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Factors in a class of regular digraphs

✍ Scribed by M. V. S. Ramanath

Publisher: John Wiley and Sons
Year: 1985
Tongue: English
Weight: 634 KB
Volume: 9
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190090113

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✦ Synopsis

For the class of 2-diregular digraphs: (1) We give a simple closed form expression-a power of 2-for the number of difactors. (2) For the adjacency matrices of these graphs, we show an intimate relationship between the permanent and determinant. (3) We give a necessary and sufficient condition for the Cartesian product of two directed circuits to have a difactor with exactly k components thereby generalizing a result of Trotter and Erdos. Our results also show that a conjecture of Bondy, regarding vertex-t ransi t ive graphs, f ai Is to hold for vertex-t ra nsi t ive dig rap h s . This work was partially supported by the Government of Canada through Grant S232A1.

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