%0 Journal Article
%T A Linear Algorithm for Computing $gamma_{_{[1,2]}}$-set in Generalized Series-Parallel Graphs
%J Transactions on Combinatorics
%I University of Isfahan
%Z 2251-8657
%A Sharifani, Pouyeh
%A Hooshmandasl, Mohammad Reza
%D 2020
%\ 03/01/2020
%V 9
%N 1
%P 1-24
%! A Linear Algorithm for Computing $gamma_{_{[1,2]}}$-set in Generalized Series-Parallel Graphs
%K domination
%K Total domination
%K [1
%K Total [1
%K 2]-set
%K Series-parallel graphs
%K Generalized series-parallel graph
%R 10.22108/toc.2019.105482.1509
%X For a graph $G=(V,E)$, a set $S subseteq V$ is a $[1,2]$-set if it is a dominating set for $G$ and each vertex $v in V setminus S$ is dominated by at most two vertices of $S$, i.e. $1 leq vert N(v) cap S vert leq 2$. Moreover a set $S subseteq V$ is a total $[1,2]$-set if for each vertex of $V$, it is the case that $1 leq vert N(v) cap S vert leq 2$. The $[1,2]$-domination number of $G$, denoted $gamma_{[1,2]}(G)$, is the minimum number of vertices in a $[1,2]$-set. Every $[1,2]$-set with cardinality of $gamma_{[1,2]}(G)$ is called a $gamma_{[1,2]}$-set. Total $[1,2]$-domination number and $gamma_{t[1,2]}$-sets of $G$ are defined in a similar way. This paper presents a linear time algorithm to find a $gamma_{[1,2]}$-set and a $gamma_{t[1,2]}$-set in generalized series-parallel graphs.
%U https://toc.ui.ac.ir/article_24185_5d3db88464af44f66f4256faa00162d7.pdf