Edge frames of graphs: A graph embedding problem Original Research Article

A nonempty graph G is edge homogeneously embedded in a graph H if for each edge e of G and each edge f of H, there exists an edge isomorphism between G and a vertex induced subgraph of H which sends e to f. A graph F of minimum size in which G can be edge homogeneously embedded is called an edge frame of G and the size of F is called the edge framing number efr(G) of G. It is shown that every graph has at least one edge frame and, consequently, that the edge framing number of a graph is a well-defined concept. Several results involving edge frames and edge framing numbers of graphs are presented.