## The automorphism group of a product of graphs

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- by Donald J. Miller
- Proc. Amer. Math. Soc.
**25**(1970), 24-28 - DOI: https://doi.org/10.1090/S0002-9939-1970-0262116-3
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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.## References

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## Bibliographic Information

- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**25**(1970), 24-28 - MSC: Primary 05.62
- DOI: https://doi.org/10.1090/S0002-9939-1970-0262116-3
- MathSciNet review: 0262116