The 
-arrangement
graph 
is defined as the graph on the vertex
set consisting of the permutations of 
containing exactly 
elements, where 
and 
are integers with 
, and 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.
