Applications of E‐graphs in Network Design

In this paper, we introduce a construction that produces graphs, called E‐graphs, by replacing the edges in a core graph with a copy of a given graph. These graphs are generalizations of several graphs that have recently been presented as models for network designs, including the G‐network and its extensions. We discuss several invariant properties of these graphs with emphasis on those of interest in network design, such as number of edges, diameter, and domination number