Strong (weak) edge-edge domination number of a graph

Abstract

For any edge x=uv of an isolate free graph G(V,E),(N[x]) is the subgraph induced by the vertices adjacent to u and v in G. We say that an edge x, e-dominates an edge y if y ? (N[x]). A set L ? E is an Edge-Edge Dominating Set (EED-set) if every edge in E-L is e-dominated by an edge in L. The edge-edge domination number ? ee(G) is the cardinality of a minimum EED-set. We find the relation ship between the new parameter and some known graph parameters.