  The closed neighborhood $N_G[e]$ of an edge $e$ in a graph $G$ is the set
consisting of $e$ and of all edges having an end-vertex in common with $e$. Let
$f$ be a function on $E(G)$, the edge set of $G$, into the set $\{-1,1\}$. If
$\sum_{x\in{N[e]}}f(x)\geq 1$ for each edge $e \in E(G)$, then $f$ is called a
signed edge dominating function of $G$. The signed edge domination number of
$G$ is the minimum weight of a signed edge dominating function of $G$. In this
paper, we find the signed edge domination number of the complete tripartite
graph $K_{m,n,p}$, where $1\leq m\leq n$ and $p\geq m+n$. This completes the
search for the signed edge domination numbers of the complete tripartite
graphs.
