1. On the Secure Total Domination Number of Graphs.
- Author
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Cabrera Martínez, Abel, Montejano, Luis P., and Rodríguez-Velázquez, Juan A.
- Subjects
- *
DOMINATING set , *GEODESICS - Abstract
A total dominating set D of a graph G is said to be a secure total dominating set if for every vertex u ∈ V (G) \ D , there exists a vertex v ∈ D , which is adjacent to u, such that (D \ { v }) ∪ { u } is a total dominating set as well. The secure total domination number of G is the minimum cardinality among all secure total dominating sets of G. In this article, we obtain new relationships between the secure total domination number and other graph parameters: namely the independence number, the matching number and other domination parameters. Some of our results are tight bounds that improve some well-known results. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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