Locally triangular graphs and normal quotients of the n-cube

  title={Locally triangular graphs and normal quotients of the n-cube},
  author={Joanna B. Fawcett},
  journal={Journal of Algebraic Combinatorics},
For an integer $$n\ge 2$$n≥2, the triangular graph has vertex set the 2-subsets of $$\{1,\ldots ,n\}$${1,…,n} and edge set the pairs of 2-subsets intersecting at one point. Such graphs are known to be halved graphs of bipartite rectagraphs, which are connected triangle-free graphs in which every 2-path lies in a unique quadrangle. We refine this result and provide a characterisation of connected locally triangular graphs as halved graphs of normal quotients of n-cubes. To do so, we study a… 
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