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

Abstract

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 $K_{n,n,n}$.