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Graphs with Given Group and Given Graph-Theoretical Properties

Published online by Cambridge University Press:  20 November 2018

Gert Sabidussi
Gert Sabidussi*
Affiliation:
University of Minnesota and Tulane University
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n 1938 Frucht (2) proved the following theorem:

(1.1). Theorem. Given any finite group G there exist infinitely many nonisomorphic connected graphs X whose automorphism group is isomorphic to G.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 515 - 525
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Dirac, G. A., The structure of k-chromatic graphs, Fund. Math., 40 (1953), 42–55.Google Scholar
2. Frucht, R., Herstellung von Graphen mit vorgegebener abstrakter Gruppe, Compositio Math., 6 (1938), 239–250.Google Scholar
3. Frucht, R., Graphs of degree 3 with given abstract group, Canad. J. Math, 1 (1949), 365–378.Google Scholar
4. König, D., Theorie der endlichen und unendlichen Graphenf (Leipzig, 1936).Google Scholar
5. Sabidussi, G., Graph multiplication. Submitted to Mathematische Zeitschrift.Google Scholar
6. Whitney, H., Congruent graphs and connectivity of graphs, Amer. J. Math., 54 (1932), 150–168.Google Scholar