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CORR
2010
Springer

On Graphs and Codes Preserved by Edge Local Complementation

12 years 1 months ago
On Graphs and Codes Preserved by Edge Local Complementation
Orbits of graphs under local complementation (LC) and edge local complementation (ELC) have been studied in several different contexts. For instance, there are connections between orbits of graphs and errorcorrecting codes. We define a new graph class, ELC-preserved graphs, comprising all graphs that have an ELC orbit of size one. Through an exhaustive search, we find all ELC-preserved graphs of order up to 12 and all ELC-preserved bipartite graphs of order up to 16. We provide general recursive constructions for infinite families of ELC-preserved graphs, and show that all known ELC-preserved graphs arise from these constructions or can be obtained from Hamming codes. We also prove that certain pairs of ELC-preserved graphs are LC equivalent. We define ELC-preserved codes as binary linear codes corresponding to bipartite ELC-preserved graphs, and study the parameters of such codes.
Lars Eirik Danielsen, Matthew G. Parker, Constanza
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CORR
Authors Lars Eirik Danielsen, Matthew G. Parker, Constanza Riera, Joakim Grahl Knudsen
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