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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The automorphism group of a product of graphs

Author: Donald J. Miller
Journal: Proc. Amer. Math. Soc. 25 (1970), 24-28
MSC: Primary 05.62
MathSciNet review: 0262116
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Abstract: In a recent paper we showed that every connected graph can be written as a weak cartesian product of a family of indecomposable rooted graphs and that this decomposition is unique to within isomorphisms. Using this unique prime factorization theorem we prove that if a graph $X$ can be written as a product of connected rooted graphs, which are pairwise relatively prime, then the automorphism group of $X$ is isomorphic to the restricted direct product of the automorphism groups of the factors with prescribed subgroups the isotropy groups of the factors at the roots. This is a generalization of Sabidussi’s theorem for cartesian multiplication.

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Keywords: Automorphism group, weak cartesian product of graphs, cartesian product of graphs, restricted direct product of groups, sum of graphs
Article copyright: © Copyright 1970 American Mathematical Society