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arXiv · 1507.01503

Locally triangular graphs and normal quotients of the $n$-cube

Joanna B. Fawcett
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Abstract

For an integer $n\geq 2$, the triangular graph has vertex set the $2$-subsets of $\{1,\ldots,n\}$ 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 parameter that generalises the concept of minimum distance for a binary linear code to arbitrary automorphism groups of the $n$-cube.

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Joanna B. Fawcett. 2015-07-06. Locally triangular graphs and normal quotients of the $n$-cube. https://doi.org/10.1007/s10801-015-0659-1

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