Total and paired domination numbers of toroidal meshes

2011/09/19 by Fu-Tao Hu, Hu, Fu-Tao, Jun‐Ming Xu +2
Computer Science · Mathematics · #05C12 #05C25 #05C40 #Advanced Graph Theory Research #Combinatorics (math.CO) #E.1 #FOS: Mathematics #G.2.2 #Graph Labeling and Dimension Problems #Interconnection Networks and Systems #acm:05C12 #acm:05C25 #acm:05C40 #math.CO #msc:05C12 #msc:05C25 #msc:05C40

paper · pdf · doi:10.48550/arxiv.1109.3928

8 pages with 2 figures

arxiv created 2011/09/19 · openalex publication_date 2011/09/19 · arxiv updated 2011/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a graph without isolated vertices. The total domination number of G is the minimum number of vertices that can dominate all vertices in G, and the paired domination number of G is the minimum number of vertices in a dominating set whose induced subgraph contains a perfect matching. This paper determines the total domination number and the paired domination number of the toroidal meshes, i.e., the Cartesian product of two cycles C_n and C_m for any n≥ 3 and m∈\3,4\, and gives some upper bounds for n, m≥ 5.

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