@article {
author = {Cabrera Martinez, Abel and Martinez Arias, Alondra and Menendez Castillo, Maikel},
title = {A characterization relating domination, semitotal domination and total Roman domination in trees},
journal = {Communications in Combinatorics and Optimization},
volume = {6},
number = {2},
pages = {197-209},
year = {2021},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2020.26892.1157},
abstract = {A total Roman dominating function on a graph $G$ is a function $f: V(G) \rightarrow \{0,1,2\}$ such that for every vertex $v\in V(G)$ with $f(v)=0$ there exists a vertex $u\in V(G)$ adjacent to $v$ with $f(u)=2$, and the subgraph induced by the set $\{x\in V(G): f(x)\geq 1\}$ has no isolated vertices. The total Roman domination number of $G$, denoted $\gamma_{tR}(G)$, is the minimum weight $\omega(f)=\sum_{v\in V(G)}f(v)$ among all total Roman dominating functions $f$ on $G$. It is known that $\gamma_{tR}(G)\geq \gamma_{t2}(G)+\gamma(G)$ for any graph $G$ with neither isolated vertex nor components isomorphic to $K_2$, where $\gamma_{t2}(G)$ and $\gamma(G)$ represent the semitotal domination number and the classical domination number, respectively. In this paper we give a constructive characterization of the trees that satisfy the equality above.},
keywords = {total Roman domination,semitotal domination,domination,trees},
url = {http://comb-opt.azaruniv.ac.ir/article_14113.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_14113_0b4f6cdb301bc12d4c4eb2b4ad659382.pdf}
}