Secure total domination in graphs

Abstract

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 γ_st) for the path P_n and obtain a sharp lower bound for γ_st for n-vertex forests with maximum degree at most Δ.