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
is constructed by making two copies of the vertex set
of 
(omitting the initial edge set entirely) and constructing
edges 
and 
for every edge 
of 
.
The bipartite double graph is equivalent to the graph
tensor product 
.
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 (2018) to suggest than one of the alternate names should be used for this concept.
Note that the bipartite double differs from the plain double graph in that the initial edge set is discarded in the bipartite double graph, while it is retained in the double graph.
The following table summarizes bipartite double graphs for some named graphs and classes of graphs.
for 
odd; 
for 
even
-
-
for 
for 
odd; 
for 
even
for 
odd; 
for 
even