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Abstract: 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 n ≤ 22 or m ≤ 30. 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 30 ≤ m ≡ 1 (mod 5) and n ≥ 22, and we provide tighter lower and upper bounds for γ(Cm □ Pn) if m ≡ 3, 4 (mod 5).
Keywords: Domination in graphs, Cartesian product graphs, tropical matrix multiplication
Published in RUP: 20.08.2026; Views: 417; Downloads: 12
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