  An edge labeling of a connected graph $G = (V, E)$ is said to be local
antimagic if it is a bijection $f:E \to\{1,\ldots ,|E|\}$ such that for any
pair of adjacent vertices $x$ and $y$, $f^+(x)\not= f^+(y)$, 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 (i) give a sufficient condition
for a graph with one pendant to have $\chi_{la}\ge 3$. A necessary and
sufficient condition for a graph to have $\chi_{la}=2$ is then obtained; (ii)
give a sufficient condition for every circulant graph of even order to have
$\chi_{la} = 3$; (iii) construct infinitely many bipartite and tripartite
graphs with $\chi_{la} = 3$ by transformation of cycles; (iv) apply
transformation of cycles to obtain infinitely many one-point union of regular
(possibly circulant) or bi-regular graphs with $\chi_{la} = 2,3$. The work of
this paper suggests many open problems on the local antimagic chromatic number
of bipartite and tripartite graphs.
