On the Outer Independent Double Roman Domination Number

A double Roman dominating function of a graph $G$ is $f:V(G)\rightarrow \{0,1,2,3\}$ having the property that for each vertex $v$ with $f(v)=0$, there exists $u\in N(v)$ $f(u)=3$, or are $u,w\in $f(u)=f(w)=2$, and if $f(v)=1$, then adjacent to assigned at least $2$ under $f$. The domination number $\gamma_{dR}(G)$ minimum weight $f(V(G))=\sum_{v\in V(G)}f(v)$ among all functions $G$. An outer independent $f$ which set vertices $0$ independent. $\gamma_{oidR}(G)$ taken over In this work, we present some contributions study in graphs. Characterizations families connected graphs small numbers, tight lower upper bounds on parameter given. We moreover bound tree $T$ from below by two times cover plus one. also prove decision problem associated NP-complete even when restricted planar maximum degree most four. Finally, give an exact formula concerning corona