Secure total domination in graphs - Benecke S.,; Cockayne E.J.,; Mynhardt C.M., (Utilitas Mathematica, 2007)
A new strategy, called secure total domination, for placing guards in order to protect a graph, is introduced. Some properties of the strategy for arbitrary graphs are determined, we evaluate the minimum number of guards (termed the secure total domination number and denoted by γst) for the path Pn and obtain a sharp lower bound for γst for n-vertex forests with maximum degree at most Δ.