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An Edge but not Vertex Transitive Cubic Graph*

  • I. Z. Bouwer (a1)
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Let G be an undirected graph, without loops or multiple edges. An automorphism of G is a permutation of the vertices of G that preserves adjacency. G is vertex transitive if, given any two vertices of G, there is an automorphism of the graph that maps one to the other. Similarly, G is edge transitive if for any two edges (a, b) and (c, d) of G there exists an automorphism f of G such that {c, d} = {f(a), f(b)}. A graph is regular of degree d if each vertex belongs to exactly d edges.

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*

The graph described in this note was discovered by Dr. Marion C. Gray in 1932. The author has independently rediscovered it and believes that it here appears in print for the first time.

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References
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1. Folkman, J., Regular line-symmetric graphs. J. Combinatorial theory 3 (1967) 215-232.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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