Restrained edge domination number of some path related graphs

Abstract

For a graph G=(V, E), a set S⊆ V (S⊆ E) is a restrained dominating (restrained edge dominating) set if every vertex (edge) not in S is adjacent (incident) to a vertex (edge) in S and to a vertex (edge) in V-S (ES). The minimum cardinality of a restrained dominating (restrained edge dominating) set of G is called restrained domination (restrained edge domination) number of G, denoted by γ r (G)(γ re (G). The restrained edge domination number of some standard graphs are already investigated while in this paper the restrained edge domination number like degree splitting, switching, square and middle graph obtained from path.