# Isomorphic components of direct products of bipartite graphs

Discussiones Mathematicae Graph Theory (2006)

- Volume: 26, Issue: 2, page 231-248
- ISSN: 2083-5892

## Access Full Article

top## Abstract

top## How to cite

topRichard Hammack. "Isomorphic components of direct products of bipartite graphs." Discussiones Mathematicae Graph Theory 26.2 (2006): 231-248. <http://eudml.org/doc/270238>.

@article{RichardHammack2006,

abstract = {A standard result states the direct product of two connected bipartite graphs has exactly two components. Jha, Klavžar and Zmazek proved that if one of the factors admits an automorphism that interchanges partite sets, then the components are isomorphic. They conjectured the converse to be true. We prove the converse holds if the factors are square-free. Further, we present a matrix-theoretic conjecture that, if proved, would prove the general case of the converse; if refuted, it would produce a counterexample.},

author = {Richard Hammack},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {direct product; tensor product; Kronecker product; bipartite graph},

language = {eng},

number = {2},

pages = {231-248},

title = {Isomorphic components of direct products of bipartite graphs},

url = {http://eudml.org/doc/270238},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Richard Hammack

TI - Isomorphic components of direct products of bipartite graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2006

VL - 26

IS - 2

SP - 231

EP - 248

AB - A standard result states the direct product of two connected bipartite graphs has exactly two components. Jha, Klavžar and Zmazek proved that if one of the factors admits an automorphism that interchanges partite sets, then the components are isomorphic. They conjectured the converse to be true. We prove the converse holds if the factors are square-free. Further, we present a matrix-theoretic conjecture that, if proved, would prove the general case of the converse; if refuted, it would produce a counterexample.

LA - eng

KW - direct product; tensor product; Kronecker product; bipartite graph

UR - http://eudml.org/doc/270238

ER -

## References

top- [1] T. Chow, The Q-spectrum and spanning trees of tensor products of bipartite graphs, Proc. Amer. Math. Soc. 125 (1997) 3155-3161, doi: 10.1090/S0002-9939-97-04049-5. Zbl0882.05089
- [2] W. Imrich and S. Klavžar, Product Graphs; Structure and Recognition (Wiley Interscience Series in Discrete Mathematics and Optimization, New York, 2000). Zbl0963.05002
- [3] P. Jha, S. Klavžar and B. Zmazek, Isomorphic components of Kronecker product of bipartite graphs, Discuss. Math. Graph Theory 17 (1997) 302-308, doi: 10.7151/dmgt.1057. Zbl0906.05050
- [4] P. Weichsel, The Kronecker product of graphs, Proc. Amer. Math. Soc. 13 (1962) 47-52, doi: 10.1090/S0002-9939-1962-0133816-6. Zbl0102.38801

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.