Advances and Applications in Discrete Mathematics
Volume 20, Issue 1, Pages 13 - 24
(January 2019) http://dx.doi.org/10.17654/ |
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SECURE DOMINATING SETS IN THE LEXICOGRAPHIC PRODUCT OF GRAPHS
Sergio R. Canoy, Jr., Seanne Abigail E. Canoy and Marlon F. Cruzate
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Abstract: Let be a simple graph. A set is a dominating (total dominating) set of G if for every there exists such that A dominating (total dominating) set S of G is a secure dominating (resp. secure total dominating) set of G if for each there exists such that is a dominating (resp. total dominating) set of G. In this paper, we characterize the secure dominating and the secure total dominating sets in the lexicographic product of connected graphs. As a consequence, we determine some (sharp) bounds for the secure domination and secure total domination numbers of the lexicographic product. |
Keywords and phrases: domination, total domination, secure domination, secure total domination, lexicographic product.
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