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Graphs, groups and polytopes

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Part of the Lecture Notes in Mathematics book series (LNM,volume 686)

Abstract

With each eigenspace of the adjacency matrix A of a graph X there is an associated convex polytope. Any automorphism of X induces an orthogonal transformation of this polytope onto itself. These observations are used to obtain information on the relation between the automorphism group of X and the multiplicities of the eigenvalues of A. This approach yields new results on this topic as well as improvements of previously known ones.

Keywords

  • Normal Subgroup
  • Weight Vector
  • Automorphism Group
  • Adjacency Matrix
  • Coxeter Group

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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© 1978 Springer-Verlag

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Godsil, C.D. (1978). Graphs, groups and polytopes. In: Holton, D.A., Seberry, J. (eds) Combinatorial Mathematics. Lecture Notes in Mathematics, vol 686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062528

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  • DOI: https://doi.org/10.1007/BFb0062528

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08953-7

  • Online ISBN: 978-3-540-35702-5

  • eBook Packages: Springer Book Archive