On the Secure Total Domination Number of Graphs
Keyword(s):
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.
2021 ◽
Vol 14
(2)
◽
pp. 578-589
2021 ◽
Vol 14
(1)
◽
pp. 149-163
2019 ◽
Vol 11
(01)
◽
pp. 1950004
2020 ◽
Vol 8
(4S5)
◽
pp. 272-276
Keyword(s):