Metadata
bibkey: luizvieira2025independentroman
authors: A. G. Luiz and F. A. S. Vieira
year: 2025
title: Independent [k]-Roman Domination on Graphs
doi: 10.7151/dmgt.2580
url: https://arxiv.org/abs/2406.11688v1
claim: The authors conjecture that gamma_[kR](G) = i_[kR](G) for k >= 2 on all generalized Blanusa snarks.
strata_touched:
- D5/S3/Combinatorics/Graph/Domination/LuizVieiraBlanusaIndependentRoman
license: citation-only
triage: anchor
Verified locator
DOI: https://doi.org/10.7151/dmgt.2580
Source: https://arxiv.org/abs/2406.11688v1
Source
A. G. Luiz and F. A. S. Vieira, “Independent [k]-Roman Domination on Graphs”, Discussiones Mathematicae Graph Theory 45 (2025), 1249–1272. The arXiv version is 2406.11688v1.
The source defines [k]-Roman dominating functions and independent [k]-Roman dominating functions in Section 1, gives the generalized Blanuša snark construction in Section 4 and conjectures in Section 6 that γ[kR](G) = i[kR](G) for k ≥ 2 on all generalized Blanuša snarks.
The closing conjecture (Section 6 of arXiv:2406.11688v1; published Section 5, p. 1270) states: “another interesting line of research is finding other classes of graphs with ∆(G) ≤ 3 for which γ[kR](G) = i[kR](G) for k ≥ 2. In fact, we conjecture that this property holds for all generalized Blanuša snarks.”