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.