Remarks on the Complexity of Non-negative Signed Domination

This paper is motivated by the concept of nonnegative signed domination that was introduced by Huang, Li, and Feng in 2013 [15]. We study the non-negative signed domination problem from the theoretical point of view. For networks modeled by strongly chordal graphs and distance-hereditary graphs, we show that the non-negative signed domination problem can be solved in polynomial time. For networks modeled by bipartite planar graphs and doubly chordal graphs, however, we show that the decision problem corresponding to the non-negative signed domination problem is NP-complete. Furthermore, we show that even when restricted to bipartite planar graphs or doubly chordal graphs, the non-negative signed domination problem is not fixed parameter tractable.