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A characterization relating domination, semitotal domination and total Roman domination in trees | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 3، دوره 6، شماره 2، اسفند 2021، صفحه 197-209 اصل مقاله (429.04 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2020.26892.1157 | ||
| نویسندگان | ||
| Abel Cabrera Martinez* 1؛ Alondra Martinez Arias2؛ Maikel Menendez Castillo2 | ||
| 1Universitat Rovira i Virgili, Tarragona, Spain | ||
| 2Departamento de Matemática, Universidad de Oriente, Cuba | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Total Roman domination؛ semitotal domination؛ domination؛ trees | ||
| مراجع | ||
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