Edge dominating graph of a graph

Abstract

The edge dominating graph $E_{D}(G)$ of a graph $G=(V,E)$ is a graph with $V(E_{D}(G))=E(G)\cup S(G)$, where $S(G)$ is the set of all minimal edge dominating sets of $G$ with two vertices $u,v\in V(E_{D}(G))$ adjacent if $u\in E$ and $v$ is a minimal edge dominating set of $G$ containing $u$. In this paper, we establish the bounds on order and size, diameter and vertex(edge)connectivity.