Journal of Algebraic Combinatorics

, Volume 44, Issue 1, pp 119–130

Locally triangular graphs and normal quotients of the n-cube

Article

DOI: 10.1007/s10801-015-0659-1

Cite this article as:
Fawcett, J.B. J Algebr Comb (2016) 44: 119. doi:10.1007/s10801-015-0659-1
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Abstract

For an integer \(n\ge 2\), 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.

Keywords

Locally triangular graph Rectagraph Normal quotient n-cube Semibiplane 

Funding information

Funder NameGrant NumberFunding Note
Australian Research Council (AU)
  • DP130100106

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Centre for the Mathematics of Symmetry and ComputationThe University of Western AustraliaCrawleyAustralia

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