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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.
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 | |
| Publication status | Published - 1 Aug 2016 |
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Dive into the research topics of 'Locally triangular graphs and normal quotients of the n-cube'. Together they form a unique fingerprint.Projects
- 1 Finished
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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