Mathematics – Combinatorics
Scientific paper
2010-06-30
Mathematics
Combinatorics
22 pages, 16 figures
Scientific paper
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 error-correcting 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.
Danielsen Lars Eirik
Knudsen Joakim Grahl
Parker Matthew G.
Riera Constanza
No associations
LandOfFree
On Graphs and Codes Preserved by Edge Local Complementation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On Graphs and Codes Preserved by Edge Local Complementation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Graphs and Codes Preserved by Edge Local Complementation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-153662