Graphs of Degree Three with a Given Abstract Group

  title={Graphs of Degree Three with a Given Abstract Group},
  author={Roberto W. Frucht},
  journal={Canadian Journal of Mathematics},
  pages={365 - 378}
  • R. Frucht
  • Published 1 August 1949
  • Mathematics
  • Canadian Journal of Mathematics
1. Introduction. In his well-known book on graphs [1] König proposed the following problem: “When can a given abstract group be represented as the group of the automorphisms of a (finite) graph, and if possible how can the graph be constructed?” To understand this problem well let us begin with the precise definition of a graph and its group (of automorphisms). 

On Graphs with Given Automorphism Group

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A One-Regular Graph of Degree Three

  • R. Frucht
  • Mathematics
    Canadian Journal of Mathematics
  • 1952
Soon after the publication of Tutte's paper [5] on m-cages, H. S. M. Coxeter asked in a letter to the author whether one-regular graphs of degree 3 exist. The purpose of the following paper is to

Topics in Graph Automorphisms and Reconstruction

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A family of cubical graphs

  • W. T. Tutte
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1947
We begin with some definitions. A cubical graph is a simplicial 1-complex in which each 0-simplex is incident with just three 1-simplexes.

Herstellung von Graphen mit vorgegebener abstrakter Gruppe

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