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- W1971297844 abstract "In a digraph G=(V,A), a vertex u is said to dominate its out-neighbors v, that is, there is an arc (u,v)∈A. A set D⊆V is a dominating set of G if each vertex of V∖D is dominated by some vertex of D. The domination number of G, denoted by γ(G), is the minimum cardinality of a dominating set of G. Generalized de Bruijn digraphs GB(n,d) are good candidates for interconnection networks. Kikuchi and Shibata show that ⌈nd+1⌉≤γ(GB(n,d))≤⌈nd⌉. In this paper, by constructing a (consecutive) dominating set of a generalized de Bruijn digraph, we prove that its domination number has exactly two values, that is, γ(GB(n,d))=⌈nd+1⌉ or ⌈nd+1⌉+1. Additionally, using a related result in number theory, we provide a complete characterization of generalized de Bruijn digraphs with the domination number equal to ⌈nd+1⌉ or ⌈nd+1⌉+1. As a consequence of the above results, we prove a conjecture posed by Kikuchi and Shibata. The conjecture says that each generalized de Bruijn digraph has a minimum dominating set that is consecutive." @default.
- W1971297844 created "2016-06-24" @default.
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- W1971297844 date "2015-08-01" @default.
- W1971297844 modified "2023-10-07" @default.
- W1971297844 title "Constructing the minimum dominating sets of generalized de Bruijn digraphs" @default.
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- W1971297844 doi "https://doi.org/10.1016/j.disc.2015.03.011" @default.
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