- - - Department of Computer Science, Yazd University, Yazd, Iran.
- - - Department of Computer Science, Yazd University, Yazd, Iran.
- - - Department of Computer Science, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
- - - Department of Computer Science, Yazd University, Yazd, Iran.
- - - Department of Computer Science, The University of Auckland, Auckland, New Zealand.

A 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.

Mixed Dominating Set, Generalized Series-Parallel, Parse Tree, Tree-width