ArticleOriginal scientific text
Title
A cancellation property for the direct product of graphs
Authors 1
Affiliations
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014, USA
Abstract
Given graphs A, B and C for which A×C ≅ B×C, it is not generally true that A ≅ B. However, it is known that A×C ≅ B×C implies A ≅ B provided that C is non-bipartite, or that there are homomorphisms from A and B to C. This note proves an additional cancellation property. We show that if B and C are bipartite, then A×C ≅ B×C implies A ≅ B if and only if no component of B admits an involution that interchanges its partite sets.
Keywords
graph products, graph direct product, cancellation
Bibliography
- R. Hammack, A quasi cancellation property for the direct product, Proceedings of the Sixth Slovenian International Conference on Graph Theory, under review.
- P. Hell and J. Nesetril, Graphs and Homomorphisms, Oxford Lecture Series in Mathematics (Oxford U. Press, 2004), doi: 10.1093/acprof:oso/9780198528173.001.0001.
- W. Imrich and S. Klavžar, Product Graphs; Structure and Recognition (Wiley Interscience Series in Discrete Mathematics and Optimization, 2000).
- L. Lovász, On the cancellation law among finite relational structures, Period. Math. Hungar. 1 (1971) 59-101.
Pages:
179-184
Main language of publication
English
Received
2007-08-13
Accepted
2007-12-05
Published
2008
DOI: 10.7151/dmgt.1400
Exact and natural sciences