DMGT

Discussiones Mathematicae Graph Theory 17(2) (1997) 301-309
DOI: https://doi.org/10.7151/dmgt.1057

ISOMORPHIC COMPONENTS OF KRONECKER PRODUCT OF BIPARTITE GRAPHS

Pranava K. Jha

Department of Computer Engineering
Delhi Institute of Technology: Delhi Kashmere Gate
Delhi 110 006, India
e-mail: pkj@dit.ernet.in

Sandi Klavžar
and
Blaž Zmazek

Department of Mathematics, PEF, University of Maribor
Koro ska cesta 160, 2000 Maribor, Slovenia
e-mail: sandi.klavzar@uni-lj.si

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.

Keywords: Kronecker product, bipartite graphs, graph isomorphism.

1991 Mathematics Subject Classification: 05C60.

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