Independent Edge Domination Topology of Some Graph Families (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.
Keywords: Complete graph; Friendship graph; Complete bipartite graph; Independent edge domination topology