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The least number of edges for graphs having automorphism group of order three

  • Roberto Frucht
  • Allan Gewirtz
  • Louis V. Quintas
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 186)

Keywords

Automorphism Group Cyclic Group Identity Group Regular Graph Combinatorial Theory 
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

  1. 1.
    Frucht, R., Herstellung von Graphen mit vorgegebener abstrakter Gruppe, Compositio Math. 6 (1938), 239–250.MathSciNetzbMATHGoogle Scholar
  2. 2.
    Frucht, R., Gewirtz, A., and Quintas, L. V., El número mínimo de líneas para grafos conexos con grupo de automorfismos de orden 3, Scientia, (in press).Google Scholar
  3. 3.
    Gewirtz, A., Hill, A., and Quintas, L. V., El número mínimo de puntos para grafos regulares y asimétricos, Scientia 138 (1969), 103–111.MathSciNetGoogle Scholar
  4. 4.
    Gewirtz, A., Hill, A., and Quintas, L. V., Extremum problems concerning graphs and their groups, Proceedings of the Calgary International Conference on Combinatorial Structures and their Applications, Gordan and Breach, New York, 1970, 103–109.Google Scholar
  5. 5.
    Gewirtz, A. and Quintas, L. V., Connected extremal edge graphs having symmetric automorphism group, Recent Progress in Combinatorics (W. T. Tutte, ed.) Academic Press, New York, 1969, 223–227.Google Scholar
  6. 6.
    Harary, F., Graph Theory, Addison-Wesley, Reading, 1969.zbMATHGoogle Scholar
  7. 7.
    Harary, F. and Palmer, E. M., The smallest graph whose group is cyclic, Czech. Math. J. 16 (1966), 70–71.MathSciNetzbMATHGoogle Scholar
  8. 8.
    Harary, F. and Prins, G., The number of homeomorphically irreducible trees, and other species, Acta Math. 101 (1959), 141–162.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Meriwether, R. L., Smallest graphs with a given cyclic group (1963) unpublished, but see Math Reviews 33 (1967) #2563.Google Scholar
  10. 10.
    Quintas, L. V., Extrema concerning asymmetric graphs, J. Combinatorial Theory 3 (1967), 57–82.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Quintas, L. V., The least number of edges for graphs having symmetric automorphism group, J. Combinatorial Theory 5 (1968), 115–125.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • Roberto Frucht
    • 1
  • Allan Gewirtz
    • 2
  • Louis V. Quintas
    • 3
  1. 1.Universidad Tecnica Federico Santa MariaValparaisoChile
  2. 2.Brooklyn College, CUNYBrooklynU.S.A.
  3. 3.Pace CollegeNew YorkU.S.A.

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