Bounds on weak and strong total domination in graphs - M.H. Akhbari; Nader Jafari Rad (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2016)
A set D of vertices in a graph G=(V,E) is a total dominatingset if every vertex of G is adjacent to some vertex in D. Atotal dominating set D of G is said to be weak if everyvertex vV-D is adjacent to a vertex uD such thatd_G(v)≥ d_G(u). The weak total domination numberγ_wt(G) of G is the minimum cardinality of a weaktotal dominating set of G. A total dominating set D of G issaid to be strong if every vertex vV-D is adjacent to avertex uD such that d_G(v)≤ d_G(u). The strongtotal domination number γ_st(G) of G is the minimumcardinality of a strong total dominating set of G. We presentsome bounds on weak and strong total domination number of a graph.