Formulas for various domination numbers of products of paths and cycles

The existence of a constant time algorithm for solving different domination problems on the subclass of polygraphs, rotagraphs and fasciagraphs, where the monograph is fixed, is shown by means of path algebras. As these graphs include products (the Cartesian, strong, direct, lexicographic) of paths and cycles, we implement the algorithm to get formulas in the case of the domination number, the Roman domination number and the independent domination number of products of paths and cycles where the size of one factor is fixed. We also show that the values of the investigated graph invariants on fasciagraphs and rotagraphs with the same monograph can only differ by a constant value.