@article {
author = {Amjadi, Jafar and Samadi, Babak and Volkmann, Lutz},
title = {Total restrained Roman domination},
journal = {Communications in Combinatorics and Optimization},
volume = {8},
number = {3},
pages = {575-587},
year = {2023},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2022.27628.1303},
abstract = {Let $G$ be a graph with vertex set $V(G)$. A Roman dominating function (RDF) on a graph $G$ is a function $f:V(G)\longrightarrow\{0,1,2\}$ such that every vertex $v$ with $f(v)=0$ is adjacent to a vertex $u$ with $f(u)=2$. If $f$ is an RDF on $G$, then let $V_i=\{v\in V(G): f(v)=i\}$ for $i\in\{0,1,2\}$. An RDF $f$ is called a restrained (total) Roman dominating function if the subgraph induced by $V_0$ (induced by $V_1\cup V_2$) has no isolated vertex. A total and restrained Roman dominating function is a total restrained Roman dominating function. The total restrained Roman domination number $\gamma_{trR}(G)$ on a graph $G$ is the minimum weight of a total restrained Roman dominating function on the graph $G$. We initiate the study of total restrained Roman domination number and present several sharp bounds on $\gamma_{trR}G)$. In addition, we determine this parameter for some classes of graphs.},
keywords = {Total restrained domination,total restrained Roman domination,total restrained Roman domination number},
url = {https://comb-opt.azaruniv.ac.ir/article_14426.html},
eprint = {https://comb-opt.azaruniv.ac.ir/article_14426_d5f2a14f23334b09e3f71e675a41e54c.pdf}
}