Information Processing Letters
Weighted independent perfect domination on cocomparability graphs
Discrete Applied Mathematics
The weighted perfect domination problem and its variants
Discrete Applied Mathematics
The algorithmic complexity of minus domination in graphs
Discrete Applied Mathematics
Weighted domination of cocomparability graphs
Discrete Applied Mathematics
Graph classes: a survey
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Effincient Domination of Permutation Graphs and Trapezoid Graphs
COCOON '97 Proceedings of the Third Annual International Conference on Computing and Combinatorics
Minus Domination in Small-Degree Graphs
WG '98 Proceedings of the 24th International Workshop on Graph-Theoretic Concepts in Computer Science
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An efficient minus (respectively, signed) dominating function of a graph G = (V,E) is a function f: V → {-1,0,1} (respectively, {-1, 1}) such that Σu∈M[v] f(u) = 1 for all v ∈ V, where N[v] = {v} ∪ {u|(u,v) ∈ E}. The efficient minus (respectively, signed) domination problem is to find an efficient minus (respectively, signed) dominating function of G. In this paper, we show that the efficient minus (respectively, signed) domination problem is NP-complete on chordal graphs, chordal bipartite graphs, planar bipartite graphs and planar graphs of maximum degree 4 (respectively, on 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 (respectively, every graph with no vertex of odd degree) has an efficient minus (respectively, signed) dominating function. We also give linear-time algorithms to find these functions. Besides, we show that the efficient minus domination problem is equivalent to the efficient domination problem on trees.