The double graph of a given graph G is constructed by making two copies of G (including the initial edge set of each) and adding edges u_1 v_2 and v_1 u_2 for every edge u v of G. Note that the double graph differs from the bipartite double graph in that the initial edge set is retained in the double graph, while it is discarded in the bipartite double graph.

bipartite double graph | cycle double cover | graph lexicographic product