Amirkabir University of TechnologyAUT Journal of Mathematics and Computing1220201001A linear-time algorithm to compute total [1, 2]-domination number of block graphs263270402910.22060/ajmc.2020.18444.1035ENPouyehSharifaniInstitute for Research in Fundamental Sciences (IPM), Tehran, Iran.MohammadrezaHooshmandaslDepartment of Computer Science, University of Mohaghegh Ardabili, Ardabil, Iran.0000-0002-3834-3610SaeidAlikhaniDepartment of Mathematics, Yazd University, Yazd, Iran.Journal Article20200519Let G = (V, E) be a simple graph without isolated vertices. A set D ⊂ V is a total [1, 2]-dominating set if for every vertex v ∈ V , 1 ≤ |N(v) ∩ D| ≤ 2. The total [1, 2]-domination problem is to determine the total [1, 2]-domination number γt[1,2](G), which is the minimum cardinality of a total [1, 2]-dominating set for a graph G. In this paper, we present a linear-time algorithm to compute γt[1,2](G) for a block graph G.https://ajmc.aut.ac.ir/article_4029_c5e379fd5ea2da4be1fd158b707875ec.pdf