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- 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.
