arXiv
Open Access
2026
Bounds for (strong) Roman $k$-dominations
Fahimeh Khosh-Ahang Ghasr
Abstrak
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.
Topik & Kata Kunci
Penulis (1)
F
Fahimeh Khosh-Ahang Ghasr
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2026
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓