On a generalization of Roman domination with more legions

DOI10.1142/S1793830923500040arXiv2212.08935OpenAlexW4312191011MaRDI QIDQ6420861

F. Khosh-Ahang

Publication date: 17 December 2022

Abstract: In this note, we generalize the concepts of (perfect) Roman and Italian dominations to (perfect) strong Roman and Roman k-domination for arbitrary positive integer k. These generalizations cover some of previous ones. After some comparison of their domination numbers, as a first study of these concepts, we study the (perfect, strong, perfect strong) Roman k-domination numbers of complete bipartite graphs.

Full work available at URL: https://doi.org/10.1142/s1793830923500040

Mathematics Subject Classification ID

Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items (1)

New bounds on the outer-independent total double Roman domination number

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