Geodesic
Isomorphic components of Kronecker product of bipartite graphs
Discussiones Mathematicae. Graph Theory, Tome 17 (1997) no. 2, pp. 301-309

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Weichsel (Proc. Amer. Math. Soc. 13 (1962) 47-52) proved that the Kronecker product of two connected bipartite graphs consists of two connected components. A condition on the factor graphs is presented which ensures that such components are isomorphic. It is demonstrated that several familiar and easily constructible graphs are amenable to that condition. A partial converse is proved for the above condition and it is conjectured that the converse is true in general.
Keywords: Kronecker product, bipartite graphs, graph isomorphism 
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Jha, Pranava; Klavžar, Sandi; Zmazek, Blaž. Isomorphic components of Kronecker product of bipartite graphs. Discussiones Mathematicae. Graph Theory, Tome 17 (1997) no. 2, pp. 301-309. http://geodesic.mathdoc.fr/item/DMGT_1997_17_2_a8/