ArticleOriginal scientific text
Title
Cancellation of direct products of digraphs
Authors 1, 1
Affiliations
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014, USA
Abstract
We investigate expressions of form A×C ≅ B×C involving direct products of digraphs. Lovász gave exact conditions on C for which it necessarily follows that A ≅ B. We are here concerned with a different aspect of cancellation. We describe exact conditions on A for which it necessarily follows that A ≅ B. In the process, we do the following: Given an arbitrary digraph A and a digraph C that admits a homomorphism onto an arc, we classify all digraphs B for which A×C ≅ B×C.
Keywords
graph direct product, graph product cancellation, digraphs
Bibliography
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- W. Imrich and S. Klavžar, Product Graphs: Structure and recognition, Wiley-Interscience Series in Discrete Mathematics and Optimization (John Wiley and Sons, New York, 2000).
- L. Lovász, On the cancellation law among finite relational structures, Period. Math. Hungar. 1 (1971) 145-156, doi: 10.1007/BF02029172.
Pages:
575-590
Main language of publication
English
Received
2009-07-16
Accepted
2009-11-18
Published
2010
DOI: 10.7151/dmgt.1515
Exact and natural sciences