On the Secure Total Domination Number of Graphs

Identifier:  imarina:5867555

Handle: https://hdl.handle.net/20.500.11797/imarina5867555

Authors:  Cabrera Martinez, Abel; Montejano, Luis P; Rodriguez-Velazquez, Juan A

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.