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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.19497 |
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| _version_ | 1866916057562742784 |
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| author | Qiao, Zhi Xia, Zheng-Jiang Hong, Zhen-Mu |
| author_facet | Qiao, Zhi Xia, Zheng-Jiang Hong, Zhen-Mu |
| contents | Let $Γ=(V,E)$ be a graph. The disjunctive domination number of $Γ$ is the minimum cardinality of a set $S\subseteq V$ such that every vertex not in $S$ is adjacent to a vertex of $S$, or has at least two vertices in $S$ at distance $2$ from it. In this paper, we give bounds for the disjunctive domination numbers of the torus grid graphs $C_m\Box C_n$, and determine the disjunctive domination numbers of $C_3\Box C_n$, $C_4\Box C_{n}$ and $C_8\Box C_{4n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19497 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the disjunctive domination numbers of the torus grid graphs Qiao, Zhi Xia, Zheng-Jiang Hong, Zhen-Mu Combinatorics Let $Γ=(V,E)$ be a graph. The disjunctive domination number of $Γ$ is the minimum cardinality of a set $S\subseteq V$ such that every vertex not in $S$ is adjacent to a vertex of $S$, or has at least two vertices in $S$ at distance $2$ from it. In this paper, we give bounds for the disjunctive domination numbers of the torus grid graphs $C_m\Box C_n$, and determine the disjunctive domination numbers of $C_3\Box C_n$, $C_4\Box C_{n}$ and $C_8\Box C_{4n}$. |
| title | On the disjunctive domination numbers of the torus grid graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.19497 |