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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.10952 |
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| _version_ | 1866911105797849088 |
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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 $T\subseteq V(G)$ is a $2$-\textit{movable total dominating set} of $G$ if $T$ is a total dominating set and for every pair $x,y \in T$, $T \backslash \{x, y\}$ is a total dominating set in $G$, or there exist $u, v \in V(G) \backslash T$ such that $u$ and $v$ are adjacent to $x$ and $y$, respectively, and $(T \backslash \{x,y\}) \cup \{u,v\}$ is a total dominating set in $G$. The $2$-\textit{movable total domination number} of $G$, denoted by $γ_{mt}^{2}(G)$, is the minimum cardinality of a 2-movable total dominating set of $G$. A 2-movable total dominating set with cardinality equal to $γ_{mt}^{2}(G)$ is called $γ_{mt}^{2}$-set of $G$. This paper present the 2-movable total domination in the join and corona of graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10952 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On 2-Movable Total Domination in the Join and Corona of Graphs Pedrano, Ariel C. Paluga, Rolando N. Combinatorics 54C05, 54C08, 54C10 Let $G$ be a connected graph. A non-empty $T\subseteq V(G)$ is a $2$-\textit{movable total dominating set} of $G$ if $T$ is a total dominating set and for every pair $x,y \in T$, $T \backslash \{x, y\}$ is a total dominating set in $G$, or there exist $u, v \in V(G) \backslash T$ such that $u$ and $v$ are adjacent to $x$ and $y$, respectively, and $(T \backslash \{x,y\}) \cup \{u,v\}$ is a total dominating set in $G$. The $2$-\textit{movable total domination number} of $G$, denoted by $γ_{mt}^{2}(G)$, is the minimum cardinality of a 2-movable total dominating set of $G$. A 2-movable total dominating set with cardinality equal to $γ_{mt}^{2}(G)$ is called $γ_{mt}^{2}$-set of $G$. This paper present the 2-movable total domination in the join and corona of graphs. |
| title | On 2-Movable Total Domination in the Join and Corona of Graphs |
| topic | Combinatorics 54C05, 54C08, 54C10 |
| url | https://arxiv.org/abs/2508.10952 |