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- W2188648465 abstract "The distance l-domination number γl(G) of a strongly connected digraph G is the minimum number γ for which there is a set DV (G) with cardinality γ such that any vertex v / 2 D can be reached within distance l from some vertex in D. In this paper, we establish a lower bound and an upper bound for γl of a generalized de Bruijn digraph and a generalized Kautz digraph, and also give a sufficient condition for these digraphs whose γ2 are equal to the lower bounds. As a consequence, for the de Bruijn digraph B(d, k), we determine that γ2(B(d, k)) = d k d2+d+1 . At the end of this paper, we conjecture γ2(K(d, k)) = d k +d k 1 d2+d+1 ." @default.
- W2188648465 created "2016-06-24" @default.
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- W2188648465 date "2006-01-01" @default.
- W2188648465 modified "2023-09-26" @default.
- W2188648465 title "Distance Domination Numbers of Generalized de Bruijn and Kautz Digraphs" @default.
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