Edge-Domsaturation Number of a Graph

The edge-domsaturation number ds(G) of a graph G=(V, E) is the least positive integer k such that every edge of G lies in an edge dominating set of cardinality k. The connected edge-domsaturation number dsc(G) of a graph G=(V, E) is the least positive integer k such that every edge of G lies in a connected edge dominating set of cardinality k. In this paper, we obtain several results connecting ds(G),dsc(G)and other graph theoretic parameters.