The bipartite double graph, also called the Kronecker cover, Kronecker double cover, bipartite double cover, canonical double cover, or bipartite double, of a given graph G is constructed by making two copies of the vertex set of G (omitting the initial edge set entirely) and constructing edges u_1 v_2 and v_1 u_2 for every edge u v of G. The bipartite double graph is equivalent to the graph tensor product G×K_2. In a non-bipartite connected graph, exactly one double cover is bipartite. However, a bipartite or disconnected graph may have more than one bipartite double graph, leading Pisanski to suggest than one of the alternate names should be used for this concept.
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