  An edge labeling of a connected graph $G = (V,E)$ is said to be local
antimagic if it is a bijection $f : E \to \{1, . . . , |E|\}$ such that for any
pair of adjacent vertices $x$ and $y$, $f^+(x) \ne f^+(y)$, where the induced
vertex label $f^+(x) = \sum f(e)$, with $e$ ranging over all the edges incident
to $x$. The local antimagic chromatic number of $G$, denoted by $\chi_{la}(G)$,
is the minimum number of distinct induced vertex labels over all local
antimagic labelings of $G$. In this paper, we first show that a $d$-leg spider
graph has $d+1\le \chi_{la}\le d+2$. We then obtain many sufficient conditions
such that both the values are attainable. Finally, we show that each 3-leg
spider has $\chi_{la} = 4$ if not all legs are of odd length. We conjecture
that almost all $d$-leg spiders of size $q$ that satisfies $d(d+1) \le 2(2q-1)$
with each leg length at least 2 has $\chi_{la} = d+1$.
