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Improved bounds on the domination number of a tree

✍ Scribed by Desormeaux, Wyatt J.; Haynes, Teresa W.; Henning, Michael A.


Book ID
124143693
Publisher
Elsevier Science
Year
2014
Tongue
English
Weight
317 KB
Volume
177
Category
Article
ISSN
0166-218X

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The k-domination number of a graph is the cardinality of a smallest set of vertices such that every vertex not in the set is adjacent to at least k vertices of the set. We prove two bounds on the k-domination number of a graph, inspired by two conjectures of the computer program Graffiti.pc. In part

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A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S and the subgraph induced by S contains a perfect matching. The minimum cardinality of a paired-dominating set of G is the paireddomination number of G, denoted by Ξ³ pr (G). In this w