%0 Journal Article 
%A Campanelli, Nicolás
%A Kuziak, Dorota
%T Total Roman domination in the lexicographic product of graphs
%D 2019
%@ 0166-218X
%U http://hdl.handle.net/10498/30893
%X A total Roman dominating function of a graph $G=(V,E)$ is a function $f: V(G)\to \{0,1,2\}$ such that for every vertex $v$ with $f(v)=0$ there exists a vertex $u$ adjacent to $v$ with $f(u)=2$, and such that the subgraph induced by the set of vertices labeled one or two has no isolated vertices. The total Roman domination number of $G$ is the minimum value of the sums $\sum_{v\in V}{f(v)}$ over all total Roman dominating functions $f$ of $G$. In this paper we study the total Roman domination number of the lexicographic product of graphs.
%K Total Roman domination
%K Roman domination
%K Lexicographic product graphs
%~ Universidad de Cádiz