Properties
- For a fixed degree and number of vertices, the Kautz graph has the smallest diameter of any possible directed graph with vertices and degree .
- All Kautz graphs have Eulerian cycles. (An Eulerian cycle is one which visits each edge exactly once-- This result follows because Kautz graphs have in-degree equal to out-degree for each node)
- All Kautz graphs have a Hamiltonian cycle (This result follows from the correspondence described above between edges of the Kautz graph and vertices of the Kautz graph ; a Hamiltonian cycle on is given by an Eulerian cycle on )
- A degree- Kautz graph has disjoint paths from any node to any other node .
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