Overview

In this paper we determine conditions for when the complete m-partite graph is not a mod sum graph. Also we show $K_{n,m}$ is a mod sum graph when $m$ is even and $m \ge 2n$ or when $m$ is odd and $m \ge 3n-3$ and $\rho (K_{n,m})=n$ when $3 \le n \le m < 2n$. In Chapter 2 we prove these results and we present conjectures and conclude with Chapter 3.