Advances and Applications in Discrete Mathematics
Volume 19, Issue 1, Pages 17 - 31
(January 2018) http://dx.doi.org/10.17654/AADMJan2018_017_031 |
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-DOMINATION IN GRAPHS UNDER SOME BINARY OPERATIONS
Shaleema A. Arriola and Sergio R. Canoy, Jr.
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Abstract: Let Gbe a simple graph. A subset Sof is a -dominating set of Gif for each there exist distinct vertices such that and The minimum cardinality of a -dominating set of Gis called the -domination number of G. In this paper, we characterize the -dominating sets in the join, corona, lexicographic product, and the Cartesian product of two graphs. As direct consequences, we determine the -domination number of each of these graphs. |
Keywords and phrases: domination, (1,2)-domination, join, corona, lexicographic product, Cartesian product. |
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