@article {
author = {Azvin, Farzaneh and Jafari Rad, Nader and Volkmann, Lutz},
title = {Bounds on the outer-independent double Italian domination number},
journal = {Communications in Combinatorics and Optimization},
volume = {6},
number = {1},
pages = {123-136},
year = {2021},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2020.26928.1166},
abstract = {An 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 $v\in V(G)$ then $\sum_{u\in N[v]}f(u)\geq3$, and the set $ \{u\in V(G)|f(u)=0\}$ is independent. The weight of an OIDIDF $f$ is the value $w(f)=\sum_{v\in V(G)}f(v)$. 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.},
keywords = {Roman domination,outer-independent double Italian domination,tree},
url = {http://comb-opt.azaruniv.ac.ir/article_14104.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_14104_674446c089f9f7401f8ddd07199d0e3c.pdf}
}