A note on domination parameters of the conjunction of two special graphs

A dominating set D of G is called a split dominating set of G if the subgraph induced by the subset V(G)-D is disconnected. The cardinality of a minimum split dominating set is called the minimum split domination number of G. Such subset and such number was introduced in [4]. In [2], [3] the authors estimated the domination number of products of graphs. More precisely, they were study products of paths. Inspired by those results we give another estimation of the domination number of the conjunction (the cross product) Pₙ ∧ G. The split domination number of Pₙ ∧ G also is determined. To estimate this number we use the minimum connected domination number ${\displaystyle {\gamma }_c\left(G\right)}$.