Advances and Applications in Discrete Mathematics
Volume 19, Issue 4, Pages 421 - 435
(October 2018) http://dx.doi.org/10.17654/AADMOct2018_421_435 |
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ANOTHER LOOK AT k-DOMINATION IN GRAPHS
Sergio R. Canoy, Jr. and Ferdinand P. Jamil
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Abstract: The closed neighborhood of a vertex vof a graph Gis the set consisting of vand all vertices of Gadjacent to v. A set Sof vertices in Gis a dominating set of Gif Given a positive integer k, a subset Sof Gis a k-dominating set if for each Scontains at least kdistinct vertices in the neighborhood of v. A k-dominating set Sof Gis a connected k-dominating set if the induced subgraph of Gis connected. The k-domination (resp. connected k-domination) number of Gis the minimum cardinality of ak-dominating (resp. connected k-dominating) set of G.
In this paper, we investigate the k-domination number and the connected k-domination number of the corona of graphs. Also, we characterize the 2-dominating sets of the lexicographic product and the Kronecker product of connected graphs and determine bounds for their 2-domination numbers. |
Keywords and phrases: k-domination, connected k-domination, corona, lexicographic product, Kronecker product.
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