Vertex-Edge Domination in Interval and Bipartite Permutation Graphs

Given a graph G =(V, E), a vertex u is an element of 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 is an element of E, there exists a vertex u is an element of 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.