The Kautz graph is a directed graph).

edges

.

Kautz graphs are closely related to De Bruijn graphs.

Properties

• , the Kautz graph has the smallest diameter.

• 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)

• .

In computing

The Kautz graph has been used as a network topology for connecting processors in high-performance computing and fault-tolerant computing applications: such a network is known as a Kautz network.

Notes