The 
-arrangement
graph 
is defined as the graph on the vertex set consisting
of the permutations of 
containing at most 
elements where vertices are connected by edges whenever two
permutations differ in exactly one of their 
positions. The 
-arrangement graph has 
nodes, is regular
of vertex degree 
, 
-connected, has graph diameter 
, and is vertex-Vertex-Transitive
Graph and edge-transitive (Day and Tripathi
1992).
The arrangement graph 
is the line graph of the
-crown graph.
Precomputed properties of arrangement graphs are available in the Wolfram Language as GraphData[
"ArrangementGraph",
n,
k
].
Special cases of 
are summarized in the following table and illustrated above.
