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Isn't this also known as a complete k-partite graph? At least Bondy and Murty (1982) call it that. Perhaps Turan's name was used for this graph after that publication? Should the article at least mention the name complete k-partite graph?
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I think a complete k-partite graph is a more general family of graphs in which the sizes of the parts need not be nearly equal. But I will look into finding a way to work that terminology into the article.
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The stated number of edges in the Turan graph is wrong. For instance, the 8-partit Turan graph on 12 vertices has only 62 edges while the formula yields 63 edges.
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