Isomorphic components of Kronecker product of bipartite graphs

Abstract

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. Math. Subj. Class. (1991): 05C60 Key terms: Kronecker product, bipartite graphs, graph isomorphism ∗This work was supported in part by the Ministry of Science and Technology of Slovenia under the grants P1-0206-101 and J1-7036.