Advertisement

Graphs, groups and polytopes

  • C. D. Godsil
Contributed Papers
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Biggs, N. Algebraic Graph Theory, C.U.P., London, (1974).CrossRefzbMATHGoogle Scholar
  2. [2]
    Coxeter, H. and Moser, W. Generators and relations for discrete groups, 2nd ed. Springer, Berlin (1965).zbMATHGoogle Scholar
  3. [3]
    Grünbaum, B. Convex Polytopes, Wiley, New York (1967).zbMATHGoogle Scholar
  4. [4]
    Harary, F. "Graph Theory", Addison-Wesley, Reading, Ma., (1969).zbMATHGoogle Scholar
  5. [5]
    Huppert, B., "Endliche Gruppen I", Springer, Berlin, (1967).CrossRefzbMATHGoogle Scholar
  6. [6]
    Mowshowitz, A. The group of a graph whose adjacency matrix has all distinct eigenvalues, in Proof Techniques in Graph Theory, Academic, New York (1969), 109–110.Google Scholar
  7. [7]
    Petersdorf, M. and Sachs, H. Spektrum und Automorphismengruppe eines Graphen, in Combinatorial theory and its applications, III, North-Holland, Amsterdam (1970), 891–907.Google Scholar
  8. [8]
    Wielandt, H. "Finite Permutation Groups", Academic Press, New York, (1964).zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • C. D. Godsil
    • 1
  1. 1.Department of MathematicsUniversity of MelbourneParkvilleAustralia

Personalised recommendations