The TuranGraph(n,k) command returns the Turán graph with parameters n, k.

The Turán graph is the complete k-partite graph on n vertices whose partitions are as close to equal in cardinality as possible.

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

$G≔\mathrm{TuranGraph}\left(5\,3\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 5\; vertices\; and\; 8\; edges}$

$\mathrm{NumberOfEdges}\left(G\right)$

$8$

$G≔\mathrm{TuranGraph}\left(5\,4\right)$

$G≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 5\; vertices\; and\; 9\; edges}$

$\mathrm{NumberOfEdges}\left(G\right)$

$9$

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

"Turán graph", Wikipedia. http://en.wikipedia.org/wiki/Turan_graph

The GraphTheory[SpecialGraphs][TuranGraph] command was introduced in Maple 2018.

For more information on Maple 2018 changes, see Updates in Maple 2018.