New upper bounds for [k]-Roman domination numbers of C_m □ P_n are obtained via linear periodic and residue-class constructions, with residue-class bounds shown asymptotically superior for large m.
Further results on [k]-Roman domination on cylindrical grids Cm□Pn
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Upper bounds for double Roman domination and $[k]$-Roman domination of cylindrical graphs $C_m \Box P_n$
New upper bounds for [k]-Roman domination numbers of C_m □ P_n are obtained via linear periodic and residue-class constructions, with residue-class bounds shown asymptotically superior for large m.