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 .
Read more about this topic: Kautz Graph
Famous quotes containing the word properties:
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)