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k-tuple total domination in cross products of graphs

โœ Scribed by Michael A. Henning, Adel P. Kazemi


Book ID
118801978
Publisher
Springer US
Year
2011
Tongue
English
Weight
343 KB
Volume
24
Category
Article
ISSN
1382-6905

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k-tuple domination in graphs
โœ Chung-Shou Liao; Gerard J. Chang ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 109 KB
Proof of a conjecture on -tuple dominati
โœ Guangjun Xu; Liying Kang; Erfang Shan; Hong Yan ๐Ÿ“‚ Article ๐Ÿ“… 2008 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 142 KB

Let G = (V, E) be a graph and N G [v] the closed neighborhood of a vertex v in G. For k โˆˆ N, the minimum cardinality of a set In this note we prove the following conjecture of Rautenbach and Volkmann [D. Rautenbach, L. Volkmann, New bounds on the k-domination number and the k-tuple domination numbe

On the domination number of cross produc
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In this communication the domination number of the cross product of an elementary path with the complement of another path is exactly determined and some inequalities for general cases are deduced. The paper ends with a Vizing-like conjecture relating the domination number of the cross product of G