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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1057,
author = {Pranava K. Jha and Sandi Klav\v zar and Bla\v z Zmazek},
title = {Isomorphic components of Kronecker product of bipartite graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {17},
year = {1997},
pages = {301-309},
zbl = {0906.05050},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1057}
}
Pranava K. Jha; Sandi Klavžar; Blaž Zmazek. Isomorphic components of Kronecker product of bipartite graphs. Discussiones Mathematicae Graph Theory, Tome 17 (1997) pp. 301-309. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1057/
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