3-tuple total domination number of rook's graphs
Copyright policy )3-tuple total domination number of rook's graphs
A $k$-tuple total dominating set ($k$TDS) 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 $k$TDS is called the $k$-tuple total dominating number and it is denoted by $��_{\times k,t}(G)$. We give a constructive proof of a general formula for $��_{\times 3, t}(K_n \Box K_m)$.
rook’s graph, Graph operations (line graphs, products, etc.), vizing’s conjecture, Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.), 05c69, QA1-939, FOS: Mathematics, 05c76, total domination, Mathematics - Combinatorics, Combinatorics (math.CO), cartesian product of graphs, Mathematics, Rooks graph, k-tuple total domination
rook’s graph, Graph operations (line graphs, products, etc.), vizing’s conjecture, Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.), 05c69, QA1-939, FOS: Mathematics, 05c76, total domination, Mathematics - Combinatorics, Combinatorics (math.CO), cartesian product of graphs, Mathematics, Rooks graph, k-tuple total domination
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