TY - JOUR
ID - 24185
TI - A Linear Algorithm for Computing $gamma_{_{[1,2]}}$-set in Generalized Series-Parallel Graphs
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Sharifani, Pouyeh
AU - Hooshmandasl, Mohammad Reza
AD - Department of Computer Science, Yazd University, Yazd, Iran
Y1 - 2020
PY - 2020
VL - 9
IS - 1
SP - 1
EP - 24
KW - domination
KW - Total domination
KW - [1
KW - Total [1
KW - 2]-set
KW - Series-parallel graphs
KW - Generalized series-parallel graph
DO - 10.22108/toc.2019.105482.1509
N2 - 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.
UR - https://toc.ui.ac.ir/article_24185.html
L1 - https://toc.ui.ac.ir/article_24185_5d3db88464af44f66f4256faa00162d7.pdf
ER -