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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2509.05301 |
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| _version_ | 1866916936967782400 |
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| author | Pedrano, Ariel C. Paluga, Rolando N. |
| author_facet | Pedrano, Ariel C. Paluga, Rolando N. |
| contents | Let $G$ be a connected graph. A non-empty $S\subseteq V(G)$ is a $2$-movable dominating set of $G$ if $S$ is a dominating set and for every pair $x,y \in S$, $S\backslash \{x, y\}$ is a dominating set in $G$, or there exist $u, v \in V(G) \backslash S$ such that $u$ and $v$ are adjacent to $x$ and $y$, respectively, and $(S \backslash \{x,y\}) \cup \{u,v\}$ is a dominating set in $G$. The $2$-movable domination number of $G$, denoted by $γ_{m}^{2}(G)$, is the minimum cardinality of a 2-movable dominating set of $G$. A 2-movable dominating set with cardinality equal to $γ_{m}^{2}(G)$ is called $γ_{m}^{2}$-set of $G$.
This paper present the 2-movable domination number in the corona and join of graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05301 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On 2-Movable Domination in the Join and Corona of Graphs Pedrano, Ariel C. Paluga, Rolando N. General Mathematics : 54C05, 54C08, 54C10 G.2 Let $G$ be a connected graph. A non-empty $S\subseteq V(G)$ is a $2$-movable dominating set of $G$ if $S$ is a dominating set and for every pair $x,y \in S$, $S\backslash \{x, y\}$ is a dominating set in $G$, or there exist $u, v \in V(G) \backslash S$ such that $u$ and $v$ are adjacent to $x$ and $y$, respectively, and $(S \backslash \{x,y\}) \cup \{u,v\}$ is a dominating set in $G$. The $2$-movable domination number of $G$, denoted by $γ_{m}^{2}(G)$, is the minimum cardinality of a 2-movable dominating set of $G$. A 2-movable dominating set with cardinality equal to $γ_{m}^{2}(G)$ is called $γ_{m}^{2}$-set of $G$. This paper present the 2-movable domination number in the corona and join of graphs. |
| title | On 2-Movable Domination in the Join and Corona of Graphs |
| topic | General Mathematics : 54C05, 54C08, 54C10 G.2 |
| url | https://arxiv.org/abs/2509.05301 |