An upper bound for the k-power domination number in r-uniform hypergraphs
نویسندگان
چکیده
Generalizing work on graphs, Chang and Roussel introduced k-power domination in hypergraphs conjectured the upper bound for number r-uniform n vertices was nr+k. This shown to be true simple graphs (r=2) it further that only a family of hypergraphs, known as squid attained this bound. In paper, conjecture is proven hold with r=3 or 4; but false, by counterexample, r≥7. Furthermore, we show are not attain original Finally, new r≥3.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2022
ISSN: ['1872-681X', '0012-365X']
DOI: https://doi.org/10.1016/j.disc.2022.113038