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.
Roman domination in graphs
2 Pith papers cite this work, alongside 61 external citations. Polarity classification is still indexing.
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math.CO 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Relates signed total Roman domination number on cubic graphs to open packing, 2-tuple total domination, and signed total domination numbers to derive bounds and NP-completeness; shows domatic number determined by degree-3 vertices; computes exact values on complete multipartite graphs.
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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.
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Signed Total Roman Domination and Domatic Numbers: Degree Three and Complete Multipartite Graphs
Relates signed total Roman domination number on cubic graphs to open packing, 2-tuple total domination, and signed total domination numbers to derive bounds and NP-completeness; shows domatic number determined by degree-3 vertices; computes exact values on complete multipartite graphs.