3-Tuple Total Domination Number of Rook’s Graphs

Abstract

A k-tuple total dominating set (kTDS) of a graph G is a set S of vertices in which every vertex in G is adjacent to at least k vertices in S. The minimum size of a kTDS is called the k-tuple total dominating number and it is denoted by γ×k,t(G). We give a constructive proof of a general formula for γ×3,t(Kn□Km).

Keywords

• k-tuple total domination
• cartesian product of graphs
• rook’s graph
• vizing’s conjecture
• 05c69
• 05c76