  Given a graph $G=(V,E)$, $f:V \rightarrow \{0,1,2 \}$ is the Italian
dominating function of $G$ if $f$ satisfies $\sum_{u \in N(v)}f(u) \geq 2$ when
$f(v)=0$. Denote $w(f)=\sum_{v \in V}f(v)$ as the weight of $f$. Let
$V_i=\{v:f(v)=i\},i=0,1,2$, we call $f$ the independent Italian dominating
function if $V_1 \cup V_2$ is an independent set. The independent Italian
domination number of $G$ is the minimum weight of independent Italian
dominating function $f$, denoted by $i_{I}(G)$. We equivalently transform the
independent domination problem of the connected block graph $G$ to the induced
independent domination problem of its block-cutpoint graph $T$, then a linear
time algorithm is given to find $i_{I}(G)$ of any connected block graph $G$
based on dynamic programming.
