The JohnsonGraph(n, k) command constructs the (n,k) Johnson graph. This is an undirected graph in which the vertices correspond to k-element subsets of {1,…,k}, and an edge exists between two vertices when the intersection of their associated subsets has cardinality k-1.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{with}\left(\mathrm{SpecialGraphs}\right)\:$

$\mathrm{J52}≔\mathrm{JohnsonGraph}\left(5\,2\right)$

$\mathrm{J52}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 10\; vertices\; and\; 30\; edge(s)}$

$\mathrm{ChromaticNumber}\left(\mathrm{J52}\right)$

$5$

$\mathrm{DrawGraph}\left(\mathrm{J52}\right)$

"Johnson graph", Wikipedia. http://en.wikipedia.org/wiki/Johnson_graph

The GraphTheory[SpecialGraphs][JohnsonGraph] command was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.