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Total restrained Roman domination | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 10، دوره 8، شماره 3، آذر 2023، صفحه 575-587 اصل مقاله (419.43 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2022.27628.1303 | ||
| نویسندگان | ||
| Jafar Amjadi1؛ Babak Samadi2؛ Lutz Volkmann* 3 | ||
| 1Azarbaijan Shahid Madani University | ||
| 2Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran | ||
| 3RWTH Aachen University | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Total restrained domination؛ total restrained Roman domination؛ total restrained Roman domination number | ||
| مراجع | ||
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