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k-tuple domination in graphs

✍ Scribed by Chung-Shou Liao; Gerard J. Chang


Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
109 KB
Volume
87
Category
Article
ISSN
0020-0190

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## Abstract A subset __S__ of vertices of a graph __G__ is __k__‐dominating if every vertex not in __S__ has at least __k__ neighbors in __S__. The __k__‐domination number $\gamma\_k(G)$ is the minimum cardinality of a __k__‐dominating set of __G__. Different upper bounds on $\gamma\_{k}(G)$ are kn

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## Abstract A graph is __k__‐domination‐critical if Ξ³(__G) = k__, and for any edge __e__ not in __G__, Ξ³(__G + e) = k__ βˆ’ 1. In this paper we show that the diameter of a domination __k__‐critical graph with __k__ ≧ 2 is at most 2__k__ βˆ’ 2. We also show that for every __k__ ≧ 2, there is a __k__‐dom