Bounds for (strong) Roman $k$-dominations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910112365412352 |
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| author | Ghasr, Fahimeh Khosh-Ahang |
| author_facet | Ghasr, Fahimeh Khosh-Ahang |
| contents | Motivated by resource defense models in networks, such as protecting territories with varying legion strengths, let $k \geq 2$ be an integer. Roman $k$-domination and strong Roman $k$-domination generalize Roman, double Roman, Italian, and double Italian domination to arbitrary number of legions. The main goal of this note is establishing sharp upper bounds for the Roman and strong Roman $k$-domination numbers of connected graphs. These bounds unify and extend prior results for $k=2$ and $k=3$. We also precisely characterize the graphs achieving these bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06818 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bounds for (strong) Roman $k$-dominations Ghasr, Fahimeh Khosh-Ahang Combinatorics 05C69 Motivated by resource defense models in networks, such as protecting territories with varying legion strengths, let $k \geq 2$ be an integer. Roman $k$-domination and strong Roman $k$-domination generalize Roman, double Roman, Italian, and double Italian domination to arbitrary number of legions. The main goal of this note is establishing sharp upper bounds for the Roman and strong Roman $k$-domination numbers of connected graphs. These bounds unify and extend prior results for $k=2$ and $k=3$. We also precisely characterize the graphs achieving these bounds. |
| title | Bounds for (strong) Roman $k$-dominations |
| topic | Combinatorics 05C69 |
| url | https://arxiv.org/abs/2604.06818 |