Graphs with equal secure total domination and inverse secure total domination numbers
V. R. Kulli, B. Chaluvaraju, M. Kumara · Journal of Information and Optimization Sciences · 2018
A secure total dominating set of a graph G = (V, E) is a total dominating set D ⊆ V(G) with the property that for each u ∈ V(G) – D, there exists v ∈ D adjacent to u such that (D – {v}) ∪ {u} is a total dominating set. If V(G) – D contains a secure total dominating set D´ of G, then D´ is called an inverse secure total dominating set with respect to D. The secure and inverse secure total domination number of G is the minimum cardinality among all secure and inverse secure total dominating sets of G and is denoted by γst (G) and , respectively. In this paper, we find some graphs for which . Also we obtain some graphs for which .