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arXiv · 2605.19497

On the disjunctive domination numbers of the torus grid graphs

Zhi Qiao·Zheng-Jiang Xia·Zhen-Mu Hong
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Abstract

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 $C_8\Box C_{4n}$.

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Zhi Qiao, Zheng-Jiang Xia, Zhen-Mu Hong. 2026-05-28. On the disjunctive domination numbers of the torus grid graphs. https://arxiv.org/abs/2605.19497

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