  Let $G = (V, E)$ be a finite simple undirected graph without $K_2$
components. A bijection $f : E \rightarrow \{1, 2,\cdots, |E|\}$ is called a
local antimagic labeling if for any two adjacent vertices $u$ and $v$, they
have different vertex sums, i.e., $w(u) \neq w(v)$, where the vertex sum $w(u)
= \sum_{e \in E(u)} f(e)$, 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 (vertex sum) $w(v)$. The local antimagic
chromatic number $\chi_{la}(G)$ is the minimum number of colors taken over all
colorings induced by local antimagic labelings of $G$. It was conjectured
\cite{Aru-Wang} that for every tree $T$ the local antimagic chromatic number
$l+ 1 \leq \chi_{la} ( T )\leq l+2$, where $l$ is the number of leaves of $T$.
In this article we verify the above conjecture for complete full $t$-ary trees,
for $t \geq 2$. A complete full $t$-ary tree is a rooted tree in which all
nodes have exactly $t$ children except leaves and every leaf is of the same
depth. In particular we obtain that the exact value for the local antimagic
chromatic number of all complete full $t$-ary trees is $ l+1$ for odd $t$.
