3 research outputs found
On Total Domination in the Cartesian Product of Graphs
Ho proved in [A note on the total domination number, Util. Math. 77 (2008) 97–100] that the total domination number of the Cartesian product of any two graphs without isolated vertices is at least one half of the product of their total domination numbers. We extend a result of Lu and Hou from [Total domination in the Cartesian product of a graph and K2or Cn, Util. Math. 83 (2010) 313–322] by characterizing the pairs of graphs G and H for which γt(G□H)=12γt(G)γt(H)
, whenever γt(H) = 2. In addition, we present an infinite family of graphs Gn with γt(Gn) = 2n, which asymptotically approximate equality in γt(Gn□Hn)≥12γt(Gn)2
On Total Domination in the Cartesian Product of Graphs
Ho proved in [A note on the total domination number, Util. Math. 77 (2008) 97–100] that the total domination number of the Cartesian product of any two graphs without isolated vertices is at least one half of the product of their total domination numbers. We extend a result of Lu and Hou from [Total domination in the Cartesian product of a graph and or , Util. Math. 83 (2010) 313–322] by characterizing the pairs of graphs and for which , whenever . In addition, we present an infinite family of graphs with , which asymptotically approximate equality in