Domination in cylindrical graphs

The domination number γ(Cm□Pn) of the Cartesian product Cm□Pn of a cycle and a path has been computed when m ≡ 0, 2 (mod 5). In the remaining cases m ≡ 1, 3, 4 (mod 5), exact formulae for γ(Cm□Pn) have been determined when either m ≤ 30 or n ≤ 22. For the rest of the cases, only lower and upper bounds for γ(Cm□Pn) are known. In this paper, we study γ(Cm□Pn) when m ≡ 1, 3, 4 (mod 5). In particular, we compute γ(Cm□Pn) if m ≡ 1 (mod 5), m ≥ 30 and n ≥ 22, and we provide tighter lower and upper bounds for γ(Cm□Pn) if m ≡ 3, 4 (mod 5).