Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21286120210601Bounds on the outer-independent double Italian domination number1231361410410.22049/cco.2020.26928.1166ENFarzanehAzvinShahed UniversityNaderJafari RadShahed UniversityLutzVolkmannRWTH Aachen University0000-0003-3496-277XJournal Article20200722An outer-independent double Italian dominating function (OIDIDF) on a graph $G$ with vertex set $V(G)$ is a function $f:V(G)longrightarrow {0,1,2,3}$ such that if $f(v)in{0,1}$ for a vertex $vin V(G)$ then $sum_{uin N[v]}f(u)geq3$, and the set $ {uin V(G)|f(u)=0}$ is independent. The weight of an OIDIDF $f$ is the value $w(f)=sum_{vin V(G)}f(v)$. The minimum weight of an OIDIDF on a graph $G$ is called the outer-independent double Italian domination number $gamma_{oidI}(G)$ of $G$. We present sharp lower bounds for the outer-independent double Italian domination number of a tree in terms of diameter, vertex covering number and the order of the tree.http://comb-opt.azaruniv.ac.ir/article_14104_674446c089f9f7401f8ddd07199d0e3c.pdf