Discussiones Mathematicae Graph Theory 30(4) (2010) 575-590
doi: 10.7151/dmgt.1515

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Richard H. Hammack  and  Katherine E. Toman

Department of Mathematics and Applied Mathematics
Virginia Commonwealth University
Richmond, VA 23284-2014, USA
e-mail: rhammack@vcu.edu
e-mail: tomanke@vcu.edu


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.

2010 Mathematics Subject Classification: Primary: 05C76; Secondary: 05C20, 05C60.


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Received 16 July 2009
Revised 18 November 2009
Accepted 18 November 2009