Vertex-edge domination in interval and bipartite permutation graphs

Abstract

Given a graph G = (V, E), a vertex u ∈ V ve-dominates all edges incident to any vertex offor 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.