Yazd UniversityAlgebraic Structures and Their Applications2382-97615120180201An efficient algorithm for Mixed domination on Generalized Series-Parallel Graphs2339120810.22034/as.2018.1208ENM.RajaatiDepartment of Computer Science, Yazd University, Yazd, Iran.M.R.HooshmandaslDepartment of Computer Science, Yazd University, Yazd, Iran.A.ShakibaDepartment of Computer Science,
Vali-e-Asr University of Rafsanjan,
Rafsanjan, Iran.P.SharifaniDepartment of Computer Science,
Yazd University, Yazd, Iran.M.J.DinneenDepartment of Computer Science,
The University of Auckland,
Auckland, New Zealand.Journal Article20180420A mixed dominating set $S$ of a graph $G=(V, E)$ is a subset of vertices and edges like $S \subseteq V \cup E$ such that each element $v\in (V \cup E) \setminus S$ is adjacent or incident to at least one element in $S$. The mixed domination number $\gamma_m(G)$ of a graph $G$ is the minimum cardinality among all mixed dominating sets in $G$. The problem of finding $\gamma_{m}(G)$ is known to be NP-complete. In this paper, we present an explicit polynomial-time algorithm using the parse tree to construct a mixed dominating set of size $\gamma_{m}(G)$ where $G$ is a generalized series-parallel graph.https://as.yazd.ac.ir/article_1208_a3d01b0ef81b9ace16f3dc16a272884d.pdf