%0 Journal Article
%T Total double Roman domination in graphs
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Hao, Guoliang
%A Volkmann, Lutz
%A Mojdeh, Doost Ali
%D 2020
%\ 06/01/2020
%V 5
%N 1
%P 27-39
%! Total double Roman domination in graphs
%K total double Roman domination
%K double Roman domination
%K total Roman domination
%K total domination
%K domination
%R 10.22049/cco.2019.26484.1118
%X Let $G$ be a simple graph with vertex set $V$. A double Roman dominating function (DRDF) on $G$ is a function $f:Vrightarrow{0,1,2,3}$ satisfying that if $f(v)=0$, then the vertex $v$ must be adjacent to at least two vertices assigned $2$ or one vertex assigned $3$ under $f$, whereas if $f(v)=1$, then the vertex $v$ must be adjacent to at least one vertex assigned $2$ or $3$. The weight of a DRDF $f$ is the sum $sum_{vin V}f(v)$. A total double Roman dominating function (TDRDF) on a graph $G$ with no isolated vertex is a DRDF $f$ on $G$ with the additional property that the subgraph of $G$ induced by the set ${vin V:f(v)ne0}$ has no isolated vertices. The total double Roman domination number $gamma_{tdR}(G)$ is the minimum weight of a TDRDF on $G$. In this paper, we give several relations between the total double Roman domination number of a graph and other domination parameters and we determine the total double Roman domination number of some classes of graphs.
%U http://comb-opt.azaruniv.ac.ir/article_13945_dce686282b94fcb96a05edec316a45ef.pdf