Twin domination in generalized Kautz digraphs |
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Authors: | DONG Yan-xia SHAN Er-fang WU Ling-ye |
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Institution: | Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China |
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Abstract: | Let G = (V,A) be a digraph. A set T of vertices of G is a twin dominating set of G if for every vertex v ∈ V \ T.
There exist u,w ∈ T (possibly u = w) such that (u, v), (v,w) ∈ A. The twin domination number γ?(G) of G is the cardinality
of a minimum twin dominating set of G. In this paper we consider the twin domination number in generalized Kautz digraphs
GK(n, d). In these digraphs, we establish bounds on the twin domination number and give a sufficient condition for the twin
domination number attaining the lower bound. We give the exact values of the twin domination numbers by constructing
minimum twin dominating sets for some special generalized Kautz digraphs. |
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Keywords: | twin dominating set generalized Kuatz digraph interconnection networks |
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