On the disjunctive domination numbers of the torus grid graphs

Zhi Qiao; Zheng-Jiang Xia; Zhen-Mu Hong

paper

On the disjunctive domination numbers of the torus grid graphs

arXiv:2605.19497

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 $C_{m} □ C_{n}$ , and determine the disjunctive domination numbers of $C_{3} □ C_{n}$ , $C_{4} □ C_{n}$ and $C_{8} □ C_{4 n}$ .