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Direct products of automorphism groups of graphs

✍ Scribed by Mariusz Grech

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 121 KB
Volume: 62
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20385

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✦ Synopsis

Abstract

In this article we study the product action of the direct product of automorphism groups of graphs. We generalize the results of Watkins [J. Combin Theory 11 (1971), 95–104], Nowitz and Watkins [Monatsh. Math. 76 (1972), 168–171] and W. Imrich [Israel J. Math. 11 (1972), 258–264], and we show that except for an infinite family of groups S~n~ × S~n~, n≥2 and three other groups D~4~ × S~2~, D~4~ × D~4~ and S~4~ × S~2~ × S~2~, the direct product of automorphism groups of two graphs is itself the automorphism group of a graph. © 2009 Wiley Periodicals, Inc. J Graph Theory 62: 26–36, 2009

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