TITLE: Why do people use "K" to represent a complete graph?
QUESTION [8 upvotes]: Why do people use the letter "K", rather than "C", to represent a complete graph? Does it come from German "komplett"?

REPLY [7 votes]: My understanding is that Harary introduced the notation $K_5$ and $K_{3,3}$ for the graphs appearing in Kuratowski's theorem, and the choice of $K$ as symbol was in honour of Kuratowski. 
I must admit that I do not have this first hand, but it was certainly the accepted explanation as I was "growing up" graph theoretically.
Edit: The story is in print on page 259 of Doug West's "Introduction to Graph Theory".