# graph.kautz

0th

Percentile

##### Kautz graphs

Kautz graphs are labeled graphs representing the overlap of strings.

Keywords
graphs
##### Usage
graph.kautz(m,n)
##### Arguments
m
Integer scalar, the size of the alphabet. See details below.
n
Integer scalar, the length of the labels. See details below.
##### Details

A Kautz graph is a labeled graph, vertices are labeled by strings of length n+1 above an alphabet with m+1 letters, with the restriction that every two consecutive letters in the string must be different. There is a directed edge from a vertex v to another vertex w if it is possible to transform the string of v into the string of w by removing the first letter and appending a letter to it. Kautz graphs have some interesting properties, see eg. Wikipedia for details.

##### Value

• A graph object.

##### concept

Kautz graph

graph.de.bruijn, line.graph
line.graph(graph.kautz(2,1))
graph.kautz(2,2)