(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Let G = (V(G),E(G)) be a nonempty graph. An independent edge dominating set is an independent set of edges which is also an edge dominating set of G. The family of independent edge dominating sets of G generates a unique topology. In this paper, we formally defined the new notion of topology generated by the family of independent edge dominating sets (IEDS) in a graph called the independent edge domination topology of E(G), denoted as τ_ID^E (G). Moreover, we characterize the subbasic sets generated from the family of independent edge dominating sets and the independent edge domination topology of some graph families.