Geodesic
Vertex-edge domination in interval and bipartite permutation graphs
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 4, pp. 947-963

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Given a graph G = (V,E), a vertex u ∈ V ve-dominates all edges incident to any vertex of N_G[u]. A set D ⊆ V is a vertex-edge dominating set if, for any edge e∈ E, there exists a vertex u ∈ D such that u ve-dominates e. Given a graph G, our goal is to find a minimum cardinality ve-dominating set of G. In this paper, we designed two linear-time algorithms to find a minimum cardinality ve-dominating set for interval and bipartite permutation graphs.
Keywords: vertex-edge domination, linear time algorithm, interval graphs, bipartite permutation graphs 
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Paul, Subhabrata; Pradhan, Dinabandhu; Verma, Shaily. Vertex-edge domination in interval and bipartite permutation graphs. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 4, pp. 947-963. http://geodesic.mathdoc.fr/item/DMGT_2023_43_4_a4/