TY - JOUR
ID - 14426
TI - Total restrained Roman domination
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Amjadi, Jafar
AU - Samadi, Babak
AU - Volkmann, Lutz
AD - Azarbaijan Shahid Madani University
AD - Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
AD - RWTH Aachen University
Y1 - 2023
PY - 2023
VL - 8
IS - 3
SP - 575
EP - 587
KW - Total restrained domination
KW - total restrained Roman domination
KW - total restrained Roman domination number
DO - 10.22049/cco.2022.27628.1303
N2 - 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.
UR - https://comb-opt.azaruniv.ac.ir/article_14426.html
L1 - https://comb-opt.azaruniv.ac.ir/article_14426_d5f2a14f23334b09e3f71e675a41e54c.pdf
ER -