TY - JOUR
ID - 14104
TI - Bounds on the outer-independent double Italian domination number
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Azvin, Farzaneh
AU - Jafari Rad, Nader
AU - Volkmann, Lutz
AD - Shahed University
AD - RWTH Aachen University
Y1 - 2021
PY - 2021
VL - 6
IS - 1
SP - 123
EP - 136
KW - Roman domination
KW - outer-independent double Italian domination
KW - tree
DO - 10.22049/cco.2020.26928.1166
N2 - 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 $vin V(G)$ 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.
UR - http://comb-opt.azaruniv.ac.ir/article_14104.html
L1 - http://comb-opt.azaruniv.ac.ir/article_14104_674446c089f9f7401f8ddd07199d0e3c.pdf
ER -