  Let $G$ be a connected graph with $|V| = n$ and $|E| = m$. A bijection
$f:E\rightarrow \{1,2,...,m\}$ is called a local antimagic labeling of $G$ if
for any two adjacent vertices $u$ and $v$, $w(u) \neq w(v)$, where $w(u) =
\sum_{e \in E(u)}f(e)$, and $E(u)$ is the set of edges incident to $u$. Thus,
any local antimagic labeling induces a proper vertex coloring of $G$ where the
vertex $v$ is assigned the color $w(v)$. The local antimagic chromatic number
is the minimum number of colors taken over all colorings induced by local
antimagic labelings of $G$. Let $m,n > 1$. In this paper, the local antimagic
chromatic number of a complete tripartite graph $K_{1,m,n}$, and $r$ copies of
a complete bipartite graph $K_{m,n}$ where $m \not \equiv n \bmod 2$ are
determined.
