From the Coxeter Graph to the Klein Graph

  title={From the Coxeter Graph to the Klein Graph},
  author={I. Dejter},
  journal={J. Graph Theory},
  • I. Dejter
  • Published 2012
  • Mathematics, Computer Science
  • J. Graph Theory
We show that the 56-vertex Klein cubic graph Γ′ can be obtained from the 28-vertex Coxeter cubic graph Γ by “zipping” adequately the squares of the 24 7-cycles of Γ endowed with an orientation obtained by considering Γ as a 𝒞-ultrahomogeneous digraph, where 𝒞 is the collection formed by both the oriented 7-cycles and the 2-arcs that tightly fasten those in Γ. In the process, it is seen that Γ′ is a 𝒞′-ultrahomogeneous (undirected) graph, where 𝒞′ is the collection formed by both the 7… Expand
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