Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24491220200901A 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, IranDepartment of Computer Science, Yazd University, Yazd, IranMohammadrezaHooshmandaslDepartment of Computer Science, University of Mohaghegh Ardabili, Ardabil, IranDepartment of Computer Science, Yazd University, Yazd, Iran0000-0002-3834-3610SaeidAlikhaniDepartment of Mathematics, Yazd University, Yazd, IranJournal Article20200519Let $G=(V, E)$ be a simple graph without isolated vertices. A set $D\subseteq V$ is a total $[1,2]$-dominating set if for every vertex $v\in V , 1\leq |N(v)\cap D|\leq 2$. The total $[1,2]$-domination problem is to determine the total $[1,2]$-domination number $\gamma_{t[1,2]}(G)$, 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 $\gamma_{t[1,2]}(G)$, for a block graph $G$.https://ajmc.aut.ac.ir/article_4029_37ba0eb98b8dee9c894950fe396e5321.pdf