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.
Sharifani, P., Hooshmandasl, M. (2020). A Linear Algorithm for Computing $\gamma_{_{[1,2]}}$-set in Generalized Series-Parallel Graphs. Transactions on Combinatorics, 9(1), 1-24. doi: 10.22108/toc.2019.105482.1509
MLA
Pouyeh Sharifani; Mohammad Reza Hooshmandasl. "A Linear Algorithm for Computing $\gamma_{_{[1,2]}}$-set in Generalized Series-Parallel Graphs". Transactions on Combinatorics, 9, 1, 2020, 1-24. doi: 10.22108/toc.2019.105482.1509
HARVARD
Sharifani, P., Hooshmandasl, M. (2020). 'A Linear Algorithm for Computing $\gamma_{_{[1,2]}}$-set in Generalized Series-Parallel Graphs', Transactions on Combinatorics, 9(1), pp. 1-24. doi: 10.22108/toc.2019.105482.1509
VANCOUVER
Sharifani, P., Hooshmandasl, M. A Linear Algorithm for Computing $\gamma_{_{[1,2]}}$-set in Generalized Series-Parallel Graphs. Transactions on Combinatorics, 2020; 9(1): 1-24. doi: 10.22108/toc.2019.105482.1509
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