 2δ-2. Super-connected if κ₁ > κ. Many regular graphs are super-connected.
Step-by-Step Instructions
- 1Select graph.
- 2Compute κ₁.
- 3Compare with κ.
- 4Check super-connected.
- 5Apply to network.