Abstract:
A set D ⊆ V of a graph G = (V,E) is called a restrained dominating set of G if every vertex not in D is
adjacent to a vertex in D and to a vertex in V \ D. The MINIMUM RESTRAINED DOMINATION problem
is to find a restrained dominating set of minimum cardinality. The decision version of the MINIMUM
RESTRAINED DOMINATION problem is known to be NP-complete for chordal graphs. In this paper, we
strengthen this NP-completeness result by showing that the problem remains NP-complete for doubly
chordal graphs, a subclass of chordal graphs. We also propose a polynomial time algorithm to solve the
MINIMUM RESTRAINED DOMINATION problem in block graphs, a subclass of doubly chordal graphs.
