Geodesic
Hop domination in chordal bipartite graphs
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 3, pp. 825-840

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In a graph G, a vertex is said to 2-step dominate itself and all the vertices which are at distance 2 from it in G. A set D of vertices in G is called a hop dominating set of G if every vertex outside D is 2-step dominated by some vertex of D. Given a graph G and a positive integer k, the hop domination problem is to decide whether G has a hop dominating set of cardinality at most k. The hop domination problem is known to be NP-complete for bipartite graphs. In this paper, we design a linear time algorithm for computing a minimum hop dominating set in chordal bipartite graphs.
Keywords: domination, hop domination, polynomial time algorithm, chordal bipartite graphs 
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Henning, Michael A.; Pal, Saikat; Pradhan, Dinabandhu. Hop domination in chordal bipartite graphs. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 3, pp. 825-840. http://geodesic.mathdoc.fr/item/DMGT_2023_43_3_a15/