Abstract
An absorbant of a digraph D is a set S ⊆ V(D) such that, for every v ∈ V(D) ∖ S, there exists an arc (v,u) with u ∈ S. We denote the cardinality of a minimum absorbant by γ a (D). An absorbant S is called a perfect absorbant if no vertex of S has an out-neighbor in S and no two vertices in S have a common in-neighbor.
In this paper, we are concerned with the perfect absorbant problem in generalized De Bruijn digraphs. We prove that some classes of generalized De Bruijn graphs have perfect absorbants. We also answer some questions asked by Shan et al. in [10], i.e., we affirm that γ a (G B (8k − 4,4k − 3)) = 3 and γ a (G B (6k,2k − 1)) = 4 for \(k\geqslant 2\).
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Wang, YL., Wu, KH., Kloks, T. (2013). On Perfect Absorbants in De Bruijn Digraphs. In: Fellows, M., Tan, X., Zhu, B. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7924. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38756-2_31
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DOI: https://doi.org/10.1007/978-3-642-38756-2_31
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