Bagging Approach for Italian Domination in $C_{n} \square\,P_{m}$

For graph
$G=(V,E)$
, the open neighborhood of a vertex
$v$
is
$N(v)=\{u\in V|uv\in E\}$
. A function
$f: V(G)\rightarrow \{0, 1, 2\}$
is called an Italian dominating function of
$G$
if
$\sum _{u\in N(v)}f(u)\geq 2$
, for each vertex
$f(v)=0$
. The weight of
$f$
is
$w(f)=\sum _{v\in V(G)}f(v)$
. The minimum weight of an Italian dominating function of
$G$
is called the Italian domination number of
$G$
, denoted by
$\gamma _{I}(G)$
. In this paper, we present a bagging approach and a partitioning approach to investigate the Italian domination number of Cartesian product of circles and paths,
$C_{n}\Box \,P_{m}$
. We determine the exact values of the Italian domination numbers of
$C_{n}\Box \,P_{3}$
,
$C_{3}\Box \,P_{m}$
. We also present some bounds on the Italian domination number of
$C_{n}\Box \,P_{m}$
for
$n, m\geq 4$
.