Locally triangular graphs and normal quotients of the n-cube

Joanna Fawcett

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    1 Citation (Scopus)
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    © 2015, Springer Science+Business Media New York.
    For an integer n≥ 2 , the triangular graph has vertex set the 2-subsets of { 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 parameter that generalises the concept of minimum distance for a binary linear code to arbitrary automorphism groups of the n-cube.
    Original languageEnglish
    Pages (from-to)119-130
    Number of pages12
    JournalJournal of Algebraic Combinatorics
    Issue number1
    Early online date21 Dec 2015
    Publication statusPublished - 1 Aug 2016


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