Let $G=(V,E)$ be graph. For any function $h:V\to \{0,1,2,3\}$, let $V_i=\{v\in V:h(v)=i\}$, $0\le i\le 3$. The function $h$ is called an outer-independent double Roman dominating function (OIDRDF) if the following conditions are satisfied.

The outer-independent double Roman domination number of $G$ is defined by ${\gamma }_{oidR}(G)=\mathrm{\text{min}}\left\{\right.{\sum }_{v\in V}h(v):h$ is an OIDRDF OF $G\left\}\right.$. We prove that the decision problem MOIDRDP, corresponding to ${\gamma }_{oidR}(G)$ is NP-complete for split graphs. We also show that it is linear time solvable for connected threshold graphs and bounded treewidth graphs. Finally, we show that the MOIDRDP and domination are not equivalent in computational complexity aspects.

让$G=（V,乙）$是图。对于任何函数$H:V\to \{0,1,2,3\}$， 让$V_{我}=\{v\epsilon V:H（v）=我\}$,$0\le 我\le 3$。功能$H$如果满足以下条件，则称为外独立双罗马支配函数（OIDRDF）。

外独立双罗马统治数$G$定义为${\gamma }_{哦我d右}（G）=\mathrm{\text{分钟}}\left\{\right.{\Sigma }_{v\epsilon V}H（v）:H$是一个 OIDRDF OF$G\left\}\right.$。我们证明决策问题MOIDRDP，对应于${\gamma }_{哦我d右}（G）$对于分割图来说是 NP 完全的。我们还表明，对于连通阈值图和有界树宽图，它是线性时间可解的。最后，我们表明 MOIDRDP 和统治在计算复杂度方面并不等效。