Locally triangular graphs and normal quotients of the n-cube

Joanna Fawcett

doi:10.1007/s10801-015-0659-1

Locally triangular graphs and normal quotients of the n-cube

Joanna Fawcett

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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Abstract

© 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 language	English
Pages (from-to)	119-130
Number of pages	12
Journal	Journal of Algebraic Combinatorics
Volume	44
Issue number	1
Early online date	21 Dec 2015
DOIs	https://doi.org/10.1007/s10801-015-0659-1
Publication status	Published - 1 Aug 2016

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10.1007/s10801-015-0659-1

Fawcett, 2016 Locally triangular graphs and normal quotients of the n-cubeAccepted author manuscript, 127 KBLicence: Unspecified

Permutation Groups & their Interrelationship with the Symmetry of Graphs Codes & Geometric Configurations
Bamberg, J. (Investigator 01), Devillers, A. (Investigator 02) & Praeger, C. (Investigator 03)
ARC Australian Research Council
1/01/13 → 31/12/17
Project: Research

Cite this

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AB - © 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.

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Locally triangular graphs and normal quotients of the n-cube

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Permutation Groups & their Interrelationship with the Symmetry of Graphs Codes & Geometric Configurations

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