A lower bound for the number of triangular embeddings of some complete graphs and complete regular tripartite graphs

We prove that, for a certain positive constant a and for an infinite set of values of n, the number of nonisomorphic triangular embeddings of the complete graph K n is at least n a n 2 . A similar lower bound is also given, for an infinite set of values of n, on the number of nonisomorphic triangular embeddings of the complete regular tripartite graph K n , n , n .