English

On a generalization of Roman domination with more legions

Combinatorics 2025-06-10 v1

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.

Keywords

Cite

@article{arxiv.2212.08935,
  title  = {On a generalization of Roman domination with more legions},
  author = {Fahimeh Khosh-Ahang Ghasr},
  journal= {arXiv preprint arXiv:2212.08935},
  year   = {2025}
}

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22pages