Efficient Minus and Signed Domination in Graphs

Authors:
Chin Lung Lu;Sheng-Lung Peng;Chuan Yi Tang
Affiliations:
-;-;-
Venue:
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
Year:
2000

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Abstract

We show that the efficient minus (resp., signed) domination problem is NP-complete for chordal graphs, chordal bipartite graphs, planar bipartite graphs and planar graphs of maximum degree 4 (resp., for chordal graphs). Based on the forcing property on blocks of vertices and automata theory, we provide a uniform approach to show that in a special class of interval graphs, every graph (resp., every graph with no vertex of odd degree) has an efficient minus (resp., signed) dominating function. Besides, we show that the efficient minus domination problem is equivalent to the efficient domination problem on trees.