Abstract | ||
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A set D⊆V of a graph G=(V,E) is called a dominating set of G if every vertex in V∖D has at least one neighbor in D. A dominating set D of G is a paired-dominating set of G if G[D], the subgraph of G induced by D, has a perfect matching. Given a graph G, Min-Paired-Dom-Set is the problem to find a paired-dominating set of G of minimum cardinality. Min-Paired-Dom-Set is known to be NP-hard for general graphs and many other restricted classes of graphs. However, Min-Paired-Dom-Set is solvable in polynomial time in some graph classes including strongly chordal graphs and chordal bipartite graphs. In this paper, we strengthen this result by proposing a polynomial time algorithm to compute a minimum paired-dominating set in the class of strongly orderable graphs, which includes strongly chordal graphs and chordal bipartite graphs. The algorithm runs in linear time if a quasi-simple elimination ordering of the strongly orderable graph is provided. |
Year | DOI | Venue |
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2019 | 10.1016/j.dam.2018.08.022 | Discrete Applied Mathematics |
Keywords | Field | DocType |
Domination,Paired-domination,Strongly orderable graphs,Polynomial time algorithm | Discrete mathematics,Graph,Combinatorics,Dominating set,Vertex (geometry),Chordal graph,Bipartite graph,Cardinality,Matching (graph theory),Time complexity,Mathematics | Journal |
Volume | ISSN | Citations |
253 | 0166-218X | 1 |
PageRank | References | Authors |
0.35 | 9 | 2 |
Name | Order | Citations | PageRank |
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D. Pradhan | 1 | 21 | 2.52 |
B. S. Panda | 2 | 99 | 21.18 |