  A graph $G$ is antimagic if there exists a bijection $f$ from $E(G)$ to
$\left\{1,2, \dots,|E(G)|\right\}$ such that the vertex sums for all vertices
of $G$ are distinct, where the vertex sum is defined as the sum of the labels
of all incident edges. Hartsfield and Ringel conjectured that every connected
graph other than $K_2$ admits an antimagic labeling. It is still a challenging
problem to address antimagicness in the case of disconnected graphs. In this
paper, we study antimagicness for the disconnected graph that is constructed as
the direct product of a star and a path.
