Non-isomorphic Minimal Colorings of $K_{4n+3}$

Abstract

We prove that the number of nonisomorphic minimal $2$-colorings of the edges of $K_{4n+3}$ is at least $2n$ less than the number of nonisomorphic minimal $2$-colorings of the edges of $K_{4n+2}$, where $n$ is a nonnegative integer. Harary explicitly gave all the nonisomorphic minimal $2$-colorings of the edges of $K_6$. In this paper, we give all the nonisomorphic minimal $2$-colorings of the edges of $K_7$.