  An \emph{antimagic labeling} of a finite undirected simple graph with $m$
edges and $n$ vertices is a bijection from the set of edges to the integers
$1,...,m$ such that all $n$ vertex sums are pairwise distinct, where a vertex
sum is the sum of labels of all edges incident with the same vertex. A graph is
called \emph{antimagic} if it has an antimagic labeling. In 1990, Hartsfield
and Ringel conjectured that every connected graph, but $K_2$, is antimagic. In
2004, N. Alon et al showed that this conjecture is true for $n$-vertex graphs
with minimum degree $\Omega(\log n)$. They also proved that complete partite
graphs (other than $K_2$) and $n$-vertex graphs with maximum degree at least
$n-2$ are antimagic. Recently, Wang showed that the toroidal grids (the
Cartesian products of two or more cycles) are antimagic. Two open problems left
in Wang's paper are about the antimagicness of lattice grid graphs and prism
graphs, which are the Cartesian products of two paths, and of a cycle and a
path, respectively. In this article, we prove that these two classes of graphs
are antimagic, by constructing such antimagic labelings.
