Saved in:
Bibliographic Details
Main Authors: Qiao, Zhi, Xia, Zheng-Jiang, Hong, Zhen-Mu
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.19497
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866916057562742784
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